BWV 38.6 · Aus tiefer Not schrei ich zu dir

How to read this

Center is the local tonic (changes across phrases as Krumhansl re-estimates the key). Radial distance is each sounding pitch's LCM measure against the local tonic. The dashed rings mark canonical LCMs — closer in is more consonant.

Angle follows the circle of fifths: 12 o'clock is the tonic, 1 o'clock is the dominant, and so on clockwise. So pitches that are tonally close also sit visually close.

Color coding: cream = ordinary pitch; gold = chord root (the lowest-LCM pitch in the texture, approximately); red = leading tone; amber = Phrygian pull (♭6̂ or ♭2̂); purple = chordal seventh; green = secondary- function tone (temporary leading tone / chordal seventh).

Green dashed circle appears when the local key differs from home (A) — it shows where the local tonic itself sits on the home-key gradient.

What to look for

Use the cadence-jump buttons. Compare a leading-tone HC (m5, m7, m11, m13 — the G♯ pitch sits on the LCM 120 ring) against a Phrygian-pull moment (m1 b3, m2 b1 — the F-natural sits on the LCM 40 ring). The Phrygian half-step from above is acoustically 3× closer to home than the leading-tone half-step from below — exactly what Claim 6 predicts.