At least one of us is very confused. I don’t think it’s me.
At the end of the toccata there is a chord containing the following notes, from bottom to top: D (in the bass, on the pedals), another D (lowest note on the manuals), F, A, D. This is a perfectly ordinary chord of D minor, of course. After that there is a semiquaver rest and then the fugue subject begins (or, perhaps better, the fugue subject begins with a semiquaver rest). At that point, as is normal in a fugue, there is only one voice sounding.
Oh, wait, you weren’t talking about the fugue at all? You meant the chord a few bars into the toccata? Well, OK then, that chord contains the notes you said it does. (Though, I repeat, it isn’t “the chord held at the start of Bach’s Fugue in D minor”; it’s in the toccata, not the fugue; in a discussion of music analysis such distinctions are really worth making.)
But there’s nothing weird about that chord! It’s a standard diminished-7th chord (everything at intervals of 3 semitones from some starting point; in this instance C#, E, G, Bb). If I may quote from that bastion of the avant garde, Wikipedia:
The most common form of the diminished seventh chord is that rooted on the leading tone [...] These notes occur naturally in the harmonic minor scale.
Diminished seventh, check. Rooted on the leading tone, check. Minor key, check. It’s perfectly commonplace. (There are plenty of much weirder things in Bach.)
The chord is in measure 2 of the piece, and contains these notes: D, C#, E, G, Bb, C#, E.
A diminished 7th in Dm should have D, F, Ab, Bb, shouldn’t it? This is a diminished 7th C#, so what’s the D doing there?
Anyway, my impression is that diminished 7ths are much more common in organ music than in piano music. I think of them as “that organ-music chord”. And if you look up diminished 7th in the same music database that komponisto linked to above, you’ll see it has a much higher fraction of baroque entries than any of the other items on that list.
Perhaps part of the issue is when I hear “baroque” I think Bach, and when I hear “classical” I think Mozart. I think Bach does more weird chords than Mozart does. Or consider Beethoven’s Moonlight Sonata—it’s chock full of different chords juxtaposed in unusual ways, but they’re almost all common chords.
Anyway, my impression is that diminished 7ths are much more common in organ music than in piano music.
I don’t share this impression at all. How much piano music do you know? There’s probably a lot more of it than there is of organ music. This is certainly the case in the nineteenth century, which was probably the heyday of the diminished seventh (while being the low point of the organ repertory).
And if you look up diminished 7th in the same music database that komponisto linked to above, you’ll see it has a much higher fraction of baroque entries than any of the other items on that list.
Eh? Among a combined total of 70-80 examples on this page and this one, I count about 7-8 Baroque examples, so about 10%. I’m not going to count through all the other 24 pages for comparison, but I don’t think this supports the thesis that the diminished seventh is particularly characteristic of the Baroque as opposed to the Classical or Romantic; indeed, it is the Romantic which dominates the examples, as I predicted above. (And note by the way that not one of the Baroque examples that I could find was specifically an organ piece!)
I think Bach does more weird chords than Mozart does.
What data is this based on? And for what definition of “weird”? Did you see the Mozart example I cited in my other comment? Do you have any reason to think that example is particularly uncharacteristic (in a way that your Bach example isn’t)?
Or consider Beethoven’s Moonlight Sonata—it’s chock full of different chords juxtaposed in unusual ways, but they’re almost all common chords.
This a piece with plenty of diminished sevenths! (And what do you mean by “juxtaposed in unusual ways”?)
Phil, in all seriousness, you really ought to look at the Westergaard book. You would like it, and it would really help clarify your thinking about music. (I believe I have already directed you to an electronic copy via e-mail.)
At least one of us is very confused. I don’t think it’s me.
At the end of the toccata there is a chord containing the following notes, from bottom to top: D (in the bass, on the pedals), another D (lowest note on the manuals), F, A, D. This is a perfectly ordinary chord of D minor, of course. After that there is a semiquaver rest and then the fugue subject begins (or, perhaps better, the fugue subject begins with a semiquaver rest). At that point, as is normal in a fugue, there is only one voice sounding.
Oh, wait, you weren’t talking about the fugue at all? You meant the chord a few bars into the toccata? Well, OK then, that chord contains the notes you said it does. (Though, I repeat, it isn’t “the chord held at the start of Bach’s Fugue in D minor”; it’s in the toccata, not the fugue; in a discussion of music analysis such distinctions are really worth making.)
But there’s nothing weird about that chord! It’s a standard diminished-7th chord (everything at intervals of 3 semitones from some starting point; in this instance C#, E, G, Bb). If I may quote from that bastion of the avant garde, Wikipedia:
Diminished seventh, check. Rooted on the leading tone, check. Minor key, check. It’s perfectly commonplace. (There are plenty of much weirder things in Bach.)
The chord is in measure 2 of the piece, and contains these notes: D, C#, E, G, Bb, C#, E.
A diminished 7th in Dm should have D, F, Ab, Bb, shouldn’t it? This is a diminished 7th C#, so what’s the D doing there?
Anyway, my impression is that diminished 7ths are much more common in organ music than in piano music. I think of them as “that organ-music chord”. And if you look up diminished 7th in the same music database that komponisto linked to above, you’ll see it has a much higher fraction of baroque entries than any of the other items on that list.
Perhaps part of the issue is when I hear “baroque” I think Bach, and when I hear “classical” I think Mozart. I think Bach does more weird chords than Mozart does. Or consider Beethoven’s Moonlight Sonata—it’s chock full of different chords juxtaposed in unusual ways, but they’re almost all common chords.
Wikipedia: pedal point
I don’t share this impression at all. How much piano music do you know? There’s probably a lot more of it than there is of organ music. This is certainly the case in the nineteenth century, which was probably the heyday of the diminished seventh (while being the low point of the organ repertory).
Eh? Among a combined total of 70-80 examples on this page and this one, I count about 7-8 Baroque examples, so about 10%. I’m not going to count through all the other 24 pages for comparison, but I don’t think this supports the thesis that the diminished seventh is particularly characteristic of the Baroque as opposed to the Classical or Romantic; indeed, it is the Romantic which dominates the examples, as I predicted above. (And note by the way that not one of the Baroque examples that I could find was specifically an organ piece!)
What data is this based on? And for what definition of “weird”? Did you see the Mozart example I cited in my other comment? Do you have any reason to think that example is particularly uncharacteristic (in a way that your Bach example isn’t)?
This a piece with plenty of diminished sevenths! (And what do you mean by “juxtaposed in unusual ways”?)
Phil, in all seriousness, you really ought to look at the Westergaard book. You would like it, and it would really help clarify your thinking about music. (I believe I have already directed you to an electronic copy via e-mail.)