The Harmonic and Melodic Equivalence Series
The Harmonic and Melodic Equivalence Series contains over 40 courses that explore three note pairs. These three note pairs form a hexatonic scale and can be used to make interesting melodies as well as being great 3 note chords. Two different types of three note pairs are explored in these courses. Tertial pairs are constructed with Major, Minor, Diminished and Augmented triads while the non-tertial pairs are constructed using various combinations of the 12 possible three note structures those are:
- 036 which is a diminished triad.
- 037 which is a major or minor triad.
- 048 which is an augmented triad.
This blog post will look at two important courses from the Harmonic and Melodic Equivalence Series. These are Volumes Seven and Eight which look at combining two 016s. The 016 is one of the most important three note combinations in music. This pitch class set has a tritone within its structure which is the backbone of dominant chords, and one of the most used intervals in music. The Harmonic and Melodic Equivalence Series looks at the possible applications of a single 016 as well as two 016s played together to form a hexatonic scale.
Exploring Two of the Courses from the Harmonic and Melodic Equivalence Series
As I just mentioned, the Harmonic and Melodic Equivalence Series has two courses that explore two 016-016 three note pairs. But that really is just the tip of a massive iceberg of sound. Let’s look at one of the most used scales in improvisation, the symmetrical diminished scale (1, b2, b3, 3, #4, 5, 6, b7). There are eight 016s found in this scale and 12 016-016 combinations:
- [C Db Gb] [A E Eb] 0 1 6 0 1 6
- [C Db Gb] [Bb E Eb] 0 1 6 0 1 6
- [C Db Gb] [A Bb Eb] 0 1 6 0 1 6
- [C Db Gb] [A Bb E] 0 1 6 0 1 6
- [C Db G] [A E Eb] 0 1 6 0 1 6
- [C Db G] [Bb E Eb] 0 1 6 0 1 6
- [C Db G] [A Bb Eb] 0 1 6 0 1 6
- [C Db G] [A Bb E] 0 1 6 0 1 6
- [C G Gb] [A E Eb] 0 1 6 0 1 6
- [C G Gb] [Bb E Eb] 0 1 6 0 1 6
- [C G Gb] [A Bb Eb] 0 1 6 0 1 6
- [C G Gb] [A Bb E] 0 1 6 0 1 6
That’s a lifetime of work right there –just to master all these combinations in all keys. The good news is, once your learn one 016-016 combination it is much easier to master the next because of the built-in symmetry of the structure.
The Nature of a Dominant Sound
One of the reasons I say that this 016-016 combination is a lifetime of work is because of the nature of a dominant sound. If you explore the reharmonization principles presented in Chord Workbook for Guitar Volume One you will see that there are 3 ways a dominant chord can resolve so in a way that triples the list above because remember, you want to think of all these relationships in the overall key center of the moment. Then if you look at the reharmonization principle presented in Chord Workbook for Guitar Volume Two which presents the idea of using reharmonizing chords based combining chord tones and tensions you exponentially increase the size of the list of possibilities. Overwhelming? Yes, but I find it more exciting that I can learn one combination on my instrument and have a plethora of applications for that one combination. And that makes practicing 016 very rewarding because by learning one thing you find multiple uses that will mushroom your sound palette.
Finding the Important Two Three Note Combinations
The Harmonic and Melodic Equivalence Series does not cover all the three note pairs that are found in music, but it does cover the combinations that I’ve found the most useful. It explores the common triadic combinations that most people have discussed in other books, but more importantly, it looks at the non-triadic combinations that have been very neglected, which is crazy because these sounds not only work wonderfully as melodic lines, but also create awesome chordal sounds. In the case of the 016 as both a melodic and chordal sound it’s a sound you are used to hearing. The common drop two C13 chord C, Bb, E, A has an 016 in its top three notes so many musicians are already using 016 –they just don’t realize it!
By exploring the 016 and all the books in the The Harmonic and Melodic Equivalence Series you will open up a whole new world of fresh sounds and a new way to look at things you commonly play. It all cases it will expand your knowledge and make you a better musician by showing you new ways to perceive and work with music.
Need Help Understanding what an 016 is?
I’ve written a book called the Sonic Resource Guide which explains pitch class set theory in very easy to understand terms. Think of pitch class set theory as a way to organize all possible scales (of which there are 220.) Using this method you can really wrap your head around all melodic and harmonic possibilities in music. Check in out it will change your whole musical life!
Bruce Arnold Music Education Genealogy Chart
You might enjoy checking out the “Music Education Genealogy Chart” located on my artist’s site. You will clearly see the historic progression of pedagogy that is the basis for Muse Eek Publishing Products. Great musicians throughout history have been studying the ideas presented by Muse-eek.com which derives its content from a a lineage that stretches back to Scarlatti!