Group Theory And Music

If you believe that I'm agreeing with you then I believe you are mistaken.  I'm just not trying to convince you otherwise, because the dialog would be beyond you and I don't mean that as an offensive jab.  In the words of Feynman (more or less) we can't talk about physics without the mathematics.  Thus, I don't believe I can talk about anything meaningful on how a topic like group theory can be useful or for that matter category theory without just talking over you.  Nevertheless, let's not confuse that with a belief that I believe mathematics in music can only bring forth trivial ideas.   

While the heyday of dodecaphony has long passed, it's not fair to assess the music in such a way, especially since it's not even possible to 'demonstrate' what is or isn't musical or meaningful since everyone has different views on the matter. Some of the most engaging pieces of music I've ever heard were constructed using set theory, pieces like Boulez's 1st Piano Sonata, Babbitt's More Melisma, Wuorinen's Chamber Concerto for Flute and Ten Players, Webern's Variations for Piano, et al.

 

Yes but were those pieces really created using set theory or adopted by analysts as examples of set theory in music so they could get a paper published? I can't speak for all of those examples but I know that Webern's Variations and Boulez's 1st piano sonata definitely were not composed with any set theory in mind. You can label certain elements in them using set theory such as the self- generating motive at the start of the Boulez or certain recurring harmonies in the Webern but you could do the same to something like Beethoven op. 131 and label every case of the augmented 2nd in its various guises and transformations and claim that he had set theory in mind when composing but that would be pointlessly anachronistic. As it happens, Babbit, Boulez and Webern are three of my favourite composers. I'm not knocking the music at all; I'm just knocking the analysts-turned-mathematicians.

 

 

 

If you believe that I'm agreeing with you then I believe you are mistaken.  I'm just not trying to convince you otherwise, because the dialog would be beyond you and I don't mean that as an offensive jab.  In the words of Feynman (more or less) we can't talk about physics without the mathematics.  Thus, I don't believe I can talk about anything meaningful on how a topic like group theory can be useful or for that matter category theory without just talking over you.  Nevertheless, let's not confuse that with a belief that I believe mathematics in music can only bring forth trivial ideas.   

 

Thus proving my point to an even greater degree that this is a piece of vanity publishing that appeals only to a niche market of mathematicians who happen to have an interest in both group theory and music theory. If we could draw a Venn diagram, the intersection would have about 5 people in it. If only you would admit that instead of pretending that there is some grand esotericism at work that us non-initiated monkeys could never wrap our little heads around.  

I can see you're not an academic otherwise the irony of niche publishing would surely have been a joke.  Anyway!  Don't get defensive because your ego is hurt.  Just because you don't find value in it, doesn't mean other people don't or can't.  I mostly suspect you find little value in it, mostly because you can't comprehend it, which is fine.  Nevertheless, I don't see why you feel the need to go out of your way to express how little value it has to you, when it's clearly something not within your realm of understanding or even familiarity?  That's like me reviewing a steakhouse, and just trying their mash potatoes (vegetarian here.)  It's just asinine on so many levels!

I can see you're not an academic otherwise the irony of niche publishing would surely have been a joke.  Anyway!  Don't get defensive because your ego is hurt.  Just because you don't find value in it, doesn't mean other people don't or can't.  I mostly suspect you find little value in it, mostly because you can't comprehend it, which is fine.  Nevertheless, I don't see why you feel the need to go out of your way to express how little value it has to you, when it's clearly something not within your realm of understanding or even familiarity?  That's like me reviewing a steakhouse, and just trying their mash potatoes (vegetarian here.)  It's just asinine on so many levels!

 

I don't understand why you've posted it on a forum for composers if, as you've already admitted, it is going to be of no use to composers. That would be like recommending a steakhouse to a vegetarian. Asinine.

This is where reading comprehension and not assuming statements would benefit you.

 

1)I never said it would have no use for a composer.  I simply said a composer clearly doesn't need it. 

 

2)I posted it here because as I stated in my first post, I believed there would exist a group ( even a 2 people form a group!) that would appreciate the book for what it is and perhaps the even more generalized idea behind it. 

 

I don't know why you assume every topic must be relevant to everyone.  Clearly, the target audience is small, I am pretty sure I more or less stated that in my first post. 

Yes but were those pieces really created using set theory or adopted by analysts as examples of set theory in music so they could get a paper published?

The first one.

While the heyday of dodecaphony has long passed, it's not fair to assess the music in such a way, especially since it's not even possible to 'demonstrate' what is or isn't musical or meaningful since everyone has different views on the matter.

 

I pretty much agree - someone, somewhere might find some kind of value or usefulness to virtually anything, musically speaking. And that's fine.

 

Some of the most engaging pieces of music I've ever heard were constructed using set theory...

 

Agreed, again.

 

Though, in my view, the sole fact of being constructed using set theory doesn't make them any more musically engaging or interesting. After all, there are a lot of masterworks which weren't built through this method, and that doesn't make any of them less of a masterpiece. And there's also a lot of crap being written, which will remain as crappy as ever, even if its composer attempts to justify it through some sort of pseudo-scientific babbling.

The first one.

 

I disagree. Not one mention of set theory in either Orientations or Boulez on Music Today. I suspect this is a case of confused nomenclature because serial and set theory aren't synonymous. You could analyse it all with set theory (and by analyse, I really mean label) but to say Boulez or Webern composed with set theory in mind is a bit of a stretch. Especially the piano sonata 1 which is from the 1940s. It predates most expositions of musical set theory by at least 20 years. Ditto Webern but even more so.

This is where reading comprehension and not assuming statements would benefit you.

 

1)I never said it would have no use for a composer.  I simply said a composer clearly doesn't need it. 

 

2)I posted it here because as I stated in my first post, I believed there would exist a group ( even a 2 people form a group!) that would appreciate the book for what it is and perhaps the even more generalized idea behind it. 

 

I don't know why you assume every topic must be relevant to everyone.  Clearly, the target audience is small, I am pretty sure I more or less stated that in my first post. 

 

 

Very well, I am being asinine, I'm incapable of understanding it and clearly don't fall within the target audience. I accept that. I'm only still on this thread because other people have chipped in and quoted me so I've had to respond to them.

I disagree. Not one mention of set theory in either Orientations or Boulez on Music Today. I suspect this is a case of confused nomenclature because serial and set theory aren't synonymous. You could analyse it all with set theory (and by analyse, I really mean label) but to say Boulez or Webern composed with set theory in mind is a bit of a stretch. Especially the piano sonata 1 which is from the 1940s. It predates most expositions of musical set theory by at least 20 years. Ditto Webern but even more so.

Oh, by 'set theory' I was assuming that we were talking about dodecaphony (as indicated by my first post). My mistake. Also, I couldn't help but notice that your example on the other page looks a lot like how many people have approached analysis of Bartok's 4th String Quartet (though I am aware of the disparity that often exists between composition and analysis).

Now after being better familiarized with what exactly is being discussed, I still don't think that anything composed using 'set theory' is fundamentally devoid of musicality. As you successfully demonstrated earlier, the same conclusions can be drawn by simply putting two-and-two together so I agree with you (and others that have posted) in that set theory isn't exactly practical. All the same, I can understand why it is appealing to some composers because of the ability to precisely control elements of their compositions from a very basic level. I was actually doing similar things for a little bit and I liked the ability I had over interval content and having total chromaticism with certain consistencies between constituent groups of pitches. I only wrote one piece in this manner (it was a flute duo I had on this site for a little bit). It didn't lack musicality, but from writing it I learned that I needed more freedom...

Oh, by 'set theory' I was assuming that we were talking about dodecaphony (as indicated by my first post). My mistake. Also, I couldn't help but notice that your example on the other page looks a lot like how many people have approached analysis of Bartok's 4th String Quartet (though I am aware of the disparity that often exists between composition and analysis).

Now after being better familiarized with what exactly is being discussed, I still don't think that anything composed using 'set theory' is fundamentally devoid of musicality. As you successfully demonstrated earlier, the same conclusions can be drawn by simply putting two-and-two together so I agree with you (and others that have posted) in that set theory isn't exactly practical. All the same, I can understand why it is appealing to some composers because of the ability to precisely control elements of their compositions from a very basic level. I was actually doing similar things for a little bit and I liked the ability I had over interval content and having total chromaticism with certain consistencies between constituent groups of pitches. I only wrote one piece in this manner (it was a flute duo I had on this site for a little bit). It didn't lack musicality, but from writing it I learned that I needed more freedom...

 

I'm sure some great music could be produced by using set theory in the compositional process but I would argue that you could create the same piece of music without the set theory. For me it's like, to get to the mathematical part, you have to go through the musical part first anyway so why turn it all into math just to turn it back into music again, if that makes sense. You can still have the same level of control of interval content and consistency without it. Music is already abstract enough without abstracting it further with mathematics in my opinion.

 

I've done it as well. I wrote a piano piece using the all-interval hexachord against it's complementary set. In the end, I found that I was largely writing exactly what I instinctively wanted to write, then attempting to shoehorn it into this set theory idea after the fact. The piece still had a certain consistency and uniformity to it because you're always going to get that from cellular or motivic development and the intuitive connections and possibilities that you see while writing anyway. Not to mention your ear, which is streets ahead of your brain when it comes to making and seeking out these sorts of connections while composing.

 

I think I'm being too strong about this but it's probably a reaction to having to put up with professional analysts using mathematical ideas to tell me things about pieces of music that are either of no musical consequence to the listener whatsoever, or can be inferred without the aid of a mathematical idea. 

I'm sure some great music could be produced by using set theory in the compositional process but I would argue that you could create the same piece of music without the set theory. For me it's like, to get to the mathematical part, you have to go through the musical part first anyway so why turn it all into math just to turn it back into music again, if that makes sense. You can still have the same level of control of interval content and consistency without it. Music is already abstract enough without abstracting it further with mathematics in my opinion.

 

I've done it as well. I wrote a piano piece using the all-interval hexachord against it's complementary set. In the end, I found that I was largely writing exactly what I instinctively wanted to write, then attempting to shoehorn it into this set theory idea after the fact. The piece still had a certain consistency and uniformity to it because you're always going to get that from cellular or motivic development and the intuitive connections and possibilities that you see while writing anyway. Not to mention your ear, which is streets ahead of your brain when it comes to making and seeking out these sorts of connections while composing.

 

I think I'm being too strong about this but it's probably a reaction to having to put up with professional analysts using mathematical ideas to tell me things about pieces of music that are either of no musical consequence to the listener whatsoever, or can be inferred without the aid of a mathematical idea.

Right, I don't think we have any disagreements. Speaking of dry essays on the subject, I have a $120 book by George Perle which deals entirely with his use of set theory in his own music, presented in the most needlessly difficult language possible. Unsurprisingly, I put up with about half of it and it has been sitting on my shelf ever since (the only music text I've ever given up reading).

Anyways, to be fair to those that are interested, I'll leave this thread to the discussion presented in the OP.