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1

Figures are used with Roman numerals to show the inversion. In their original function as performance shorthand, the figures accompany a bass part, so they indicate which chord to play. For example, given a C bass note and a key signature of one sharp, a 6 means the chord is A minor while the absence of a figure means it's C major. If the key is G major, ...

4

The Roman numeral label describes the function of the chord; the figures describe the inversion or other modifications. Figures by themselves only describe which notes to play, and Roman numerals by themselves only describe the basic function of the chord. The two together give a more complete description of the specific way in which the notes of the chord ...

6

These numbers indicate what we call octave designation, which these authors discuss in their chapter on key/scale/modes (depending on what edition of the book you have, these chapters may be separated). With that said, the system they're using treats Middle C as C1. This means that Middle C is C1, the C an octave above that (the third space in treble clef) ...

8

The figures show intervals relative to the given bass note. Unaltered figures generally mean the diatonic pitch at that interval. Therefore, for example, in a piece in A minor, whether the bass is G or G♯, the E is indicated with a 6. It is not particularly fruitful to try to understand figured bass in the context of inversions. Figured bass was developed ...

7

Since figured bass shows the intervals above the bass, it only shows chromatic alterations for intervals above the bass. As such, if the only chromatic pitch is itself the note in the bass, there's no need for any chromatic alterations in the figures, since the figures apply to notes above the bass, not the bass itself. The accidental in front of that bass ...

4

It's reasonably clear that what's happening harmonically is that a first inversion B# diminished seventh chord is moving through a passing-tone C# in the pass to a root position B# diminished seventh chord. An experienced continuo player, seeing a 6-5 indication of a B# diminished chord, followed by a 7 over a B#, would recognize the change in inversion, so ...

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