Mathematics and music

[albion]

Quote from: Alan Howe on Yesterday at 21:35

    Schoenberg's Op.31 is never going to be 'accessible' because it speaks an alien language; by contrast, Berg preserves enough musical language that is accessible in his VC for it to be appreciated. Sure, this language can be learned, but for me that's the point - it doesn't come at all naturally...


Perhaps the allusion is to the mathematical formulae inherent in Serialism and the aural phenomena that result from its practical application.

It should be remembered that in terms of pitch-sounds all music is essentially a Pythagorean mathematical conceit (http://www.davesabine.com/Music/Articles/PythagorasMathematicalTheoruminMusic/tabid/169/Default.aspx). Mathematics in some form has always been used to create music: medieval composers including Machaut, Dufay and Dunstable composed isorythmic motets and Bach clearly used mathematical constructs (http://www.harpsichord.org.uk/EH/Vol2/No2/bachmath.pdf). Messiaen used prime numbers and there has been much discussion on the links between the Fibonacci Sequence and compositions as different as Debussy's La Mer and the final movement of Bartok's Music for Strings, Percussion and Celesta.

There is some excellent introductory discussion in a Radio 4 programme, Mathematics and Music in 2006, which is still available from the BBC (http://www.bbc.co.uk/programmes/p003c1b9). Although not covered in any depth, a wide range of topics is discussed including numerology and the Golden Section.

I would also encourage anybody specifically interested in Serialism and its reception to read Schoenberg, Serialism and Cognition: Whose Fault if No One Listens? by Philip Ball (http://www.philipball.co.uk/docs/pdf/Ball_atonalism2.pdf).

In very basic terms, music is mathematical constructs and formulae: for example there is nothing inherently 'sad' in a minor triad or 'happy' in a major triad beyond our own conditioned extra-musical associations.

[Delicious Manager]

For those who find Schoenberg's serial music 'difficult', the Variations for Orchestra Op 31 is one of the pieces I direct them to. I don't know why some find it hard to listen to - it is a colourful, varied and ingenious piece to which i return often. Perhaps I should quote Charles Ives: "Open your ears and listen like a man!" (or was that Carl Ruggles?).

[Alan Howe]

Well, all I can say is that there's maths I can learn to understand and there's maths it takes an expert to understand...

BTW, Schoenberg's Op.31 has to be one of the most ugly pieces of music ever written!

[Delicious Manager]

Sounds like a case of 'agree to disagree' to me.

Of course, there have been plenty of people who have accused JS Bach's music of being too mathematical...

[eschiss1]

I was reading a collection of letters Berg and Schoenberg wrote to each other and remember (inexactly) a quip Schoenberg made about his Variations for Orchestra (while he was writing it, or just after): something along the lines of
"both those who admire his music and otherwise, agree that his new work [the variations] is as good as anything else he's written."


(which I took to be in a false-newspaper-clipping/review style for fun, fwiw.)
Eric (who didn't start out an admirer or Schoenberg fan but obviously based on past posts rather is one now. at least, of the music.)

[sdtom]

I understand and correct me if I'm wrong but wasn't Taneyev a mathematician? Didn't he incorporate a certain amount into his composing.
Thomas

[Amphissa]

 
Mathematics can be used to describe and analyze most anything, from natural phenomena to behavioral patterns to the products of human enterprise. But its use as a tool for creation (to me) leads in directions that undermine the humanity of the arts -- the emotional context, the experience of human passage. Yes, there can be beauty in mathematics, and some composers have become fascinated by the use of mathematics in composition. But (to me) mathematics is better for analysis and description, not for creation. To me, mathematics is not art.

[Alan Howe]

I agree. No amount of mathematical education is going to get me - and, I supect, many, many others - to appreciate, let alone like where the music of the 2VS has led us...

[eschiss1]

Nor will it get anyone to like Bach who doesn't already. How fortunate that mathematical education has nothing to do with the appreciation of either Bach or the 2nd Vienna School...