Progressions
Numbers are chord-root offsets. The chord quality comes from the mode. Two roots are often enough; four-root loops are reference shapes, not obligations.
0 → 8 → 10 → 70 → 3 → 10 → 80 → 10 → 8 → 50 → 50 → 10 → 7 → 0| Fast lookup | Roots | Character |
|---|---|---|
| one change | 0 → 8 | minor i ↔ VI |
| one change | 0 → 10 | minor i ↔ VII |
| one change | 0 → 5 | Dorian i ↔ IV |
| synthwave | 0 → 8 → 3 → 10 | i · VI · III · VII |
| major/trance | 0 → 7 → 9 → 5 | I · V · vi · IV |
Pedal root: movement without losing the center
0000325377710Voice leading
0 3 78 12 1510 14 170 3 70 3 82 5 10Σ motion = 250→8 · 3→12 · 7→15Σ motion = 10→0 · 3→3 · 7→8d(A, B) = Σ |aᵢ − bᵢ|Pair voices, measure each semitone displacement, then sum. Root position costs 25; the close inversion costs 1.| Space can identify | Operation | Livecoding meaning |
|---|---|---|
| octave-related pitches | x ≡ x + 12 | same pitch class, different register |
| reordered chord tones | permutation | same unordered chord, different voicing path |
| the same shape at another root | transposition | add one offset to every voice |
| mirrored interval direction | inversion | optional equivalence; useful for finding related shapes |
A full chord space is multidimensional. This two-column projection keeps only the part needed here: every line is one voice, and the whole chord transition is the collection of those lines.
prefer ±1 or ±2 per voiceIf a voice can move 1–2 semitones instead of 5–7, test the closer inversion first.Attraction & potential
“Wants to resolve” means “listeners have learned to expect one continuation more than others in this context.” It is a tendency, not a universal law. The same pitch can feel stable in one mode and unstable in another.
Note tendencies
11 → 121 → 08 → 76 → 7| Signal | Default tendency | What can override it |
|---|---|---|
leading tone 11 | up to root 12 | descending line or a different tonal center |
| chordal seventh | down one scale step | revoicing, suspension or non-functional harmony |
| chromatic neighbor | return to the note it surrounds | repetition can turn it into a new stable pitch |
| common tone | stay while other voices move | register, melody and bass may make a leap preferable |
From notes to chord potential
P(A → B)=common tonesidentity+semitone resolutionslocal pull+style priorlearned grammar−total voice motioneffortThis is a ranking model, not physics. The weights change with the mode and style. In modal techno, common tones and short motion may matter more than a classical dominant–tonic function.
| From G7 | Candidate voicing | Motion | Potential in C minor | Why |
|---|---|---|---|---|
7 11 14 17 | 7 12 15 19 · Cm | 0 +1 +1 +2 | high | 11→12, common G, dominant → tonic |
7 11 14 17 | 7 10 15 19 · E♭ | 0 −1 +1 +2 | medium | equally smooth geometry, weaker closure |
7 11 14 17 | 8 12 15 20 · A♭ | +1 +1 +1 +3 | medium | deceptive color; three semitone resolutions |
7 11 14 17 | 8 12 17 20 · Fm | +1 +1 +3 +3 | low | one common tone but more total motion |
- Generate candidate chord shapes from the current pitch collection.
- Create inversions near the current register.
- Measure the shortest voice-to-voice motion.
- Add bonuses for common tones, tendency resolutions and style-specific moves.
- Rank candidates; keep several possible next moves instead of declaring one answer.
The chord-space view follows Dmitri Tymoczko’s A Geometry of Music. The language of tendency remains deliberately contextual: see Style and tendency and Tendency tones.