VIII. Scale & Mode Terminology
Parent Scale
A traditional scale (pentatonic, diatonic, whole-tone, etc.) that contains an orbit’s pitch-class set as a subset. Parent-scale containment is a set-theoretic fact, not a claim about derivation.
Step Sequence
The ordered tuple of semitone gaps between consecutive pitch classes of a chord (within one octave, including wrap-around). Always sums to 12.
Mode
A cyclic rotation of the step sequence — starting on a different note of the chord. Each mode is a different “entry point” into the same pitch collection.
Step-Size Multiset
The step sequence sorted in ascending order. Rotation-invariant. Characterizes the orbit’s melodic vocabulary regardless of mode. Two orbits may share a multiset (multiset collision) while having different cyclic orderings.
Multiset Collision
Two orbits sharing the same step-size multiset but different cyclic orderings. Collisions: {2,2,3,5} = Summit Q777 and Plateau Q877; {2,3,3,4} = Plateau Q787 and Upper Slope Q786; {2,2,4,4} = Saddle Q686 and Precipice Q688; {1,3,3,5} = Valley Q878 and Lower Slope Q876. Used compositionally for “shadow” effects.
Scale Families
The eight parent scales of OTH, organized into four families:
| Family | Scale | Notes | Modes | Orbits |
|---|---|---|---|---|
| I | Major Pentatonic | 5 | 5 | Summit, Plateau Q877 |
| I | Minor Pentatonic (rotation) | 5 | 5 | Plateau Q787 |
| II | Chromatic-Pentatonic (D♭) | 6 | 6 | Upper Slope Q776, Valley Q878, Lower Slope Q876 |
| II | Chromatic-Pentatonic (E♭) | 6 | 6 | Upper Slope Q786 |
| II | All-Interval Heptatonic | 7 | 7 | Lower Slope Q867 |
| III | Whole-Tone | 6 | 1 | Saddle Q686, Valley Q868, Precipice Q688 |
| IV | Heptatonic Chromatic-Pentatonic | 7 | 7 | Valley Q767, Precipice Q788 |
| IV | Narrows Hexatonic | 6 | 6 | Narrows Q676 |
Total: 8 distinct parent scales, 43 distinct modes.
Cadential Scalar Arc
The characteristic progression of scale families through a full OTH cadence: Pentatonic → Chromatic-Pentatonic → Whole-Tone → Chromatic-Pentatonic → Pentatonic
The whole-tone region at the center is the “eye of the storm” — structurally the highest tension (Saddle, structural dominant), but melodically the smoothest (no semitones, no direction). Character lives at home; the dominant is the void you pass through.