You’ve completely misunderstood my claim, as arundelo pointed out. It’s like accusing moridinamael of denying the atomic theory of matter (or worse, being opposed to scientific inquiry) because he/she criticized the Bohr model.
I.e. you’re taking for granted the very thing I’m claiming is wrong, and then somehow using my statement to deduce other unrelated beliefs that I don’t in fact hold.
(I’m somewhat surprised, because we had some fairly extensive discussions about all this in person a couple months ago. )
I’m afraid my brain chose to remember the jogging path, the view of the Potomac, the bridges, and some of the joggers, but nothing about what we said. If you converted me to your view, I have lapsed back into my old ways. I have to learn everything several times.
I don’t see how I’ve misunderstood your claim. I realize you claim harmony doesn’t cut reality at the joints. I think that’s an aesthetic judgment. You say that Westergardian theory allows one to treat the music of Berg, Schoenberg, and Webern as belonging to the same school as earlier Western music, as if this were a point in favor of that theory. To me, it is a proof that the theory is both wrong and destructive, because my aesthetic sense says that music is crap. We agree that the test of a theory of music is whether it helps one compose good music. I’ve never tried to write music using either theory, but if using Westergardian theory allows one to write music like that of Berg, my aesthetic judgements, which are different than yours, say that proves it is a bad theory.
Perhaps if I had been raised in a culture that used Westergardian composition techniques, I would be acclimatized to it, and would appreciate that music, and have a low opinion of harmonic theory. Even supposing that were true, which I doubt, it would only mean that this is culturally relative. Not a failure of rationality.
It seems to me that to claim that harmonic theory is objectively wrong, you must also claim that the tastes of people like me, who like things written using harmonic theory and dislike things not using harmonic theory, are also objectively wrong.
If you showed that Westergardian theory gave a simpler explanation of the music that I like, that would help convince me that it was a superior theory. (I don’t expect you can do this in a blog post.) But even then, calling it a bad concept would be like calling Newtonian physics a bad concept because it doesn’t explain motion at relativistic speeds.
You say that Westergardian theory allows one to treat the music of Berg, Schoenberg, and Webern as belonging to the same school as earlier Western music, as if this were a point in favor of that theory. To me, it is a proof that the theory is both wrong and destructive, because my aesthetic sense says that music is crap.
This is not really true, for a variety of reasons:
Schenker and Westergaard do not claim that their theory can explain atonal music. A claim that Schenckerian/Westergaardian analysis helps explain tonal music is much stronger than the claim about atonal music, and should be evaluated on its own merits. In particular, we know that Schencker was aware of early atonal music, and didn’t like it.
People’s “aesthetic sense” seems to be quite dependent on their musical experience. Modern atonal music was the result of a very gradual development of taking existing (e.g. tonal) music and adding more and more “atonality” (whatever that means: some would say dissonance, others would talk about modulation, or complexity). People generally learn to appreciate atonal music by retracing these developments gradually, and listening to more and more challenging pieces. Thus, while your aesthetic sense says that this music sucks, this may not prove much.
There is plenty of music that was clearly “not written using harmonic theory” insofar as harmonic theory (e.g. as detailed by Rameau’s Treatise on Harmony) postdates it. And yet, Renaissance and Baroque period music (and even a lot of secular Medieval music) is generally appreciated, just as much as music written after harmony-based theories became established.
If you showed that Westergardian theory gave a simpler explanation of the music that I like, that would help convince me that it was a superior theory.
I understand and sympathize. (It wasn’t that I thought I converted you to my view, but that I thought I had done a better job of conveying what my complaints about harmonic theory were.)
I don’t see how I’ve misunderstood your claim.
The misunderstanding is most evident when you write a phrase like:
things written using harmonic theory
which begs the whole question. You assume that harmonic theory is an accurate description of “how those things are written”, which is the very thing I deny. You seem to be confusing music theory with music, which is like mixing up the map and the territory.
We agree that the test of a theory of music is whether it helps one compose good music
Not quite. At least, the emphasis is on “helps”, not on “good”. You should think of a work of music (including its aesthetic qualities) being held fixed when we evaluate theories; the parameter we’re measuring that determines how good the theory is is how easily the theory allows us to produce the music in question.
(Furthermore, it certainly can’t be the case that harmonic theory’s classifications track your likes and dislikes. After all, you apparently don’t like Beethoven’s Great Fugue, and yet as far as harmonic theory is concerned it’s in the same category as his other works, which you do like.)
But even then, calling it a bad concept would be like calling Newtonian physics a bad concept because it doesn’t explain motion at relativistic speeds.
I disagree that harmonic theory is anywhere near as good as Newtonian physics. I would instead compare it—unfavorably—to pre-Darwinian theories of biodiversity. I specifically believe it to be one of the worst theories of all time (whereas Newtonian physics is one of the best).
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?
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.
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.
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?
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.
This chord has its origins in the Renaissance, further developed in the Baroque, and became a distinctive part of the musical style of the Classical and Romantic periods.
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.
the chord held at the start of Bach’s Fugue in D minor
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.
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:
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.)
That’s an argument that classical music uses more augmented sixths chords, which are not especially uncommon
“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).
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?
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).
Classical music moves from one resolved chord to another thru a series of pivot chords.
“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).
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
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.
Baroque music sometimes… pass[es] through intermediate states that aren’t any kind of recognized chord
Indeed! Thus harmonic theory is inadequate even to the description (mere description, mind you) of Baroque music, let alone Classical or Romantic.
You’ve completely misunderstood my claim, as arundelo pointed out. It’s like accusing moridinamael of denying the atomic theory of matter (or worse, being opposed to scientific inquiry) because he/she criticized the Bohr model.
I.e. you’re taking for granted the very thing I’m claiming is wrong, and then somehow using my statement to deduce other unrelated beliefs that I don’t in fact hold.
(I’m somewhat surprised, because we had some fairly extensive discussions about all this in person a couple months ago. )
I’m afraid my brain chose to remember the jogging path, the view of the Potomac, the bridges, and some of the joggers, but nothing about what we said. If you converted me to your view, I have lapsed back into my old ways. I have to learn everything several times.
I don’t see how I’ve misunderstood your claim. I realize you claim harmony doesn’t cut reality at the joints. I think that’s an aesthetic judgment. You say that Westergardian theory allows one to treat the music of Berg, Schoenberg, and Webern as belonging to the same school as earlier Western music, as if this were a point in favor of that theory. To me, it is a proof that the theory is both wrong and destructive, because my aesthetic sense says that music is crap. We agree that the test of a theory of music is whether it helps one compose good music. I’ve never tried to write music using either theory, but if using Westergardian theory allows one to write music like that of Berg, my aesthetic judgements, which are different than yours, say that proves it is a bad theory.
Perhaps if I had been raised in a culture that used Westergardian composition techniques, I would be acclimatized to it, and would appreciate that music, and have a low opinion of harmonic theory. Even supposing that were true, which I doubt, it would only mean that this is culturally relative. Not a failure of rationality.
It seems to me that to claim that harmonic theory is objectively wrong, you must also claim that the tastes of people like me, who like things written using harmonic theory and dislike things not using harmonic theory, are also objectively wrong.
If you showed that Westergardian theory gave a simpler explanation of the music that I like, that would help convince me that it was a superior theory. (I don’t expect you can do this in a blog post.) But even then, calling it a bad concept would be like calling Newtonian physics a bad concept because it doesn’t explain motion at relativistic speeds.
This is not really true, for a variety of reasons:
Schenker and Westergaard do not claim that their theory can explain atonal music. A claim that Schenckerian/Westergaardian analysis helps explain tonal music is much stronger than the claim about atonal music, and should be evaluated on its own merits. In particular, we know that Schencker was aware of early atonal music, and didn’t like it.
People’s “aesthetic sense” seems to be quite dependent on their musical experience. Modern atonal music was the result of a very gradual development of taking existing (e.g. tonal) music and adding more and more “atonality” (whatever that means: some would say dissonance, others would talk about modulation, or complexity). People generally learn to appreciate atonal music by retracing these developments gradually, and listening to more and more challenging pieces. Thus, while your aesthetic sense says that this music sucks, this may not prove much.
There is plenty of music that was clearly “not written using harmonic theory” insofar as harmonic theory (e.g. as detailed by Rameau’s Treatise on Harmony) postdates it. And yet, Renaissance and Baroque period music (and even a lot of secular Medieval music) is generally appreciated, just as much as music written after harmony-based theories became established.
I do agree that this would be quite relevant.
I understand and sympathize. (It wasn’t that I thought I converted you to my view, but that I thought I had done a better job of conveying what my complaints about harmonic theory were.)
The misunderstanding is most evident when you write a phrase like:
which begs the whole question. You assume that harmonic theory is an accurate description of “how those things are written”, which is the very thing I deny. You seem to be confusing music theory with music, which is like mixing up the map and the territory.
Not quite. At least, the emphasis is on “helps”, not on “good”. You should think of a work of music (including its aesthetic qualities) being held fixed when we evaluate theories; the parameter we’re measuring that determines how good the theory is is how easily the theory allows us to produce the music in question.
(Furthermore, it certainly can’t be the case that harmonic theory’s classifications track your likes and dislikes. After all, you apparently don’t like Beethoven’s Great Fugue, and yet as far as harmonic theory is concerned it’s in the same category as his other works, which you do like.)
I disagree that harmonic theory is anywhere near as good as Newtonian physics. I would instead compare it—unfavorably—to pre-Darwinian theories of biodiversity. I specifically believe it to be one of the worst theories of all time (whereas Newtonian physics is one of the best).
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.)
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.)
“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.