Harmonic and Melodic Equivalence V10B Trichord Pair

This course works with a trichord pair consisting of a two 025 pitch class sets an augmented 4th apart. These six notes are also part of a diminished scale so they can be used anywhere that you might apply a diminished or symmetrical diminished scale. This makes them extremely useful for an improvising musician.

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 V10B 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 025 pitch class sets. An example of that would be C, G, A and D, E, B. As you probably notice these six notes form a major scale minus the 4th. 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 V10B 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 V10B 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

  • 01-025-025-Degree-1-b2-b3-b5-5-6-Closed-Position-Key-C-Harmonic-and-Melodic-Equivalence-V10B-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

1st Inversion Exercise

  • 02-025-025-Degree-1-b2-b3-b5-5-6-1st-Inversion-Key-F-Harmonic-and-Melodic-Equivalence-V10B-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

2nd Inversion Exercise

  • 03-025-025-Degree-1-b2-b3-b5-5-6-2nd-Inversion-Key-Bb-Harmonic-and-Melodic-Equivalence-V10B-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

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

  • 04-025-025-Degree-1-b2-b3-b5-5-6-Random-Inversions-Key-Eb-Harmonic-and-Melodic-Equivalence-V10B-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

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

  • 05-025-025-Degree-1-b2-b3-b5-5-6-Random-Inv-Rhy-Key-Ab-Harmonic-and-Melodic-Equivalence-V10B-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

2nd Set of Exercises in Harmonic and Melodic Equivalence V10B Course

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

Atomic Scales 1st Rotation

  • 01-025-025-Degree-1-b2-b3-b5-5-6-Atomic-Scale-Ex-1-Key-C-Harmonic-and-Melodic-Equivalence-V10B-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

Atomic Scales 2nd Rotation

  • 02-025-025-Degree-1-b2-b3-b5-5-6-Atomic-Scale-Ex-2-Key-F-Harmonic-and-Melodic-Equivalence-V10B-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

Atomic Scales 3rd Rotation

  • 03-025-025-Degree-1-b2-b3-b5-5-6-Atomic-Scale-Ex-3-Key-Bb-Harmonic-and-Melodic-Equivalence-V10B-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

Atomic Scales 4th Rotation

  • 04-025-025-Degree-1-b2-b3-b5-5-6-Atomic-Scale-Ex-4-Key-Eb-Harmonic-and-Melodic-Equivalence-V10B-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

Atomic Scales 5th Rotation

  • 05-025-025-Degree-1-b2-b3-b5-5-6-Atomic-Scale-Ex-5-Key-Ab-Harmonic-and-Melodic-Equivalence-V10B-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

Atomic Scales 6th Rotation

  • 06-025-025-Degree-1-b2-b3-b5-5-6-Atomic-Scale-Ex-6-Key-Db-Harmonic-and-Melodic-Equivalence-V10B-by-bruce-arnold-for-muse-eek-publishing-inc

MP3 example

TOC in the Harmonic and Melodic Equivalence V10B Trichord Pair Course:

  • How to Use This Course
  • Harmonic/Melodic Possibilities of an 025 and 025 combination.
  • Chord Possibilities of this 025 and 025 combination
  • Two triad pairs rotations Starting on Every Eighth Note
  • How to think of these an 025 and 025 combinations that are used in this course
  • The 025 and 025 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, G, A and Db, Eb, Gb 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 V10B Trichord Pair Today!

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

Additional Information for Harmonic and Melodic Equivalence V10B Trichord Pair:

  • Digital Edition 978-1-59489-256-1
  • 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 MetroDrone®

What people are saying:

Hey Bruce, I just wanted to report in on the 10B course. I’m really starting to feel like an expert on these combinations but you completely blew me away with this 025-025 combination for a diminished sound. First I never in a million years would have even thought that 025 could be used with a diminished scale which has really opened my eyes to a lot of cool sounds. I love it when I get turned on to something completely unexpected so you really hit it out of the park on this one! J. Ogland

Got to tell you guys that these Harmonic and Melodic Equivalence books are a game changer for me. Especially as you point out in the books that you should think of these combinations in relationship to the key center. I hadn’t been doing that to start but now I am and starting to apply that idea to everything that I practice. You are correct that this makes improvising with crazy note combinations much easier. Right now I’m also working with the altered scale and was having a real problem with it until I started thinking and hearing it in an overall key center. It’s making much more sense now and I’m creating melodic lines that are much more musical. Thanks for all your help. L. Tanning

One thing I’m noticing is these different shapes are easily transferable. If you learn the 025 for 10A then applying it to the 10B combination is much easier. I originally was thinking that every new book was a steep new learning curve but that really isn’t true in many cases. Thanks for pointing that out and all your other guidance via my emails. J. Van Dyke

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Muse-Eek Publishing Company is a publishing house with a broad focus on music education. Muse-Eek also publishes fine art and poetry books, and has its own record label, Muse-Eek Records. Our online presence, Muse-Eek.com specializes in the publication of music workbooks, video courses and sound and video recordings that teach the foundation of good musicianship through groundbreaking and innovative methods along with traditional methods that have been taught for centuries. These historic methods date back through centuries of great musicians and educators. To see these interesting relationship please see Bruce Arnold's Music Education Genealogy Chart which tells you a lot about the where many of his educational ideas took root and some of the educational pillars that are evident throughout the books you find on this website. The Muse-Eek Records catalogue contains a diverse selection of music much of it by Bruce Arnold in collaboration with some of today's best players in classical, jazz, rock and avant-garde music. These are available in CD, DVD and mp3 formats. We believe in a working relationship with our music education customers; they are free to interact with the author after purchasing a book to help them through any material they don’t understand or which they need further clarification. We also have a member's area which contains a wealth of free information to help a student understand music at a deeper level and access additional files for our books. Many of our books offer cutting edge ideas regarding ear training, guitar technique, rhythm and time. These methods have a proven track record. Our main author Bruce Arnold has taught at some of the most prestigious music schools in the world, including Princeton, Dartmouth, Berklee College of Music, New England Conservatory, The New School and NYU. Along with Mr. Arnold's publications on the Muse-eek.com website he has also written books and appeared in educational DVDs for MelBay and Truefire. Over the years Mr Arnold has used his experiences with his students to develop a program that can elevate a musician's ability to world class caliber. If you have questions about any of our books or recordings please send us an email. Along with general questions about either our record label or our publishing company we also welcome questions to help a student choose the proper materials to reach their goals. We have over 300 products to help you learn any style of music and to develop your musicianship to its peak. We also make recommendations for practice schedules for students who use our methods to get the most out of their study time. This, along with personal interaction with Bruce through email, nurtures the student's ability through a closely monitored situation, ensuring there is no wasted time or misunderstanding.