INTRODUCTORY TEXT

With the utilization of symmetrical unities in the form of scales, we can free ourselves from pure generative thinking. We can superimpose these scales as well without the pure generation of inversions. Of course the exposition of the entire scale must occur. This insures us of a collection of pitches, irrelevant of the generative process, resulting eventually in a perfect symmetrical unity. Here I have, in letters, an example exhibiting this method.

C- F#-G-Bb followed by D-E-A-C. The entire collection is symmetrical to the note D however is not generated from D. This collection is randomly chosen from a symmetrical unity as a heptatonic scale. This reads as such D-E-F#-G-A-Bb-C. Therefore we can generate asymmetrical figures or chords with the manifestation of symmetrical scales as resources instead of separate pitches.

A random collection is also possible by rearranging a generated inversion with member substitution. One example could be D-F-F#-A followed by a generation D-B-Bb-G.

Now we can freely rearrange the perfect generation and construct two random groups that also eventually create a symmetrical unity. For example B-D-F#-Bb followed by G-A-D-F.

Now I will illustrate, in Roman numerals, all the possible scales inversely constructed to the beginning pitch.

SYMMETRIC UNITIES AS SCALES

TRITONIC SCALES
I-bII-VII
I-II-bVII
I-bIII-VI
I-III-bVI
I-IV-V

QUADRATONIC SCALES
I-bII-#IV-VII
I-II-#IV-bVII
I-bIII -#IV-VI
I-III -#IV-bVI
I-IV-#IV-V

PENTATONIC SCALES
I-bII-II-#VI-VII
I-bII-bIII-VI-VII
I-bII-III-bVI-VII
I-bII-IV-V-VII
I-II-bIII-VI-bVII
I-II-III-bVI-bVII
I-II-IV-V-bVII
I-#II-III-#V-VI
I-bIII-IV-V-VI
I-III-IV-V-bVI

HEXATONIC SCALES
I-bII-II-#IV-#VI-VII
I-bII-bIII-#IV-VI-VII
I-bII-III-#IV-bVI-VII
I-bII-IV-#IV-V-VII
I-II-bIII-#IV-VI-bVII
I-II-III-#IV-bVI-bVII
I-II-IV-#IV-V-bVII
I-#II-III-#IV-#V-VI
I-bIII-IV-#IV-V-VI
I-III-IV-#IV-V-bVI

HEPTATONIC SCALES
I-bII-II-bIII-VI-bVII-VII
I-bII-II-III-bVI-bVII-VII
I-bII-II-IV-V-bVII-VII
I-bII-bIII-III-bVI-VI-VII
I-bII-bIII-IV-V-VI-VII
I-bII-III-IV-V-bVI-VII
I-II-bIII-III-bVI-VI-bVII
I-II-bIII-IV-V-VI-bVII
I-II-III-IV-V-bVI-bVII
I-#II-III-IV-V-bVI-VI

OCTATONIC SCALES
I-bII-II-bIII-#IV-VI-bVII-VII
I-bII-II-III-#IV-bVI-bVII-VII
I-bII-II-IV-#IV-V-bVII-VII
I-bII-bIII-III-#IV-bVI-VI-VII
I-bII-bIII-IV-#IV-V-VI-VII
I-bII-III-IV-#IV-V-bVI-VII
I-II-bIII-III-#IV-bVI-VI-bVII
I-II-bIII-IV-#IV-V-VI-bVII
I-II-III-IV-#IV-V-bVI-bVII
I-#II-III-IV-#IV-V-bIV-IV

NONETONIC SCALES
I-bII-II-bIII-III-bVI-VI-bVII-VII
I-bII-II-bIII-IV-V-VI-bVII-VII
I-bII-II-III-IV-V-bVI-bVII-VII
I-bII-bIII-III-IV-V-bVI-VI-VII
I-II-bIII-III-IV-V-bVI-VI-bVII

DECATONIC SCALES
I-bII-II-bIII-III-#IV-bVI-VI-bVII-VII
I-bII-II-bIII-IV-#IV-V-VI-bVII-VII
I-bII-II-III-IV-#IV-V-bVI-bVII-VII
I-bII-bIII-III-IV-#IV-V-bVI-VI-VII
I-II-bIII-III-IV-#IV-V-bVI-VI-bVII

UNDECATONIC SCALES
I-bII-II-bIII-III-IV-V-bVI-VI-bVII-VII

© Copyright by Paul Amrod