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Comment by beefman | Hacker News Reader

The earliest tritone substitution I know of appears in Scarlatti K420

https://www.youtube.com/watch?v=Nf3_NfuvK8Y

There are two tritones in 7-limit just intonation (7/5 and 10/7) and therefore two possible tritone substitutions. Here they're played successively

http://lumma.org/music/theory/demo/progs/TritoneProgressions...

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I didn't hear that spot as a tritone substitution, personally, but a sort of non-harmonic counterpoint move ("passing tones" or "setup tones" to 19th century theorists).

More broadly, a lot of people like to point out wild 20th century chords in baroque music, but they really didn't think in terms of chords, and as such these pseudo-chords don't have the same function that modern versions of chords do. In particular, Scarlatti was a prolific user of the partimento method of composition, which is a slightly of abstracted version of counterpoint, and his sonatas are pretty good examples of pieces written with this in mind. The method revolves around intervals and movement between voices rather than chords. It's normal for someone thinking in counterpoint to produce some very "modern" "chords" because that's a common consequence of following nothing but voice leading to produce a piece of music.

https://en.wikipedia.org/wiki/Partimento

See also Rick Beato mis-analyzing Bach's counterpoint as containing a very "modern" maj7#5 chord: https://www.youtube.com/watch?v=d1f_tzBx6ko&t=1s

But JS Bach apparently did love those modern sounds, see BWV 542/I But indeed it doesn't make much sense to apply jazz theory on classical or early music.

I've never quite understood that POV, although my piano teacher had it. Clearly she had another way of understanding it which I'm sure is more useful. I lack that training.

Pick an example everyone knows: Bach's Prelude in C. I wrote in chord symbols over every bar of that, except for that one very weird bar near the end. It helped me a lot in memorizing it.

IMO when you're playing music, everything you want to do is on the table. If you're going to make music theory and music history arguments, you should be sensitive to the theory and history you are arguing about.

By the way, a 19th century functional harmonist would also find that prelude sort of odd. Not in terms of the chords themselves, but they don't always obey their usual functions.

Also, many modern players and theorists reach toward Schenkerian analysis and its derivatives to sort of explain why music sounds the ways it does. Unlike counterpoint and harmony, Schenkerian analysis is almost entirely descriptive, not prescriptive. I have no idea what your teacher would have suggested.

> IMO when you're playing music, everything you want to do is on the table. If you're going to make music theory and music history arguments, you should be sensitive to the theory and history you are arguing about.

I don't even understand this paragraph. I'm not arguing.

That wasn't directed to you, but rather toward your teacher and the OP. The intent was that as a player, I think you should go ahead and use roman numerals or jazz theory or any other form of analysis that helps you think about things. However, if you are publishing an analysis of a piece (which you did not do), you should be thinking differently than that.

As someone with a significant background in historical performance, my books of Bach preludes are still full of Roman numerals because that is a really good way to "compress" information about what notes to play.

OK. For sure I wouldn't publish that set of chords, since anyone could create it as a shorthand.

I'm actually interested in other ways of analyzing it.

I mentioned this in a sister comment, but I will add:

* Schenkerian analysis is probably the modern method of looking at Bach. A sister comment also indicates that Schenker was a controversial figure (he was a German fascist), but I believe the follow-ups from other theorists on his methods are the modern ones to use for analysis.

* Analyzing otherwise in the context of counterpoint and intervals - see Gradus ad Parnassum and Kennan's book on counterpoint.

I guess you could use figured bass notation. It's more complex than modern chord notation because it tells you which inversion to use, and it notates secondary dominants (e.g. V of V, which you'd write simply as D7 in jazz notation if you're in C). Personally I know too little about it to use it effectively and therefore I would stick with modern chord notation even when talking about classical pieces.

While not disagreeing with anything you’ve said (music theory is one part acoustic physics to several parts history and sociology), the specific primacy of Schenkerian analysis is a particularly American trait.

It’s also, interestingly, illustrative of your argument. Musical analysis is necessarily socially contextual and therefore revealing of the author’s values and priorities, and Schenkerian arguments often imply, or directly come with, some really quite right-wing positions. Schenker was very much into motivated reasoning to defend his deep-rooted racism; many Schenkerian analysts have, deliberately or otherwise, wound up following in those footsteps.

Schenkerian analysis is, broadly speaking, a rediscovery and popularization of melodic reduction approaches that were well known to composers and performers in the 18th century. There's very little that's specifically American about it, let alone German. See Nicholas Baragwanath, The Solfeggio Tradition: A Forgotten Art of Melody in the Long Eighteenth Century. And of course, Schenker's "imaginary continuo" is readily understood as a popularization of historical partimento (and closely comparable approaches such as the so-called Partitura known from German sources).

It's true though that Schenker's treatises included plenty of political asides of such an extreme chauvistic character that to call them "quite right wing" is a huge understatement. (It's also true that, as scholarly research has pointed out in recent years, he seems to have expressed similarly extreme views in his private correspondence and other private writings.) Part of this might perhaps be explained as Schenker's awkward overcompensation for what would've been his remarkably humble origins back then (he came from a small village in what was then Austrian Galicia, now in modern Ukraine). Regardless, I think we nowadays have so many sources proving the relevance of melodic reduction/elaboration approaches (some of them quite early indeed, from the 16th-17th centuries) that to tie these analytical approaches polemically to Schenker and his specificities is really quite pointless, perhaps even misleading.

Ah yes, the good old "fascist dog whistle" argument. Schenker himself was an outright fascist. However, many theorists from the late 20th century who have come up with methods for analyzing tonal music have done so mostly on the back of Schenker's work. I'm also not suggesting you should read Schenker himself - his own work on what we call "Schenkerian analysis" is quite primitive and limited.

I'm curious what you would suggest to perform a modern analysis of Bach (what the original comment chain on this was about) if not Schenkerian analysis. I didn't see any alternative analysis tools proposed in your post, even though it sounds like you are educated on the subject.

Ethan Hein, who teaches music and blogs about it, comes from a jazz background and wrote out chord symbols when he was trying to learn Bach’s Chaconne on the guitar: https://www.ethanhein.com/wp/2019/chord-progressions-in-the-...

See also BWV 903 and BWV 1079.

Andras Schiff playing BWV 903 (there are some REALLY bad performances of this piece out there): https://www.youtube.com/watch?v=SNWOhm5iXxs

BWV 1079 wasn't necessarily written with musical instruments proscribed, but here's a good French group's performance: https://www.youtube.com/watch?v=tfMQ-AYiuJw

For an alternative (but still very valid) interpretation, Wanda Landowska playing BWV 903 on a harpsichord in 1935 totally blew my mind: https://www.youtube.com/watch?v=h-tsbumcyVc

My piano teacher pointed me to this recording when I studied the piece with him. It was scandalizing at first, but the free improvisation in the arpeggiated chords is almost miraculous. (I also love Paul Badura-Skoda's take on the piece: https://www.youtube.com/watch?v=Xx5gojkXdeI)

Scarlatti's sonatas contain many chords, apart from pure polyphony. In fact they're particularly notable for their early inroads toward functional harmony. The tritone substitution in K420 is a clear example of this. Bach much less so, and certainly not in the case highlighted by Beato there.

Whether it contains what a modern ear hears as chords or not, he wrote the piece using polyphonic methods. Bach's music also contains plenty of chords, but that doesn't change how it was written.

When theorists talk about Scarlatti laying the foundation of harmony, partimento is probably the foundation they are referring to. Functional harmony of the 19th century is just a more powerful abstraction.

I don't get how it depends on "how it was written." First, Bach did write chords. Bar 2 of the famous Toccata and fugue ends in a chord. Bar 10/11 has a big chord. Bar 12 starts with a chord. There are chords everywhere. In case you doubt the authorship, plenty of other toccatas have chords. The whole idea of figured bass is chords.

Second, while they did think differently about harmony, you can describe it in modern terms. A description like Cmaj7 doesn't mean anything else than a set of pitches.

A tritone substitution is somewhat different, since it depends on what the analyzer thinks the chord could/should have been. There's a recent YouTube video (by David Bennett, IIRC) that shows tritone substitutions in songs, but he mentions that he doubts Paul McCartney knew he was writing one. But does that mean it isn't? No, it means you can see it as a tritone substitution.

Music theory is a subjective tool to describe and compare, nothing else.

It's interesting that you cite the Toccata and Fugue in D minor because some theorists believe that was actually written much later. The original theory was that Mendelssohn wrote it in the 19th century, but I believe there were some sources from the 1700s. It clearly has a very non-Bach character, including the octave doublings in the chords you mention.

It's very clear that the man wrote chords. It's also very clear that harmony (ie vertical music theory) was not the tool used to write those chords. If you listen to BWV903, for example, there is a long section of arpeggiated chords that defy 18th and 19th century harmony.

The OP's idea of a tritone substitution from Scarlatti does not have the same harmonic function as a tritone substitution in modern music. I would agree with you that if the function matches, you can certainly analyze things in the context of a later theory, but the function does not match.

Finally, figured bass notates intervals, not chords. A crude realization can neglect voice leading in the upper voices, but more skilled realizers of figured bass will preserve voice leading between the intervals in the upper voices. The idea that figured bass is about chords sort of maps backwards the modern abuses of figured bass (which IMO should not be taught as a "basic music theory" subject - but that is for another day) onto the original method.

> The whole idea of figured bass is chords.

I think this might be missing the point a little bit - the bassline in figured bass has more primacy than any of the sonorities above it. The most relevant feature of "chord"-based approaches to music (as found historically, e.g. in performance methods for the Baroque guitar, and to a far lesser extent in repertoire for the lute) is that the vertical sonority (such as "Cmaj7") is all that matters; individual "voices" or "parts" are of secondary importance at best. This maps well enough to how lute- or guitar-like instruments might be played in an accompaniment role (since these instruments obscure the sense of a "melodic line" or a "part" the most, for a variety of reasons) but music includes a whole lot more than that.

Can you recommend any good books or resources for learning polyphonic compositional methods and/or about the other known methods?

Fux's Gradus ad Parnassum is something you can find. A lot of the partimento stuff was practical in nature, and consisted of some rules and several exercises. A great online source on Partimento and historical solfege:

https://partimenti.org/

Thanks!

That's a qualitatively different "tritone substitution" than what the author describes.

author: spice up your jazz by simply replacing one dominant 7th chord with another a tritone away!

Scarlatti: You thought I was aiming toward D-flat? Bitch, I'm surfing in G major! Your puny diatonic expectations cannot contain me.

Put simply-- you can use regular expressions to try out the author's substitutions, but you'll need to build your own parser to try out Scarlatti's.

If you think of a dominant 7th chord as four notes in a 4:5:6:7 resonance, then it seems the 7/5 interval is the "correct" tritone in this context. But a proper tritone substitution means turning the 7/5 into a 10/7 or a 10/7 into a 7/5, which means one or the other of the chords will be out of tune with itself.

Alternatively, one could just hold one note fixed and move the other three, so you end up with both chords being self-consistent. That seems more mathematically satisfying at least.

Ultimately, though, I suppose the only real standard of correctness in music is whatever you can get away with.

"Whatever you can get away with" is the entire basis of equal temperament.

It is, but in just intonation it's harder to get away with certain things when the math doesn't quite work out.

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