Non-Equivalents
Regarding tone, there are 224 non-equivalents, (NEqu) in a single chromatic scale. All the music from the 4th Repertoire, Book For…., are from the 12 codes of three toned NEqu’s presented in example #8. Note, to the left of the second code in rounded brackets; (13) = EFG, E to F is one semitone and E to G is 3 semitones, these three tones can then be subjected to circular permutation, 1x2x3 = 6 providing the following outcomes:
E F G
E G F
F G E
F E G
G E F
G F E
With transpositions and inversions included (13) equates to 12 x 6 = 72. These are considered the equivalents of the initial NEqu code. When intervals are inverted within an octave, where a 5th equates to a fourth we conclude that there are 6 intervals: semitone, tone, minor third, major third, fourth and tritone. Again refer to Example #8, the symbols in square brackets to the right of code five;[100011] reveal the interval content of: 1 semitone, 0 tones, 0 minor 3rds, 0 major 3rds, 1 fourth and 1 tritone. One can surmise two groups of intervals here. Group 1: those that expand the interval of a tone to become a major third being two tones and a tritone having three tones. The 2nd group is what remains: one semitone, a minor third, three semitones and a fourth, five semitones. Refer to our 12 NEqu examples, these NEqu’s are made up of combinations of these two groups, eight from the 1st group and four from 2nd group. For more, search rpmacromusic.com.au Book 9. These observations inform the extrapolation of codes which are asked for in each suite. Although the NEqu parameter of three tones is minimal we are able to expand the intervalic palette by introducing secondary intervals that don't appear in the original code while still holding the concentration of a particular chroma. Nevertheless, be alert to the ambiance of the code as it may become blurred by ill-conceived extensions.