Theory of harmony, through the patterning of musical symmetries

[ contemporary music ]

PAUL AMROD
... CONTEMPORARY COMPOSER

PAUL AMROD´S THEORY OF HARMONY
THROUGH THE PATTERNING OF MUSICAL SYMMETRIES

Through my explorations into the new harmony at the begin of the 20th Century and my passion for the hard-bop modern jazz from 1965-1975, I have formulated a new concept as an alternative to the “equal importance” of notes, as found in dodecaphony.

Through the observance of musical symmetries I began to pattern simply tritones following typical serial methods. For Example C-F#, E-A#, Eb-A, B-E#, G-C#, A-D#, F-B I would utilize for the building of the first row. Then one can simply, like a twelve-tone row, invert the row. This results in seven new tritones which are structurally related. C-F#, Ab-D, A-D#, Db-G, F-B, Eb-A, G-C#.

At this point I distribute notes around the tritones and develop modes for a melodical and harmonical resource.

In other words each modal resource will be built with the tritone as a nucleus. One can think of it like a solar system where the tritone is the sun and the other chosen notes are planets.

I will now give a written example of some modal structures which are held together by their tritonic relationships. One also needn’t be irritated if more than one tritone appears in a scale. Only the ordered tritones build this structuring.

C-Db-E-F#-G-Ab-Bb. This mode belongs to tritone C-F#.
E-F#-G-A#-B-D-D#. This mode belongs to tritone E-A#.
Eb-F#-G-A-Bb-C-Db .This mode belongs to tritone Eb-A.
B-C#-D-E#-F#-A-A#. This mode belongs to tritone B-E#.
G-A#-B-C#-D-Eb-F. This mode belongs to tritone G-C#.

Every following tritone can build with its planets therefore a new mode as well. I personally stay with three various modes and their transpositions per piece or movement. This is highly helpful for melodic and harmonic homogeny. For my scheme above I will have fourteen modes eventually which are all related to each other through the patterning of the tritone. The choice of notes around a symmetry is personal. If you wish to write mostly darker intervals, fine. If you wish to be diatonic, fine.

The point of the concept is to move modes with structured symmetries instead of the equality of pitches utilized in dodecaphony. One can simply choose his harmonic palette by arranging the wished pitches around a symmetry. When utilizing this method one will hear, as each symmetry moves one to another, a clear and logical harmonic movement.

The tritone is not the only symmetry in a twelve-note well-tempered environment. We have as well the augmented triad (C-E-G#).This triad can be used to control chromatics exactly in the same manner as I have already shown with the tritone.

INTRODUCTORY TEXT TO THE EXPOSITION OF PATTERNS

Here I have various examples of the patterning of symmetries resulting in a logical harmonic environment. One may ask himself what about a symmetrical movement from the tritone or augmented triad. If one wishes to move a harmony, for example an augmented fourth then one must consider the distribution of notes around the tritone. This is in a diatonic example completely clear.

From C Lydian to F# Lydian we see that each structure has seven notes. In C we have D and E above C and G, A and B over F#. If we reverse the distribution over C and F# we will hear the harmonic movement of an augmented fourth. In other words then three notes over C and two over F#.

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