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III. The Ridgeline

Ridge

Not a single orbit but a structural feature of the degree landscape: the connected path of degree-8 orbits that forms the “spine” of the terrain.

Three orbits share the maximum degree of 8: Summit (Q777), upper Plateau (Q787), and Saddle (Q686). These three orbit types form the high ground of B — the continuous elevated terrain from which all descents begin and to which all ascents return.

The ridge is the path along this high ground. In mountain geography, a ridgeline is a continuous line of high elevation connecting peaks, with the terrain falling away on both sides. In OTH:

  • The Summit is the true peak (maximum stability, pentatonic parent, all-P5).
  • The upper Plateau Q787 is the adjacent peak at the same elevation (degree 8) but with different character (one A5, minor-seventh flavor, minor-pentatonic parent).
  • The Saddle is the low point on the ridge — still at degree 8, but functionally a pass rather than a peak (maximum betweenness, whole-tone parent, structural dominant).

The ridge separates the two wings of the space:

  • To one side: the d5-wing (Q767, Q686, Q676 — orbits rich in tritones, descending from the ridge through darker, more dissonant territory)
  • To the other side: the A5-wing (Q878, Q788, Q688, Q868 — orbits rich in augmented fifths, descending through brighter, more expansive territory)

Walking along the ridge (Summit ↔ Plateau Q787 ↔ Saddle) maintains maximum connectivity while shifting harmonic color. Walking off the ridge in either direction descends into one of the two wings. This is the fundamental topographic metaphor of OTH: the ridge is the high road; the wings are the slopes falling away on either side; the Saddle is the pass where the ridge dips and the two sides come closest together.

Note: The ridge is an emergent structural feature, not a formally defined term in the same sense as the orbit function names. It names a relationship between orbits rather than a single orbit. Whether “ridge” or “ridgeline” should be promoted to a primary structural term alongside the orbit function names is a compositional and pedagogical question — does calling attention to the connected high ground help composers navigate the space?