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The opening harmonic progression of the B minor mass:

Bm moves to a C# half-diminished 7th — a ii7 chord, nothing unusual yet. To put it in root position is a bit unconventional for the style, but the stepwise motion in the bass is worth it. A common predominant chord.

Instead of the expected dominant, however, Bach throws in a V7-iv chord, a B7. This does move to Em as expected, but to shift from a ii7 to a secondary dominant isn't something you see very often, especially not a V7-iv.

The rest of the opening is pretty conventional, with a V7, i, VI, very brief ii7, and finally resolving to a V. I'm mainly asking about the ii7 to V7-iv, which seems like it should sound very abrupt, yet it does not. Why does this progression make sense to our ears?

3 Answers 3

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Structurally, the second chord is not a C♯ half-diminished seventh but an A♯ diminished seventh in first inversion. The B in the second soprano is a suspension. The harmonic rhythm is in half notes but with some embellishment.

The first four measures are basically

i          viiº(6)
V(6/5)/vi  iv
V(6/5)     i
iv(6)      V

or

Bm      A♯º7/C♯
B7/D♯   Em
F♯7/A♯  Bm
Em/G    F♯

This fits a classic functional harmonic analysis: tonic to dominant, secondary dominant of subdominant to subdominant, dominant to tonic, subdominant to dominant.

But, perhaps more significantly, the theory of functional harmony was only in its infancy in Bach's day. Jean-Philippe Rameau was promoting the innovative idea that E-G-C was the same chord as C-E-G, but it hadn't yet reached broad acceptance, and in fact Bach was resistant to it.

Rather, Bach was coming from the tradition of partimenti, of which a prominent element was the "rule of the octave," essentially a template for harmonizing ascending and descending scales, often with a series of suspensions. Typically, those suspensions are embellishments of a series of stepwise 6/3 chords (except the first and last, because the 6/3 chord isn't stable). Here, Bach gives us a stepwise ascending bass with the figures

8     7
7     6
(7/5) 6
9     8

Ignoring the embellishments, that's

[5/3]
6
6
[5/3]

...bog standard stuff.

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    in fact Bach was resistant to it. An interesting thesis! Do we have historical evidence of this? Jan 20, 2023 at 15:07
  • @AlbrechtHügli apparently CPE wrote about Rameau's theory while noting that he (CPE) and his father (JS, of course) disagreed with it. But I haven't found a primary source nor a secondary source with a citation. I did scan and search the Versuch über die wahre Art das Clavier zu spielen without finding the name "Rameau," but I haven't found the whole text in a single file, so I'm not confident that I've searched it effectively, and furthermore it is of course possible that this is the document in which he said this but that he didn't mention Rameau by name.
    – phoog
    Jan 20, 2023 at 19:58
  • I was probably misunderstanding ... you don't man that Bach was Jan 20, 2023 at 22:14
  • @AlbrechtHügli that comment appears to be incomplete. Is it?
    – phoog
    Jan 21, 2023 at 10:54
  • A bit of a nitpick, I think there's a little mistake in the functional harmonic analysis. vii°(6) implies just a diminished chord. I think it would be more accurately shown as vii°(6+ 5) to show the 7th G and the sharpened A.
    – OprenStein
    Jan 21, 2023 at 22:53
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As phoog already pointed out the second chord is not in fact C# half diminished, but A# diminished with root suspension, effectively the dominant 7 b9 with omitted root.

But this is not actually what makes the progression work (as it works totally fine if you do keep that b on the second chord). What makes this work is the ambiguity between the tonic b minor and a secondary tonic e minor. Now, we usually consider the half diminished 7 chord a characteristic chord, as it only occurs in one position in a diatonic scales. But if you consider a melodic minor scale you will actually see that a natural half diminished 7 happens on the raised VI. And this is exactly the type of movement we have here:

The bass forms a line from B to E using the notes of E melodic minor. And the chords on top somehow do represent that. This is quite a strong move, as is forms a strong cadence towards that E minor, creating lots of tension.

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  • Glad someone agrees.
    – Aaron
    Jan 20, 2023 at 13:14
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It's because of the A-natural passing tone in the tenor, combined with smooth voice leading.

A-natural is native to E minor, which is where we're headed in this brief segment, and the brief presence of a i7 chord slightly undermines the sense of B minor. (This, as opposed to Bach using A# as the leading tone to strongly confirm B minor.) This subtly prepares the ear for the upcoming E minor chord, even whispering that we might be in the key of E minor, starting on its v chord.

What's more, the bass outlines ^5 - ^6 - ^7 - ^1 in E minor, while the soprano outlines b^7 - ^1 - ^2 - ^3. The parallel between the soprano and bass gives the effect of v - vi - viio - i in E minor.

D  E  F#  G
B  C# D#  E

In fact, the apparent ii7 chord — the result of the suspension of B from the first chord — is also the vi7 chord in E minor. So the progression can be interpreted as v(7) vi7 viio7 i in E minor.

Below is a reduction showing the analysis in both B minor and E minor.

Bach B minor mass, mm. 1-2, reduction

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    We're not headed to E minor; E minor is present only as the subdominant of B minor: the entire four measure section moves decisively to the dominant of B minor to introduce the fugue, which is very squarely in B minor. Also the A natural doesn't make this harmonic progression work, as you can see by substituting a B there for the A. You lose the rich dissonance of the minor seventh chord, but the progression from i to iv still works perfectly well from a functional standpoint.
    – phoog
    Jan 20, 2023 at 8:50
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    @phoog You've misunderstood. I don't mean we're headed to E minor as a cadence point or modulation. I just meant that in the limited segment presented by OP, we're going to wind up on an E minor chord. And your own comment makes my point about the A — without it, the progression loses some of its richness. The sound of the progression has to be considered in any analysis. Analysis is interpretive as much as rule-based. However, it would be clearer, I think, if I put the ii7 in parentheses and comment on the suspension. I left it as is to offer consistency with the OP's understanding.
    – Aaron
    Jan 20, 2023 at 12:48
  • Fair enough. I read it in the sense one might find in a classical or romantic sonata where it would mean "preparing for a new large section in [the named key]." It also occurred to me that you could see the whole first two measures as an extended iv subdominant, followed by the third and fourth measures as an extended V dominant, followed by the fugue opening in i. So I'd remove my downvote but the answer hasn't been edited since then so I can't. If you do edit it, ping me so I can change my vote.
    – phoog
    Jan 20, 2023 at 20:07
  • @phoog Done. I also tried to clarify the limits of the analysis to the two measures rather than in the larger context. Other clarifications I'll get to a bit later. But you've understood me in suggesting the possibility of viewing the passage as an extended subdominant.
    – Aaron
    Jan 20, 2023 at 20:14
  • @phoog I think I've got this cleaned up now. Should be more clear.
    – Aaron
    Jan 21, 2023 at 3:45

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