Dominant seventh and inversions

The dominant seventh in root position: the triad takes its seventh as the doubled root falls a step, and the new tone must fall again into the tonic chord.

The root-position dominant seventh in minor: the figures carry both the sharp and the 7 — the raised third and the falling seventh, tension from both sides.

The 6/5: the dominant seventh standing on its leading tone. The bass itself must rise a half step, while the seventh falls in an upper voice.

The 6/5 in minor, where the bass stands on the raised leading tone — printed on the staff, not in the figures — and rises home.

The 4/3 as a passing chord: the bass walks from the tonic to its first inversion, and the dominant seventh on the second degree is the step between.

The 4/3 in minor, written out in full as ♯6/4/3 — the accidental that raises the dominant’s third falls on the sixth above the bass, so the shorthand will not do.

The 4/2: the seventh slips into the bass in passing, and the bass inherits its obligation — down a step, onto the first inversion.

The 4/2 in minor, figured ♯4/2: the raised leading tone now sits a fourth above the bass-borne seventh, and the figure must say so.

The tour: one dominant seventh through all four positions, the bass climbing its own chord while the seventh is held — the obligation deferred until the harmony finally changes.

The tour in minor, where every position must account for the raised third: sharp beside the 7, plain under the leading-tone bass, ♯6 in the middle of the stack, ♯4 over the seventh.

Three ways in, one way out: the seventh entering prepared, in passing, and freely — and falling by step every single time.

The deceptive resolution with the seventh aboard: V7 resolves to the submediant, every tendency tone keeping its promise — the promise broken is only the bass’s.