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Harmonic and Melodic Equivalence V9D Trichord Pair

This course works with a trichord pair consisting of a two 024 pitch class sets an augmented 4th apart. This forms a whole tone scale and is one of the few instances within this series where we are dealing directly with a common scale. This presents a challenge because the whole tone scale is such a recognizable sound. Using two trichords, in this case 024s, can really help to disguise the pervasive sound of the whole tone scale. Within this course you will find a discussion on how to deal with symmetrical scales like the whole tone and diminished to make them less obvious when you use them in an improvisational setting.

Two Trichords

Two trichords which unlike a two triad pair are not build in thirds. The term was coined by Milton Babbitt to distinguish a three note collection from a triad built in 3rds. Trichords form a sound that is very useful to a modern improviser both as melodic and harmonic content. Through the Harmonic and Melodic Equivalence Series these trichords are studied in-depth. I think you will find them to be a welcome addition to your improvisational palette.

Harmonic and Melodic Equivalence V9D Trichord Pair

Status: In stock, Digital book is available for immediate access.

Background Information on a Two Triad Pair or Two Trichords

“Harmonic and Melodic Equivalence Trichord Pair” is a series of books that will help you to develop many different musical skills simultaneously. The source materials for this book are exercises that contain two 3 note groupings which are not built in thirds. First a little background, “two triad pairs” consist of two 3 note groupings that are built in 3rds. These combinations typically use a major, minor, diminished or augmented triad and when grouped into a collection of two are called a “two triad pair.”

A trichord pair on the other hand takes any of the 9 other possible 3 note combinations and builds pairs using these pitch class sets. These include 012, 013, 014, 015, 016, 024, 025, 026 and 027. Any three note group can be referred to as a “trichord” but is more commonly used when speaking of a three note grouping not built in thirds. Trichords can also be referred to as non-tertial two triad pairs.

The exercises found in this course use many different types of harmonic and melodic ideas that can be superimposed over common chord progressions, scales and other musical situations. This course concentrates on using a two 024 pitch class sets. An example of that would be C, D, E and Gb, Ab, Bb. As you probably notices these six notes are half of a chromatic scale. While this combination isn’t great for playing over chords each trichord can form the sound of many typical chords and therefore it is great as a tool to superimpose chord changes. The course contains many ideas on how to implement this idea. There are also many charts included in this course to show you how these notes function in all 12 keys.

Unique Aspect of These Two Trichord Books

The two trichord books are pretty unique to the Muse Eek Publishing Inc. catalog. The various non-tertial two triad pairs found in this collection are both beautiful and highly applicable to modern improvisation. They work well as a melodic and harmonic device and Mr. Arnold has written a body of work through both recordings, videos and books dedicated to these non-tertial combinations. As with all of Mr. Arnold’s books there is a sharp focus on the ear training and the “Harmonic and Melodic Equivalence Two Trichord” Series is no different. Each exercise or chart is always relating back to the idea of how you would hear these notes within a key center. This book includes a section where the two trichord pair are put into common chord progressions but more importantly shows you how these progressions relate to the overall key center. Learning music based on how your hear it rather than relating everything to a chord by chord approach is the rosetta stone of music. This is the secret to the previously undecipherable mystery of understanding music from an aural perspective.

Harmonic and Melodic Equivalence Series

This course is part of the Harmonic and Melodic Equivalence Series which explores over 50 different either trichord pairs or two triad pairs. To see all volumes follow the link above to explore each volume and hear examples from each course as well as finding links to compositions that I’ve written using each combination.

Harmonic and Melodic Equivalence Exercises

This course is divided up into two sets of exercises written in treble and bass clef. The 1st set of exercises gets gradually harder but also more musical. Depending upon your musical skills you can start anywhere you want but for beginners I would recommend starting from the 1st exercise of the five. The 2nd set of exercises are called “Atomic Scales.” These exercises are a technical exercise that really helps you to learn these ideas but also sound great as a melody right off the bat. There are 6 different types of “Atomic Scales” exercises in this course. You don’t have to play every exercise in every key. But doing this will greatly increase the likelihood of you using it in real music in the future. Below is a listing of the exercises found in this course:

  • Closed position studies.
  • 1st inversion studies.
  • 2nd inversion studies.
  • Random combinations of closed position along with 1st and 2nd inversion.
  • Random combinations of closed position along with 1st and 2nd inversion with rhythmic displacement.
  • Atomic Scales Exercise 1
  • Atomic Scales Exercise 2
  • Atomic Scales Exercise 3
  • Atomic Scales Exercise 4
  • Atomic Scales Exercise 5
  • Atomic Scales Exercise 6

Explanation of 2nd Set of Exercises in Harmonic and Melodic Equivalence V9D Trichord Pair Course

Below is an explanation for each set of the 6 different atomic scale exercises found in this course. Three octave sequences that move back and forth between the two 3 note groups are presented in six different configurations. These exercises are highly melodic and can be used verbatim as melodies when soloing. If we thought of the three notes as A,B,C then there would be six different ways to combine these notes. i.e. ABC, ACB, BAC, BCA, CAB and CBA. All exercises include MP3s as well as midi files so that you can hear and play these exercises at any tempo as well as versions in all 12 keys.

  • Three octave sequences that move back and forth between the two 3 note groups in the ABC sequence
  • Three octave sequences that move back and forth between the two 3 note groups in the ACB sequence
  • Three octave sequences that move back and forth between the two 3 note groups in the BAC sequence
  • Three octave sequences that move back and forth between the two 3 note groups in the BCA sequence
  • Three octave sequences that move back and forth between the two 3 note groups in the CAB sequence
  • Three octave sequences that move back and forth between the two 3 note groups in the CBA sequence

1st Set of Exercises in Harmonic and Melodic Equivalence V9D Trichord Pair Course

Here are a few examples from the 1st set of exercises. A complete list of the different types of exercises can also be found below.

Closed Position Exercise

  • 01-024-024-Degree-1-2-3-b5-b6-b7-Closed-Position-Key-C-Harmonic-and-Melodic-Equivalence-V9D-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

1st Inversion Exercise

  • 02-024-024-Degree-1-2-3-b5-b6-b7-1st-Inversion-Key-F-Harmonic-and-Melodic-Equivalence-V9D-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

2nd Inversion Exercise

  • 03-024-024-Degree-1-2-b3-3-4-5-2nd-Inversion-Key-Bb-Harmonic-and-Melodic-Equivalence-V9D-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

Random combinations of closed position along with 1st and 2nd inversion.

  • 04-024-024-Degree-1-2-3-b5-b6-b7-Random-Inversions-Key-Eb-Harmonic-and-Melodic-Equivalence-V9D-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

Random combinations of closed position along with 1st and 2nd inversion and rhythm permutation

  • 05-024-024-Degree-1-2-3-b5-b6-b7-Random-Inv-Rhy-Key-Ab-Harmonic-and-Melodic-Equivalence-V9D-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

2nd Set of Exercises in Harmonic and Melodic Equivalence V9D Course

Here are a few examples from the 2nd set of exercises.

Atomic Scales 1st Rotation

  • 01-024-024-Degree-1-2-3-b5-b6-b7-Atomic-Scale-Ex-1-Key-C-Harmonic-and-Melodic-Equivalence-V9D-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

Atomic Scales 2nd Rotation

  • 02-024-024-Degree-1-2-3-b5-b6-b7-Atomic-Scale-Ex-2-Key-F-Harmonic-and-Melodic-Equivalence-V9D-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

Atomic Scales 3rd Rotation

  • 03-024-024-Degree-1-2-3-b5-b6-b7-2nd-Inversion-Key-Bb-Harmonic-and-Melodic-Equivalence-V9D-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

Atomic Scales 4th Rotation

  • 04-024-024-Degree-1-2-3-b5-b6-b7-Atomic-Scale-Ex-4-Key-Eb-Harmonic-and-Melodic-Equivalence-V9D-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

Atomic Scales 5th Rotation

  • 05-024-024-Degree-1-2-3-b5-b6-b7-Atomic-Scale-Ex-5-Key-Ab-Harmonic-and-Melodic-Equivalence-V9D-by-bruce-arnold-for-muse-eek-publishing-incc

MP3 example

Atomic Scales 6th Rotation

  • 06-024-024-Degree-1-2-3-b5-b6-b7-Atomic-Scale-Ex-6-Key-Db-Harmonic-and-Melodic-Equivalence-V9D-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

TOC in the Harmonic and Melodic Equivalence V9D Trichord Pair Course:

  • How to Use This Course
  • Harmonic/Melodic Possibilities of an 024 and 024 combination.
  • Chord Possibilities of this 024 and 024 combination
  • Two triad pairs rotations Starting on Every Eighth Note
  • How to think of these an 024 and 024 combinations that are used in this course
  • The 024 and 024 combination Daily Exercise-Atomic Scales
  • Thinking of these two triad pairs as applications to Modes
  • Thinking of these two triad pairs as One Scale
  • C, D, E and Gb, Ab, Bb as One Scale in All Keys
  • Forming chord progressions with two triad pairs
  • Forming extended chord progressions with two triad pairs
  • Choosing chord progressions from two triad pairs
  • Additional practice ideas

Get Harmonic and Melodic Equivalence V9D Trichord Pair Today!

Status: In stock, Digital book is available for immediate access.

Additional Information for Harmonic and Melodic Equivalence V9D Trichord Pair:

  • Digital Edition 978-1-59489-254-7
  • One 14 page PDF explaining exercises, 5 different types of exercises, 328 pages of exercises in PDF format in treble and bass clef.
  • Information and examples of forming extended chord progressions with this two triad pair.
  • MP3’s and Midi files for all exercises.
  • 12 MP3s from Tuba MetroDroneĀ®

What people are saying:

Bruce, this is one of the most interesting books in this series. Not so much about the segmenting of the whole tone scale but with the information you supply on how to disguise common scales like whole tone and diminished. Totally agree with your idea that you don’t want to sound like your playing licks when you improvise and your suggestions are great on how to get around that with these highly recognizable scales. As always I appreciate your insights. J. Ogland

Just wanted to drop you guys an email and tell you how much I enjoying this Harmonic and Melodic Equivalence Series. I appreciate you being so thorough by including so many different ways to combine two triad pairs or two trichords. I’m familiar with the two triad pairs but these two trichord books are really a new thing for me. I’m a guitarist so I’m applying these ideas both as melodic lines and chords. Really digging the juxtaposition of the 024 chords with these various scales. I would have never thought of doing this so I appreciate you opening up my eyes to some new sounds. Looking forward to the next book in the series! U. Anders

Hi Mr. Arnold, I wanted to get in touch to express my thanks for these triad pair books. I studied with Charlie Banacos back in the day and did quite a bit of work with his double mambos and non-tertial double mambos. This series in taking those ideas and really organizing them into a system by using pitch class sets which was something that Charlie never talked about with me so I’m glad you are filling in the blanks with your information. Looking forward to the next book in the series. F. Anderson