II. The Topographic Landscape — Functional Regions
All function names are terrain features — natural landforms, not human constructions.
Summit
Orbit: Q777 — [7,7,7] | Forte: 4-23 | Degree: 8 | Size: 12 chords Fiber class: A | Step sequence: [2,5,2,3] | Parent scale: Major Pentatonic
The all-perfect-fifth orbit. Maximum connectivity, maximum stability. The OTH tonic — the point of arrival and departure. The word evokes the apex of the degree landscape: a vantage from which one can move in many directions (unlike “tonic,” which implies gravitational pull toward). The 12 Summit chords define the 12 quintal keys of OTH.
Example: C–G–D–A (the “C stack”)
Plateau
Two orbits sharing the name, distinguished by degree:
Upper Plateau — Q787 — [7,8,7] | Forte: 4-26 | Degree: 8 | Size: 12 chords Palindromic. Shares degree 8 with the Summit. The minor seventh chord type (Cm7). The “other peak” — same elevation, different color. Parent scale: minor pentatonic rotation.
Plateau — Q877 — [7,7,8]/[8,7,7] | Forte: 4-22 | Degree: 6 | Size: 24 chords Non-palindromic. One step from pure quintal. Parent scale: major pentatonic.
Plateaus are stable enough to linger on but not the final destination. Moderate tension, multiple available paths. The OTH analogue of the subdominant region.
Slope
Four orbits at two degree levels, functioning as transitional terrain:
Upper Slope — Q786 — [7,8,6]/[6,8,7] | Forte: 4-27 | Degree: 6 | Size: 24 chords The dominant/half-diminished seventh chord type. Bridges the quintal core to the d5-containing chords. Parent scale: chromatic-pentatonic (E♭ variant).
Upper Slope — Q776 — [7,7,6]/[6,7,7] | Forte: 4-16 | Degree: 5 | Size: 24 chords The first orbit with a semitone step. Parent scale: chromatic-pentatonic (D♭ variant).
Lower Slope — Q876 — [8,7,6]/[6,7,8] | Forte: 4-18 | Degree: 5 | Size: 24 chords Maximally heterogeneous — one each of d5, P5, A5. Parent scale: chromatic-pentatonic (D♭ variant).
Lower Slope — Q867 — [8,6,7]/[7,6,8] | Forte: 4-Z15 | Degree: 4 | Size: 24 chords The all-interval tetrachord. Maximum interval diversity. Parent scale: All-Interval Heptatonic (7 notes, 7 modes — the richest scale in the system).
Slopes are the connector tissue of OTH — transitional chords mediating between the stable upper regions and the tense lower regions. The OTH analogue of the pre-dominant.
Valley
Three orbits sharing the name, all at degree 4:
Valley — Q767 — [7,6,7] | Forte: 4-8 | Degree: 4 | Size: 12 chords The “pinched” quintal chord — two d5-adjacent pairs. The most dissonant playable scale in the system (heptatonic chromatic-pentatonic with twin semitone clusters). d5-wing.
Valley — Q868 — [8,6,8] | Forte: 4-21 | Degree: 4 | Size: 12 chords The whole-tone tetrachord. Symmetric but constrained. Parent scale: whole-tone (shared with Saddle). Cross-wing bridge.
Valley — Q878 — [8,7,8] | Forte: 4-17 | Degree: 4 | Size: 12 chords Two A5 intervals flanking P5. Parent scale: chromatic-pentatonic (D♭ variant). A5-wing.
Valleys are low points in the degree landscape — maximum tension, minimum connectivity. Chords that demand resolution.
Saddle
Orbit: Q686 — [6,8,6] | Forte: 4-25 | Degree: 8 | Size: 6 chords (T₆ symmetric) Fiber class: B (2 inversions in [6,8]) | Step sequence: [2,4,2,4] (period-2) Parent scale: Whole-tone (6 notes, 1 mode)
Formerly “Crossroads.” Renamed to maintain the terrain-only naming principle — a saddle is a natural landform; a crossroads is human infrastructure.
The structural dominant of OTH. A saddle point in the mathematical sense: a critical point of the degree landscape that is simultaneously the low point along the ridge connecting two Summits and the high point of the pass between two lower regions. The saddle has maximum betweenness centrality (~9.1% of all shortest paths per chord, ~54.8% total for the 6-chord orbit) — more paths through the space flow through the Saddle than through any other orbit.
The terrain metaphor is precise: in mountain geography, a saddle (also called a col or pass) is the low point on a ridge between two peaks, and simultaneously the high point of the route between two valleys. It is the natural transit point — the place where paths converge, the pass through which travelers must go. Every geodesic between two Summit chords in different keys passes through a Saddle chord. This makes the Saddle the structural bottleneck of the space: it creates directed tension because, once you arrive at the Saddle, the paths forward are constrained (degree 8, but limited orbit-level exits), and the most natural exit is upward to a Summit — the OTH cadence.
The Saddle’s T₆ symmetry means each Saddle chord belongs to exactly two quintal keys simultaneously (it equals its own tritone transposition). This dual allegiance is the OTH mechanism for modulation: the Saddle is the pivot through which key changes flow.
The 6 Saddle chords are: {C,D,F♯,A♭}, {C,E,F♯,B♭}, {D♭,F,G,B}, {E♭,F,A,B}, {D♭,E♭,G,A}, {D,E,A♭,B♭}.
Tertian identity: French augmented sixth chord.
Precipice
Two orbits at the extreme edge of the degree landscape:
Precipice — Q688 — [6,8,8]/[8,8,6] | Forte: 4-24 | Degree: 6 | Size: 12 chords Fiber class B. Parent scale: whole-tone. The “edge of stability” — low-degree, A5-dominant.
Precipice — Q788 — [7,8,8]/[8,8,7] | Forte: 4-19 | Degree: 4 | Size: 24 chords The augmented-major seventh chord type (Cm(maj7)). Extreme chromatic tension. Parent scale: heptatonic chromatic-pentatonic.
Precipices are chords teetering at the edge — very few exits, strong directional tendency. The word conveys the sense of standing at a cliff face before a dramatic resolution.
Narrows
Orbit: Q676 — [6,7,6] | Forte: 4-9 | Degree: 4 | Size: 6 chords (T₆ symmetric) Fiber class: B (2 inversions in [6,8]) | Step sequence: [1,5,1,5] (period-2) Parent scale: Octatonic only
The most constrained chord in B — a geographic bottleneck with minimal options. Only two exit orbits at the orbit level (both to the Upper Slope Q776). The OTH analogue of the fully diminished seventh chord’s extreme restlessness, but even more constrained. The most extreme step distribution: two semitone clusters separated by perfect fourths.
The Narrows is the most isolated orbit scalarly — it has no pentatonic, diatonic, whole-tone, or blues parent. Only octatonic containment.