On Sun, 1 Oct 2000 10:29:07 +0100, "David Webber"
<dave at musical.demon.co.uk> wrote:
>> I find it interesting to see that a discussion of music and IQ can
>> turn into a discussion about tuning....
>>The route is (mathematically) clear. Most of us start to learn music based
>on 12 tone equal temperament. Most people never realise that this is
>different from harmonic tuning. Those of us that do, fairly naturally then
>start to assume that there is something special which uniquely defines 12
>tones, and those with a mathematical bent then naturally assume that there
>must be a mathematical proof that 12 is somehow unique. It comes as a shock
>to find that there isn't.
>>In fact I'm still shocked by it. All that music with amazingly beautiful
>mathematical structure (forgetting for the moment - but only for the
>moment - what it sounds like) is based on a crude approximation which is
>permitted only by the inaccuracy of our ears and which is encouraged by the
>rather small number of fingers we have to play a musical instrument. The
>whole of western music is an amazingly complex and weighty structure built
>on foundations of sand - and yet it stands up.
>>Anyway once you have established all that, you find there are vaious weirdos
>around, the existence of whom you never hitherto perceived, who either
>insist on playing old music with old tunings (shock horror!) or start making
>new music with 19, 31, or 53 notes in an octave.
>>So from music and IQ we go to music and mathematics, and from there to the
>lack of mathematical precision an the idea that there is no unique tuning.
>And all the underlying mathematics does not close the system but leaves it
>open for endless arguments - which have to be settled on a basis of artistic
>judgement (another shock!). <g>.
David - all of your comments have to do with the technicalities of
keyboard tuning. While that may be a very interesting subject, it is
not the primal expression of musical IQ. For starters, singers and
violinists generally have no use for 12TET and its calculations unless
they're forced by some piano accompanying them. Secondly, don't forget
that there is an amazing amount of musical cultures that have nothing
like our concept of fixed intonation. Third, no-one singing a fifth is
calculating frequencies.
There are questions that I find more interesting, or basic, to adress
in comparing musical and mathematical thought. For instance, when I am
thinking about the relationships between form and the possibilities of
transforming materials, I generally think in a way that feels similar
to some thinking I did when still into maths. For example, the basic
material and its potential transformations often feel to me to set up
a musical space with certain 'topological' properties: I think in
terms of dimension, of coherence, of 'circularities' in the shape of
the set of musical transformations of material. Group theory can
provide strong analogies as well. And these shapes and spaces then
correspond to shapes and spatial properties of the development of the
music 'in-time' (to use a word coined by Xenakis).
Do mind, I am not making claims for strict mathematicality of musical
form processes (you can't 'prove' form), it's rather I sense a very
eneral type of connection, a visualizing of abstract structure.
--
Samuel
A prelude by Johann Sebastian Bach performed by the guitarist, Lord Baden Powell
- Chr. J. van Geel