# New complexity, atonality and other maths versus music ideas



## Drowning_by_numbers

I've just seen a thread loosely debating the popular maths versus music and thought it warranted a topic of it's own. 

This is a tricky subject to approach but I am just opening the arena for healthy debate on how much maths you believe music can hold. I am thinking specifically of serial composers, or at least those in that vein. Often people say that atonal music is "not music" and I just wondered what the thoughts on this are in this forum. For example a composer such as Brian Ferneyhough who obviously uses complex mathematics in his music, and insane rhythms, nested tuplets etc that are almost impossible to play. I often wonder in his music if the rhythm was less specific if it would detract from the music. 

Thoughts anyone??


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## Herzeleide

Ferneyhough doesn't use complex maths in his music.


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## Bach

Not ridiculously complex, but maths nonetheless. http://en.wikipedia.org/wiki/Etudes_Transcendantales


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## Herzeleide

Well, one could say that there's maths involved in all music... every literate musician has to learn how to divide and subdivide bars and beats one way or another, even if it's the stuff we take for granted like dividing 4/4 into sixteen.


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## Bach

> For example, for the oboe part in the first song, the rhythm is almost totally determined by a strict system, with five stages of complexity, each determined by another cycle of numbers:
> dividing each measure into a number of notes
> subdividing chunks of those notes into another layer
> adding dots so that 4 notes fit where 3 did previously
> tie some notes with each other and replace others with rests
> replace two consecutive notes with a triplet in which one beat is a rest


That's a rather mathematical approach to composition.


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## Herzeleide

It's a very systematic way of dealing with rhythm.



> 34) Do your works have variations of some sort (perhaps some changing of previous material)? Are they generated mathematically?
> 'Variations' is a species of form; 'variation' is a manner of working. Surely all music deals with the latter. Likewise mathematics (except that most music probably deals with a sort of elevated arithmetic).
> 
> 35) Did you ever study math or science?
> Not willingly. I did study mathematical logic for a brief period back in the 60s, but never systematically.
> 
> 36) Is math or science important when performing or listening to your works?
> No, except sometimes as helpful metaphor. .


http://en.wikipedia.org/wiki/Talk:Brian_Ferneyhough


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## Bach

Yes, but you're really using systematic and mathematical synonymous - Messiaen, for example, did not deal with rhythm in such a way.


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## Herzeleide

Well, I think 'systematic' is a more accurate description. I'm not sure what 'mathematical' actually means really; he's manipulating the rhythm in a very elaborate way, and dealing with it seemingly for its own sake. I know other composers haven't/don't deal with rhythm in the way Ferneyhough does in this piece.

Anyway... this is just semantics. I feel the original poster is wrong to posit a dichotomy between maths and music. It doesn't even make sense because the stuff Ferneyhough produces clearly is music. His music is the _Ars Subtilior_ of our time.

Would his music suffer if the rhythm were less specific? Well... yes. It's a silly question really. I'm not fond of hypothetical questions. Like, would Berg have written _Lulu_ if the twelve-tone technique was never invented? It doesn't matter.


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## Drowning_by_numbers

This are all vast assumptions you are making, and although I may have expressed myself poorly they are certainly not what I suggested. I do not believe what you seem to be implying I belive. I was simply asking for a view as to whether you believe music has become too intellectual, relying to much on mathematical concepts and not enough on emotional value.

In no way did I suggest Ferneyhough does not write music. You have made a lot of incorrect assumptions if you don;t mind me saying. I am incredibly passionate about contemporary music but I worry about the majority of it being assessable to the wider public.. and in a concert of Ferneyhough's music which I enjoyed I was sat with another friend of mine who is a professional musician but not a particular fan of contemporary music and he hated the concert. I found myself wondering whether if trained musicians cannot understand or appreciate what a great deal of contemporary composers are doing, what hope do the general public have?

So that is my question. I believe that maths and music are inseparable, but in recent years has music relied too much on mathematical concepts and not enough on emotional value and the actual product - i.e. the sound. It is not a hypothetical question.


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## sam richards

Not just in classical, some of the mathematical ideas are in the popular music too, it just a experimentation on the part of the composers. 

Talking about emotional values is, frankly, stupid. Music is just an assortment of sound waves, and the emotion is subjective. Some may feel a particular emotion when listening to a piece of music while others will not.


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## PostMinimalist

Extra musical ideas are fine as a basis for musical composition as long as they finally produce music. When Bach writes a canon in crab diminution at the sixth he is using maths but he will make sure that the math is slave to the music and not the other way around. If his canons sounded **** 'cos they were full of parallel fifths, unresolved clashes and weird clusters etc, then I think he would have thrown them in the trash (which he might well have done with a lot of stuff we don't know about).

As Hezeleide says (can I paraphrase here?) all music that we think of as 'Non math' music is actually governed by a deeper more subtle math than we can imagine. So I say why not try to add to that rather than pile in some math you picked up at a bar (cloud theory, fractals, calculus etc.)?

There has been much speculation as to how much cryptonumerology Bach used and some of his works have been analysed to show that they contain references to the fibonacci serires and the golden section and other 'Sacred' numbers. The wonderful thing is however that we don't hear, at least on a conscious level, these references where as in much of todays 'math based' music it is all too obvious.

So either it's the wrong math or the wrong compostion technique, since the beauty of Bach is his apparent simplicty which, when analysed, turns out to be extrememly complex; today we suffer from music which sounds complex and when analysed turns out to be based on some dull, dry mathematical system and not those systems which were (and still are in many circles) regarded as sacred and the key to deeply understsnding nature, not just catagorizing or cataloging it. 

Bach may express and almost Pythagorean understanding of something simple like 1,2,3 whereas Xenakis just catalogs a mess like 75.455x^34{x*e45 (34π^2)} figuatively speaking, of course.

FC


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## Herzeleide

Drowning_by_numbers said:


> I do not believe what you seem to be implying I belive. I was simply asking for a view as to whether you believe music has become too intellectual, relying to much on mathematical concepts and not enough on emotional value.


Again, I'm afraid you're making the same mistake that I've already criticised. The notion of 'maths versus music' that you mention in the thread title appears to posit a dichotomy between the two: that they're mutually exclusive. For example, the algorithmically derived series of durations used in Messiaen's _Chronochromie_ does nothing to prevent the awesome expressiveness of this piece (in fact, I would say that this is his best orchestral piece). Likewise, the serial processes used to generate the material Boulez uses in _Le marteau sans Maitre_ are very elaborate, and yet the music is beautiful and very expressive. I also love the music of Xenakis.

Music can be dry and dull, yes. There has always been dry, academic music. This is a failure of a composer's inventiveness, it's not that the composer is using compositional techniques too 'consciously' rather than relying on intuition. I completely reject these polarities.



Drowning_by_numbers said:


> In no way did I suggest Ferneyhough does not write music. You have made a lot of incorrect assumptions if you don;t mind me saying.


Again, I was led to believe this by your phrase 'maths versus music'; as though one cannot accommodate the other.



Drowning_by_numbers said:


> I am incredibly passionate about contemporary music but I worry about the majority of it being assessable to the wider public.. and in a concert of Ferneyhough's music which I enjoyed I was sat with another friend of mine who is a professional musician but not a particular fan of contemporary music and he hated the concert. I found myself wondering whether if trained musicians cannot understand or appreciate what a great deal of contemporary composers are doing, what hope do the general public have?
> 
> So that is my question. I believe that maths and music are inseparable, but in recent years has music relied too much on mathematical concepts and not enough on emotional value and the actual product - i.e. the sound. It is not a hypothetical question.


Ferneyhough doesn't (most the time) use mathematical concepts in his music, unless you think all the stuff involving tuplets is maths.

Ferneyhough's music is the opposite of arid calculations. His music has a thrilling electricity about it; a hyper-expressive, hyper-sensitive aesthetic devoid of banalities, dryness or theoretical exaggerations. This is its problem. There's nothing easy about his music: it _is_ intrinsically difficult, like a lot of modern music: it's part of the experience and appeal of the music. It's hardly surprising that even educated musicians find it too difficult, let alone the general public; I see nothing problematic about this. Ferneyhough is who he is, and if someone wants contemporary music that dilutes itself to fit the tastes of the general public, there are people out there like Phillip Glass for them to gorge themselves on.


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## Herzeleide

post-minimalist said:


> So either it's the wrong math or the wrong compostion technique, since the beauty of Bach is his apparent simplicty which, when analysed, turns out to be extrememly complex; today we suffer from music which sounds complex and when analysed turns out to be based on some dull, dry mathematical system and not those systems which were (and still are in many circles) regarded as sacred and the key to deeply understsnding nature, not just catagorizing or cataloging it.
> 
> Bach may express and almost Pythagorean understanding of something simple like 1,2,3 whereas Xenakis just catalogs a mess like 75.455x^34{x*e45 (34π^2)} figuatively speaking, of course.
> 
> FC


Xenakis is awesome.

You're using the words 'simplicity' and 'complexity' as some form of value-judgement; something I've argued against in another thread (which you have no doubt seen).


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## PostMinimalist

Xenakis is indisputably awesome. In his early works, based on architectural principals hwever he allowed his bluepirnts to govern and not his ears. Of course when he was designing his buildings he allowed his 'eye' to govern the math involved but his application of this to music requires that another organ (the ear) be allowed to govern. When he invented the UPIC I was at the first demonstration in Britain given at the Barbican Centre by Peter Nelson (who I knew from Edinburgh University Experimental Arts Group). It was very beguiling being able to draw a face and then have a computer 'translate'the drawing directly into music. This was a stream-lined version of his own (Xenakis' not Nelson) methods of composition. But it was 'music' as the result of a visually inspired creation and any 'intentional' musical or aural intervention in the creeative process immediately required concessions in the visual input. The more you wanted to really get into the resulting sound the more you ended up drawing something that looked more and more like music notation (Ala guido d'Arezzo). Complexity is not so much a value judgement here as an expression of how aurally unintuitive the process of musical creation has become.


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## Herzeleide

post-minimalist said:


> Complexity is not so much a value judgement here as an expression of how aurally unintuitive the process of musical creation has become.


'Has become': you missed off the 'for Xenakis' qualifier there.

Xenakis may use stochastic processes to generate material, and he may have used a computer programme to help him with this, but the crucial point is that *he* decided what went into the computer.

His musical decisions are not arbitrary, otherwise he wouldn't have developed his own style (which is very recognisable).

I'm uneasy about the distinction between 'conscious' compositional thought and 'intuitive' - both (if we accept the division) ultimately are hard to explain and rationalise.


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## PostMinimalist

H. I Agree with most of what you say here. Just one thing though, Xenakis may have decided what went into the computer but defered to the computer as to what came out thereof!  Ha
FC


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## Drowning_by_numbers

Herzeleide said:


> Ferneyhough's music is the opposite of arid calculations. His music has a thrilling electricity about it; a hyper-expressive, hyper-sensitive aesthetic devoid of banalities, dryness or theoretical exaggerations. This is its problem. There's nothing easy about his music: it _is_ intrinsically difficult, like a lot of modern music: it's part of the experience and appeal of the music. It's hardly surprising that even educated musicians find it too difficult, let alone the general public; I see nothing problematic about this. Ferneyhough is who he is, and if someone wants contemporary music that dilutes itself to fit the tastes of the general public, there are people out there like Phillip Glass for them to gorge themselves on.


I resent the arrogant assumption that music that appeals to a wider variety of people than Ferneyhough it is therefore diluted. So many composers appeal to a wider audience and yet mantain intergrity as composers and don't "dilute" there ideas. As a composer, I want to write for people, as opposed to people with a degree in music, but that doesn't mean I will write less complex music. Composers like Ligeti and Messiaen for example attract larger audiences because there is still something about there music that is a) appealing and b) understandable. Not that I am suggesting that Ferneyhough is anything but a great composer. I guess it just depends why you write music and what you want to get out of it.


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## Herzeleide

Drowning_by_numbers said:


> I guess it just depends why you write music and what you want to get out of it.


Yes, precisely. Composers are who they are, whether the upshot is that they're liked by lots of people or only an initiated few. Which is why it's redundant speculating about Ferneyhough's music as though there is a problem with the fact that it doesn't appeal to a wider audience (which you have done: 'I worry about the majority of it being assessable to the wider public.')


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## Herzeleide

post-minimalist said:


> H. I Agree with most of what you say here. Just one thing though, Xenakis may have decided what went into the computer but defered to the computer as to what came out thereof!  Ha
> FC


I deferred to what the computer came out with when typing this sentence.


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## PostMinimalist

Herzeleide said:


> I deferred to what the computer came out with when typing this sentence.


The difference being that you had a really good idea what it was going to be at the exit door! Xenakis (at least at first) did not.


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## Herzeleide

post-minimalist said:


> (at least at first)


This is the crucial datum.

Yes, he experimented. We all do. That's how one learns.


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## Drowning_by_numbers

Leaving Xenakis aside, what do you feel about total serialism, where composers serialised every aspect of the music then? "If it moves, serialise it." Can it be argued that composers who used this method are not making a musical choice?


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## danae

Drowning_by_numbers said:


> Leaving Xenakis aside, what do you feel about total serialism, where composers serialised every aspect of the music then? "If it moves, serialise it." Can it be argued that composers who used this method are not making a musical choice?


Based on what has already been said until now on this thread, how can you ask this question? Bottom line for me is this: if it results in music, then it IS a musical choice. And don't ask what music is... for obvious reasons!


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## Herzeleide

danae said:


> Bottom line for me is this: if it results in music, then it IS a musical choice.


Precisely.


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## Drowning_by_numbers

danae said:


> Based on what has already been said until now on this thread, how can you ask this question?


Becuase I don't agree with your answer. But apparently this is not the place to disucss this. I don't believe there is one correct answer either so I didn't expect such a black and white response.



danae said:


> And don't ask what music is... for obvious reasons!


I didn't.


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## sam richards

*TS fails*



danae said:


> Based on what has already been said until now on this thread, how can you ask this question? *Bottom line for me is this: if it results in music, then it IS a musical choice.* And don't ask what music is... for obvious reasons!











Danae summed this up.


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