LCM trajectory · time-series view

← polar view

BWV 38.6 · LCM over time

The 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.

Pitch LCM per voiceChord LCM · root + internalRegion LCM · vs ATension envelope · Σ voice LCM61220407212060210420161230φ1φ2φ3φ4φ5m1m2m3m4m5m6m7m8m9m10m11m12m13♭6̂ → 5̂secondary 7̂♭6̂ → 5̂♭6̂ → 5̂7̂ → 1̂7̂ → 1̂7̂ → 1̂7̂ → 1̂7̂ → 1̂secondary 7̂secondary 77̂ → 1̂7̂ → 1̂7 of V → ♭3̂7̂ → 1̂unclearI → I — does not match a standard cadence patternHCiv⁷ → V — half cadence (ends on V)uncleari → i — does not match a standard cadence patternunclearV⁷/V → ? — does not match a standard cadence patternHCi → V — half cadence (ends on V)
Legend
SopranoAltoTenorBasschord rootregionleading-tonePhrygian-pullchordal-7
Current event
m1 · b1.0 · event 1/57 · dur 2♩
I⁴⁄₂ in E major
Tempo60 bpm (1.00×)

How to read this

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.