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LCM trajectory · time-series view
← polar viewThe four voices' distance from the local tonic, traced through the chorale as one line per voice. The polar plot showed whereeach chord sits in the gradient at one moment; this view shows how the gradient moves through time.
Four tracks, shared X-axis (absolute beat). The piece runs left to right. Measure markers along the bottom (m1, m2, …). Phrase boundaries are vertical dashed lines (φ1, φ2, …, φ5). Cadences are gold triangles at the top.
Track 1 — Pitch LCM per voice. Each voice (S/A/T/B) traces its own line through the gradient. The Phrygian (LCM 40) and leading-tone (LCM 120) reference lines are accent-colored. Watch the tenor (G♯) spike up to LCM 120 at every HC. Watch the alto (F natural) sit at LCM 40 across the Phrygian-flavored passages of phrase 1.
Track 2 — Chord LCM. Gold line is the chord-root's distance from local tonic. Dashed faint line is the chord's own internal dissonance (4:5:6 triad = 60; V⁷ = 420). The internal dissonance spike at m11 b4.5 is the V⁷ approach.
Track 3 — Region LCM. Green step function showing when Krumhansl re-estimates the local key. m1–3 at LCM 6 (E major ≈ Phrygian on E), m4–8 at LCM 1 (A minor home), m9–10 at LCM 30 (briefly C major), m11–13 at LCM 1 (back home).
Track 4 — Tension envelope. Sum of voice LCMs at each moment, filled. The hills are where the texture is acoustically spread; the valleys are arrivals on tonic-anchored chords.
Click anywhere on the chart to jump the playhead. Click a cadence triangle to jump to that cadence.