The emergence of the starting point as a symmetrical root

A starting point is represented in the thesaurus with the Roman numeral (I). The term “unequal” represents the method of distributing pitches around a given symmetry. Each mode consists of a prime-numerical symmetry and an unequal distribution of pitches. This also enables each mode to be transposed on all half-steps from the original.

The inequality is either reached through the number of pitches between each part of a given symmetry, as a pure Lydian mode or through an intervallic distance which is greater or smaller. An example of the use of intervallic distance could read as such, I-II-#IV-V. In the case of the augmented triad the distance below also can play a factor. In this particular mode, I-#II-III-IV-#V-VII, the distance above both the (I) and the (#V) are equal however because the intervallic distance is greater beneath (#V) the number (I) becomes the starting point.

An interesting acoustical phenomenon occurs if we listen closely to each member of a given mode. We could for starters examine all of the tritonic modes. We will arbitrarily arrange the notes and place the Roman number (I) within a given chord as the second voice.

Now I will list all five modal variations in this fashion. V-I-#IV, #V-I-#IV, VI-I-#IV,
bVII-I-#IV, VII-I-#IV. Now we shall play each chord firstly and then isolate each separate pitch. We will notice a special dominance of the number (I). This dominance I describe as a symmetrical root solidifying the entire transpositional process.

I will now develop a transpositional scheme in which we can follow the appearance of various symmetrical roots. This scheme would be in letters G-C-F#-; Db-Eb-A; Bb-D-G#;
A-Bb-E; G-A-D#; E-Ab-D. Now we will move to F# as our first starting point and invert our scheme. C#-F#-B#; Db-Eb-A; C-E-A#; G-Ab-D; G-A-D#.Gb-Bb-E. One can hear that in each of our triads the second voice emerges as the symmetrical root.

This principle can therefore be expanded from just three-note modes to encompass all distributions around a particular symmetry possible in our twelve note system. Therefore the generation of quadratonic, pentatonic, hexatonic, heptatonic, octatonic, nonetonic, decatonic, and undecatonic modes. I propose that each mode, because of the exercising of this distributive method, results in the emergence of a symmetrical root as a starting point represented, in this thesaurus, by the Roman numeral (I).

The redistribution of modal members through harmonic structures and with the isolation of a given starting point, this pitch always will be audible as possessing dominance even in complex ten or eleven note chords.