This system consists in symmetrically dividing the octave in three or four parts. If we consider C to be used as octave, then we will get the pitches C, E and G# or Ab. When using these three pitches harmonically, we get the C augmented chord which is ambiguous due to its symmetrical nature – if we invert any of its chord pitches, it always implies the same sonority.
This means that any chord pitch can be considered as the root with the underlying whole-tone or the augmented scale.
In the sense that these tonics are connected because each may have its own harmonic pull at any given time in the musical piece, it means that the respective chords from each derived tonic system will also be connected. Therefore, we would be working the tonalities C major, E major and Ab major, using each respective major chord as a potential tonic.
The same principle applies if the octave is symmetrically divided in four parts. In C, we will get the pitches C, Eb, Gb and Bbb which constitutes the diminished seventh chord.
In part, because the octave is divided in third intervals, this approach resembles the chromatic mediants relationships and how these can be used to introduce non-diatonic or chromatic pitches into a closed tonal system, that is, without losing the sense of tonal center.
In practice, the multi-tonic system is presented as a tool to re-harmonize or create variations of an otherwise simple chord progression, in any given key center, and use the multiple tonics as reference for substitute chords. In jazz, this approach is commonly used for the ii-V-I chord progression and it can be distinguished by its unusual tonal root movement:
A series of ii-V-I chord progressions where the ii related to G maj7 and Eb maj7 (in the end) were substituted with augmented sixth chords. The highlighted chords are the target chord tones used to divide the Eb octave.
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