Orbit Interval recipe Forte Degree Function
Q777 (Summit) [7,7,7] 4-23 8 Tonic Q787 (Plateau) [7,8,7] 4-26 8 Stable plateau (Cm7-flavored) Q686 (Saddle) [6,8,6] 4-25 8 Structural dominant (max betweenness) Q877 (Plateau) [8,7,7] / [7,7,8] 4-22 6 Stable plateau (one A5) Q786 (Upper Slope) [7,8,6] 4-27 6 Connector (dominant-7-flavored) Q688 (Precipice) [6,8,8] / [8,8,6] 4-24 6 Edge of stability Q776 (Upper Slope) [7,7,6] 4-16 5 Slope (one d5) Q876 (Lower Slope) [8,7,6] 4-18 5 Slope (max heterogeneity) Q767 (Valley) [7,6,7] 4-8 4 Valley (pinched) Q676 (Narrows) [6,7,6] 4-9 4 Most constrained Q878 (Valley) [8,7,8] 4-17 4 Valley (two A5s) Q868 (Valley) [8,6,8] 4-21 4 Whole-tone tetrachord Q788 (Precipice) [7,8,8] 4-19 4 Augmented-major-7-flavored Q867 (Lower Slope) [8,6,7] 4-Z15 4 All-interval tetrachord
Species Notes per chord Allowed motions Allowed non-chord tones
1st 1 single-edge cantus motion none 2nd 2 single-edge cantus motion passing, anticipation 3rd 4 single-edge cantus motion passing, neighbor, anticipation, cambiata 4th mixed single-edge cantus motion + fiber inversions suspension (held across bar) 5th free all motion types all categories, with stepwise treatment
Step Chord Function
Penultimate-1 Saddle ([6,8,6]) Maximum tension; two d5s Penultimate Slope ([7,8,6] or [7,7,6]) Partial resolution; one d5 remains Cadence Summit ([7,7,7]) Full resolution; three P5s
The voice motion across this two-edge cadence is two single-semitone descents (or ascents), each widening a tritone (d5→P5) or contracting an augmented fifth (A5→P5). When both motions occur simultaneously across the two-edge cadence, the listener perceives a unified resolution event — the OTH analog of the V→I tonal cadence.
Path Continuity. Every transition between successive chords is a legal chord-graph motion type.Cadential Direction. Cadences are approached through tension chords (Saddle, Slope, or related).Tension Preparation. Saddle chords should be preceded by a chord at chord-graph distance 1 from them.Resolution Pacing. From a Saddle, both tritones should resolve to perfect fifths within two chord-graph edges.Avoid Orbit-Persistence. Three or more consecutive chord-graph edges within the same orbit produce voice fusion.Wing Awareness. The piece should have a coherent wing-color identity, with wing crossings made deliberately.Degree-Gradient Direction. Phrase-level motion should follow a meaningful trajectory through the degree landscape.Fiber as Color, Not Function. Fiber inversions vary registral character without altering harmonic identity.