The circle of falling fifths
GVL-045Roots falling by fifths — each chord’s root becoming the fifth of the next — is the strongest progression the diatonic system has, and run in sequence it visits every chord in the key before arriving home.
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The bass moves in a pattern — what do the upper voices do?
The stock progressions of the partimento tradition: basses falling in fifths or thirds, rising by step under 5–6 exchanges, descending by step under chains of sevenths, and the sequential formulas every keyboard student memorized. Each bass motion binds the upper voices to a small set of correct continuations.
Roots falling by fifths — each chord’s root becoming the fifth of the next — is the strongest progression the diatonic system has, and run in sequence it visits every chord in the key before arriving home.
Add a seventh to every chord of the falling-fifths circle and the sequence becomes self-perpetuating: each seventh is prepared as a common tone from the chord before, strikes with the new root, and falls by step to become the third of the chord after — which has meanwhile acquired its own seventh the same way.
A bass that wants to climb by step cannot carry parallel triads — the fifths would march in parallel.
A bass descending by step may carry a chord of the sixth on every tone: because the 6/3 contains no perfect fifth against the bass, the whole texture can move in parallel — thirds and sixths all the way down — without breaking a rule.
Roots falling by thirds — I to vi to IV to ii — share two tones at every join, so the harmony changes color more than it changes place: each step keeps most of the previous chord and lowers its foundation.
Riepel’s “mountain”: a two-chord model — an applied dominant resolving up a fourth — stated and then restated one step higher, so the bass climbs do–fa, re–sol.
Riepel’s “well”: a two-chord model — an applied dominant resolving down into its chord — stated on the supertonic and then restated one step lower on the tonic.
Riepel’s “bridge”: the harmony stands on the dominant and waits — a prolongation of 5̂, often gathering the seventh as it goes, spanning the gap between one section and the next.