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komponisto comments on Bad Concepts Repository - Less Wrong
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I don't understand music theory enough to continue the debate. I don't even understand what you mean by harmonic theory, since I assume you don't mean we should throw away 1-3-5 chords. I have noticed that Baroque music tends more often than classical or romantic music to have passages that starts on one chord, and the different parts walk their different ways to another chord with no pivot chords, just walk the bass and damn the torpedoes in between. is that related to what you're talking about?
By harmonic theory I mean the idea proposed by Jean-Philippe Rameau in 1722 of analyzing music as a succession of simultaneities ("chords"), to each of which is assigned a "root", and with the order of chords being governed by relationships among the roots.
The above doesn't make any literal sense, but if what you mean by this is that Baroque music violates Rameau's rules of root progression more often than later music (which, believe it or not, is actually what I think you mean), then this is almost certainly not the case: generally speaking, music gets more complex as you go forward in history, and the more complex it is, the more likely it is to crash Rameau's theory.
(Yes, I know that popular histories tell you that Classical music was simpler than Baroque. This is wrong.)
The reality is that the torpedoes were always damned. Rameau and his theoretical successors mistook certain superficial patterns (which automatically arise in particularly simple musical contexts) for underlying laws. The actual underlying laws were discovered by Schenker and Westergaard.
Would you deny that Baroque music deviates from common chords more often than classical music does?
Yes. Look at how many Baroque vs. Classical entries there are on this list of examples of augmented sixth chords, for instance.
That appears to be an effect of the data compiler's bias. This list of I-5-7 chords from the same source has the same ratio.
From Wikipedia:
This implies that its use increased over time, and in particular was greater in the Classical and Romantic periods than in the Baroque.
That's an argument that classical music uses more augmented sixths chords, which are not especially uncommon. Contrast that with something like the chord held at the start of Bach's Fugue in D minor -- it's got a C#, a D, and an E it in; what the hell is it?
That's what I was talking about when I said "I have noticed that Baroque music tends more often than classical or romantic music to have passages that starts on one chord, and the different parts walk their different ways to another chord with no pivot chords, just walk the bass and damn the torpedoes in between," which makes perfectly simple literarl sense. Classical music moves from one resolved chord to another thru a series of pivot chords. Baroque music sometimes just walks the bass, and maybe the top note also, by one half-step per "chord" until it arrives at the destination chord, passing through intermediate states that aren't any kind of recognized chord, certainly nothing so common as an augmented 6th.
Now, if when we say Baroque you're thinking Vivaldi and I'm thinking Bach's organ music, that could account for the difference of opinion.
Bach wrote umpteen different fugues in D minor, none of which is so obviously better or more important than the others as to deserve the title "Bach's Fugue in D minor". And it's kinda unusual for a fugue to begin with any sort of held chord, though maybe whichever one you're thinking of does.
Would you care to be more specific?
I bet PhilGoetz is talking about the toccata in the famous Toccata and Fugue in D minor, BWV 565, which has a C# diminished 7 over a D pedal tone (about 30 seconds into this recording).
Yeah, I thought he might be talking about that too, so I looked at the score. The chord immediately before the start of the fugue doesn't fit Phil's description.
Yes, I'm taking about BWV 565. I was too lazy to look up the number, and I should have said "Tocatta and Fugue in Dm". He only wrote two things called "Tocatta and Fugue in Dm", and this is the more famous one.
And, YES, the chord does fit my description. I don't have to look it up; I play it, and I know you begin by striking a very low D, then the C# almost an octave above it, then the E just above that, and more notes beyond as well.
AND I just went downstairs and checked the score, just in case you were actually right. I think you may be talking about the next chord. What I'm calling the "chord" is written as an ascending series of notes, but most players hold them all down until the last one. It's the weird one, not the "pivot" & not the resolution.
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.)
"Uncommon" doesn't mean anything without reference to a time period; the point is that they are more uncommon in the Baroque period than in the Classical. The Classical period uses a richer "vocabulary of chords" than the Baroque, if one insists on thinking in such terms (as a Westergaardian, I don't think in terms of a "vocabulary of chords", of course).
First of all "Bach's Fugue in D minor" is highly ambiguous; Wikipedia lists 10 such works by J.S. Bach alone (BWV 538, 539, 554, 565, 851, 875, 899, 903, 905, and 948).
But you can find a chord containing those same three pitch-classes (along with G# and B) in the first movement of Mozart's Symphony No. 29 (p.4, second system, 4th measure, 1st and 3rd quarter).
"Pivot chord" is a technical term in harmonic theory (which, again, I don't subscribe to) meaning a chord shared by two different keys which is used in modulating between them. You don't appear to be using this term correctly here (we're not talking about key changes), and I'm not sure exactly what you do mean. "Resolved chord" is not a standard term at all, but maybe you mean "consonant chord". (?) However, both Baroque and Classical music "move from one [consonant] chord to another" (well, except when moving to dissonant chords, which also occurs in both periods...) So this sentence reads like confused gobbledygook to me. A musical example of the phenomenon which you think occurs in Baroque music but not Classical would help (but we know it isn't "a chord with C#, D, and E", as the Mozart example I gave shows).
You just have to compare apples to apples. If the most complex works of J.S. Bach are what you mean by "Baroque", then the most complex works of Haydn, Mozart, and (at least early) Beethoven have to be what you mean by "Classical".
I think what actually accounts for the "difference of opinion" is that you underestimate the complexity of Classical works.
Indeed! Thus harmonic theory is inadequate even to the description (mere description, mind you) of Baroque music, let alone Classical or Romantic.