What do you think about Set Theory?

I feel like Set Theory, to a mathematician, would feel like Numerology, and often times while analyzing music with it, it really just felt silly. There's also rules to Set Theory that I feel lack a solid reason. But eh, I haven't spent that much time studying it compared to other people who do support it, so I could be missing something.

Anyways, discuss.

http://en.wikipedia.org/wiki/Set_theory_(music)
It seems rather useless to me. I mean, it's sort of like examining things that regular music theory already does.
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It seems rather useless to me. I mean, it's sort of like examining things that regular music theory already does.

No it's not. It's examing things that "regular" music theory can't. That's the whole point.

It's not always useful, but there are a lot of situations where it comes in handy to make sense of the pitch material of a piece. I usually avoid using it unless the piece really obviously calls for it though because doing a full set analysis is a huge pain.

There's also rules to Set Theory that I feel lack a solid reason.

Like what?
I don't know what music theory is.

Quote by jazz_rock_feel
Like what?
Take a chord and its inversion and the "best normal order" is the one with the smallest interval on the bottom two pitches.

Plus I don't think there's any audible significance to the inversion of a lot of chords or rows.
Take a chord and its inversion and the "best normal order" is the one with the smallest interval on the bottom two pitches.

Take a chord, put the third in the bass and it's in first inversion. It's just called best normal order because that's what some dude in 1940 decided to call it. Plus it makes sense to have a standard system where you convert all sets to have the same spacing to compare them. It could've just as easily been the other way around, but it inherently makes sense to say that the smallest intervals go in the bottom of the set.

Plus I don't think there's any audible significance to the inversion of a lot of chords or rows.

That's really arguable. Inverted sets typically sound very similar.

But whatever, set theory can be useful, but it's often not at all. I don't mind when people say it's pointless, but I do mind when people say it's turning music into math because it's really really really really not.
I don't know what music theory is.

Quote by jazz_rock_feel
Take a chord, put the third in the bass and it's in first inversion. It's just called best normal order because that's what some dude in 1940 decided to call it. Plus it makes sense to have a standard system where you convert all sets to have the same spacing to compare them. It could've just as easily been the other way around, but it inherently makes sense to say that the smallest intervals go in the bottom of the set.
It's essentially "just 'cus." Not a fan of that. Especially because very different chords will be classified the same, which is already a common criticism.
Quote by jazz_rock_feel
That's really arguable. Inverted sets typically sound very similar.

But whatever, set theory can be useful, but it's often not at all. I don't mind when people say it's pointless, but I do mind when people say it's turning music into math because it's really really really really not.
I think if there is a similarity, it's from something that can be examined with traditional theory (like how Berg would use more familiar idioms), but I don't think there is an audible significance with more atonal rows, like the ones exercising pointillism. And if there is, honestly it's probably just a placebo effect, or you could create a similar audible significance to the listener with a row that isn't related to that matrix.
Quote by jazz_rock_feel
No it's not. It's examing things that "regular" music theory can't. That's the whole point.

It's not always useful, but there are a lot of situations where it comes in handy to make sense of the pitch material of a piece. I usually avoid using it unless the piece really obviously calls for it though because doing a full set analysis is a huge pain.

Eh, fair enough.
lol @ Sam butting into everything even when he has no idea.

Anyways set theory is meh. I'm more drawn towards the idea of using tone rows in a functional or at least triadic way and ignoring the strict consistency devised with set theory.

...modes and scales are still useless.

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Last edited by Xiaoxi at May 29, 2013,
I think it's important to point out that set theory and serialism are not dependent on one another. I mean, they're not mutually exclusive, like you can obviously apply set theory to serial music and rows, but to me it's much more usefully applied outside of that. Like pre-serial Webern and Schoenberg and some post-serial music too.

I totally get the criticism of it, but after getting over the intial clumsiness of it it comes in handy.

It's essentially "just 'cus." Not a fan of that. Especially because very different chords will be classified the same, which is already a common criticism.

Those are two different criticisms though. When you were talking about normal order, you were just talking about conventions (which exist all over the place in theory). As for sets that aren't similar being grouped together artificially, that can be true, but you're also sort of missing part of the point. Sets aren't necessarily grouped together because they sound the same as a whole, it's sometimes about looking at intervals present in a set which can also create relationships.

Here's the bottom line. Set theory allows us to manipulate musical motives outside of the context of pitch, which is obviously the main way we look at tonal music, and in the context of intervals, which is much more applicable when you're outside of the context of a key.

In a tonal piece, the relationship between F and C doesn't matter because they both have defined functions in the key. Just the fact that they are F and C tells us a lot about what's happening. In post-tonal music, F and C mean nothing on their own because they're floating out of context, but saying they're a perfect fourth apart means a lot because that puts them in context.

That's the part of set theory that people don't get. They get bogged down in the numbers and the brackets, but they don't see the forest for the trees.

I used the word context 5 times in this post.
I don't know what music theory is.

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I think it's important to point out that set theory and serialism are not dependent on one another.

Serialism is dependent on set theory.

...modes and scales are still useless.

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Those are two different criticisms though. When you were talking about normal order, you were just talking about conventions (which exist all over the place in theory).
I pointed out what I believe to be something negative about the convention. Which I think is a result of the convention not having any real reason to it. By considering one order the "best" for no real reason, a different order which potentially has a much more different sound is shadowed and classified the same.
Quote by jazz_rock_feel
As for sets that aren't similar being grouped together artificially, that can be true, but you're also sort of missing part of the point. Sets aren't necessarily grouped together because they sound the same as a whole, it's sometimes about looking at intervals present in a set which can also create relationships.

Here's the bottom line. Set theory allows us to manipulate musical motives outside of the context of pitch, which is obviously the main way we look at tonal music, and in the context of intervals, which is much more applicable when you're outside of the context of a key.

In a tonal piece, the relationship between F and C doesn't matter because they both have defined functions in the key. Just the fact that they are F and C tells us a lot about what's happening. In post-tonal music, F and C mean nothing on their own because they're floating out of context, but saying they're a perfect fourth apart means a lot because that puts them in context.

That's the part of set theory that people don't get. They get bogged down in the numbers and the brackets, but they don't see the forest for the trees.
I understand this, yeah, but you assign a number like F and C, a 5, and then what? These numbers have no significance on their own. All that's done is stating the obvious. You're simply defining the piece rigidly while not giving any information on the audible significance of the piece. The vocabulary you end up with in set theory in meaningless. All it seems to be able to come up with is if there's any mathematical structure or recurring harmonic pattern in the piece, but most of the time these events don't have any audible significance or recognizability to the unaware listener. And if there is always supposed to be a significance for listerners behind different sets of pitches because they have been "inverted" or transposed/planed chromatically and they share a numerical value is numerology.

You might be defining what the composer is thinking, but you aren't defining what the audio is creating for the listener.
Last edited by The Madcap at May 29, 2013,
Apparently I become a huge set theory apologist after midnight. I don't even like set theory. **** it, too late now.
Quote by Xiaoxi
Serialism is dependent on set theory.

How? You can analyze serial music without set theory.

I pointed out what I believe to be something negative about the convention. Which I think is a result of the convention not having any real reason to it. By considering one order the "best" for no real reason, a different order which potentially has a much more different sound is shadowed and classified the same.

Sets are unordered. You only put them in normal order to compare them on the same level with one another. The order that you put them in has no bearing over how the composer uses them. You're thinking serially, where order matters, not in terms of sets where it doesn't.

I understand this, yeah, but you assign a number like F and C, a 5, and then what? These numbers have no significance on their own. All that's done is stating the obvious. You're simply defining the piece rigidly while not giving any information on the audible significance of the piece. The vocabulary you end up with in set theory in meaningless. All it seems to be able to come up with is if there's any mathematical structure or recurring harmonic pattern in the piece, but most of the time these events don't have any audible significance or recognizability to the unaware listener. And if there is always supposed to be a significance for listerners behind different sets of pitches because they have been "inverted" or transposed/planed chromatically and they share a numerical value is numerology.

You might be defining what the composer is thinking, but you aren't defining what the audio is creating for the listener.

So you're telling me that if I take a Webern piece and see that he uses three different sets that all use interval class 1 twice that doesn't tell me anything about what the piece sounds like? Again, this isn't math. Outside of the use of numbers and some of the same basic concepts as mathematical set theory the two have nothing in common. I don't know how you could analyze something with sets and think you've arrived at any mathematical conclusion about a piece. What you've done is found out the groups of intervals that define a piece. If you don't think that's useful, then don't use it.

And numerology is finding some kind of meaning or divinity in numbers, which has nothing to do with this. All you do with set theory is convert note names to numbers so you can manipulate them easier, because notes don't matter anymore, only intervals. You're not assigning special meaning to the numbers any more than you assign special meaning to the letters of the musical alphabet.
I don't know what music theory is.

Not a big fan of set theory. It's kind of useful in a few instances (mid era 20th century music) but I think there are better theories. And I don't think anyone should ever compose according to rules (compose by ear, write down what you want to hear), although the rules can be useful for learning and training composition.
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How? You can analyze serial music without set theory.

How do you analyze something like Webern's Piano Variations without set theory?

...modes and scales are still useless.

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Sets are unordered. You only put them in normal order to compare them on the same level with one another. The order that you put them in has no bearing over how the composer uses them. You're thinking serially, where order matters, not in terms of sets where it doesn't.
I don't really understand this.
Quote by jazz_rock_feel
So you're telling me that if I take a Webern piece and see that he uses three different sets that all use interval class 1 twice that doesn't tell me anything about what the piece sounds like? Again, this isn't math. Outside of the use of numbers and some of the same basic concepts as mathematical set theory the two have nothing in common. I don't know how you could analyze something with sets and think you've arrived at any mathematical conclusion about a piece. What you've done is found out the groups of intervals that define a piece. If you don't think that's useful, then don't use it.

And numerology is finding some kind of meaning or divinity in numbers, which has nothing to do with this. All you do with set theory is convert note names to numbers so you can manipulate them easier, because notes don't matter anymore, only intervals. You're not assigning special meaning to the numbers any more than you assign special meaning to the letters of the musical alphabet.
I don't think there is anything mathematical about Set Theory. I said that thing about mathematical structure just because you can have a row or something that follows some really simple numerical pattern and that's it. But that doesn't really matter. I simply don't think people hear music in these terms. Yeah, people will hear stuff like a chromatic interval in Webern, true. But regardless, yeah, I don't think finding the intervals alone really tells us what the notes is doing for the listener.

The comparison to numerology is meant to be more in terms of logic.
Quote by Xiaoxi
How do you analyze something like Webern's Piano Variations without set theory?

Dunno, I've never looked at it specifically, but it's serial, so I would start by looking at the row(s) he used and how he used them. Knowing Webern he probably used only one and probably a small number of transformations. It could be interesting to see which he chose and look at their relationships.

Isn't that the mirror one though? You don't need set theory to know what a palindromic row is. Sets could be part of the equation, but all I'm saying is you don't NEED sets to look at serial music and you can use sets outside of serial music. And I can tell you I've analyzed serial music without the use of formal set theory. Serialism existed before set theory was around.
I don't know what music theory is.

^ true. I don't really like set theory... but I do like palindromic sets. They are kind of cool >_< and aren't always atonal.