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The overall key of this piece in A minor (it is Bach's prelude from Prelude and Fugue in A minor BWV 895). Here is what I understood :

At the end of bar 6, there seems to be a change of key: this might be conceivable because of the very last G natural and the 2nd inversion of the dominant seventh chord without its root (D, F, B) which belongs to C major. That being said, the fact that C is not part of bar 7's second chord creates a kind of ambiguity: it could thus conceal an E minor triad which, followed by a D natural, could lead very well to the following chord: a nice A major triad. However, neither the chord progression C major-A major nor E minor 7-A major sound very baroque to me.

For the next part, I am convinced that this A major triad goes on a D minor modulation (with the leading tone of the scale be that C♯). The next chords belongs entirely to D minor (1st inversion of its triad, then A major [dominant triad] as bar 8's second chord). And so on until the first chord in bar 9, G major triad followed by a F (to form the dominant seventh of C major) which naturally leads to a nice C major triad, whose dominant is immediately substitued with an A. Finally, this takes us back to our first key (A minor), as the G♯ reappears on the last beat of bar 9 – back home!

I have to say that I find myself a bit confused about the whole thing and I would like to read a more precise and accurate analysis of these 4 measures.

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    The second inversion of the dominant seventh chord without a root is usually analyzed as the first inversion of the viiº chord, or, in minor keys, of iiº. The diminished trial is most commonly seen in first inversion.
    – phoog
    Commented Jul 3, 2023 at 21:43
  • So this chord is not really a reason to think that we have modulated towards C major?
    – Lava
    Commented Jul 3, 2023 at 21:47
  • Possibly not -- I am analyzing it in my head so it's slow going. I'll post an answer when I have something more concrete.
    – phoog
    Commented Jul 3, 2023 at 21:54

2 Answers 2

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In brief

  • m6 = a minor
  • m7, m8 = d minor
  • m9 = a minor.

My more complete analysis goes like this (measure-beat):

                     incidental
                    |-----------|
m6-1  -2      -3.0  -3.5     -4.0  4.5
Bm    E7/B    A     Dm/A     A     Am
ii    V[6/4]  I     iv[6/4]  I     i

          transition toward D minor
         |--------------...
m7-1     -2                   -3         -4
Bm7b5/A  Em7                  A7         Dm/F
ii[4/2]  v[6/5] = ii[6/5]/iv  V[4/2]/iv  iv[6]

    Cadence in Dm
|------------------
m8-1    -2     -3
Em7     A7b9   Dm
ii7/iv  V7/iv  iv

 Brief tonicization of C major    Transition back to A minor
|-----------------------------   |--------------------------
m9-1                      -2      -3                -4
G7                        C       B-7b5             E7/B
IV[6/5]/iv = V[6/5]/bIII  bIII    vii7/III = ii7/i  V[4/3]
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I agree with Aaron's broad analysis that measures 7 and 8 are in D minor, but I disagree on the detail. Essentially this is built from sequences of 7-6 suspensions, a very common way to deal with a descending scale.

Starting with measure 5, we have Dm, Dm7, E7/D, Am/C. In figured bass terms, E7/D, a seventh chord in third inversion, is figured 4/2 (with the sixth implicit), and Am/C, a triad in first inversion, is figured with a 6. In Roman numeral analysis, therefore, this is V(4/2) to i6.

In measure 6, we start with an ornamented 7-♯6 suspension over B, namely A-G♯. You could analyze this as Bø7 or Bm7 going to E7 in the second inversion or as G♯º (viiº) in first inversion with a suspension of the root, or just as an inverted E7 with a 4-3 suspension (in lead sheet terms, Esus4add7/B to E7/B), depending on how much weight you want to give to which of the sixteenth notes. For Bach it's just a 7-6 suspension; he was not fond of Rameau's theory that led eventually to Roman numeral analysis.

The third beat is difficult to describe with Roman numeral analysis, but it's not so complicated with figures. The soprano has ♯3-4-♮3 while the tenor has ♮6-5. With a raised third at the end of the measure, this would be a standard cadence to D minor, but the lowered third sends us somewhere else. If we look at it in chordal terms, it's Am7, setting us up for the third-inversion Bø7 on the downbeat of measure 7.

Continuing with measure 7 in figures, we have (4/2) followed by either 6 or (6/4), then (4/2) and 6. Three things suggest that the second beat is a 6 chord (Em/G) instead of a (6/4) chord (C/G). First, second-inversion triads are very rare. Second, it reflects the repeating nature of the harmonic and contrapuntal sequence, and, third, it gives us a nice circle-of-fifths progression of Bø7-Em-A7-Dm (where the seventh chords are both in third inversion and the triads are both in first inversion). It is also noteworthy that this is a sequence of inverted 7-6 suspensions — that is, the suspended voice is the bass.

In measure 8, we have Em7, A (or A7 or A7♭9, again depending on how much weight you want to give to the 16th notes) and Dm, a firm cadence on the minor subdominant, where we stay for two beats.

Measure 9 is also hard to describe in functional terms. I make it out roughly as (with the second and third chords as eighth notes) G/B - C/B - Am - Bø7 - G♯º/B, which gives figures of 6 - (4/2) - (nothing) - 7 - ♯6.

You could call the first half of the measure ♭VII (or V/III) to III7 to i, but again the C/B is more of a suspension in the bass than a structural harmony. Reducing it to quarter notes, I'd call the second beat i, giving us a fairly standard i-viiº6-i progression liberally embellished with suspensions.

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