Search Results for “amp” – Muse Eek https://muse-eek.com Bruce Arnold Innovation in Music Education Sat, 25 Apr 2026 15:18:09 +0000 en-US hourly 1 https://muse-eek.com/wp-content/uploads/2020/08/cropped-Muse-eek-logo-512X512-300dpi-32x32.jpg Search Results for “amp” – Muse Eek https://muse-eek.com 32 32 Ultimate Guide to Octatonics and Bebop Scales https://muse-eek.com/ultimate-guide-to-octatonics-and-bebop-scales/ Tue, 21 Apr 2026 19:04:38 +0000 https://muse-eek.com/?page_id=1429835 Continue reading →]]>



The Ultimate Guide to Octatonics and Bebop Scales

Master the “New Path” to Modern Linear Phrasing and Harmonic Symmetry

Welcome to the Bebop & Octatonic Scale Mastery section of Muse-Eek. This category is dedicated to the specialized study of eight-note structures—a critical “New Path” for any musician looking to master linear phrasing and sophisticated jazz improvisation vocabulary.

While traditional Western theory often focuses on seven-note heptatonic scales, the leap to 8-note scales is what defines the professional “Bebop sound” and the modern textures of fusion and rock. Here, we move beyond basic patterns to explore the mathematical symmetry and rhythmic perfection that octatonic systems provide.

What You Will Discover in This Category:

The 124 Bebop Scales: Most players only know two or three bebop scales. This collection reveals the full spectrum of 124 permutations, teaching you how to use chromatic passing tones to ensure chord tones always land on the downbeat.

495 Octatonic Permutations: Explore the vast universe of 495 possible eight-note scales. Using Pitch Class Set (PCS) theory, we simplify these into 29 Prime Forms, making complex harmonic data manageable and actionable.

Advanced Application & Phrasing: From Segmenting Bebop Scales with approach notes to mastering the Tertial Octatonics used by icons like Allan Holdsworth, these resources bridge the gap between abstract theory and real-world performance.

Rhythmic Symmetry: Learn why 8-note scales are the secret to maintaining a perfect “pocket” in 4/4 time, allowing for seamless tension and release in your solos.

Whether you are a jazz traditionalist or a fusion explorer, these courses provide the technical drills, MIDI files, and structural insights needed to revolutionize your approach to the fretboard or keyboard. Dive into our Ultimate Guide to Octatonics and Bebop Scales to begin your journey toward total melodic and harmonic mastery.

Octatonic and Bebop Resource Guide Index

Click any title below to jump directly to that study deep-dive.

Where to Use Them: Common Progressions

  • Major ii-V-I: Use the Dorian Bebop on the ii chord and the Dominant Bebop on the V chord. This ensures your transition from the b7 of the ii chord to the 3rd of the V chord is smooth and rhythmically perfect.
  • Minor ii-V-I: This is where Octatonic Symmetrical Diminished scales shine. Over the V7alt chord (like a G7b9), the symmetrical diminished scale provides the b9, #9, and #11 tensions that define the modern jazz sound.
  • Static Dominant Chords: In funk or fusion (like a static C7 groove), the Mixolydian Bebop allows you to play long, continuous descending lines that never lose their “pocket” because the root always returns to the downbeat every two measures.

Advanced Bebop Scale Substitutions

Once you are comfortable with the standard application of bebop scales, the next step in your jazz improvisation vocabulary is learning how to “substitute” one scale for another to create sophisticated tension. This is a hallmark of the modern “New Path” approach.

The Minor-Major Swap: One of the most effective substitutions is playing a Melodic Minor Bebop scale over a dominant chord starting from the same root. For example, over a C7 chord, try playing the C Melodic Minor Bebop scale. This naturally highlights the natural 7th against the b7 of the chord, creating a sophisticated “shifting” sound often heard in the playing of Joe Henderson.

The Tritone Substitution: You can also apply the tritone principle to your 8-note scales. If you are playing over a G7 chord, try using the Db Dominant Bebop scale. Because both scales share the same 3rd and 7th (just inverted), the extra chromatic notes in the Db scale will function as altered tensions (b9, #11) over the G7. This is the fastest way to add “outside” flavors to your linear phrasing while keeping your rhythmic placement perfectly symmetrical.

Foundations & Bebop Methods

Octatonic Theory & Practice

Practice Guidance

Foundations & Bebop Methods

The logic of the “Jazz Sound.” Bebop scales are the bridge between linear scale runs and functional chordal playing. By adding one chromatic note, you unlock a world of perfect rhythmic placement.

Foundations & Bebop Methods

The Logic of the “Extra” Note

Understanding the “Extra” note is the key to rhythmic mastery. When moving from a typical seven-note scale to an eight-note **octatonic** or **bebop** system, there are crucial differences in how that added pitch functions.

An octatonic scale is essentially a seven-note scale with an added pitch. By identifying the seven-note “subsets” hidden within an eight-note scale, you gain immediate insight into where that scale will sound best. While my courses provide this detailed structural mapping for you, the process is simple: first, listen to the key you are in; second, pick a functional seven-note scale that works; and third, branch into octatonic scales that contain that seven-note scale as a subset. This method yields incredibly interesting and modern results.

On the other hand, **Bebop scales** are traditionally designed to ensure chord tones land on the downbeats. Any scale you choose in this style must conform to this rhythmic logic to sound authentic. However, the end result isn’t always about strictly outlining changes. In contexts like free improvisation, you can use the Bebop scale as a unique melodic effect, exploring the sound of the eight-note structure without the constraints of traditional functional harmony.

Bebop Method
Midi Files Included

Bebop Scales: 124 Bebop Scales and Their Application

124 Bebop Scales and Their Application by Bruce Arnold

Most musicians work with only a handful of Bebop scales. This course reveals that there are 124 useful Bebop scales. By following the logic of adding one chromatic note to common seven-note structures, you gain total control over the Bebop sound across every musical situation.

Course Highlights:

  • Deep Integration: Learn how all 124 scales relate back to the 29 Eight-Note Prime Forms through Pitch Class Set Theory.
  • Rhythmic Mastery: Master the technique of placing chord tones on the downbeat for a professional jazz flow.
  • Comprehensive Assets: Includes a 95-page PDF, 495 MIDI files, and Jam Tracks in all 12 keys.

Linear Phrasing
11,904 Exercise Files

Segmenting Bebop Scales

Segmenting Bebop Scales by Bruce Arnold

Segmenting is the secret weapon of modern jazz phrasing. By breaking the scale into 5-note groups and adding 3-note approach figures, you transform predictable scale runs into sophisticated, “anticipating” lines that sound like they’re coming off a classic record.

  • Much more useful application: Segmenting allows the scale to be played in multiple places creating interesting new melodic phrases.
  • Rote Internalization: Massive library of PDFs and MIDI files to help you automate these movements in all keys.

Linear Phrasing
11,904 Exercise Files

Segmenting Bebop Scales with Approach Notes

Segmenting Bebop Scales with Approach Notes by Bruce Arnold

Segmenting is the secret weapon of modern jazz phrasing. By breaking the scale into 5-note groups and adding 3-note approach figures, you transform predictable scale runs into sophisticated, “anticipating” lines that sound like they’re coming off a classic record.

  • Phrasing Shifts: Approach the Bebop scale before beat one to totally change your melodic flow.
  • Rote Internalization: Massive library of PDFs and MIDI files to help you automate these movements in all keys.

Octatonic Theory & Practice

The architecture of melody and symmetry. Octatonic scales provide the exotic, symmetrical sounds used by fusion masters like Allan Holdsworth and contemporary classical composers.

Theory Encyclopedia
744 Pages of PDFs

495 Eight-Note Scales in All 12 Keys

495 Eight-Note Scales Encyclopedia by Bruce Arnold

Explore the full universe of octatonic possibilities. While the diminished scale is common, there are 495 total eight-note scales. This course organizes them through Pitch Class Set theory, reducing the overwhelming volume into 29 Prime Forms.

  • Structural Insights: Master internal structures, chords, and available tensions for every possible 8-note combination.
  • Compositional Inspiration: List of compositions and composers (including Allan Holdsworth) who utilize these scales.

Advanced Harmony
Chordal Symmetry

Octatonic Chords: Diatonic 8-Note Harmony

Octatonic Chords and Diatonic Harmony by Bruce Arnold

How do you harmonize an eight-note scale? Traditional music theory focuses on seven-note diatonic harmony, but the Octatonic universe requires a different approach. This course explores how to derive 3 and 4-note chords (tetrads) directly from octatonic structures.

  • Diatonic Analysis: See the chords that naturally occur within the Diminished and Symmetrical Diminished systems.
  • Modal Movement: Learn to play these chords modally up and down the guitar neck or piano to create head-turning modern textures.
  • Vertical Mastery: Move beyond linear playing by internalizing the vertical “stacks” found in each of the 29 Prime Forms.

Modern Improvisation
267 Page Method

Tertial Octatonics: The “Two Tetrad” Method

Tertial Octatonics Two Tetrad Method by Bruce Arnold

Want to create a modern sound from those tired old arpeggios? Tertial Octatonics is the answer. By combining two common 7th chords (tetrads), you can form complete Octatonic scales that are much easier to access and sound significantly more modern than standard linear runs.

What this course covers:

  • Comprehensive Pairs: Every possible combination of two 7th chords that form an Octatonic scale, covering Major 7, Dominant 7, Minor 7b5, and more.
  • Targeted Practice: Exercises for over 11 common chord types (page 4 to 267) including Dominant 7b5 and Minor Major 7.
  • The Modern Sound: Hints and applications to use these structures over Dominant 7th and 7sus4 key centers for a “liquid” modern texture.

How to Choose the Right 8-Note Scale

Choosing between a Bebop scale and an Octatonic scale depends entirely on your musical intent. While both are eight-note structures, they function differently within a harmonic progression. Understanding these nuances is the hallmark of a mature improviser.

1. The Bebop Intent (Linear Flow)

Use Bebop scales when your goal is linear clarity. Because Bebop scales are designed to put chord tones on the downbeats, they are the best choice for “straight-ahead” jazz playing where you want to clearly outline the harmony while maintaining a fluid, eighth-note stream.

Primary Rule: If the chord change lasts for at least one full measure, a Bebop scale allows you to “spell out” the chord (1, 3, 5, 7) rhythmically. This is the “Bebop Effect” that makes your lines sound authentic to the era of Charlie Parker and Bud Powell.

2. The Octatonic Intent (Modern Color)

Use Octatonic scales (like the Symmetrical Diminished) when you want harmonic tension and modern texture. These scales are built on symmetrical intervals, which creates a “shifting” sound that doesn’t resolve as predictably as a Bebop scale.

Primary Rule: Use these over dominant chords to add “outside” colors like the #9, b9, or #11. They are also excellent for modal “planing,” where you move the same chord voicing up or down in minor thirds—a staple of fusion and modern jazz piano.

The “Previous Sound” Principle

One critical concept explored in the Scale Analysis course is how the previous sound affects your choice. For example, if a previous chord contained a b5 or a b6, selecting a Bebop scale that also features those degrees will make your transition sound much more logical and “musical” to the listener.

Always analyze the internal structure of the scale. A scale like #115 (Lydian Dominant Bebop) features both the #4 and the b7, making it the perfect tool for a IV7 chord in a blues or a dominant chord that doesn’t resolve to the tonic.

The 29 Octatonic Prime Forms

By using Pitch Class Set Theory, we can simplify the massive universe of 495 scales into 29 parent structures. Understanding these Prime Forms is the key to 8-note mastery.


Modern Applications: Holdsworth and Messiaen

The “New Path” approach bridges the gap between 20th-century classical theory and modern fusion. Oliver Messiaen’s Modes of Limited Transposition and Allan Holdsworth’s Jazz Dominant textures both rely on the symmetrical beauty of the octatonic system…

Appendix: 124 Bebop Scale Reference

This list identifies the 124 primary Bebop permutations. The Chord Structure column identifies the 4-note structure formed by the 1st, 3rd, 5th, and 7th scale degrees.

# ID Scale Degrees (Intervals) Chord Structure (1,3,5,7) Common Name / Note
81 1, 2, 3, 4, 5, b6, 6, 7 1, 3, 5, 6 Major Bebop
51 1, 2, 3, 4, 5, 6, b7, 7 1, 3, 5, b7 Dominant Bebop
48 1, 2, b3, 3, 4, 5, 6, b7 1, b3, 4, 6 Dorian Bebop
75 1, 2, b3, 4, 5, b6, 6, 7 1, b3, 5, 6 Melodic Minor Bebop
83 1, 2, b3, 4, 5, b6, b7, 7 1, b3, 5, b7 Harmonic Minor Bebop
49 1, 2, 3, 4, b5, 5, 6, 7 1, 3, b5, 6 Lydian Bebop
104 1, b2, 3, 4, 5, b6, b7, 7 1, 3, 5, b7 Mixolydian b2, b6 Bebop
42 1, b2, b3, 3, b5, b6, b7, 7 1, b3, b5, b7 Altered Bebop
87 1, 2, 3, 4, b5, 5, 6, 7 1, 3, b5, 6 Whole Tone Bebop
1 1, b3, 3, 4, b5, 5, b6, 6 1, 3, b5, b6 Non-Traditional (*)

*Note: The full 124 list continues with permutations for every possible 7th chord quality. Reference the Bebop Scales course for the complete 11,000+ exercise file set.

Appendix: Essential Octatonic Scale Reference

While there are 495 possible combinations, these are the high-utility octatonic scales used in modern Jazz, Fusion, and 20th-century classical music. Use these to move beyond traditional “scale-wise” sounds.

Scale Type Scale Degrees (Intervals) Prime Form / PCS Best Application
Symmetrical Diminished 1, b2, b3, 3, b5, 5, 6, b7 0, 1, 3, 4, 6, 7, 9, T Dominant 7th (Altered)
Diminished (Whole-Half) 1, 2, b3, 4, b5, b6, 6, 7 0, 2, 3, 5, 6, 8, 9, E Diminished 7th Chords
Holdsworth Jazz Major 1, 2, 3, 4, 5, b6, 6, 7 0, 1, 3, 4, 5, 7, 8, T Major 7th / Major 6th
Holdsworth Jazz Dominant 1, 2, 3, 4, 5, 6, b7, 7 0, 1, 2, 3, 5, 7, 8, T Dominant 7th / 7sus4
Mixob2b6 Bebop 1, b2, 3, 4, 5, b6, b7, 7 0, 1, 2, 3, 5, 6, 8, 9 Dominant 7 (b9, b13)
Locrian Nat 2 Bebop 1, 2, b3, 4, b5, b6, b7, 7 0, 1, 2, 4, 5, 7, 8, T Minor 7b5 Chords
WT Bebop (Messiaen 6) 1, 2, 3, 4, b5, b6, b7, 7 0, 1, 2, 4, 6, 7, 8, T Whole Tone / Dominant #5

For the complete listing of all 495 scales, including MIDI files and key-by-key transpositions, please refer to the “495 Eight-Note Scales” course materials.

Expert FAQ & Practice Guidance

Common hurdles and professional strategies for mastering 8-note scales, straight from Bruce Arnold’s experience at Berklee and beyond.

Q: I’ve been playing a few bebop scales up and down for a few months now but don’t really know what else to do to get them into my playing.
A: Start by playing the scales in all keys using Cycle 5 (C, F, Bb, etc.). Next, sequence the bebop scale into groups of 5 notes and play them as eighth notes, ensuring the first and last notes are chord tones. Finally, start writing out solos over jazz standards using these segmented bebop scales—a technique Jerry Bergonzi had me do to truly internalize these segments.
Q. I’ve used the diminished and symmetrical diminished scale; that’s about it for octatonic scales. Why are there so many other octatonic scales that you recommend and which ones should I work on?
A. Start with the diminished and symmetrical diminished in all keys, Cycle 5. Beyond those, concentrate on octatonic scales that work over dominant chords, such as the Mixolydian b2, b6 scale with an added b3, or the Mixolydian b2, b6 scale with a b5 replacing the 5. These provide immediate “head-turning” utility.
Q. I’ve been segmenting Bebop scales but would like to take it one step further. What do you recommend?
A. Add 3-note approach figures to the beginning of the segmented Bebop scale. This changes your phrasing by approaching the scale before it starts on beat one. For deep dives on this, see the “Approach Notes” course.
Q. Are octatonics just for jazz musicians? I’m a fusion/rocker and want to add new sounds.
A. They are great for rock/fusion! Allan Holdsworth used octatonic scales extensively. Start with the diminished systems and branch out, but don’t forget the chords derived from these scales. Playing them modally up and down the neck will create a very fresh, sophisticated sound.
Q. I have a real problem keeping diminished and symmetrical diminished scales straight. How do I fix this?
A. I had that problem back at Berklee too. Two things helped: 1) Every day as I walked, I’d pick a scale and say the note names or degrees for each step I took. 2) I spent 3 months playing only these two types of scales every day, moving through Cycle 5. That immersion clears the confusion immensely.
Q. I’m burnt out on these scales after many years. Any ideas for expanding my use of them?
A. Work with two tetrads and pivot back and forth between them. My “Tertial Octatonics” course is designed for exactly this. Using these tetrads creates a fresh new sound and they make for fantastic, modern chord voicings.

Ready to Begin Your 8-Note Journey?

Mastering these scales is a lifetime pursuit, but the results in your playing are immediate. Whether you’re using the 124 Bebop Scales for authentic jazz flow or Tertial Octatonics for modern fusion, the “New Path” starts here.

The 8-Note Mastery Roadmap: A 90-Day Plan

Mastering 495 scales can feel like an impossible task. The secret is not to learn more, but to learn deeper. Follow this structured roadmap to integrate these sounds into your DNA.

Phase 1: The Foundation (Days 1-30)

Focus exclusively on the Major and Dominant Bebop scales.

  • The Drill: Play one key per day following the Cycle of 5ths.
  • The Goal: Use the “walking recitation” method to say the note names aloud while playing. Ensure chord tones (1, 3, 5, 7) always land on the beat.

Phase 2: Symmetrical Immersion (Days 31-60)

Introduce the Symmetrical Diminished and Whole Tone Bebop scales.

  • The Drill: Practice 3-notes-per-string patterns on guitar or “pivoting” tetrads on piano.
  • The Goal: Transition from a ii-V-I using a Bebop scale on the ‘ii’ and a Symmetrical Diminished on the ‘V’. Listen for the “tension shift.”

Phase 3: Vocabulary & Application (Days 61-90)

Start Segmenting and using Approach Notes.

  • The Drill: Write out one 16-bar solo per week over a standard like “Autumn Leaves” or “Blue Bossa” using only 8-note segments.
  • The Goal: Break out of “scale-wise” playing. If you feel burnt out, move to the Tertial Octatonics and explore the world of tetrad pivots.

“Consistency beats intensity. One key, fifteen minutes, every single day.” — Bruce Arnold

Glossary of 8-Note Concepts

To master the “New Path,” you must understand the terminology that bridges traditional jazz theory and modern pitch class analysis. Use this glossary as a quick reference guide.

Approach Note Figure
A melodic ornamentation technique where a target note (usually a chord tone) is preceded by one or more non-harmonic tones. In 8-note phrasing, a 3-note approach figure is often used to delay the start of a scale until a specific downbeat, creating a more sophisticated, “anticipating” rhythmic feel.
Bebop Chord
The four-note structure formed by the 1st, 3rd, 5th, and 7th degrees of a bebop scale. The genius of the 8-note bebop system is that it allows these “Bebop Chord” tones to land consistently on downbeats, providing a strong harmonic foundation during rapid linear runs.
Cycle 5 (Cycle of Fifths)
The movement of root notes in descending perfect fifths (C, F, Bb, Eb, etc.). This is the primary practice vehicle for jazz musicians, as it mimics the most common functional harmonic movement (V to I) found in the Great American Songbook.
Pitch Class Set (PCS)
A method of musical organization that treats notes as numbers (0-11). By using Pitch Class Sets, we can identify the “Prime Form” of a scale—its most basic structural identity—allowing us to see the relationship between 495 different scales and their 29 parent structures.
Prime Form
The most compact version of a Pitch Class Set. Identifying the Prime Form of an 8-note scale is essential for “New Path” students because it simplifies complex harmonic data into manageable, mathematical patterns that can be transposed to any key.
Symmetrical Diminished
An 8-note scale built on an alternating pattern of half-steps and whole-steps (or vice versa). Because of its perfectly symmetrical structure, this scale creates a highly modern, “ambiguous” sound that is widely used in fusion, rock, and modern jazz to provide altered tensions over dominant chords.
Tetrad
A four-note chord or melodic structure. In the study of Tertial Octatonics, we break an 8-note scale into two distinct tetrads. Pivoting between these two four-note groups is a key technique for breaking out of linear, scalar habits and creating angular, modern lines.
Tritone Substitution
A harmonic concept where a dominant chord is replaced by another dominant chord located a tritone (six semitones) away. In an 8-note context, applying a tritone substitution to your bebop scale choice allows for sophisticated chromaticism while maintaining the same rhythmic resolution.

]]> Ultimate Guide to Ear Training: Master the Key Center Method https://muse-eek.com/ultimate-guide-to-ear-training/ Sat, 18 Apr 2026 18:35:59 +0000 https://muse-eek.com/?page_id=1429621 Continue reading →]]>  

 

The Ultimate Guide to Ear Training through the Contextual Ear Training Method

Master the ability to hear music in real-time. This lineage-tested roadmap provides the exact path to reflexive hearing, based on 40 years of expertise from Bruce Arnold and the legendary methods of Charlie Banacos.”

Ultimate-Guide-to-Ear-Training

Stop calculating and start hearing. Achieve instant recognition of every note within a key center through the proven Muse-Eek method. Follow the roadmap developed Bruce Arnold to master the same techniques used by the students of Charlie Banacos.”

The Key Center Philosophy: Hearing in Real Time

Ear training is the fundamental bridge between the musical concepts in your mind and the physical execution on your instrument. However, the vast majority of music students are taught using the Interval Method. This mathematical approach focuses on the distance between two notes. While this is helpful for visual analysis on a staff, it is functionally useless for real-time performance. In a professional setting, music moves too fast for calculation. If you have to think, “That note was a Major 6th above the last one,” you have already missed the next three beats.

The Key Center Method, also known as Contextual Ear Training, treats music as a functional language rather than a math problem. In this system, every note has a unique “color” or “gravity” relative to the tonal center (the Key). For example, an ‘E’ in the key of C is not just a distance of four half-steps; it is the specific, emotional sound of a Major 3rd. It has a distinct character that your brain can learn to recognize as an instant reflex. Think of it like color recognition: when you see the color “red,” you don’t measure its light frequency or compare it to “orange”—you simply know it is red. This guide is designed to take you to that exact level of “reflexive hearing”.

Achieving this requires a specific kind of dedication. I recommend practicing for one hour a day, but—crucially—this hour should be broken into 10-minute intervals. This frequent repetition prevents mental fatigue and ensures that the “color” of the pitches stays fresh in your subconscious mind. If you want to progress faster, you can certainly practice more, but the secret lies in the frequency of the sessions, not just the duration.

The Ultimate Guide to Ear Training Roadmap: Understanding Your Journey

Every musician arrives at my door with a different background. Identifying where you are currently is the only way to choose the right path forward. Here are the three primary stages of the ear training journey.

1. The Beginning Student: Beyond the Apps

Many students come to me having already done ear training either in college or more commonly an app that they downloaded from the internet. The first problem with the app from the internet is an author usually knows how to build an app and is copying an idea for ear training to make some money but really doesn’t have the pedigree to help you if you have problems. The other problem is students will start with interval ear training but don’t get informed that you could use intervals for certain things but really you need to hear what all 12 notes sound like in a key center.

Many beginning students show up with a good knowledge of interval ear training but can’t figure out why they can’t hear anything when they play or listen to music. This is because you need Contextual Ear Training where you learn the sound of all 12 notes and then you will see that you start to hear things when you are playing or listening. Even with the basic courses I’ve provided, students can have many problems that need further help. I’ve created many other books to help students when they are having problems. Some of these problems are weak key retention, too much prior interval training, and poor pitch discrimination (can’t tell if a note is higher or lower in pitch). I have courses to correct these and other situations that arise during your ear training journey.

2. The Intermediate Student: Bridging the “Context Gap”

I get many students that have a good grasp of relative pitch ear training; they can identify most notes against a key center with a mistake here and there but still can’t hear anything or very little when they are listening to music or playing it. This is usually caused by “Context.” In other words, you can do a technique ear training exercise but you can’t apply it to real music. To fix this, I’ve created a large resource of “Direct Application” ear training courses that have you identify notes or sing notes in real musical situations.

These courses vary greatly from jazz to classical to heavy metal to movie scores and beyond. Each of these courses helps you bridge the gap between an “Exercise” and a “real world music situation.” One other problem that comes up with intermediate students is bad habits that they have engrained into their mind. Many times we spend more time unlearning than learning. Finding these bad habits is why an app isn’t going to get you there. You need an experienced teacher to help you find the issue and fix it. That is why I offer free email support for students working with my courses.

3. The Advanced Student: Mastering Modulations and Complexity

Advanced students are usually students that have worked through many of my methods but want to go even further with their Contextual Ear Training education. Students in this category usually can hear all 12 notes against a key center, can do the Key Note Recognition so their Key Retention is good, and can identify short melodies without modulating. But they lack the ability to modulate correctly, have little experience with more complicated music like Pitch Class Set Improvisation ideas or advanced jazz harmonies.

They also lack the ability to hear complicated chord progressions or the understanding of how extensive key center recognition can go. For instance, they have never worked with a course like “Scale Analysis” which shows you how to hear scales on one key throughout an entire chord progression. I’ve created this and many courses to help these students master their weak points.

Direct Application: Real-World Musical Fluency

Where ear training gets to be exciting is when you can start to hear real music in real time. The key behind this is speed in recognition. You have to develop the ability to instantly hear notes or chords. There are, of course, limits because we are only human and part of this is about your memory skills. But that said, remember when you see the color “red” you don’t sit and ponder “What is that color?” you just know it’s red. This is how you need to get to with ear training, and I can show you the process of getting there. It takes dedication, but if you can put in an hour a day broken up into 10-minute intervals of practice, you can get there. Want to get there quicker? Practice more!.

Direct application of movie scores is a great place to start. Usually movie scores start pretty simple like a low note followed by a few notes. That low note gives you the key, so it helps you to identify the notes. I’ve created a new course called Serial Ear which gives you the same type of practice where you hear a low pitch (Key Center) and then you have to guess what the notes are. Keep in mind that using a direct application like Serial Ear, it is a really great idea to play along with your instrument. Let’s say you hear C, E, G; well, then you can play those notes, but you could then start improvising with other scales that contain C, E, G. I give you 18 inversions so pianists and guitarists can find new chords.

For students who are intermediate jazz, classical, rock, country, or metal players, spend a massive amount of time working with Direct Application courses so that you can listen to a standard jazz tune, a Bach Chorale, or a heavy metal groove and identify or sing notes when prompted. This goes well beyond what Charlie Banacos taught; he didn’t have the technical resources to create courses like this. He would just say, “You need to play, man!”—which is true. If you don’t play with others, it will be very difficult to get over that hurdle of hearing at an advanced level.

When you enter an advanced level like trying to hear the key centers in Schoenberg’s 5 Piano Pieces or Webern’s Fünf Canons, you need to get your key retention on a much higher level. Charlie Banacos used to have me sing through these pieces either all in one key or following the key center changes in my mind through the use of solfeggio. When I would change keys, I would change the solfeggio to match, which told him how I was modulating.

Rock music can also be deceptively difficult. In “All Along the Watchtower” (G to D to Am), are you in G or Am?. Only through building your key retention will you be able to answer that question. Music doesn’t have to be complex to fool your ear, but through working with key retention and direct application, you will fix these issues.

4 Common Pitfalls & Practice Mistakes that the Ultimate Guide to Ear Training can fix

Over 40 years of teaching, I have seen these recurring mistakes that stall progress:

1. Resolving Tension Notes

Students often hear a difficult note (like a #11) and resolve it to a “safe” note (the 5th) in their head to identify it. This is a “crutch” that slows you down. You must learn the sound of the #11 as its own standalone color.

2. Mental Counting

If you are counting up from the root (1, 2, 3…) to find a note, you are using logic, not your ears. This method focuses on bypassing the intellect to reach a natural reflex.

3. Poor Key Retention

If you lose the “feeling” of the key by the time the target note plays, you are guessing in a vacuum. Targeted exercises in the Key Retention Builder series help fix this.

4. Ignoring Your Instrument

You must bridge the gap between audio files and your fingers. Use a MetroDrone® while you practice scales to relate every technical move to a functional key. I would also recommend Long Line Rhythm® Feel Time Don’t Count Time to see all the amazing things you can do with the MetroDrone®

The Key Center Philosophy: Hearing in Real Time

Ear training is the fundamental bridge between the musical concepts in your mind and the physical execution on your instrument. However, the vast majority of music students are taught using the Interval Method. This mathematical approach focuses on the distance between two notes. While this is helpful for visual analysis on a staff, it is functionally useless for real-time performance. In a professional setting, music moves too fast for calculation. If you have to think, “That note was a Major 6th above the last one,” you have already missed the next three beats.

The Key Center Method, also known as Contextual Ear Training, treats music as a functional language rather than a math problem. In this system, every note has a unique “color” or “gravity” relative to the tonal center (the Key). For example, an ‘E’ in the key of C is not just a distance of four half-steps; it is the specific, emotional sound of a Major 3rd. It has a distinct character that your brain can learn to recognize as an instant reflex. Think of it like color recognition: when you see the color “red,” you don’t measure its light frequency or compare it to “orange”—you simply know it is red. This guide is designed to take you to that exact level of “reflexive hearing”.

Achieving this requires a specific kind of dedication. I recommend practicing for one hour a day, but—crucially—this hour should be broken into 10-minute intervals. This frequent repetition prevents mental fatigue and ensures that the “color” of the pitches stays fresh in your subconscious mind. If you want to progress faster, you can certainly practice more, but the secret lies in the frequency of the sessions, not just the duration.

The Ultimate Guide to Ear Training Roadmap: Understanding Your Journey

Every musician arrives at my door with a different background. Identifying where you are currently is the only way to choose the right path forward. Here are the three primary stages of the ear training journey.

1. The Beginning Student: Beyond the Apps

Many students come to me having already done ear training either in college or more commonly an app that they downloaded from the internet. The first problem with the app from the internet is an author usually knows how to build an app and is copying an idea for ear training to make some money but really doesn’t have the pedigree to help you if you have problems. The other problem is students will start with interval ear training but don’t get informed that you could use intervals for certain things but really you need to hear what all 12 notes sound like in a key center.

Many beginning students show up with a good knowledge of interval ear training but can’t figure out why they can’t hear anything when they play or listen to music. This is because you need Contextual Ear Training where you learn the sound of all 12 notes and then you will see that you start to hear things when you are playing or listening. Even with the basic courses I’ve provided, students can have many problems that need further help. I’ve created many other books to help students when they are having problems. Some of these problems are weak key retention, too much prior interval training, and poor pitch discrimination (can’t tell if a note is higher or lower in pitch). I have courses to correct these and other situations that arise during your ear training journey.

2. The Intermediate Student: Bridging the “Context Gap”

I get many students that have a good grasp of relative pitch ear training; they can identify most notes against a key center with a mistake here and there but still can’t hear anything or very little when they are listening to music or playing it. This is usually caused by “Context.” In other words, you can do a technique ear training exercise but you can’t apply it to real music. To fix this, I’ve created a large resource of “Direct Application” ear training courses that have you identify notes or sing notes in real musical situations.

These courses vary greatly from jazz to classical to heavy metal to movie scores and beyond. Each of these courses helps you bridge the gap between an “Exercise” and a “real world music situation.” One other problem that comes up with intermediate students is bad habits that they have engrained into their mind. Many times we spend more time unlearning than learning. Finding these bad habits is why an app isn’t going to get you there. You need an experienced teacher to help you find the issue and fix it. That is why I offer free email support for students working with my courses.

3. The Advanced Student: Mastering Modulations and Complexity

Advanced students are usually students that have worked through many of my methods but want to go even further with their Contextual Ear Training education. Students in this category usually can hear all 12 notes against a key center, can do the Key Note Recognition so their Key Retention is good, and can identify short melodies without modulating. But they lack the ability to modulate correctly, have little experience with more complicated music like Pitch Class Set Improvisation ideas or advanced jazz harmonies.

They also lack the ability to hear complicated chord progressions or the understanding of how extensive key center recognition can go. For instance, they have never worked with a course like “Scale Analysis” which shows you how to hear scales on one key throughout an entire chord progression. I’ve created this and many courses to help these students master their weak points.

Direct Application: Real-World Musical Fluency

Where ear training gets to be exciting is when you can start to hear real music in real time. The key behind this is speed in recognition. You have to develop the ability to instantly hear notes or chords. There are, of course, limits because we are only human and part of this is about your memory skills. But that said, remember when you see the color “red” you don’t sit and ponder “What is that color?” you just know it’s red. This is how you need to get to with ear training, and I can show you the process of getting there. It takes dedication, but if you can put in an hour a day broken up into 10-minute intervals of practice, you can get there. Want to get there quicker? Practice more!.

Direct application of movie scores is a great place to start. Usually movie scores start pretty simple like a low note followed by a few notes. That low note gives you the key, so it helps you to identify the notes. I’ve created a new course called Serial Ear which gives you the same type of practice where you hear a low pitch (Key Center) and then you have to guess what the notes are. Keep in mind that using a direct application like Serial Ear, it is a really great idea to play along with your instrument. Let’s say you hear C, E, G; well, then you can play those notes, but you could then start improvising with other scales that contain C, E, G. I give you 18 inversions so pianists and guitarists can find new chords.

For students who are intermediate jazz, classical, rock, country, or metal players, spend a massive amount of time working with Direct Application courses so that you can listen to a standard jazz tune, a Bach Chorale, or a heavy metal groove and identify or sing notes when prompted. This goes well beyond what Charlie Banacos taught; he didn’t have the technical resources to create courses like this. He would just say, “You need to play, man!”—which is true. If you don’t play with others, it will be very difficult to get over that hurdle of hearing at an advanced level.

When you enter an advanced level like trying to hear the key centers in Schoenberg’s 5 Piano Pieces or Webern’s Fünf Canons, you need to get your key retention on a much higher level. Charlie Banacos used to have me sing through these pieces either all in one key or following the key center changes in my mind through the use of solfeggio. When I would change keys, I would change the solfeggio to match, which told him how I was modulating.

Rock music can also be deceptively difficult. In “All Along the Watchtower” (G to D to Am), are you in G or Am?. Only through building your key retention will you be able to answer that question. Music doesn’t have to be complex to fool your ear, but through working with key retention and direct application, you will fix these issues.

Course Deep-Dives: Choosing Your Path at the Ultimate Guide to Ear Training page

Because I have created over 300 courses, students often ask which specific book will solve their current plateau. Below is a detailed breakdown of the “Core Nine” courses that form the backbone of the Muse-Eek method. Keep in mind that there are many more books on ear training lists here.

Many students have problems that need extra courses to solve their specific issue. Send me an email if you run into any problems. If you are just starting with this ear training get One Note Complete and Contextual Ear Training. These two courses are the core study and can be practiced anywhere that you can listen to an MP3. Try to do an hour a day practice and break that up into 10 minute sessions.

Book cover for Ear Training One Note Complete by Bruce Arnold, a foundational course for hearing pitches within a key center.

1. Ear Training One Note Complete

This is the “Level 0” for every student, regardless of their technical ability on their instrument. The goal here is simple but profound: to hear a cadence and identify a single pitch. This course removes the variables of rhythm and movement, forcing your brain to memorize the functional gravity of the 12 chromatic notes. We use the Key of C to provide a stable reference point for the brain’s long-term memory.

This course is usually paired with the singing course: Contextual Ear Training/strong>

Book cover for Contextual Ear Training by Bruce Arnold, a course focused on singing scale degrees within a key center to develop reflexive hearing.

2. Contextual Ear Training

If One Note Complete is the “Listening” pillar, this is the “Internalization” pillar. You must be able to generate these sounds from within. In this course, you are prompted to sing a specific scale degree against a cadence. This course is vital for improvisers because it develops the “Pre-Hearing” reflex—the ability to hear a line in your head a split second before your fingers play it.

This course is usually paired with the listening course: One Note Ear Training/strong>

Graphic for The MetroDrone practice tool by Bruce Arnold, a specialized metronome providing a constant tonal center for contextual ear training.

3. The MetroDrone®

The MetroDrone is a metronome that provides a constant tonal center. By practicing your regular technical exercises—scales, arpeggios, sequences—over the MetroDrone, you are doing Ear Training and Technical Practice simultaneously. It forces every note you play to have a functional meaning. I use this course everyday it builds both ear training and rhythm/time ability simultaneously. It available as MP3s or you can buy the app in the apple store.

Book cover for Key Note Recognition Ear Training by Bruce Arnold, an advanced course for identifying key centers and modulations in complex music.

4. Key Note Recognition

This is the “Level 2” transition. Once you can hear 12 notes in one key, we start “Key Jumping.” In this course, you hear a cadence in one key, a note, and then a cadence in a different key. This develops **Elite Key Retention**, preventing you from being “thrown off” by modulations in complex music.

Book cover for Serial Ear Training by Bruce Arnold, an advanced course for identifying long sequences of pitches without a recurring cadence.

5. Serial Ear

Serial Ear tests you melodically on every possible 3 note combination through 18 possible inversions and all transpositions. It is the ultimate ear training course for nailing down every 3 note melodic possibility. This is the ultimate test of your functional memory.

Book cover for Scale Analysis by Bruce Arnold, teaching musicians how to hear chord progressions within a single parent scale.

6. Scale Analysis

One of the most advanced concepts I teach is Scale Analysis. This course teaches you how to hear one parent scale—like C Major—across an entire progression. It moves you away from “chord-scale” theory and into “functional-key” theory, which is how the masters actually heard music.

Book cover for Direct Application Ear Training by Bruce Arnold, a guide to applying ear training to real music situation.

7. Direct Application Ear Training

Once single notes are a reflex, you should start working with the Direct Application courses so that you can work on ear training with real music. There are many courses available for this I’ve given a list below. There are multiple courses within each of the links below which can be purchases separately or as a bundle.

Book cover for Two-Note Harmonic Ear Training by Bruce Arnold, a guide to identifying two simultaneous pitches within a key center.

8. Two-Note Harmonic Ear Training

Once single notes are a reflex, you must learn to hear two things at once. This course is the gateway to hearing chords. By moving from one note to two, you are doubling the data your brain has to process, which is the final step before full harmonic recognition. There are many versions of 2 note ear training I recommend the complete 2 note collection shown in the link below.

LEARN MORE → BUY COMPLETE 2 NOTE COLLECTION NOW

Book cover for Two-Note Melodic Ear Training by Bruce Arnold, a guide to identifying two simultaneous pitches within a key center.

9. Two-Note Melodic Ear Training

Once single notes are a reflex, you must learn to hear two two or more notes melodically. There are many books in this series and I’ve listed links below. Within these links you will find multiple purchase options.

Master FAQ: Technical Troubleshooting for All Levels

This section addresses the deep technical questions I’ve received over 40 years of teaching. For more, visit the Full Muse-Eek FAQ Archive.

1. “I can identify notes in the car, but not when I’m holding my guitar. Why?”

This is a classic ‘application gap.’ When you hold your instrument, your brain defaults to physical muscle memory—you are thinking about fretboards or keys rather than sound. To fix this, you must stop ‘thinking’ and start ‘singing.’ I recommend singing the note you want to play *before* you play it. Use the Direct Application courses to force your brain to connect the functional sound to the physical location on your instrument. This is how you bridge the gap between being a ‘practicer’ and a ‘musician.’

2. “How do I know if I’m accidentally using the Interval Method?”

If you find yourself comparing the current note to the note right before it, you are using intervals. If you hear the note as a ‘feeling’ or ‘color’ against the opening cadence, you are using relative pitch. A Major 3rd has a sunny, stable quality; a b2 has a dark, pressing quality. If you aren’t hearing those emotional ‘colors,’ you are likely still calculating distances. Go back to One Note Beginning and focus on the ‘feeling’ of the pitch.

3. “Why is Key Retention so difficult for me?”

Key retention is a mental muscle. If you lose the key, it means your brain is being distracted by the ‘last note played.’ This is very common in Rock and Jazz where chords move quickly. You need to practice with a drone. The MetroDrone is specifically designed to keep the fundamental present in your ear while you move through complex scales. This ‘anchoring’ effect eventually becomes permanent, allowing you to hold a key for minutes at a time without a reference.

4. “Should I practice in different keys every day?”

Actually, no. In the beginning, stay in the Key of C. We are training your **brain’s perception**, not your hands. All keys are functionally identical. Once you recognize a #11 in C, you will recognize a #11 in F#. By changing keys too often early on, you introduce a variable that can confuse the brain. Once you are at 80% accuracy in C, then move to the Key Note Recognition course to begin ‘Key Center Jumping.’

5. “What did Charlie Banacos mean when he said ‘No Intervals’?”

Charlie understood that music is a language. When you speak, you don’t calculate the distance between words. Charlie’s method was about ‘instant recognition.’ He wanted his students to be so grounded in the key center that they could hear a Schoenberg piece and understand exactly where the tonal shifts were happening through functional solfeggio. He moved beyond the clinical and into the artistic.

6. “Why does a 10-minute session work better than an hour?”

Cognitive science tells us that the brain’s ability to create new neural pathways is strongest during short bursts of high focus. When you do ear training for an hour, your brain gets tired and starts ‘guessing’ or using ‘logic’ to find the answer. This reinforces bad habits. By doing 10 minutes, you keep your ‘listening reflex’ sharp. It’s like lifting weights—you don’t lift for 5 hours straight; you do sets and reps.

Complete Ear Training Course Directory at Ultimate Guide to Ear Training page

Foundations

Many of the links below have multiple courses within. It is always a good idea to ask about what course(s) would be good for you based on your current level by sending a email. There is also an Ear Training: A Guided Tour page to see the bigger picture. Some learn better by watch videos. 25 Ear Training Tips is a nice addition to the books below to explain the process.

Direct Application

Advanced Singing

Advanced Listening

Advanced Theory

Developing Key Retention Skills

Pitch Class Set Ear Training

A Proven Educational Lineage

The methods found on muse-eek.com are part of a historical musical lineage stretching back to the 18th-century masters.

By using Muse-Eek books and courses, you are now a part of this lineage—a tradition of excellence passing through legends like Charlie Banacos and Jerry Bergonzi.

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Hexatonic-and-Trichord-resource-guide

Hexatonic and Trichord Resource Guide Index

Click any title below to jump directly to that course deep-dive.

Beginning Methods (0 Theory)

Theory & Reference

Improvisational Studies

Technique

Guitar Studies

Ear Training

Composing

Hextonic and Trichord Resource Guide by Bruce Arnold for Muse-eek.com

Hexatonic and Trichord Resource Guide

The Comprehensive Guide to Modern Melodic and Harmonic Mastery

Welcome to the Hexatonic and Trichord Resource Guide, your definitive portal for mastering the “New Path” to modern improvisation. Whether you are diving deep into pitch class set theory or looking for specialized trichord ear training, this page organizes over 30 years of pedagogy into a clear, actionable roadmap.

For a deep dive into the underlying theory, please refer to our pillar resources:
Hexatonic and Pitch Class Set Improvisation | Hexatonics Scales the Complete Guide

Beginning Methods

Modern sound doesn’t have to be complicated. These courses are designed for musicians who want to start using exotic colors and contemporary textures immediately, with zero prior knowledge of Pitch Class Set theory required.

Chord Voicings MP3 Samples Included Midi Files Included

Applying Chord Voicings to Traditional Harmony

Applying Chord Voicings to Traditional Harmony

Applying Chord Voicings to Traditional Harmony

“Applying Pitch Class Set Chord Voicings to Traditional Harmony” provides a student interested in modernizing their chord playing with four pitch class sets that effective create a new and intriguing sound for playing traditional harmony. Common jazz standards are used to give you a fresh new sound. These voicings of course could be applied to any idiom.

Course Highlights:

  • Examples of using these pitch class set is shown through common chord progressions.
  • A Direct Application Course spending most of the time directly apply these pitch class set chords.
  • Common re-harmonization principles have been avoided so the student will find this to be a quick method in applying pitch class sets to traditional harmony
  • With marginal practice should find with that their ability to complete this book will only take a few months.

Midi Files Included MP3 Jam Tracks Included For Piano or Guitar

Applying 013 Chord Voicings

Applying 013 Chord Voicings-Application of pitch class sets to traditional harmony by Bruce Arnold for Muse Eek Publishing Company Applying Pitch Class Set Chord Voicings

Applying 013 Chord Voicings

Applying 013 Chord Voicings bridges the gap between abstract pitch class sets and practical performance. Through 12 comprehensive études (one in every key), this course demonstrates how to apply 013 voicings to the standard II7–V7–I-7–VI7 progression. Perfect for guitarists, pianists, and composers, these lessons focus on sophisticated voice leading and re-harmonization techniques to create smooth, modern movement within traditional harmonic frameworks.

Course Highlights:

  • Real-World Application: Master 12 detailed études (one in every key) that apply 013 voicings to the essential II-V-I-VI progression, bridging the gap between theory and performance.
  • Expert Voice Leading & Re-harmonization: Overcome the “013 challenge” with clear examples of smooth voice leading and modern tension combinations that sound professional, not just dissonant.
  • Instrument-Specific Tools: Includes specialized charts with guitar chord diagrams for easy fretting and grand staff notation for pianists, ensuring playability regardless of your primary instrument.
  • Complete Practice Suite: Train with versatile audio assets, including MIDI files for tempo adjustment and MP3s featuring bass and cymbal accompaniment for a full ensemble feel.

Theory & Reference

The architecture of the method. These resources provide the mathematical and structural maps for all 924 hexatonic scales and their internal trichord relationships, serving as the definitive reference for the modern improviser.

Lists All Possible Scales Table to Find Any Scale Chord and Scale Application

Sonic Resource Guide

“The Sonic Resource Guide is the definitive roadmap for modern improvisation, distilling all possible pitch combinations into 220 manageable scales. This essential reference empowers musicians to derive every possible chord from any scale and master “outside” playing through advanced concepts like symmetric differences and subset groupings. Whether you are seeking new structural approaches or looking to enrich your harmonic vocabulary, this guide provides the deep technical insights needed to transform your improvisational voice.

Course Highlights:

  • Comprehensive Scale Encyclopedia: Master all 220 possible pitch class combinations, each detailed with note names, prime forms, scale degrees, and related jazz chords for every key.
  • Advanced Improvisational Tools: Unlock “hidden” relationships within scales, including 3 and 4-note subsets and “Symmetric Difference” sets for sophisticated outside playing.
  • Bridges Theory and Performance: Translates complex mathematical set theory into user-friendly musical concepts, perfect for Jazz, Progressive Rock, and Contemporary Classical musicians.
  • Dynamic Compositional Resource: Easily create and analyze new scales on the fly using the included simplified set list index, allowing for a truly unique and varied harmonic palette.

All Possible Chords 012 Jam Tracks and Études Chord and Scale Application

Ultimate 3 Note Chord Lexicon Volume One “012”

Ultimate 3 Note Chord Lexicon: Volume One, 012

Ultimate 3 Note Chord Lexicon Volume One “012”

The Ultimate 3 Note Chord Lexicon series moves beyond traditional chords built in 3rds to explore all 11 alternative ways to construct 3-note structures. These compact voicings are incredibly versatile, offering more substitution possibilities than larger chords across any musical style. Each volume provides specialized piano and guitar voicings, practical application charts, and études to help you master these modern sounds. (Note: Guitarists are encouraged to pair this with our Guitar Technique and Physiology course for optimal execution.)

Course Highlights:

  • Genre-Defying Études: Master “012” pitch class sets through diverse musical styles, including Funk, Swing, and Shuffle, to see how these modern sounds work in any groove.
  • Multi-Tempo Training: Every exercise includes three progressively faster MP3s and MIDI files, allowing you to develop fluency from a slow crawl to high-speed musicality.
  • Comprehensive Ear Training: Use the included rhythm section tracks to ingrain new sounds into your “inner ear” through sight-singing, transcription, and focused listening.
  • Flexible Study Tools: Includes 12-key chord cycles for piano and guitar, bass charts for most exercises, and count-offs that establish a clear key center for every practice session.

All Possible Chords 013 Jam Tracks and Études Chord and Scale Application

Ultimate 3 Note Chord Lexicon Volume Two “013″

Ultimate 3 Note Chord Lexicon: Volume Two "013"

Ultimate 3 Note Chord Lexicon Volume Two “013″

Volume Two: The 013 Chord Lexicon is an essential resource focusing on what is arguably the most versatile structure in modern music. Historically significant and used extensively by John Coltrane, the 013 pitch class set can replace any chord type, functioning as both a consonant and dissonant texture depending on its voicing. Because it is found within Major, Melodic Minor, Harmonic Minor, and Diminished scales, the 013 is an easy-to-play yet powerful substitution tool for every improviser.

Course Highlights:

  • 18 Powerful Modal Frameworks: Master advanced chromatic combinations (like 027-016 and 026-026) to add modern, sophisticated “color” to any song or progression.
  • The Ultimate Chord Substitute: Learn how the “013” can replace nearly any chord type, serving as a powerful tool to modernize “tired” progressions like the I-vi-ii-V turnaround.
  • Seamless Scale Integration: Discover how to use 013s as natural substitutions for Major, Melodic Minor, and Symmetrical Diminished scales to create sophisticated, Coltrane-inspired textures.
  • Diverse Practice Études: Master seven sets of musical études covering everything from Funk to Symmetrical Diminished dominant harmony, all with included bass charts and transposition options.
  • Complete Audio Mastery: Develop fluency with three-speed MP3s and MIDI files for every exercise, allowing you to focus on ear training, transcription, or high-speed performance at your own pace.

Midi Files Included MP3 Jam Tracks Included For Piano or Guitar

Ultimate 3 Note Chord Lexicon Volume Three “014″

Ultimate 3 Note Chord Lexicon: Volume Two "013"

Ultimate 3 Note Chord Lexicon Volume Three “014″

Volume Three: The 014 Chord Lexicon explores one of the most evocative and “edgy” structures in music. Famous for its heavy use in Thelonious Monk’s dissonant textures and Anton Webern’s compositions, the 014 is a powerhouse for modern Jazz and Heavy Metal. While primarily used as a striking dominant 7th substitute, it also functions perfectly as a Diminished 7 or Minor-Major 7 chord, making it an essential tool for creating sophisticated hexatonic scales and Symmetrical Diminished harmonies.

Course Highlights:

  • Modernize Your Harmony: Use the “014” structure to replace tired dominant chord voicings with a sharp, evocative sound reminiscent of Thelonious Monk and Anton Webern.
  • Versatile Modal Tools: Master five sets of études that demonstrate how 014s function as Diminished 7th or Minor-Major 7th substitutes, perfect for Jazz, Blues, and Heavy Metal.
  • Integrated Skill Building: Beyond standard chord diagrams, these études are designed for ear training, sight-reading, and transcription, helping you internalize these dissonant sounds in any key.
  • Pro Practice Assets: Includes rhythm section MP3s at three different tempos and MIDI files for every exercise, plus specialized bass charts and transposed piano p

Midi Files Included All Keys Represented Treble and Bass Clef

COMING SOON: 924 Hexatonic Scales in All 12 Keys

924-Hexatonic-Scales-in-all-keys

924 Hexatonic Scales in All 12 Keys

Finding the specific hexatonic scale you need shouldn’t be a hurdle to your practice. We’ve organized all 924 scales into a streamlined, searchable reference designed for the modern improviser. By focusing on the 50 Prime Forms, you’ll learn to see the underlying architecture behind every scale.

Course Highlights:

  • Architectural Organization: Simplifies the massive library of 924 hexatonic scales by grouping them into 50 Prime Forms, helping you understand the underlying structure and hidden relationships between scales.
  • Comprehensive Coverage: Includes 720 permutations per scale with all 12 keys fully represented to ensure total fretboard or keyboard mastery.
  • Detailed Theoretical Analysis: Provides a deep dive into each scale with Scale Degrees, Forte numbers, and harmonic possibilities for advanced melodic organization.
  • Practical Subset Mapping: Organizes scales as subsets of common structures—such as Major, Melodic Minor, Harmonic Minor/Major, Diminished, and Whole Tone—for easier integration into your vocabulary.

< !-- 5th THEORY AND PRACTICE: 5th THEORY AND PRACTICE BOOK-->

Midi Files Included All Keys Represented Treble and Bass Clef

COMING SOON: 36 Atomic Scale Permutations

36 Atomic Scale Permutations by Bruce Arnold for Muse-eek.com

36 Atomic Scale Permutations

“Atomic Scales” is the definitive term for Charlie Banacos’ specialized patterns for hexatonic mastery. This course is crucial for internalizing scales by dividing them into two distinct trichords (triad pairs), providing a clear, systematic path to fluid execution.

Course Highlights:

  • The “Atomic Scales” Method: Master Charlie Banacos’ specialized hexatonic patterns by breaking scales into two distinct trichords (triad pairs) for a systematic approach to fluid execution.
  • Comprehensive Drill Library: Includes 36 permutations per scale, meticulously transposed across every key to ensure total technical internalization.
  • In-Depth Theoretical Analysis: Gain a deeper understanding of your melodic tools with detailed breakdowns of Scale Degrees, Forte numbers, and Harmonic possibilities.
  • Universal Accessibility: Designed for all instrumentalists with complete Treble and Bass clef compatibility for every exercise.

Midi Files Included All Keys Represented Treble and Bass Clef

COMING SOON: 9240 Trichord Permutations

9240 Trichord Permutations by Bruce Arnold for Muse-eek.com

9240 Trichord Permutations

Explore the full spectrum of 36 trichord pair permutations derived from all 924 possible hexatonic combinations. Scales are categorized into seven harmonic families (Major, Melodic Minor, Harmonic Minor, etc.) for targeted practice. Available in Treble and Bass clef with full MIDI support.

Course Highlights:

  • Total Trichord Spectrum: Explore a massive library of 9,240 trichord pairs derived from all 924 possible hexatonic combinations, offering unparalleled melodic variety.
  • Harmonic Categorization: All scales are organized into seven primary harmonic families (including Major, Melodic Minor, and Harmonic Minor) for highly targeted and efficient practice.
  • Systematic Patterns: Features 36 distinct permutations per hexatonic scale, providing a structured path to internalizing complex interval relationships.
  • Modern Digital Integration: Includes full Treble and Bass clef compatibility for all instruments, plus complete MIDI support for seamless integration into your digital workflow.

Midi Files Included All Keys Represented Treble and Bass Clef

COMING SOON: 10 Trichord Pairs for 924 Hexatonic Scales

10-Trichord-Pairs-for-924-Hexatonic-Scales by Bruce Arnold for Muse-eek.com

10 Trichord Pairs for 924 Hexatonic Scales

A streamlined, essential listing of the 10 specific trichord pairs that comprise each of the 924 hexatonic scales. This is a vital resource for players looking to break down complex scales into manageable, “grippable” three-note cells across all keys.

Course Highlights:

  • Modular Scale Breakdown: Master the essential 10 trichord pairs for each of the 924 hexatonic scales, turning complex structures into manageable, three-note “cells.”
  • Precise Pitch Mapping: Includes detailed Pitch Class Designations and Scale Degrees for every combination to ensure exact melodic accuracy.
  • Advanced Structural Insights: Access a comprehensive technical profile for each scale, including Prime Forms and Forte numbers for deeper harmonic analysis.
  • Full Key & Digital Support: Fully transposed across all 12 keys and includes MIDI files, making it easy to practice or integrate into your digital workstation.

Midi Files Included All Keys Represented Treble and Bass Clef

COMING SOON: 924 Hexatonic Scales Grouped by Prime Form

924-Hexatonics-Grouped-by-Prime-Form by Bruce Arnold for muse-eek.com

924 Hexatonic Scales Grouped by Prime Form

Master the internal architecture of melody. By grouping all 924 scales into their 50 parent Prime Forms, this course reveals the hidden relationships between seemingly unrelated scales, allowing you to organize your harmonic vocabulary more efficiently.

Course Highlights:

  • Architectural Mastery: Master the internal structure of melody by grouping all 924 scales into their 50 parent Prime Forms, revealing the hidden relationships between seemingly unrelated sounds.
  • Efficient Vocabulary Organization: Grouping scales by shared Prime Forms allows you to categorize and internalize your harmonic vocabulary more systematically.
  • Comprehensive Technical Profile: Provides deep analytical insights for every scale, including Scale Degrees, Forte numbers, and Prime Form designations.
  • Universal Practice Tools: Every scale is represented in all 12 keys and includes MIDI files for seamless practice and digital integration.

Midi Files Included All Keys Represented Treble and Bass Clef

COMING SOON: Hexatonic Chords: Root, 1st, and 2nd Inversions

Hexatonic-Chords-Root-1st-2nd-Inversions by Bruce Arnold for muse-eek.com

Hexatonic Chords: Root, 1st, and 2nd Inversions

A complete guide to the vertical application of hexatonic scales. Learn to voice and play every possible three-note chord derived from the hexatonic system across all 12 keys and inversions.

Course Highlights:

  • Vertical Harmonic Mastery: A comprehensive guide to the vertical application of hexatonic scales, teaching you to voice and play every three-note chord possible within the system.
  • Complete Inversion Library: Master 9,240 patterns covering Root, 1st, and 2nd inversions for every trichord pair, ensuring total fretboard or keyboard fluency.
  • Structured Chord Groupings: Organizes the 924 hexatonic scales into 10 specific trichord pair groupings per scale, transposed across all 12 keys.
  • Precision Practice Tools: Includes MIDI files for every key to ensure accurate pitch representation and a streamlined practice experience.

Midi Files Included All Keys Represented Treble and Bass Clef

COMING SOON: Hexatonic Modal Sequencing of Trichords

Hexatonic-Modal-Sequencing-of-Trichords by Bruce Arnold for muse-eek.com

Hexatonic Modal Sequencing of Trichords

The first level of Charlie Banacos’ “Double Mambos” concept. This course presents six essential sequencing patterns across all keys and harmonic categories. It is the perfect entry point for musicians seeking to move past simple scale runs into sophisticated modal shapes.

Course Highlights:

  • Intro to “Double Mambos”: Master the first level of Charlie Banacos’ legendary concept, using six essential sequencing patterns to move beyond simple scale runs into sophisticated modal shapes.
  • Comprehensive Modal Permutations: Includes 6 specific modal sequencing patterns per scale, fully transposed across all 12 keys for total technical command.
  • Harmonic Framework: Scales are strategically organized by their relationship to common seven-note scales, making it easier to apply these shapes to familiar chord progressions.
  • Universal Compatibility: Written with complete Treble and Bass clef support, ensuring accessibility for all instrumentalists looking to expand their melodic vocabulary.

Midi Files Included All Keys Represented Treble and Bass Clef

COMING SOON: Hexatonic Modal Sequencing with 2-Note Approach Patterns

Hexatonic-Modal-Sequencing-of-Trichords-with-Approach-Notes by Bruce Arnold for muse-eek.com

Hexatonic Modal Sequencing with 2-Note Approach Patterns

An advanced fusion of two classic Banacos techniques. By adding approach notes to the Level 1 Atomic Scales, this course builds the “Post-Bebop” vocabulary used by icons like John Coltrane and Eric Dolphy. Gain complete control over chromaticism and scale-degree targeting.

Course Highlights:

  • Advanced Technique Fusion: Combines two legendary Banacos methods by adding chromatic approach notes to Level 1 Atomic Scales, creating a sophisticated “Post-Bebop” vocabulary.
  • Iconic Melodic Vocabulary: Master the chromaticism and scale-degree targeting techniques used by jazz icons like John Coltrane and Eric Dolphy.
  • Extensive Pattern Library: Features 12 trichord patterns utilized as approach note figures, with 6 distinct permutations for every scale to build fluid control.
  • Universal Instrumental Support: Provides complete Treble and Bass clef compatibility, making these advanced concepts accessible to all musicians.

Midi Files Included All Keys Represented Treble and Bass Clef

COMING SOON: 924 Hexatonic Triples

924-Hexatonic-Triples by Bruce Arnold for muse-eek.com

924 Hexatonic Triples

This course divides each scale into three distinct 2-note patterns. This unique approach opens up a new melodic universe, offering intervals and contours that standard scale-wise playing cannot achieve. Includes PDF and MIDI for all 12 keys

Course Highlights:

  • New Melodic Horizons: Discover a unique “Triples” approach that divides each hexatonic scale into three distinct two-note patterns, unlocking intervals and contours beyond standard scale-wise playing.
  • Extensive Permutation Library: Master 60 permutations per scale, organized into structured two-note groups to help you navigate a “new melodic universe.”
  • In-Depth Theoretical Breakdown: Includes detailed analysis of Scale Degrees, Forte numbers, and harmonic possibilities for every scale combination.
  • Full Digital & Notation Support: Features complete Treble and Bass clef compatibility, high-quality PDFs, and MIDI files for all 12 keys.

Improvisational Studies

Transform theory into melody. This section features our extensive series of études and application guides, teaching you how to use specific pitch class sets to navigate modern jazz, modal, and chromatic environments.

Midi Files Included All Keys Represented Treble Clef Études in 3/4,4/4,5/4,6/4,7/4

Time Transformation

Time Transformation by Bruce Arnold for Muse Eek Publishing Company

Time Transformation

Time Transformation is designed for students ready to move beyond conventional melodic and rhythmic patterns. This course explores a new frontier of improvisation based on contemporary pitch class sets, asymmetrical phrasing, and time-level superimposition. By utilizing 027 trichords and 12-tone aggregates, students will develop the technical and conceptual tools required for modern performance.

Course Highlights:

  • Contemporary Melodic Theory: Explore hexatonic scales and trichord-based melodic construction.
  • Advanced Rhythmic Concepts: Learn time-level superimposition and improvising across different rhythmic levels.
  • Complex Phrasing: Break away from standard patterns with targeted etudes in 3/4, 4/4, 5/4, 6/4, and 7/4 time signatures.
  • Sight Reading: Develop proficiency with etudes covering all key centers.
  • Interactive Audio Study: Practice with downloadable MP3s featuring modal vamps and superimposed metronome clicks (3 to 7 clicks per measure).

Midi Files Included All Keys Represented Treble Clef Études in 3/4,4/4,5/4,6/4,7/4

Set Theory for Improvisation Ensemble Method: Hexatonic 027 027

Set Theory for Improvisation 027 027 by Bruce Arnold for Muse Eek Publishing Company

Set Theory for Improvisation Ensemble Method: Hexatonic 027 027

The Set Theory Ensemble Book series provides a roadmap for musicians looking to break free from traditional patterns. By focusing on non-tertial melodic lines that weave in and out of tonal centers, this course teaches you the backbone of modern improvisation. Through 12 targeted etudes using 027 027 pitch class sets, you will discover fresh melodic possibilities for Major 7, Minor 7, and Dominant 7th sus4 chords.

Course Highlights:

  • Modern Melodic Construction: Develop hexatonic melodies using contemporary music theory constructs.
  • 12 Key Mastery: Includes 12 etudes (one in every key) that progress from highly diatonic to advanced non-diatonic structures.
  • Versatile Application: Learn to apply these lines over various chord types to control and explore different levels of dissonance.
  • Comprehensive Concept Study: Each etude explores unique combinations of note groupings, rhythmic density, and melodic range.
  • Foundational Learning: Perfect for students seeking a focused deep-dive into the concepts expanded upon in Time Transformation.

Midi Files Included All Keys Represented Treble Clef Études in 3/4,4/4,5/4,6/4,7/4

Set Theory for Improvisation Ensemble Method: Hexatonic 027 016

Set Theory for Improvisation 027016 by Bruce Arnold for Muse Eek Publishing Company

Set Theory for Improvisation Ensemble Method: Hexatonic 027 016

Ready to develop a groundbreaking approach to your solos? The Set Theory Ensemble Book series teaches you to build modern, hexatonic melodies using non-tertial lines that move fluidly in and out of the key center. By focusing on 027 016 pitch class sets, this volume provides the essential tools for creating sophisticated melodic lines over complex chord structures.

Course Highlights:

  • Targeted Chord Mastery: Discover highly effective melodies specifically designed for Dominant 7th, Minor 7b5, and Minor 6th chords.
  • 027 016 Pitch Class Exploration: Master 12 etudes that utilize this specific set theory construct to expand your harmonic vocabulary.
  • Progressive Difficulty: Studies range from diatonic foundations to high-level non-diatonic examples, allowing you to control the level of dissonance.
  • Dynamic Musicality: Every etude explores unique combinations of rhythmic density, metric levels, and melodic range across all 12 keys.
  • Modern Melodic Backbone: Shift away from traditional scales toward the “modern sound” used by contemporary improvisers.

Midi Files Included All Keys Represented Treble Clef Études in 3/4,4/4,5/4,6/4,7/4

Tertial Intervallics Volume One

Tertial Intervallics Volume One by Bruce Arnold for Muse Eek Publishing Company

Set Theory for Improvisation Ensemble Method: Hexatonic 027 016

Tertial Intervallics Volume One teaches you to harness the power of repetitive intervals to create cohesive, modern melodic lines. By utilizing consistent four-note structures (7th chords) over varying harmonic backgrounds, your ear begins to perceive the “pattern” as the primary logic, allowing for sophisticated movement through any key center.

Course Highlights:

  • Comprehensive Chord Coverage: Master intervallic patterns for 13 essential structures, including Δ7, -7, 7sus4, -7b5, °7, Δ7#5, Δ7#11, and more.
  • Pattern-Based Logic: Learn how to use interval repetition to make complex or “outside” melodic lines sound musically sensible to the listener.
  • Multifaceted Application: A versatile resource perfect for improving sight reading, understanding chordal relationships, and developing a contemporary intervallic vocabulary.
  • Ear Training Integration: Optimized for use with drones and vamps to help you internalize the relationship between intervallic lines and tonal centers.

Included Materials:

  • 200-Page PDF: Extensive written exercises and conceptual guides.
  • Audio & MIDI Suite: 18 MP3s and 18 MIDI files to hear patterns at various tempos and harmonic settings.
  • Rhythm Tools: Includes “Long Line Rhythm” PDF and Video to help master phrasing.
  • MetroDrone: Specialized MP3 to facilitate the recommended “drone-based” practice method.

Midi Files Included All Keys Represented Treble Clef Études in 3/4,4/4,5/4,6/4,7/4

013 Hexatonic Études: Pitch Class Set Exercises for Dominant 7th Key Center

Ultimate 3 Note Chord Lexicon

Set Theory for Improvisation Ensemble Method: Hexatonic 027 016

Unlock a modern, sophisticated sound with 013 Hexatonic Études. This course focuses on the “pivot” technique—alternating between two three-note groups (013 pitch class sets) to create fresh, non-traditional melodies. Designed specifically for Dominant 7th chords, these exercises help you break out of common patterns and master one of music’s most essential harmonic structures.

Course Highlights:

  • 336 Comprehensive Études: Explore 28 unique hexatonic scales across all 12 keys, providing a massive library of modern sounds.
  • Advanced Melodic “Pivoting”: Learn to alternate between two 013 pitch class sets (half-step and minor third intervals) for a cutting-edge improvisational feel.
  • Multi-Speed Learning: Each étude is recorded at three different tempos, making the material accessible for everyone from beginners to advanced professionals.
  • Ear Training & Key Recognition: Use these exercises to improve your ability to identify hexatonic intervals and strengthen your dominant key center recognition.
  • Sight Reading Mastery: All études are written at a 16th-note metric level, serving as an excellent daily tool for improving rhythmic reading speed.

Included Materials:

  • Digital PDF: 336 pages of exercises (one page per étude).
  • High-Quality MP3s: Audio examples for every étude at three different speeds.
  • MIDI Files: Total flexibility to practice at any tempo using your favorite software.
  • Pitch Class Set Guide: A clear explanation of how to think in and apply pitch class sets to your playing.

Midi Files Included All Keys Represented Treble Clef Études in 3/4,4/4,5/4,6/4,7/4

Symmetrical Trichord Pairs

Symmetrical-Trichord-Pairs by Bruce Arnold for Muse Eek Publishing Company Symmetrical Trichord Pairs

Symmetrical Trichord Pairs

Symmetrical Trichord Pairs is an 847-page exhaustive reference guide exploring the formation of two three-note groups with identical structures. By focusing on chord tones and available tensions (avoiding “avoid notes”), this book provides a roadmap for “safe” yet highly sophisticated modern improvisation. From the 027 structures favored by modern jazz and metal players to the dissonant 013 sets used in avant-garde rock, this book helps you find your personal sonic identity within 574 possible combinations.

Course Highlights:

  • 847-Page PDF Reference: An immense library exploring 11 different symmetrical structures across all 12 keys.
  • Iconic Sound Analysis: Learn the structures used by legends: 014 and 016 (Thelonious Monk), 013 (John Coltrane), and 037 (McCoy Tyner).
  • Practical Sequencing: Every pair is sequenced up one octave to help you visualize and execute fluid melodic lines immediately.
  • Targeted Chord Application: Focuses strictly on “tension-free” improvisation, ensuring every note you play fits perfectly over your chosen chord type.
  • Strategic Learning Path: Includes guidance on choosing structures that work across multiple chord types to maximize your practice time.

How to Master Symmetrical Pairs:

  • Versatility Training: Identify pairs that function over Major, Minor, and Dominant chords for seamless soloing.
  • Genre Adaptation: Discover which pitch class sets best fit your style, from Blues-based Dominant structures to Heavy Metal quartal (027) sounds.
  • Interval Consistency: Match specific trichords to the internal interval logic of the music you are performing.

Midi Files Included All Keys Represented Treble Clef Études in 3/4,4/4,5/4,6/4,7/4

Trichord Sweep Pairs Guitar Instrumentalist Sweep Arpeggios

Trichord Sweep Pairs Guitar Instrumentalist Sweep Arpeggios by Bruce Arnold for Muse Eek Publishing Company

Trichord Sweep Pairs Guitar Instrumentalist Sweep Arpeggios

Trichord Sweep Pairs is the ultimate resource for guitarists and instrumentalists looking to master modern sweep picking. By stacking two identical 3-note structures (trichords), this course moves past basic triads into 2,440 pages of unique, cutting-edge sweep patterns. Whether you play Jazz, Metal, or Fusion, these patterns provide a logical, mathematical approach to mastering the entire fretboard.

Course Highlights:

  • 2,440 Pages of Patterns: An exhaustive exploration of every possible sweep combination based on 12 essential pitch class sets.
  • Guitar-Specific Diagrams: Includes optimized fretboard diagrams and suggested fingerings to help guitarists implement these sweeps immediately.
  • Pitch Class Set Logic: Organized by “Prime Form” (012 through 048), allowing you to understand the internal interval relationships of every sweep.
  • Video Masterclasses: Includes 80 minutes of video, featuring live performances and demonstrations of 012, 013, 014, 015, and 016 sets.
  • Multi-Genre Application: Master the “027” and “037” sounds common in Metal and Jazz, or explore the “013” sounds used in avant-garde compositions.

What’s Included:

  • Technical PDFs: Divided into “Diagrams” (choice patterns) and “Suggested Fingerings” (all possible structures) for focused study.
  • 12 Études: Musical studies designed to help you read and apply these sweeps in real-world situations.
  • Audio Suite: 6 MP3s of professional recordings demonstrating these concepts in action.
  • Theory Guide: Simple, slow-paced video explanations of Pitch Class Set Theory—no prior theory knowledge required.

Midi Files Included All Keys Represented Treble Clef Études in 3/4,4/4,5/4,6/4,7/4

Tertial Octatonics

Tertial Octatonics by Bruce Arnold for Muse Eek Publishing Company

Tertial Octatonics

Are you ready to move past tired arpeggio patterns? Tertial Octatonics provides a modern alternative by exploring the full potential of eight-note scales. By using two tetrads (4-note chords) as a vehicle, this course teaches you how to create cutting-edge sounds over Dominant 7th and Dominant 7sus4 key centers, expanding your harmonic palette far beyond the standard diminished scales.

Course Highlights:

  • Tetrad Combination Mastery: Learn every possible way to combine two 7th chords to form unique octatonic scales.
  • 29 Octatonic Scales: Explore a vast library of scales that serve as professional alternatives for modern improvisation and composition.
  • Enhanced Chord Knowledge: Use “two tetrad” combinations to master your 7th chords while simultaneously building complex melodic lines.
  • Practical Application: Get specific hints and exercises on applying these structures to real-world chord progressions for a “modern” sound.
  • Comprehensive Reference: Detailed coverage of combinations for 11 common 7th chords, including Major 7th, Minor 7b5, Diminished 7th, and Major 7#11.

What You’ll Receive:

  • Extensive Exercise Library: Over 250 pages of possibilities and targeted exercises across all major chord types.
  • Aural Training: Specialized information on how to hear and internalize these advanced eight-note structures.
  • Practice Strategies: Clear, step-by-step guidance on how to practice and implement these scales into your playing.
  • Theoretical Foundation: Background information on the origin and construction of each octatonic scale.

Midi Files Included All Keys Represented Treble and Bass Clef

COMING SOON: 924 Hexatonics with 24 Aggregate Patterns

924-Hexatonics-with-Aggregate-Patterns by Bruce Arnold for muse-eek.com

924 Hexatonics with 24 Aggregate Patterns

Using the concept of “Symmetrical Difference,” this course presents all hexatonic scales as part of 12-tone aggregate lines. The result is a collection of melodic phrases of immense complexity and modern beauty.

Course Highlights:

  • The Symmetrical Difference Concept: Experience a modern approach that presents all hexatonic scales as part of 12-tone aggregate lines, resulting in melodic phrases of immense complexity and beauty.
  • Extensive Aggregate Library: Master 24 aggregate permutations per scale, fully transposed into every key to build a truly modern melodic vocabulary.
  • Detailed Analytical Profile: Gain deep structural insights with detailed breakdowns of Scale Degrees, Forte numbers, and Set Class listings for every scale.
  • Digital Practice Integration: Includes MIDI files for every exercise, ensuring total pitch accuracy and an efficient workflow for mastering these complex lines.

Technique

Bridging the gap between the mind and the fingers. These technical manuals focus on the physical mechanics required to execute 3-note and 6-note groupings with speed, clarity, and rhythmic precision.

Midi Files Included Technical Studies No book just exercise

ChopBusters

ChopBusters

ChopBusters

The ChopBuster series is a comprehensive collection of 18 specialized volumes designed to bridge the gap between abstract set theory and fluid physical execution. By focusing on specific pitch-class sets (such as 013, 027, and 013679) and structured “Pyramid” or “Rotation” routines, these exercises provide a systematic path to mastering modern improvisational shapes. Whether you are navigating diatonic chords of the major modes, symmetrical diminished structures, or complex trichord sequences, the series offers a rigorous workout for all instrumentalists looking to expand their technical and harmonic range.

Course Highlights:

  • Comprehensive Pitch-Class Mastery: A rigorous 18-volume series dedicated to internalizing advanced structures like 013, 025, 027, and complex hexatonic sets through targeted technical drills.
  • Multi-Dimensional Study Patterns: Features a wide variety of exercise types, including Ascending/Descending sequences, “Pyramid” routines, rotations, and octave displacements for total fretboard and keyboard fluency.
  • Harmonic & Melodic Versatility: Designed for all instrumentalists, these exercises cover everything from closed-position chord voicings for chordal instruments to sophisticated “sweeps” and modal sequences for melodic players.
  • Deep Modal Integration: Systematically explores every key and mode—including Major, Symmetrical Diminished, and more—to ensure you can apply modern intervals naturally in any musical context.
  • Integrated Digital Practice Tools: Every volume is supported by MIDI files and multi-tempo MP3s, allowing students to verify pitch accuracy, develop their ear, and progressively build speed from a crawl to professional tempos.

44 specific two-triad/trichord combinations All (Treble and Bass clef included) MetroDrone® MP3s for all 12 keys

Improvisation, Composition, Ear Training, Sight Singing

Harmonic and Melodic Equivalence

Harmonic-and-Melodic-Equivalence-Series-BUNDLE-by-Bruce-Arnold-for-Muse-Eek-Publishing-Inc-Harmonic-and-Melodic-Equivalence-Series-Series

Harmonic and Melodic Equivalence

The Harmonic and Melodic Equivalence Series is a groundbreaking collection of courses dedicated to the art of Pitch Class Set Improvisation. By isolating and exploring 44 unique two-triad and two-trichord pairs, this series provides a systematic bridge between abstract set theory and practical application. These combinations are selected specifically for their modern melodic contours and harmonic depth, reflecting the sophisticated vocabulary used by advanced composers and improvisers.

More than just a technical manual, this series serves as a high-level ear training and sight-singing resource. By working through these exercises against a fixed key center (supported by MetroDrone® technology), musicians learn to internalize complex structures without losing their harmonic anchor. Whether you are a composer looking for new textures or a performer aiming for “Post-Bebop” fluency, this series offers a unique and comprehensive path to mastery that is currently unmatched in contemporary music education.

Course Highlights:

  • Advanced Pitch Class Set Improvisation: A groundbreaking series of books exploring 44 unique two-triad and two-trichord pairs, offering a comprehensive roadmap for modern melodic and harmonic development.
  • Holistic Musical Development: While designed for advanced improvisation, these exercises serve as a powerful tool for sight singing and ear training, specifically engineered to improve key retention and intervallic awareness.
  • Systematic Key Center Mastery: Each course includes 12 MetroDrone® MP3s and specific technical exercises to help you internalize complex structures within a stable key center.
  • Practical Application & Background: Every volume includes a detailed PDF providing theoretical background and clear instructions on applying these shapes to various chord types in all 12 keys.
  • Versatile Learning Formats: Available as individual volumes or a complete bundle, each course features treble and bass clef exercises and MIDI support for all instrumentalists.

Midi Files Included Technical Studies No book just exercise

Trichord Pairs: Scale & Prime Form Reference

Trichord-Pairs-Scale-and-Prime-Form-Reference by Bruce Arnold for muse-eek.com

9240 Trichord Pairs: Scale & Prime Form Reference

This massive resource provides a “birds-eye view” of the entire 12-tone system by organizing a vast collection of trichord pairs under their respective parent scales and Prime Forms. By understanding the “parent” structure of a trichord pair, musicians can better organize their practice and see the hidden connections between different melodic shapes. This course is essential for players who want to simplify complex harmonic relationships and develop a more structured approach to modern improvisation across the entire chromatic spectrum.

Course Highlights:

  • Comprehensive Trichord Mapping: A massive library of trichord pairs systematically grouped by their parent scales and Prime Forms for a structured view of the 12-tone system.
  • Universal Harmonic Relationships: Includes all 12 trichords, meticulously categorized by their specific relationships to eight common 7th chord types to ensure practical application.
  • Detailed Structural Analysis: Features an in-depth breakdown for every combination, including precise Scale Degrees and Prime Form designations for advanced study.
  • Optimized Practice Tools: Every exercise is presented in Treble Clef and includes high-quality MIDI files to help you master these complex shapes with total pitch accuracy.

Midi Files Included Technical Studies No book just exercise

COMING SOON: Trichord Harmonic Analysis

Trichord-Harmonic-Analysis by Bruce Arnold for muse-eek.com

Trichord Harmonic Analysis

This course provides a systematic map of every three-note subset hidden within Charlie Banacos’ legendary chord tone and tension lists. Designed to help musicians “mushroom” their existing vocabulary, the system shows you how to take a simple melodic idea and transpose it onto sophisticated harmonic structures to create cutting-edge colors with ease. By bridging the gap between basic shapes and complex tensions, this resource allows you to navigate modern jazz and contemporary fusion harmonies with total confidence and a refined sonic palette.

Course Highlights:

  • Complete Harmonic Analysis: Gain a deep understanding of all 12 trichords meticulously analyzed in every key for total melodic flexibility.
  • Systematic Chord Categorization: Each of the 12 trichords is categorized by its relationship to eight common 7th chord types, making it easy to apply these shapes to standard progressions.
  • Vocabulary Expansion (Mushrooming): Learn to map simple three-note ideas onto complex tension lists to generate sophisticated, “post-bebop” melodic lines effortlessly.
  • Digital Practice Tools: Includes professional Treble Clef notation and MIDI files for every exercise to ensure absolute pitch accuracy and faster technical mastery.

Midi Files Included Technical Studies No book just exercise

COMING SOON: Turnarounds with Trichords

Turnarounds-with-Trichords by Bruce Arnold for muse-eek.com

Turnarounds with Trichords

This course is designed to bridge the gap between abstract theory and real-world performance. By applying the “mushrooming” concept to standard turnaround progressions, these etudes provide a practical path to mastering modern jazz colors. The curriculum is structured to challenge your fluency, moving from exercises with a full-measure focus to rapid, two-beat changes. This systematic approach ensures that you can navigate common harmonic shifts with the sophisticated, cutting-edge vocabulary used by today’s top improvisers.

Course Highlights:

  • Functional Progression Mastery: Bridge the gap between theory and performance by applying advanced trichord “mushrooming” techniques directly to standard turnaround patterns.
  • Progressive Rhythmic Challenges: Develop fluid execution by moving from full-measure focus to rapid two-beat changes, ensuring you can handle fast-moving harmonic environments.
  • Internalize Modern Colors: Learn to naturally weave sophisticated jazz and post-bebop colors into your improvisations through targeted, musical etudes.
  • Digital Practice Support: Includes MIDI files for every exercise, allowing you to practice at any tempo and verify your pitch accuracy in every key.

Guitar Studies

Fretboard-specific mastery. These resources translate complex hexatonic concepts specifically for the guitar, focusing on unique fingerings, arpeggio shapes, and fretboard visualization techniques.

Midi Files Included Technical Studies No book just exercise

COMING SOON: 013 Hexatonic Études for Dominant 7th

Turnarounds-with-Trichords by Bruce Arnold for muse-eek.com

013 Hexatonic Études for Dominant 7th

Unlock the potential of the most influential pitch class set in modern jazz and contemporary music. This course provides a deep dive into the 013 structure, specifically targeting its application over Dominant 7th chords to create high-level melodic vocabulary. Through a series of specialized études, you will learn to navigate these sophisticated shapes with confidence, gaining the “cutting-edge” sound used by elite modern improvisers to break away from traditional scale-based playing.

Course Highlights:

  • Contextual Application: Master the 013 pitch class set through musical études written over standard vamps and progressions, ensuring immediate real-world usability.
  • High-Level Melodic Vocabulary: Develop sophisticated lines specifically designed for Dominant 7th chords, providing you with modern “post-bebop” colors that cut through any musical mix.
  • Rhythmic Diversity: Move beyond predictable eighth-note patterns with modern phrasing and rhythmic variations that reflect contemporary improvisational styles.
  • Massive Audio Support: Includes an expansive library of over 12,000 MP3s, serving as a powerful tool for both ear training and immersive play-along practice.

Ear Training

If you can’t hear it, you can’t play it. Using the renowned Muse-Eek method, these courses train your ear to recognize modern tonal relationships and internalize the unique “colors” of every trichord and hexatonic scale.

MP3 Files Included Ear Training Studies An Important Ear Training Course

COMING SOON: SerialEar: The Tonal Relationship Method

Turnarounds-with-Trichords by Bruce Arnold for muse-eek.com

SerialEar: The Tonal Relationship Method

Inspired by the legendary Charlie Banacos, SerialEar is a transformative ear training method that moves beyond isolated intervals to teach you how to hear the fundamental three-note “DNA” of modern music. By practicing these sounds against a constant drone, you learn to map the entire 12-tone clock relative to a singular harmonic “Home.” This course functions as a daily meditation on resonance, designed to create total transparency between your ear, your mind, and your instrument. It is an incredibly rich resource that bridges the gap between pure ear training and high-level improvisation, allowing you to master every possible three-note combination found in music.

Course Highlights:

  • Beyond Interval Training: Move past “intervals in a vacuum” to internalize the 3-note DNA that forms the building blocks of modern harmonic structures.
  • Relative Pitch Mastery: Map the 12-tone clock against a fixed drone to develop a deep, visceral understanding of how every note resonates relative to a tonal center.
  • Dual-Purpose Practice: Use these files as a powerful ear training tool or as a play-along resource to improve your ability to improvise around any 3-note combination.
  • Total Musical Transparency: A “daily meditation” on sound designed to remove the barriers between what you hear in your head and what you execute on your instrument.

Advanced Identification 9240 Files

2. COMING SOON: Hexatonic One-Note Ear Training

A high-level challenge for the serious ear. You are presented with a trichord-pair key center—ranging from standard progressions to highly dissonant clusters—and asked to identify a single pitch. This builds the ability to recognize tonal centers in even the most exotic harmonic environments.

 

Composing

Beyond improvisation. Explore how to use these modern tools to craft original music, using symmetrical logic and set theory to develop a unique and sophisticated compositional voice.

MP3 Files of Compositions Composing Studies Scores for Compositions

Tools for Modern Improvisation

cover for Tools for Modern Improvisation by Bruce Arnold exploring hexatonic and pitch class set uses for composition and improvisation

Tools for Modern Improvisation

This course is a comprehensive collection of the advanced methods I’ve employed over the last 25 years to push the boundaries of improvisation. It bridges the gap between high-level theory and practical facility, providing technical exercises, scores from my original compositions, and 20 audio recordings to demonstrate these systems in rock, blues, jazz, and classical idioms.

Course Highlights:

  • 23rd Chords: A 12-tone aggregate technique learned from Charlie Banacos, including 10,368 pages of facility exercises and 12-tone combination PDFs.
  • Extensive Pitch Class Set Analysis: In-depth application and etudes for 013, 014, 015, 016, 025, 026, and 027 sets.
  • Composition Scores & Transcriptions: Full scores for “Blue Eleven,” “12 Tone Boogie,” “Blue Lotus,” and a transcribed guitar solo for “A Few Dozen.”
  • Modern Standards: Solo guitar arrangements for “Stella by Starlight” and “A Child is Born” using modern applications.
  • 12-Tone Boogie: Practical facility exercises with specific fingering included for guitarists.
  • Application Charts: Master guides showing how to apply various pitch class sets to chords in all twelve keys.
  • Advanced Scale Theory: Detailed lessons on Symmetrical Diminished scales, altered dominants, and intervallic applications.

Midi Files Included MP3 Audio of Compositions Scores for Compositions

My Music: Exploration in the Application of 12 Tone Technique to Jazz Composition and Improvisation

book cover for My Music: Explorations in the application of 12 tone techniques to jazz composition by Bruce Arnold for Muse Eek Publishing Company

My Music: Exploration in the Application of 12 Tone Technique to Jazz Composition and Improvisation

Achieve a strikingly original sound by applying late 20th-century 12-tone compositional methods to jazz improvisation. Bruce Arnold explains how to move past traditional tertial harmony using trichords to create fresh, non-standard musical structures. Whether you want to replace traditional chords entirely or find sophisticated substitutes for forms like the 12-bar blues, this book provides a highly organized roadmap for the contemporary composer and improviser.

Course Highlights:

  • Pitch Class Set Application: In-depth use of sets 013, 014, 015, 016, and 027 in live improvisational settings.
  • Trichord Harmony: Methods for using four-trichord arrays and non-symmetrical groupings to replace standard chord voicings.
  • 23rd Chords: Sophisticated 12-tone aggregate techniques applied to modern jazz composition.
  • Serial Improvisation: Techniques for creating “pseudo 12-tone improvisational fields” that move beyond typical chord charts.
  • Reimagined Standards: Applications of trichord structures to classic forms like Giant Steps and the 12-bar blues.
  • Scores & Audio: Includes full scores for all discussed compositions and accompanying audio files (MP3 for digital, CD for physical).
  • Theory Simplified: Clear explanations of Post-Tonal Theory and Integer Notation for the practical musician.

Pitch Classes used in Each Composition MP3 Audio plus some Video Scores for Compositions

Bruce Arnold Composition Compilation 2nd Edition

Book cover for Bruce Arnold Composition Compilation by Bruce Arnold for Muse Eek Publishing

Bruce Arnold Composition Compilation 2nd Edition

Spanning nearly 30 years of creative output (1990–2018), this collection features 90 compositions across a vast landscape of styles, including Jazz, Funk, Rock, Metal, Country, and Blues. This is an essential resource for any musician looking to see the real-world application of Pitch Class Set theory, with many charts including specific set listings and improvisational guides used by Bruce Arnold himself.

Course Highlights:

  • 90 Full Compositions: A massive library of music ranging from trio settings to intricate solo guitar pieces.
  • Pitch Class Integration: Most charts supply the specific sets used for construction, providing a direct roadmap for improvisers.
  • Multi-Genre Application: Demonstrates how 12-tone and serial techniques can be applied to everything from “WoodPecker Blues” to Metal and Modern Jazz.
  • Interactive Audio/Video: The Audio and Video edition includes a full live performance at the Provincetown Playhouse.
  • Cross-Referenced Study: Designed to work alongside Tools for Modern Improvisation and My Music for deep-dive technical study.
  • Comprehensive 013 Blues: Includes a complete series of 013-based Blues compositions in all twelve keys.

]]> Hexatonics & Pitch Class Set Improvisation https://muse-eek.com/hexatonic-scales-the-pitch-class-set-approach/ Sun, 05 Apr 2026 05:47:43 +0000 https://muse-eek.com/?page_id=1429286 Continue reading →]]>

Hexatonics and Pitch Class Set Improvisation Workshop

A Universal Language for Modern Improvisation & Composition

Hexatonic-and-Pitch-Class-Set-Improvisation

For decades, Pitch Class Set (PCS) theory was confined to academic analysis of 20th-century classical music. I’ve spent my career proving it is a living, breathing language for any genre. From heavy metal and rock to avant-garde jazz and early music, PCS provides the structural DNA for modern expression.

What is Pitch Class Set Improvisation?

At its core, Pitch Class Set Improvisation (PCSI) is a method of organizing musical ideas by looking at the DNA of a sound. Instead of thinking in traditional scales or chords, we categorize groups of notes based on the specific intervals (half-steps) between them.

Whether it’s something as familiar as a C Major scale or as modern as superimposing “015” clusters over a jazz standard, Pitch Class Set Improvisation provides a unified language for it all.

How the Math Works

We use a basic numbering system to identify these sets. For example, the notes C, D, and G form the set 027:

C = 0 (Starting point) | D = 2 (Half-steps above C) | G = 7 (Half-steps above C)

If you can follow that logic, you’ve already mastered the foundation of the system.

I. Core Theoretical Foundations of Pitch Class Set Improvisation

What is a Trichord? Beyond the Traditional Triad

For most musicians, the word “chord” immediately brings to mind tertian harmony—chords built by stacking thirds (Major, Minor, Augmented, or Diminished). While this system has served Western music for centuries, it is only one way to organize sound.

A Trichord is simply any collection of three distinct pitch classes. By moving beyond thirds, we open the door to “intervallic thinking.” Instead of thinking “Root, 3rd, 5th,” we begin to think in terms of intervals (half-steps, whole-steps, fourths, etc.). This shift is revolutionary for an improviser: it frees you from the gravity of “key centers” and allows you to navigate the chromatic scale with structural logic rather than just “playing outside.”

The 12 Essential Pitch Class Sets: A Master List

In the world of Pitch Class Set (PCS) theory, we use a concept called “Prime Form” to categorize sounds. Think of Prime Form as the “musical DNA” or the most condensed version of a chord. Because we treat all octaves as equal and ignore the order of the notes, there are mathematically only 12 unique three-note shapes (trichords) possible in our 12-tone system.

Whether you play a C Major triad (C-E-G), an F Major triad, or a G Major triad in second inversion, they all share the same Prime Form: [0,3,7]. By mastering these 12 basic “formulas,” you aren’t just learning 12 chords; you are learning the structural foundation for every possible three-note combination in existence. This radical simplification allows you to see the entire fretboard as a finite, manageable map of sonic possibilities.

Unordered vs. Ordered Sets: Understanding the Musical DNA

To truly master Pitch Class Set Improvisation using hexatonics and pitch class sets, one must understand the difference between Ordered and Unordered sets.

  • Ordered Sets: This is what we typically think of as a melody or a specific voicing. The sequence of notes matters.
  • Unordered Sets: This is the “cloud” of notes available to you. Much like a master chef looks at a basket of three ingredients and sees infinite ways to combine them, an improviser looks at an unordered pitch class set as a source of raw material.

The set remains the same regardless of inversions, registers, or octaves. This is why the system is so powerful for the guitar: a “set” isn’t a “grip” or a “fingering”—it is a harmonic identity. When you internalize the sound of an [0,1,3] set, you recognize it whether it’s played as a tight cluster in the low register or as a wide-interval skip across three octaves. You are no longer playing shapes; you are playing meaning.

Why Organize Sound with Pitch Class Set Improvisation Ideas?

The biggest advantage of Pitch Class Set Improvisation is efficiency. It drastically reduces the number of “shapes” you need to learn. In Pitch Class Set Improvisation, any combination or inversion of C, D, and G is simply an 027. By identifying these core identities, we discover there are only 12 possible three-note combinations (trichords) in total.

“Learning 12 identities is much easier than memorizing hundreds of disconnected melodic and harmonic fragments.”

Another way you could think about this is: Wouldn’t it make sense to have all 3 note melodies and harmonies at your fingertips? That would be a pretty powerful tool and a great way to organize your practice because you are working on two things at once. All 12 trichords make up the universe of sound that can be created by 3 notes. Studying these trichords opens up so much in your playing. You will see new pathways and expand your melodic and harmonic pallette.

“All 12 trichords make great melodies and chords. By using them in every transposition and inversion you really have the whole world of a 3 note chord or motif at your disposal”

Expanding the Horizon with Pitch Class Set Improvisation

Pitch Class Set Improvisation doesn’t just simplify what you already know; it unlocks sounds you haven’t discovered yet. A perfect example is “Triad Pairs,” which I refer to as Trichord Pairs. Those are pretty common but if you dig deeper inside the “Triad Pairs,” concept there is a plethora of ways you could organize or alter this concept to get new sounds and ideas. I explore a lot of this in my various books the Harmonic and Melodic Equivalence Series comes to mind for that. But in general, some macro ideas for “Triad Pairs,” or Trichord Pairs would be permute the rhythm, melodic contour and expand past chords/melodies built in 3rds to the 12 trichord patterns. The list goes on of ways to develop these types of sounds.

“Pitch Class Set Improvisation can really open up a lot of new pathways in your music. It’s all about making a slight change in how you think about music can open up a whole new world”

The 12 Foundational Trichords: The Building Blocks of Pitch Class Set Improvisation

In the world of Pitch Class Set theory, every possible three-note combination can be reduced to one of these 12 “Prime Forms.” Mastering these is the key to unlocking the hexatonic universe. Think of these as the primary colors from which all other harmonic shades are mixed.

Set (Prime Form) Interval Structure Musical Character
(012) Three half steps The Chromatic Cluster: Maximum dissonance; used for 12-tone clusters or “gritty” modern textures. See Ultimate 3 Note Chord Lexicon for Course
(013) Half step + Whole step The Universal Set: Versatile; core segment of the Octatonic scale. Works over Major, Minor, and Dominant 7ths. See Ultimate 3 Note Chord Lexicon for Course
(014) Half step + Major 3rd The “Monk” Sound: Angular and evocative. Used frequently by Thelonious Monk and Anton Webern. See Ultimate 3 Note Chord Lexicon for Course
(015) Half step + Perfect 4th The Hybrid: A modern replacement for standard triad-based Major or Minor chords.
(016) Half step + Tritone The Viennese Trichord: Aggressive and modern. Perfect for altered Dominant 7th or Minor 7b5 situations.
(024) Two whole steps Whole Tone Segment: Open and lyrical. Ideal for floating, “ballad” sounds.
(025) Whole step + Fourth The Modern Pentatonic: Provides an open, “outside” flavor compared to standard pentatonic scales.
(026) Whole step + Tritone Dominant Whole-Tone: Offers sophisticated, suspended tension for Dominant 7b5 sounds.
(027) Whole step + Fifth The “Sus” Sound: The classic “quartal” sound used by players like McCoy Tyner. see “Time Transformation” course for études.
(036) Two minor thirds Diminished Triad: Familiar tension that drives strongly toward resolution.
(037) Minor third + Major third The Standard Triad: Contains both Major and Minor triads—seen here as the same “DNA.”
(048) Two Major thirds The Augmented Triad: A symmetrical set creating a sense of endless suspension.

Technical Spotlight: The (013) Trichord

The (013) pitch class set is perhaps the most versatile tool in the modern improviser’s kit. On the guitar, it is easily visualized as a half-step followed by a whole-step (for example: C, Db, Eb). Because it contains both a minor and major third relationship depending on the root, it acts as a harmonic chameleon.

In my 013 Hexatonic Études, I explore how 28 different hexatonic scales built from this single set can be applied to a Dominant 7th chord. It creates a shimmering, sophisticated effect that sounds “modern” without feeling mathematically cold.

Technical Spotlight: The (014) Trichord

The (014) set (a half-step and a major third, e.g., C, Db, F) is the gateway to the “Modernist” sound. It is dark, crunchy, and inherently dissonant. This set is a favorite of the Second Viennese School because it lacks a perfect fifth, immediately stripping away the “safety” of traditional tonal harmony.

For guitarists, (014) is highly ergonomic for sweep patterns and wide intervallic leaps. It is a “shortcut” to the sound of the early 20th-century avant-garde, providing immediate tension that sounds intentional rather than accidental.

III. Advanced Improvisation Techniques: Hexatonic Construction

The transition from a three-note trichord to a six-note hexatonic scale is where the true power of Pitch Class Set Improvisation theory is unleashed. By combining two trichords, we create a specialized six-note “vocabulary” that provides more melodic movement than a simple chord, but more structural focus than a standard seven-note scale.

Building the ‘Magic’ Hexachords

A “Magic Hexachord” occurs when you combine two non-overlapping trichords to form a unique six-note set. The beauty of this approach is that it allows you to superimpose complex sounds over simple harmonies. For example, by combining an (027) trichord (C, D, G) with another (027) trichord starting a whole-step higher (D, E, A), you create a highly modern, open sound that floats beautifully over a C Major 7 or D Minor 7 chord.

This method moves you away from the “all-you-can-eat” buffet of the chromatic scale and gives you a specific “palette” of six notes. This limitation is actually a creative catalyst—it forces you to find new melodic shapes within a defined harmonic container.

Superimposition: One Set, Many Colors

One of the most efficient ways to use these sets is through < strong>Superimposition. A single hexatonic set can take on completely different “colors” depending on the bass note or underlying chord. Consider the (013) trichord pair:

  • Over a Dominant 7th chord: It creates a sophisticated “altered” sound that highlights the b9 and #9.
  • Over a Minor 7th chord: It creates a dark, “Phrygian” or “Dorian” hybrid texture.
  • Over a Major 7th chord: It introduces Lydian-style tensions that push the harmony toward the avant-garde.

In my Sonic Resource Guide, I map out every possible hexatonic pair, providing a master roadmap for how these sets interact with standard jazz and rock harmonies. This allows the improviser to stay “inside” the logic of the set while being “outside” the traditional key signature.

The ‘Atomic Scales’ Method: Technical Mastery

How do you actually play this on a guitar at 200 BPM? You use what I call Atomic Scales. These are short, condensed fingerings designed to fit the specific architecture of the guitar’s fret board. Instead of thinking of long, linear scales, we think of these hexatonics as “clusters” of information that can be moved vertically and horizontally. See: Harmonic and Melodic Equivalence Courses for examples of Atomic Scales.

By breaking the 12-tone aggregate into these six-note “atoms,” the fret board stops being a mystery. You begin to see the geometry of music. You aren’t memorizing scales; you are internalizing the physical relationship between intervals. This is the key to the effortless, high-speed intervallic playing found in modern jazz and tech-metal.

IV. Practical Application and Resources for Pitch Class Set Improvisation

Theory remains an academic exercise until it is applied to the music you play every day. Whether you are a jazz guitarist re-imaging a standard, a metal player looking for a more “sinister” harmonic palette, or a composer seeking new textures, the following methods provide the bridge to mastery.

Reharmonization: Replacing Traditional Chords

One of the most immediate ways to modernize your sound is to replace traditional tertial chords (Major, Minor, Dominant) with pitch class set voicings. In my Applying Pitch Class Sets to Improvisation series, I show students how to swap out standard “stock” chords for modern trichords like (015), (016), or (027).

This isn’t about complexity for complexity’s sake—it’s about harmonic character. A standard G7 chord has a very specific “pull” toward C. However, if you replace that G7 with an (013) trichord pair, you retain the function of the dominant chord while introducing a sophisticated, shimmering tension that traditional chords simply cannot provide. This allows you to play “inside” the progression while sounding “outside” the clichés.

The Ear Training Key: Hearing the ‘Color’ of the Set

To improvise effectively with these sets, you must be able to hear them in real-time. My method of ear training—famously used at NYU and Princeton—moves away from interval-counting and toward Key Center Recognition.

Using tools like the Ear Training One Note Complete, students learn to identify the unique “sound” or “color” of each pitch class set against a static key center. If you can’t hear the tension of an (014) set against a key center, you won’t be able to use it authentically in a solo. True mastery comes when you can hear a complex hexatonic scale as a single, unified “sound” rather than six individual notes. This is the difference between “math” and “music.”

Also using tools like the MetroDrone®, students learn to “Feel Time not Count Time. I should also mention the “Long Line Rhythm®” course which teaches you the method in further detail. The MetroDrone® can also be used as a drone so everything you are practicing you can hear in a key center which has you doing ear training with everything you practice. Again, if you can’t hear the tension of an (014) set against a key center, you won’t be able to use it authentically in a solo.

The Sonic Resource Guide: Your 800-Page Roadmap

For those ready to truly master this language, the Sonic Resource Guide is the ultimate reference. It reduces the infinite combinations of the 12-tone system into 220 “Prime Forms.” This book maps out every possible chord, scale, and trichord pair, allowing you to look up any group of notes and instantly see its harmonic potential.

Think of it as a dictionary for the modern improviser. It bridges the gap between high-level mathematics and the practical needs of a working musician, providing the structural DNA for a lifetime of musical exploration.

Case Study: “Art of the Blues” – Applying the (013) Set to a Living Tradition

Theory is often best understood through its application and I’ve had a lot of experience with Pitch Class Set Improvisation. In my project Art of the Blues, I set out to create a modern parallel to J.S. Bach’s Art of the Fugue. While Bach explored the exhaustive possibilities of a single fugal subject, I chose to explore the exhaustive possibilities of the (013) Pitch Class Set within the framework of the 12-bar blues.

The Harmonic Foundation: 12 Keys, One DNA

The album consists of 12 blues compositions—one in every key. Each piece is strictly built using the (013) trichord as the primary melodic and harmonic generator. By limiting the “musical DNA” to this specific set, I was able to prove that a single three-note cell can generate an entire universe of blues expression without ever repeating a “lick” or a cliché.

The (013) set acts as a harmonic chameleon here; in some keys, it feels dark and “minor-leaning,” while in others, it creates a shimmering, modern dominant tension. This demonstrates the Superimposition theory discussed earlier: the set doesn’t change, but its relationship to the blues key center creates 12 distinct emotional landscapes.

Rhythmic Serialization and Metric Pivoting

Beyond the pitch organization, Art of the Blues utilizes partially serialized rhythm. I employed a consistent use of dotted-quarter notes throughout all 12 compositions. This wasn’t just a stylistic choice—it was a structural tool for Metric Pivoting.

By establishing a steady pulse of dotted quarters, the music allows the listener (and the performers) to pivot into a new time field where the dotted quarter note becomes the new quarter note. This creates a sophisticated “poly-temporal” feel that stretches the traditional blues shuffle into a modern, elastic rhythmic space. It challenges the improviser to maintain the (013) logic while navigating shifting rhythmic gears.

Why This Matters for the Student

For students of hexatonics and Pitch Class Set Improvisation, Art of the Blues serves as a roadmap. It shows that you don’t have to abandon “the groove” or “the soul” of music to use high-level theory. Instead, these tools—the (013) set and rhythmic serialization—provide a way to honor the blues tradition while pushing it into the 21st century. It is a living example of how intervallic thinking replaces pattern playing.

Explore the full scores and recordings of this project at the Art of the Blues project page.

The Path to Pitch Class Sets: A Personal and Musical Evolution

For over thirty years, my musical life has been defined by a single, obsessive pursuit: the integration of 20th-century compositional systems into the visceral world of improvisation. This wasn’t a choice made in a vacuum, but rather a slow-motion collision between high-level jazz pedagogy and the radical structures of the European avant-garde.

1. The Banacos Foundation: Double Mambos and Hexatonic Seeds

My deep dive into this world began around 1990, after spending five formative years studying with the legendary Charlie Banacos. Charlie had a unique way of codifying complex sounds into actionable exercises. He assigned me concepts he called “Double Mambos” and “Non-Tertial Double Mambos.”

In the Banacos system, a “Double Mambo” is essentially a pair of triads or structures that form a larger six-note set—a Hexatonic. While many jazz players use triad pairs (like Eb and F over an F7 chord), Charlie pushed me toward the non-tertial variety. These weren’t just chords; they were pitch class sets that broke the traditional “stack of thirds” logic. They forced me to hear intervals as independent cells rather than just “extensions” of a root. I questioned Charlie a lot on how he knew so much about music. He made many book recommendations. If you are interested check out the Charlie Banacos recommended reading list.

2. The Second Viennese Influence: Schoenberg, Berg, and Webern

As I practiced these hexatonic structures, I started noticing their architectural shadows in the music of the Second Viennese School. The works of Arnold Schoenberg, Alban Berg, and particularly Anton Webern became my primary listening. I realized that Webern’s highly distilled style was almost entirely built on the interaction of small trichords—the same three-note building blocks that make up a hexatonic set.

Webern’s influence was the “Rosetta Stone” for my playing. His music demonstrated that you could achieve incredible emotional depth and structural integrity without relying on traditional functional harmony. I saw a direct line from his 12-tone rows to the improvisational “cells” I was developing on the guitar. This led me to the concept of Pitch Class Set Improvisation.

3. Spooky Actions: Improvising with the Modernists

To put these theories into practice, I co-founded the ensemble Spooky Actions with woodwind specialist John Gunther. Our goal was audacious: we didn’t want to just “play jazz” over classical themes; we wanted to learn to improvise within the specific set structures used by the composers. On our debut recordings of Webern, we used the exact trichords found in his scores to inform our solos.

This forced me to abandon “pattern playing.” If a piece was built on a [0, 1, 4] trichord, my improvisation had to honor that interval set. This realization shifted my focus from what scales to play to how melodic ideas must reference the music being played, ensuring the improvisation is an organic extension of the composition rather than a collection of generic licks.

4. A Unified Theory: Melodic and Harmonic Synthesis

This journey eventually led me to a radical conclusion: if my melodies were organized by trichords and hexatonics, my chords had to reflect that same organization. Traditional jazz voicings often felt “out of place” against these modern melodic lines. I began using trichords to replace standard chords entirely, creating a unified harmonic language where every voicing and every melody line shared the same DNA.

Mastering this has been my central mission since 1990. It is a “whole new world” that requires a complete re-mapping of the fret board, moving away from scale-shapes and toward a deep, intervallic understanding of the 12-tone aggregate.

5. Proving the Living Language: From Metal to Early Music

Since those early days, I’ve spent my career proving that Pitch Class Set Theory is a living language applicable to any genre. I’ve used these hexatonic constructs in everything from Heavy Metal and Rock to Avant-Garde Jazz and even Early Music. Whether I’m performing with the Boston Symphony Orchestra or playing a distorted guitar solo, these sets provide a structural rigour that allows for total creative freedom.

PCS in Action: The Recordings

Classical & Early

Heavy Metal & Rock

Jazz & Blues

Free Improvisation

Master the System: Instructional Books

1. The Foundation

Sonic Resource Guide

The definitive reference for every possible scale and set application in modern music.

→ Master the Master Map

Applying Pitch Class Sets to Improvisation

The core method for hearing and executing these sets in real-time performance.

→ Start the Core Series

2. The Equivalence Cluster

Harmonic and Melodic Equivalence Series

A massive collection of hexatonic scales exploring how Trichord Pairs and triad pairs generate sophisticated melodic textures. These books also explore how these pairs are related to traditional harmony.

→ Master Trichord Equivalence

3. The Aggregate Cluster

Hexatonic Scales: The Complete Guide

The definitive entry point for modern six-note melodic control. There are books here for the very beginner and for someone looking for more complex ways to use pitch class set improvisation.

→ Access the Hexatonic Guide

Octatonics & Tertial Octatonics & Bebop Scales

You will find a deep dive into Bebop Scales and Octatonic Scales by following the links provided. The Bebop scale courses in particular give you some advanced applications not found in any other course. The Octatonic courses give you all possible 8 notes scales, how to use them and much more!

→ Explore 8-Note Sets

4. Technical Application

ChopBusters Series

Pitch Class Set Improvisation Series

High-intensity studies designed to turn abstract sets into physical facility on your instrument.

→ Develop Professional Chops

Not sure where to start? Choose Your Path:

I’m New to Modern Sounds

If you want to start from the ground up, not get too involved in theory and use PCS in your chords and melodic patterns, start with our Applying Pitch Class Set Series.

Start Here

I Want Technical Mastery

Focus on the ChopBusters and Pitch Class Set Improvisation Etude Series to get these sets into your fingers immediately or explore more books below:

Get Technical

I Want the Deep Theory

Start with the Sonic Resource Guide to understand the mathematical and architectural logic of music or explore more below:

Learn the Theory

Frequently Asked Questions

Q: Isn’t Pitch Class Set theory just for “atonal” or “classical” music?

A: Absolutely not. While the theory was popularized by analysts of the Second Viennese School, it is a universal labeling system for any 12-tone music. Whether you are playing Heavy Metal, Blues, or Avant-Garde Jazz, these sets provide a way to organize your melodic ideas that traditional “major/minor” theory cannot reach. As shown in Art of the Blues, it is a powerful tool for modernizing any genre.

Q: Why should I learn a “Set” instead of just learning a new Scale?

A: A scale is often tied to a specific “shape” or “pattern” on the fret board. A Pitch Class Set is the “DNA” of the sound itself. When you learn a set like (013), you aren’t just learning a fingering; you are learning an intervallic relationship that remains the same regardless of octaves, inversions, or registers. This frees you from “shape-based” playing and allows for true intervallic improvisation.

Q: Is this “math” going to kill my creativity?

A: On the contrary, it provides the structure that leads to total freedom. Much like a poet uses the structure of a sonnet to find new ways to express emotion, an improviser uses Pitch Class Sets to find notes they would never find through “intuition” alone. The math is just the map; the music is what you do once you know the territory.

Q: How do I actually start practicing this on the guitar?

A: Start small. Choose one trichord—like the (027) “Sus” sound—and learn to play it in every position on the neck using Atomic Scale fingerings. Once you can hear and play that three-note cell, try combining it with another trichord to form a hexatonic scale. I should mention that there is 44 books in my Harmonic and Melodic Equivalence Series that give you the Atomic Scale for each of the hexatonics scales used in each book. Check out each page of the 44 books there are examples of Atomic Scale but many more techniques with examples to consider for practice. I have found all the examples presented in those books to be highly useful in my development.

The goal also is to move from “calculated” playing to “aural” playing, where you hear the sound of the set before you play it. I personally found that my book “Time Transformation” was very helpful because it gave me a set of études that I could play over a one chord vamp so that I could hear how the 027 would sound. That was a crucial breakthrough for me and that’s why that book exists.

Speaking of hearing my recommendation is to work with my ear training series so that you can hear music correctly and develop your ear so you can function with these advanced ideas presented in Pitch Class Set Improvisation. I’d recommend starting with Ear Training One Note Complete and Contextual Ear Training if you are just getting started with learning how to hear all 12 notes in a key center. There are many more books specifically for Pitch Class Set Improvisation and other aspects of developing this type of ear training this page.

Q: Do I need to understand “Prime Form” to use these sounds?

A: While you don’t need to be a mathematician, understanding Prime Form is incredibly helpful for organization. It allows you to group hundreds of seemingly different chords into just 12 unique categories. It’s the ultimate “shortcut” for your brain, reducing the complexity of the 12-tone system into manageable building blocks.

Still have questions?

Check out the more extensive Bruce Arnold FAQ for deep dives into rhythm, ear training, and technical exercises.


← Back to Hexatonic Scales: The Complete Guide

A Proven Educational Lineage

The methods found on this website are part of a historical musical lineage stretching back to the 18th-century masters.

By using Muse-Eek books and courses, you are now a part of this lineage—a tradition of excellence passing through legends like Charlie Banacos and Jerry Bergonzi.

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]]> Hexatonic Scales: The Complete Guide https://muse-eek.com/hexatonic-scales-the-complete-guide/ Fri, 27 Mar 2026 04:40:26 +0000 https://muse-eek.com/?page_id=1429255 Continue reading →]]>



<a href="https://muse-eek.com/wp-content/uploads/2026/03/hexatonic-scales-complete-guide.jpg"><img decoding="async" src="https://muse-eek.com/wp-content/uploads/2026/03/hexatonic-scales-complete-guide-300x300.jpg" alt="Hexatonic Scales: A Complete Guide to Pitch Class Sets - Muse-Eek" width="300" height="300" class="aligncenter size-medium wp-image-1429257" data-wp-pid="1429257" srcset="https://muse-eek.com/wp-content/uploads/2026/03/hexatonic-scales-complete-guide-300x300.jpg 300w, https://muse-eek.com/wp-content/uploads/2026/03/hexatonic-scales-complete-guide-1024x1024.jpg 1024w, https://muse-eek.com/wp-content/uploads/2026/03/hexatonic-scales-complete-guide-150x150.jpg 150w, https://muse-eek.com/wp-content/uploads/2026/03/hexatonic-scales-complete-guide-768x768.jpg 768w, https://muse-eek.com/wp-content/uploads/2026/03/hexatonic-scales-complete-guide-600x600.jpg 600w, https://muse-eek.com/wp-content/uploads/2026/03/hexatonic-scales-complete-guide-100x100.jpg 100w, https://muse-eek.com/wp-content/uploads/2026/03/hexatonic-scales-complete-guide.jpg 1080w" sizes="(max-width: 300px) 100vw, 300px" /></a> | Bruce Arnold

Hexatonic Scales: A Complete Guide

Hexatonic scales are six-note structures—often termed "hexachords"—that offer a sophisticated, open sound, effectively bridging the gap between five-note pentatonics and seven-note diatonic scales. These scales are frequently organized around trichords: three-note subsets, such as the "027" structure used in quartal harmony. These subsets serve as melodic fragments that allow you to create unique, non-traditional shapes. Beyond simple note selection, the internal interval content (or interval vector) defines the scale's emotional color, moving your playing away from traditional third-based harmony and into modern, open sonic landscapes.

There are three primary ways to choose the sound you want to create with hexatonic scales and trichords:

  • Traditional Harmony: Base your scale or trichord selection on chord tones and available tensions. This approach sounds fresh and modern without being overbearing.
  • Modal Organization: Derive your structures directly from the specific mode you are utilizing.
  • Intervallic Approach: Use a purely intervallic logic that intentionally moves in and out of the key center. This is the path to creating highly dissonant and evocative sounds.

That said, keep in mind that there are hundreds of techniques and combinations of techniques that you could use with hexatonics and trichords.

Whether you prefer a grounded approach or a more "outside" intervallic sound, both require a specific set of tools and a mastery of the underlying structures. By understanding these three paths, you can tailor your improvisations to be either subtly modern or boldly avant-garde.

Free Hexatonic Materials: Sign up to receive sample PDF exercises and MIDI files to start your journey. Sign up here.

The Influence of Charlie Banacos

Much of the methodology presented here was developed during five years of study with the legendary music guru Charlie Banacos. Charlie used "Double Mambos"—pivoting between two 3-note groups—to teach students how to create modern, non-tertial sounds instantly.

Whether you are a beginner or a professional at Berklee or NYU, these systems break down complex pitch class theory into manageable "pivoting" movements that define your unique voice as a musician.

The 12 Foundational Trichords

In 20th-century Pitch Class Set Theory, every possible 3-note combination can be reduced to one of these 12 "Trichords." Mastering these is the key to unlocking the hexatonic universe.

Set Interval Structure Musical Characteristic
012 Three half steps Maximum dissonance; 12-tone clusters
013 Half + Whole step The "Universal" set for all chord types
014 Half + Major 3rd Thelonious Monk sound; Diminished/Minor-Major
015 Half + Perfect 4th Beautiful replacement for Major/Minor chords
016 Half + Tritone Aggressive Dominant 7th or Minor 7b5 sound
024 Two whole steps Open, consonant sound for ballads
025 Whole + Fourth Modern pentatonic sound
026 Whole + Tritone Whole-tone dominant structures
027 Whole + Fifth The quintessential modern "Jazz" Sus4 sound
036 Two minor 3rds Symmetrical diminished triad
037 Minor + Major 3rd The traditional Major/Minor triad
048 Two Major 3rds The traditional Augmented triad
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A Deep Dive into the Characteristics of each Trichords

Usage & Characteristics
012: The Chromatic Cluster

The 012 (e.g., C-Db-D) is arguably the least utilized trichord, yet it possesses striking features. While its harmonic use is primarily limited to Dominant 7 or 7sus4 contexts, it is highly effective as a "burst" of unusual color. It is particularly useful when arranging for horns or strings, as the human ear tends to tolerate this dense dissonance better through orchestral timbres. When voiced with wide octave displacements, it can sound surprisingly ethereal.

Special Note: Within the 012 matrix, there are three specific "atonal" areas where traditional chords do not apply: (4, b5, 5), (b7, 7, 1), and (7, 1, b2). While these don't function as standard chords, in a blues context, the (4, b5, 5) sounds excellent as a melodic line because those notes are integral to the blues scale.
013: The Universal Set The 013 (e.g., C-Db-Eb) is unique because it is the only trichord compatible with every standard chord type. Because of this versatility, it can shift from hauntingly beautiful to aggressively dissonant depending on the voicing and the bass note beneath it. Interestingly, a vast majority of "Great American Songbook" melodies rely heavily on 013 movement. Given that many of those composers were classically trained, one wonders if this was a conscious choice or simply an intuitive grasp of how a beautiful melody unfolds.
014: The Monk Chord The 014 (e.g., C-Db-E) This is my "go-to" for dissonant harmony, especially when performing the music of Thelonious Monk. By emphasizing the Major 7th or b9 intervals within the voicing, you can achieve maximum tension. Yet, the 014 can also be haunting and delicate. Along with the 013, 015, 016, 025, 026, 036, and 037, the 014 can be moved in minor thirds to form a symmetrical diminished scale—an essential technique for the modern improviser.
015: The Modern Substitute The 015 (e.g., C-Db-F) A simply beautiful sound that works in every idiom. I often use it as a sleek substitute for standard major or minor triads. I particularly like superimposing 015s over dominant chords. For example, the structures (1, b2, b6), (b2, 2, 6), (2, b3, b7), (b5, 5, 9), and (5, b6, #9) are all 015s that sound fantastic over a Dom7. Additionally, the 015 can be moved in minor thirds to create a 12-tone aggregate.
016: The Dominant Powerhouse The 016 (e.g., C-Db-F#) is a foundational dominant sound. When voiced as (3, 6, b7), it provides a classic Dominant 13th color. Conversely, using (1, b2, 5) yields a biting, altered dominant sound. Its versatility is vast; it functions equally well as a -7b5 structure. The great lesson of the 016 is that learning a single voicing can unlock a dozen different harmonic functions.
024: The Lyrical Cluster The 024 (e.g., C-D-F) is rarely thought of as a chordal structure, but if you voice it with the middle note dropped an octave, it becomes a lush, open sound. I have used this with great effect in ballads. It is also a powerful melodic tool; by combining two 024s (e.g., C-D-E and G-A-B), you can navigate a C Major scale while skipping the "avoid note" (F). This allows you to stop or rest on any note without the immediate need for resolution.
025: The Pentatonic DNA I view the 025 (e.g., C-D-G) as the integral core of the major pentatonic scale. If you analyze a C Major Pentatonic, it is essentially a succession of 025s: (E, G, A), (G, A, C), (A, C, D), and (C, D, G). Because it can move in minor thirds within a symmetrical diminished scale, it has the unique ability to make a dissonant scale sound surprisingly consonant due to its familiar, open structure.
026: The Symmetrical Whole-Tone 026 (e.g., C-D-F#) is one of the most functional structures in this collection. It is a staple for dominant chords, but its symmetry is its greatest asset. It can be moved in whole steps to create a whole-tone scale. Less commonly known is its presence within the symmetrical diminished scale, a characteristic many jazz musicians exploit to create "inside-outside" lines.
027: The Quartal Sound 027 (e.g., C-D-G) is my primary choice for a modern Major or Minor sound. It provides that "modern 4th" or quartal stack sound (e.g., C-F-Bb). Like the 015, it can be moved in minor thirds to form a 12-tone aggregate. Two 027s paired together create a stunning Major sound—I often pivot between (1, 2, 5) and (3, 6, 7) when a Major quality is required. Shift that entire concept down a minor third, and you have two perfect Minor chord voicings.
036: The Diminished Triad As one of the four "common" triads, the 036 (e.g., C-Eb-Gb) needs little introduction. It is the essential sound of the diminished chord and a key component of the dominant 7b9 sound. Its symmetrical nature (moving in minor thirds) is a hallmark of Western music, appearing in everything from Bach to bebop.
037: The Major/Minor Triad This is often confusing to students new to pitch-class theory: the 037 (e.g., C-Eb-G or C-E-G) represents both the Major and the Minor triad. They are the same "structure," just inverted. This is the foundation of tertian harmony. A Major and Minor triad sound so cohesive together because they share this identical DNA. This is a vital lesson: whenever you pair a trichord with another of its same type, you achieve a similar structural logic and beauty. This also gives you an insight into why tertial harmony sounds so harmonious. The structures of the four common triads are either identical or very closely related.
048: The Augmented Triad The 048 (e.g., C-E-G#) is the augmented triad, the last of the four common triads. Beyond its obvious use in augmented harmonies, it is highly effective over Dominant 7th chords, Major 7#5 chords, and Minor-Major 7th chords. The beauty of the 048 lies in its perfect symmetry; because it functions in so many contexts, it is one of the most "portable" structures an improviser can learn.

Replacing Your "Tired" Old Chords

Instead of playing a standard C Major (C, E, G), try pivoting between 015, 025, or 027 structures. By leaving out the 3rd or adding specific tensions, you create a fresh musical palette that works in any style—from Heavy Metal to Contemporary Classical.

  • For Major/Minor sounds: Use 015, 024, 025, or 027.
  • For Dominant sounds: Use 012, 013, 014, 016, or 026.
  • For Minor 7b5: Stick with 016 to start.

Genre-Specific Applications: A Universal Language

One of the most powerful aspects of the Hexatonic system is its universality. Because we are dealing with interval vectors and Pitch Class Sets, the theory remains constant while the "accent" changes depending on the musical style. Whether you are using a high-gain amplifier or a grand piano, these six-note structures provide a fresh architectural framework.

1. Modern Jazz & The Avant-Garde

In the jazz tradition, hexatonics serve as the primary vehicle for "outside" playing. By moving between trichords that are semitonally related (e.g., a C Major triad and a Db Major triad), you create the intense tension and release patterns found in the late-period works of John Coltrane and McCoy Tyner. Tyner’s "quartal" sound is essentially the mastery of the 027 trichord pair. At Muse-Eek, we teach you to see these not as "random outside notes," but as a disciplined, mathematical approach to pure musicality.

2. Heavy Metal & Progressive Rock

For the modern guitarist, hexatonics offer a way to escape the "box" patterns of standard pentatonics. Metal players often use these as high-speed "shred" scales, but the true power lies in the wide-interval leaps. By prioritizing 4ths, 5ths, and tritones (sets like 016 or 027), a guitarist can create evocative, dark, and sophisticated riffs that avoid the clichés of the natural minor scale. If you are finding your technical facility is a "tall hill to climb" for these intervals, the ChopBusters series is designed specifically to build the physical strength required for these non-linear movements.

3. Contemporary Classical Composition

From the Greeks to the 2nd Viennese School, hexatonics have provided the foundation for non-traditional harmony. Using Symmetric Difference Analysis, a composer can map out an entire movement based on a single 6-note set. My group, Spooky Actions, has recorded dozens of CDs demonstrating how these mathematical sets can be the foundation for an entire composition, bridging the gap between historical tradition and the avant-garde. For the improvising classical musician these hexatonic scales and in particular the 12 trichords are immensely useful for improvising on various genres of classical music. Obviously they work really well with the 2nd Viennese school composers but equally as well with Messiaen, Stravinsky, Elliot Carter etc...

The 20/10 Practice Rule: A Pedagogical Requirement

Mastering hexatonic scales and trichords is a monumental task that requires more than just "playing." It requires a structured, pedagogical system to ensure the information moves from your brain to your hands and, ultimately, your ears. At Muse-Eek, we advocate for the 20/10 Rule, a method refined through my decades of teaching at institutions like Berklee and Princeton. I outline various ways to learn each aspect of hexatonics and trichords in various courses but I should also mention the importance of listening. You need to listen to music that has been composed with hexatonics and trichords in order to get a deep aural understanding of the sound. Listen to some of the tracks listed further below and seek out other recordings that use pitch class sets and trichord.

  • 20 Minutes of Focused Physical Practice: Spend this time on the physical facility of a specific trichord pair. Do not deviate. Focus on the "ChopBusters" approach—clear, clean, and rhythmic execution of the 924 hexatonic scales.
  • 10 Minutes of Active Aural Rest: Put the instrument down. This is the most critical part. Use these 10 minutes for Ear Training. Listen to the specific interval color you just practiced. If you can't hear it in your head, you will never truly "own" it during an improvisation.

This cycle prevents the "mental fatigue" that often accompanies high-level theory study. It ensures that your ear is always the primary driver of your musical development, just as Charlie Banacos taught: "Your ear is your most important vehicle."

PCS in Action: The Recordings

As I mentioned earlier it is important to hear hexatonics and trichords in music. Take some time and listen to these recordings. The full audio is available on youtube.com if you find a certain recording to be intriguing.

Classical & Early

Heavy Metal & Rock

Jazz & Blues

Free Improvisation

The Aural Path: Ear Training

As Charlie Banacos taught, your ear is your most important vehicle. To master hexatonics, you must recognize these sounds within a Key Center.

Are your ears ready for Hexatonics?
Before diving into advanced pitch class sets, we highly recommend you test your 12-note foundation.


Take the Aural Diagnostic Test here →

Ear Training & Singing

Explore Ear Training Series

The Physical Path: Technique Books

Technique is about developing the "chops" to play what you hear. Our 2026 curriculum includes thousands of permutations based on the Banacos approach.

Sequencing & Permutations

  • Hexatonic Modal Sequencing (36 Permutations)
  • 9,240 Permutations (Banacos Style)
  • ChopBusters for Hexatonics
  • 924 Scales: Ascending & Descending

View Technique Books

Theory & Composition

  • 924 Aggregates (12-Tone Coverage)
  • 924 Hexatonics Grouped by Prime Form
  • The Sonic Resource Guide
  • Symmetric Difference Analysis

View Theory Library

FAQ Questions about Hexatonics and Trichords

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Question Answer
Where do I start with hexatonics? Start with two 027 structures (e.g., C-D-G and E-A-B). This works as a great replacement for a CΔ7 or an A minor chord.
How do I bridge the gap between names (Major/Minor) and intervals? This can be a stumbling block. I recommend Music Theory Workbooks to help strengthen your theoretical foundation if this feels difficult to adjust to.
This process has my head spinning. How can you help? Focus on chord tones, tensions, and basic scales (Major, Melodic Minor, etc.). I recommend Essential Scales for the modal side and Chord Workbook for Guitar V1 & V2 for the harmonic side.
I like 013s on guitar; should I start there? Not necessarily. 013 is a "tall hill to climb." Start with 027 and 016 first, as they are more common and easier for intermediate players to apply immediately.
Can I use these in a traditional jazz band? Yes. Focus on 015, 016, 026, and 027 to replace traditional chords. Explore all 3 inversions, specifically on the D, G, and B string sets.
How should a horn player approach these? Use 015/027 for major sounds and 016/026 for dominant or -7b5. Try to practice these in 18 different inversions across your range.
How do I get into the "Spooky Action" style of improvisation? Master 013, 014, and 026. Check out the Chopbuster courses for specific patterns related to this 20th-century classical sound.
Will this help an acoustic guitarist playing with an avant-garde singer? Definitely. Try replacing major/minor chords with 015s (e.g., C major becomes B-C-E or B-C-G). It creates a very modern, supportive color.
Any recommendations for using this in ProgRock? 025 is key. Check out Live at Provinceton Playhouse on YouTube or the Heavy Mental CD (lots of 027). The Bruce Arnold Composition Course is also a great resource for this idiom.
You mention hundreds of techniques with hexatonics and trichords. Care to elaberate? Well you could write many books on the possible techniques. Oh wait... I already did that :) I think one way to think about hexatonics and trichords you could use them in any technique you already know. Play them as modal sequences, put approaches notes before key notes, do harmonic superimposition using trichords rather than triads or 7th chords... As you can see the list goes on and on. That said, I really think the important thing to do is learn to hear hexatonics and trichords, particularly trichords. If you went through every trichord in every key in let's say 18 inversions you are covering basically all possible 3 note chords. Obviously if you can hear all of that against a key center you are in a whole new place musicianship wise. I have a course call SerialEar that does just that and is amazing for getting your ear together with harmony and melody regardless of hexatonics or trichords.

Historical Context: Jazz & Classical

From McCoy Tyner's "Passion Dance" (Eb and F triads) to the complex 12-tone rows of Schoenberg and Webern, hexatonics bridge the gap between tradition and the avant-garde. My group "Spooky Actions" has recorded many of these applications to show how a single hexatonic scale can be the foundation for an entire composition.

Listen to original recordings and 50+ CDs of hexatonic applications at the Muse-eek store.


← Back to Hexatonic Scales: The Pitch Class Set Approach

A Proven Educational Lineage

The methods found on this website are part of a historical musical lineage stretching back to the 18th-century masters.

By using Muse-Eek books and courses, you are now a part of this lineage—a tradition of excellence passing through legends like Charlie Banacos and Jerry Bergonzi.

  • Historically Validated
  • University-Level Pedagogy
  • Professionally Proven



VIEW THE LINEAGE CHART

]]> Octatonic Chords https://muse-eek.com/octatonic-chords/ https://muse-eek.com/octatonic-chords/#respond Wed, 11 Jun 2025 04:29:57 +0000 https://muse-eek.com/?p=1428446 Continue reading →]]>

Octatonic Chords by Bruce Arnold

Diatonic Chords for 124 Eight Note Scales

From the Pitch Class Set Improvisation Series

Add digital copy to cart – $24.99

Buy on Bruce Arnold Patreon Site

Octatonic Chords, Diatonic Chords for 124 Eight Note Scales is a course that I recommend working on in tandem with the Bebop Scale Courses or the 475 Octatonic Scales book.  This course is part of a series of books on octatonics. Learning to hear the harmony for eight note scales in crucial to using them musically.  I’ve also included some very useful information on how you might approach using not only the chords but the eight note scales in a musical way and some of the pitfalls that you might encounter.

This course takes a subset of the 495 possible eight note scales and looks at diatonic chords found in 124 octatonic scales. Some of these scales have been chosen because they are commonly used, like the diminished scale. Others are typical Bebop scales while others are scales that I have found interesting, but are also part of other courses I’ve created such as the series of books on Bebop scales.

This course looks at the 3 and 4 note chords derived from these 124 octatonic scales in several ways. The 3 note diatonic chords are grouped by root, 1st and 2nd inversion, while the 4 note chords are grouped by root, 1st, 2nd and 3rd inversion but also include these voicings ascending through each eight note scale. In all of these cases you will find all 3 and 4 note chord voicings in all keys so it’s a quite a large resource that makes it very easy to organize and dig into the chords quickly.

Midi Files are included for all exercises so you can listen to these chord voicings.  I would highly recommend singing through these voicings and singing the scale over these voicings as an ear training exercise.  This will really help to ingrain the sound of the chords.

Many world-class musicians and legendary educators often recommend that you spend a significant amount of time mastering chord voicings—specifically diatonic chord voicings—to truly ingrain the unique harmonic fingerprint of a scale into your subconscious mind. By exploring the vertical structures (chords) of a scale, you develop a much deeper “inner ear” for its horizontal possibilities (melodies). This holistic approach is essential for any improviser looking to move beyond simple patterns and start playing with genuine musical intent.

This deep integration of harmony and melody helps immensely when you are attempting to craft compelling, memorable lines. There is a common wisdom among masters that any truly great melody can be distilled into a logical chord progression, and conversely, any sophisticated chord progression contains a beautiful, singing melody hidden within its voice leading. I have found this to be an absolute truth in my own journey as a performer and composer.

When you understand how an octatonic or bebop scale generates its own unique set of diatonic chords, you stop guessing and start hearing. Working through this comprehensive chord voicing resource will bridge the gap between your technical knowledge and your creative output. I highly recommend dedicating consistent practice time to these exercises; the rewards for your ears, your hands, and your musicality will be profound and long-lasting.

Below is a link to my Blog where you can find out more information about this course and other octatonic courses:

Bruce Arnold's BlogRead more at Bruce Arnold’s Blog.

Table of Contents:

Composers and Musicians who have used Octatonic Scales
Diatonic Octatonic Chord Voicings
Course Breakdown
Ways to Implement Octatonic Chords
124 Octatonic (Eight Note Scales) Used in this Book
Conclusion

List of Contents for the Octatonic Chord Course:

73 Page PDF
Octatonic Chords 4 Note Ascending for 124 Scales: 1860 Pages plus Midi Files
All 495 Eight Note Scales in all keys. 372 Pages with Midi Files

ISBN: 978-1-59489-291-2

Add digital copy to cart – $24.99

Buy on Bruce Arnold Patreon Site

What people are saying:

“Well this is a tour de force if there ever was one. Highly Recommend!” T. Roland

“Finally a course where this is made easy. Thanks Bruce!” D. Raskin

A Proven Educational Lineage

The methods found on muse-eek.com are part of a historical musical lineage stretching back to the 18th-century masters.

By using Muse-Eek books and courses, you are now a part of this lineage—a tradition of excellence passing through legends like Charlie Banacos and Jerry Bergonzi.

  • Historically Validated
  • University-Level Pedagogy
  • Professionally Proven

VIEW THE LINEAGE CHART

Octatonic Chords

Bruce Arnold Guitarist

]]> https://muse-eek.com/octatonic-chords/feed/ 0 495 Eight Note Scales https://muse-eek.com/495-eight-note-scales/ https://muse-eek.com/495-eight-note-scales/#respond Wed, 11 Jun 2025 03:22:07 +0000 https://muse-eek.com/?p=1428442 Continue reading →]]>

495 Eight Note Scales

in all 12 keys by Bruce Arnold

This is part of the Octatonics Series of Courses.

 

Add digital copy to cart – $24.99

 

Buy on Bruce Arnold’s Patreon Site

 

495 Eight Note Scales takes a deep look at using octatonic (eight note) scales.  This course is part of a series of books on octatonics. The best way to start this course is to pick an octatonic scale and learn it on your instrument. Sing it over a drone, and explore the chord voicings for the scale. The symmetrical diminished or diminished scale will of course be on of the first scales students work on because it is so prevalent in contemporary music. It will give you a sense of improvement quickly, and that will encourage you to take things further.

On the first few pages I’ve presented a lot of ways you could approach this course and a series of lists that can help explore eight note scales and the chords that can be used with them.

This course looks at 495 octatonic scales, their internal structure, which chords they can be played over and much more information to help you organize your study. These 495 possible eight note scales can be reduced down the 29 prime forms using pitch class set theory that can be helpful when you are organizing how these octatonic scales interrelate. I’ve include references to these throughout this course. The pitch class set theory information is by no means crucial to working with this course but over time you will see its usefulness. If you want to learn more about pitch class set theory and how it can be used by an improvising musician I recommend the “Sonic Resource Guide.”

Included in this course is a list of compositions by various composers who have used octatonic scales. I highly recommend listening to this music to give you ideas and inspiration. You should also check out the music and improvisations of guitarist Alan Holdsworth. His use of octatonic scales in his compositions and improvisations is one of the reasons his music sounds so unique.

This course also contains a list of the two tetrad (4 note) chords that form the complete eight note scale. This list shows the Two Tetrad combinations for the 29 possible pitch class sets. This list comes from the “Sonic Resource Guide” which I highly recommend if you want to dig deeper into all scales. The Two Tetrad list can be used to find two four note structures that contain all the notes of an eight note scale. In any case these chord structures will help to give you the “octatonic sound” and get past some of the common pitfalls.

It’s also important to do some ear training with these segmented Bebop Scales. My teachers had me play but also sing these segmented Bebop scales with approaches all in one key. So for instance, if you were playing these over “Donna Lee” you would sing all the segmented scales in the key of Ab. This will not be easy for most musicians but will really ingrain the information and help improve your key retention.

 

Read More about this course at Bruce Arnold’s Blog

495 Eight Note Scales in all 12 keys from Bruce Arnold's Blog

Table of Contents:

Composers and Musicians that have used Octatonic Scales
495 Eight Note Scales
How to Work with this Course
“Derivative” Composition
Chords and Available Tensions
Ways to Implement Diatonic Octatonic Chords
495 Eight Note Scales with Prime Form
Diatonic Chords of Eight Note Scales
Diatonic Chords of the Key of C
Conclusion

 

List of Contents for 495 Eight Note Scales Course:

 
24 Page PDF
 
“Octatonics Prime Form, Degrees, Forte Number, Chord Application” PDF 260 pages
 
495 Scales with All 12 Chromatic Modes
 
All 495 Eight Note Scales in all keys 372 Pages of PDFs with Midi Files
 
All 495 Eight Note Scales in all Keys Ascending-Descending 744 Pages of PDFs with Midi Files
 
29 Two Tetrad Combinations 29 Eight Note Prime Forms 29 Page PDF
 
Three Tetrad Combinations Page 30-58 of above PDF.

Jam Tracks V1 (MP3’s of 10 chord types in all 12 keys)

ISBN: 978-1-59489-292-9

 

Add digital copy to cart – $24.99
 
 
 
 

What people are saying:

Very large course.  I like how it’s broken down with pitch class sets.  Thinking of the 495 scales all coming from a collection of 29 prime forms really helps me not to freak out on the possible combinations.  This course is a real eye opener to future possibilities… R. Franks

The Octatonics Prime Form, Degrees, Forte Number, Chord Application PDF is really the key to this course.  A well laid out PDF where you can search for the scale you want or even what chord works with what scale.  Also the Two Tetrad Combination PDF is awesome for putting together two chords that help me work with each scale.  I hope to see full blown course on this in the future. W. Fields

Thanks Bruce!  This is a course for a lifetime.  I glad someone finally wrapped their head around eight note scales.  I’ve been using the diminished modes but this really has a lot of cool scales like the “1, 2, b3, 4, b5, 5, 6, 7” which I’m now using over a minorMajor7 chord and don’t even get me started on all the cool dominant scales…  B. Edmonds

<

A Proven Educational Lineage

The methods found on muse-eek.com are part of a historical musical lineage stretching back to the 18th-century masters.

By using Muse-Eek books and courses, you are now a part of this lineage—a tradition of excellence passing through legends like Charlie Banacos and Jerry Bergonzi.

  • Historically Validated
  • University-Level Pedagogy
  • Professionally Proven

VIEW THE LINEAGE CHART

495 Eight Note Scales in all 12 keys by Bruce Arnold

Guitarist and Author Bruce Arnold Photo

]]> https://muse-eek.com/495-eight-note-scales/feed/ 0 Segmenting Bebop Scales with Approach Notes https://muse-eek.com/segmenting-bebop-scales-with-approach-notes/ https://muse-eek.com/segmenting-bebop-scales-with-approach-notes/#respond Wed, 11 Jun 2025 02:16:53 +0000 https://muse-eek.com/?p=1428435 Continue reading →]]>

Segmenting Bebop Scales with Approach Notes by Bruce Arnold

by Bruce Arnold

124 Eight Note Scales with 12 Diatonic and Chromatic Approaches

is part of the: Octatonics Courses

Add digital copy to cart – $19.99

 

Buy this course at Bruce Arnold’s Patreon Page

Segmenting Bebop Scales with Approach Notes by Bruce Arnold for Muse Eek Publishing Inc. uses the same 124 octatonic (eight note) scales as the “Segmenting Bebop Scales” course. The main difference is the inclusion of 11,904 PDFs and Midi files for the exercises and an explanation of approach notes. “Segmenting Bebop Scales with Approach Notes” will of course get you using approach notes but it will also change your ability to play over chord changes and more importantly, how it will change your phrasing.  This course is part of a series of books on octatonics

The use of approach notes with these segmented Bebop scales requires a whole new set of skills which will become apparent as you read through the course. If you haven’t worked with approach notes previously you will find this will be a pretty step learning curve especially when you start applying these figures within real music.

I spent many years working on the similar rote exercises as found in this book. I also spent a lot of time applying these figures to jazz standards. Most of the chord progressions I used were from the Bebop lexicon; songs such as “Confirmation,” “Donna Lee,” and Rhythm Changes. It is also a great idea to play these progression in all 12 keys.

You will quickly find that not only do these segmented Bebop scales with approaches gives you a strong “Jazz Sound” but they also help your understanding phrasing in a whole new way. By anticipating the segmented Bebop line you create a whole new way to phrase. More on this in the course.

With the addition of this course you now have three method books that you can use to get a deeper understanding of Bebop scales and two different ways to play them, with and without approaches.

It’s also important to do some ear training with these “Segmenting Bebop Scales with Approaches”. My teachers had me play but also sing these segmented Bebop scales with approaches all in one key. So for instance, if you were playing these over “Donna Lee” you would sing all the segmented scales in the key of Ab. This will not be easy for most musicians but will really ingrain the information and help improve your key retention.

Below is an excerpt from the Foreword of “Segmenting Bebop Scales with Approach Notes” 

“Segmenting Bebop Scales with Approach Notes” is very similar in written content to the “Segmenting Bebop Scales” course. The main difference is the inclusion of 11,904 PDFs and Midi files for the exercises and an explanation of approach notes. Although the application of Bebop scales with approaches is very similar to the directions used for the “Segmenting Bebop Scales” course, one of the crucial differences is how this course will change your ability to play over chord changes and more importantly, how it will change your phrasing.

The use of approach notes with these segmented Bebop scales requires a whole new set of skills which will become apparent as you read through the course. If you haven’t worked with approach notes previously you will find this will be a pretty step learning curve especially when you start applying these figures within real music.

I spent many years working on the similar rote exercises as found in this book. I also spent a lot of time applying these figures to jazz standards. Most of the chord progressions I used were from the Bebop lexicon; songs such as “Confirmation,” “Donna Lee,” and Rhythm Changes. It is also a great idea to play these progression in all 12 keys.

You will quickly find that not only do these “Segmenting Bebop Scales with Approach Notes” gives you a strong “Jazz Sound” but they also help your understanding phrasing in a whole new way. By anticipating the segmented Bebop line you create a whole new way to phrase.

With the addition of this course you now have three method books that you can use to get a deeper understanding of Bebop scales and two different ways to play them, with and without approaches.

It’s also important to do some ear training with these segments. My teachers had me play but also sing these segmented Bebop scales with approaches all in one key. So for instance, if you were playing these over “Donna Lee” you would sing all the segmented scales in the key of Ab. This will not be easy for most musicians but will really ingrain the information and help improve your key retention.

This course contains a lifetime of practice. Mastering 124 segmented Bebop scales will take many years. I recommend you use some of the popular Bebop scales first and then branch out over time to some of the more esoteric examples.

You can find out more information on this course at Bruce Arnold Blog

Segmenting Bebop Scales with Approach notes by Bruce Arnold

 

Table of Contents:

Segmenting Bebop Scales with Approach Notes
Common Bebop Scales
Approach Notes
Course Breakdown
124 Bebop Scales
Bebop Scales and Chords They Work Over
How to Practice with this Course
Segmenting Bebop Scales with Approaches
Conclusion

 

List of Contents for Segmenting Bebop Scales with Approach Notes Course:

 
62 Page PDF
 
Ascending Bebop Lines with 12 Different Chromatic Approaches all keys 124 Scales
 
Ascending Bebop Lines with 12 Different Diatonic Approaches all keys 124 Scales
 
Descending Bebop Lines with 12 Different Chromatic Approaches all keys 124 Scales
 
Descending Bebop Lines with 12 Different Diatonic Approaches all keys 124 Scales

Jam Tracks V1 (MP3’s of 10 chord types in all 12 keys)

ISBN: 978-1-59489-290-5

 

What people are saying:

OK I got a sneak preview of this course from Bruce.  This is a heavy weight look at the ultimate way to play Bebop Scales.  Bruce said he learned the concept from the great tenor player Jerry Bergonzi back in the day.  Bruce Arnold also said it really helped him to play over jazz tunes but also totally revolutionized his phrasing.  Highly recommend!. J. Johnson

Totally killing course.  I think this is my favorite in the Bebop Series.  I’ve worked with Bruce’s Approach Note course so this is really great to dig into some more esoteric Bebop Scales.  Love the idea of using these types of scales in a more modern way. T. Barnett

OK this is it.  If you want to get Bebop Scales into your playing this mammoth undertaking will get you there.  The hippest thing for me is taking some of these esoteric Bebop scales and applying them to dominant chords.  Holy Crap that sounds great!  A. Victors

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By using Muse-Eek books and courses, you are now a part of this lineage—a tradition of excellence passing through legends like Charlie Banacos and Jerry Bergonzi.

  • Historically Validated
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Segmenting Bebop Scales with Approach Notes by Bruce Arnold for Muse Eek Publishing Inc.

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]]> https://muse-eek.com/segmenting-bebop-scales-with-approach-notes/feed/ 0 Segmenting Bebop Scales 124 Ascending and Descending Permutations https://muse-eek.com/segmenting-bebop-scales-124-ascending-and-descending-permutations/ https://muse-eek.com/segmenting-bebop-scales-124-ascending-and-descending-permutations/#respond Wed, 11 Jun 2025 01:24:01 +0000 https://muse-eek.com/?p=1428426 Continue reading →]]>

Segmenting Bebop Scales 124 Ascending and Descending Permutations

by Bruce Arnold

Part of the Octatonics Series

 

Add digital copy to cart – $19.99

 

Buy at Bruce Arnold’s Patreon Page

 

“Segmenting Bebop Scales 124 Ascending and Descending Permutations” is a crucial part of using these scales effectively. As you learned in the “124 Bebop Scales” course, Bebop scales are eight note scales where there is an added note, usually from a common seven note scale. When musicians apply Bebop scales they tend to gravitate towards the segment of the scale that contains the added note because otherwise the Bebop effect is lost.  This course is part of a series of books on octatonics. 

“Segmenting Bebop Scales 124 Ascending and Descending Permutations” will be working with the additional folders for the ascending and descending segments of each Bebop scale. These files present the segmented Bebop scale in 12 keys for all 124 Bebop Scales.  I’d recommend starting with the more common Bebop scales which are listed on page 2.  I would learn to segment two or three Bebop scales before moving on the “Segmenting Bebop Scales with Approach Notes.“

You will quickly find that not only do these segmented Bebop scales give you a strong “Jazz Sound” but they also help your understanding of time and groove. In the traditional way of using these scales you need to put the chord tones of the Bebop scale on the beat. This takes a while especially if you have never thought of playing scales this way. 

Most inexperienced players don’t realize where their melodies exist in time.  With Bebop scales you need this ability so that you can get the correct chord sound.  Bebop scales of course can also just be played as scales but if you want the “Jazz Sound” then there are some additional requirements which are explored in the course.

The meat of “Segmenting Bebop Scales 124 Ascending and Descending Permutations” is found in the segmentation of the Bebop scales found in the additional files with this course.  Being able to segment a Bebop scale means you know the scale in a much deeper way.   Being able to start in 4 different places within the scale will prepare you for the next course “Segmenting Bebop Scales with Approach Notes.”

You can find out further information on the Segmenting Bebop Scales 124 Ascending and Descending Permutations” course at Bruce Arnold’s Blog
 
Segmenting Bebop Scales 124 Ascending and Descending Permutations by Bruce Arnold

Table of Contents:

Segmenting Bebop Scales
Common Bebop Scales
Course Breakdown
124 Bebop Scales
Bebop Scales and Chords They Work Over
How to Practice with this Course
Segmenting Bebop Scales Examples
Conclusion

List of Contents for Segmenting Bebop Scale Course:

 
60 Page PDF
 
124 Bebop Scales Ascending (248 pages) with midi files
 
124 Bebop Scales Descending (248 pages) with midi files
 
Jam Tracks V1 (MP3’s of 10 chord types in all 12 keys)

ISBN: 978-1-59489-289-9

 

Add digital copy to cart – $19.99
 
 
 
 

What people are saying:

This idea of segmenting Bebop scales is totally new to me.  I can see how it will make the scales much more useful because I’ll be only playing a part of the scale.  It will also allow me to insert Bebop Scales when there is fast moving harmony. J. Brookmeyer

Hey Bruce, just wanted to let you know first how much I appreciate you making all of these courses available worldwide.  I’m in Singapore so not the music capital of the world exactly but being able to study this advanced information is really helping me become a great musician.  I haven’t worked much with eight note scales but looking forward to diving into these new books. A. Thurmond

I studied with you back at Berklee and you touch on this idea of segmenting Bebop scales.  At the time I was just trying to graduate but now I’m ready to really dig in with this idea.  Thanks for the great resource!  A. Samuels

A Proven Educational Lineage

The methods found on muse-eek.com are part of a historical musical lineage stretching back to the 18th-century masters.

By using Muse-Eek books and courses, you are now a part of this lineage—a tradition of excellence passing through legends like Charlie Banacos and Jerry Bergonzi.

  • Historically Validated
  • University-Level Pedagogy
  • Professionally Proven

VIEW THE LINEAGE CHART

Segmenting Bebop Scales 124 Ascending and Descending Permutations by Bruce Arnold

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]]> https://muse-eek.com/segmenting-bebop-scales-124-ascending-and-descending-permutations/feed/ 0 Bebop Scales 124 Bebop Scales and Their Application https://muse-eek.com/bebop-scales-124-bebop-scales-and-their-application/ https://muse-eek.com/bebop-scales-124-bebop-scales-and-their-application/#respond Tue, 10 Jun 2025 12:51:31 +0000 https://muse-eek.com/?p=1428411 Continue reading →]]>

Bebop Scales 124 Bebop Scales and Their Application

Add digital copy to cart – $19.99

Purchase this book at Bruce Arnold’s Patreon Page

Bebop Scales 124 Bebop Scales and Their Application works with 124 Bebop scales but is also an overview of other octatonic courses.  Bebop scales are some of the most commonly known octatonic scales and are one of the techniques used by jazz musician to create a “Bebop Sound.”  They are used in a very specific way so they are in a special class of octatonic (eight note) scales. 

Most musicians are familiar with a small subset of Bebop scales.  This course looks at the common Bebop scales as well as many more. You can see from the Table of Contents below that many aspects of Bebop scales are covered as well as an introduction to some of the future courses which cover; “Segmenting Bebop Scales” and Segmenting Bebop scales with Approaches.

The other courses mentioned above will really help you to see all the applications of Bebop scales and are very important concepts to grasp their full potentials. Overall this is a great course to get started learning Bebop Scales, understanding their use and seeing future ways that you can practice and apply them.

Excerpt from Bebop Scales 124 Bebop Scales and Their Application

Bebop scales have traditionally been a collection of eight note scales where a chord is spelled out on the 1st, 3rd, 5th and 7th position in a scale. For example, 1,2,3,4,5,b6,6,7 is a Major Bebop Scale. You can see that the 1st, 3rd, 5th and 7th position in the scale spell out a Major 6th chord.

There are 495 possible octatonic (eight note) scales. After the 330th scale you have eight note scales that do not contain the root. Many of the 495 possible eight note scales have the characteristic where every other note spells a common chord form, as I referenced in the first paragraph. Traditionally there have been approximately 10 Bebop scales that are not commonly used. I’ve listed these and a few others on page 2 of this course.

I would recommend starting with these if you are new to Bebop scales. If you already use these scales, feel free to look at the 124 Bebop scales that I’ve included in this course. Most of these 124 Bebop scales have the same characteristic where the 1st, 3rd, 5th and 7th position spell out a common chord. (See page 3 for common chord types.)

If you consider chords that are not built in 3rds as your criteria for creating a Bebop scale, that opens up a whole new world of possible scales. I’ve included some of these in the 124 Bebop scales and made a note of their uniqueness on page 8-9. If you would like to explore other possibilities there is a list of all 495 scales found in this course as well as a folder with these scales in all keys.

Bebop scales have a specific way that they are usually played, which I discuss on page 1 of this course. But there are actually many other ways to use Bebop scales. I’ve created other courses using eight note scales where you can explore such things as the chords derived from these scales, as well as common ways Bebop scales are applied in a jazz idiom.

All of the 495 possible octatonic (eight note) scales can be reduced down the 29 prime forms using pitch class set theory. I’ve include references to these throughout this course and you can find a breakdown of these relationships on pages 66-68.

Read more about this course and see example pages at Bruce Arnold’s Blog

bebop-scales-124-bebop-scales-and-their-application/

Table of Contents:

Bebop Scales
Common Bebop Scales
Course Breakdown
29 Octatonic Scales
Seventh Chords Continued
124 Bebop Scales
Chromatic Modes of Bebop Scales
Bebop Scales and Chords They Work Over
495 Eight Note Scales with Prime Form
How to Practice with this Course
Segmenting Bebop Scales; an introduction
Approaching Bebop Scales; an introduction
Going Beyond Bebop Scales
Diatonic Chords of Eight Note Scales; an introduction
Chord Tones and Available Tensions
Passing Diminished
Chords Derived from an Eight Note Scale; an introduction
Application of Eight Note Scales; an introduction

As you can see from the TOC “Bebop Scales 124 Bebop Scales and Their Application” goes explores Bebop Scales on a very deep level.  It also includes references to Pitch Class Set Theory so that you can see how all scales are related back to the 29 Eight Note Scale Prime Forms.

 

List of Contents for the Bebop Scale Course:

95 Page PDF

All 495 Eight Note Scales in all keys 372 Pages with midi files.

Jam Tracks V1 (MP3’s of 10 chord types in all 12 keys)

ISBN: 978-1-59489-288-2

Add digital copy to cart – $19.99
 

What people are saying:

Wow Bruce!  “Bebop Scales 124 Bebop Scales and Their Application.” You are blowing the top off this idea…  I love this concept that looks at the traditional Bebop Scales but then shows you how you could expand this idea to songs composed in a more modern style.  Looking forward to the future courses on this subject. B. Devon

This is a very heavy book!  You could spend a lifetime learning all this information.  I contacted Bruce and he recommended using this book to learn Bebop scales for 4 common chords: Major, Minor, Dominant, minor7b5 and then move on to the Segmenting Bebop Scales (learn same 4 Bebop Scales) then finally Segmenting Bebop Scales with Approaches.  Makes sense because most tunes will have mostly those chords. K. George

Really appreciate how this course is laid out.  There is the PDF giving you the information and history of segmenting Bebop Scales and then the extra folders with the exercises.  I also like playing along with the midi files.  I play and sing the melodies over a MetroDrone® which helps me with my ear training.  F. Foster

A Proven Educational Lineage

The methods found on muse-eek.com are part of a historical musical lineage stretching back to the 18th-century masters.

By using Muse-Eek books and courses, you are now a part of this lineage—a tradition of excellence passing through legends like Charlie Banacos and Jerry Bergonzi.

  • Historically Validated
  • University-Level Pedagogy
  • Professionally Proven

VIEW THE LINEAGE CHART

Bebop Scales 124 Bebop Scales and Their Application by Bruce Arnold

Guitarist-and-Author-Bruce-Arnold-Performing-at-Provincetown-Playhouse-in-NYC-with-Music-Man-Guitar

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