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.
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 |
| 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
- Vanishing Point / Heavy Mental
- Lavadura
- Live at Provincetown Playhouse NYC
- Heavy Mental
- Eclectic Electric Guitar Trio
(w/ Skolnick & Getter)
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.
Before diving into advanced pitch class sets, we highly recommend you test your 12-note foundation.
Ear Training & Singing
- 3-Note Melodic & Harmonic Training
- 9,240 Hexatonic Key Center Files
- Trichord Singing Exercises (All Keys)
- 18 Inversions per Trichord
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
Theory & Composition
- 924 Aggregates (12-Tone Coverage)
- 924 Hexatonics Grouped by Prime Form
- The Sonic Resource Guide
- Symmetric Difference Analysis
FAQ Questions about Hexatonics and Trichords
| 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.