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 III. Primodality and Nonrooted Chord Construction

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

Explicit Functions

Implicit Functions

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

Chapter VII. Overview on Microtempering

Appendix A. List of Chords

Appendix B. JI Redux of Prelude in C Major (BWV 846)

Appendix C. Harmonic Identities of Individual Harmonics

Notes

Release Notes