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 chordFigure: 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. 1–4Figure: official FJS rendition of BWV 846 b. 1–4Figure: I–ii making up a long chain of fifthsFigure: 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