User:FloraC/Analysis on the 13-limit just intonation space: episode ii

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Chapter I. Ionian versus Mode 8

Figure: first 16 harmonics in neutral circle-of-fifths notation on C

Brightness of diatonic modes

Mode	UDP	Average Brightness
Lydian	0	+3
Ionian	1	+2
Mixolydian	2	+1
Dorian	3	0
Aeolian	4	-1
Phrygian	5	-2
Locrian	6	-3

Chapter II. Generic Rooted Chord Construction

Interval	Notation	Interval Class
3/1	C–G	Perfect twelfth
5/3	G–E	Major sixth
7/5	E–Bb	Subdiminished fifth
9/7	Bb–D	Supermajor third
11/9	D–F+	Neutral third
13/11	F+–Ad	Subminor third
15/13	Ad–B	Superultramajor second

Figure: double-octave voicing of mode 8

Interval	Notation	Interval Class
5/4	C–E	Major third
6/5	E–G	Minor third
7/6	G–Bb	Subminor third
9/7	Bb–D	Supermajor third
11/9	D–F+	Neutral third
13/11	F+–Ad	Subminor third
15/13	Ad–B	Superultramajor second

Figure: just major chord and just minor chord

Figure: illustration of tonalities resulted from octave subdivision

Chapter IV. Diminished Chords and Augmented Chords

Interval Category Characteristics	Layer of Tonality	Contrasting Pair Examples
Pivotal harmonics	Tonality	5/4 vs 6/5
Ambitonal harmonics	Microtonality	11/10 vs 12/11
Pseudoambitonal harmonics	Pseudotonality	30/17 vs 17/10
	Pseudomicrotonality	17/16 vs 18/17

Chapter V. Things Repel the Similar but not Identical

Figure: BWV 846 b. 1–4

Figure: official FJS rendition of BWV 846 b. 1–4

Figure: I–ii making up a long chain of fifths

Figure: Flora's rendition of BWV 846 b. 1–4

Chapter VI. Overview on Functional Harmony

Figure: Flora's function map

Composite Functions

Harmonic Functions of Septimal Intervals

Ratios	Functions
8/7, 7/6	Subvaricant
9/7, 21/16	Covaricant
32/21, 14/9	Covaricant
7/4, 12/7	Varicant