Paul Davis<p...@linuxaudiosystems.com>:
this might be how users of ableton live think about making music, and more 
generally, users of computer software aimed at pattern-based music 
composition/creation.

but i would submit that if you offered this description of making music to 
musicians who play instruments or sing, they would find it unrecognizable.
Well... I guess one important element in the tiling/sequencing issue (forgive me for my lack of the exact mathematical knowledge) is time-domain. Much of Music and it's drama, versus for instance painting, is time: suspense, arousal/relaxation etc. have to do with time. So if you take a piece which are the 'tiles'? Measures? themes of the 'sonata' form? Simply recurring elements? So if on the one hand many academics disregard 'quality' composition as a mere juxtaposition of cool sounding melodies or progressions, on the other hand it's true that the time-domain calls for some sort of tiling in the sense that something comes after something
Mathematics is fundamental to music -- everything from the
relationship of notes to frequency, to what people consider musical,
or rhythmic... has to do with math, group theory, etc.

This is putting the cart before the horse. People were making music
long before there was any remotest concept of mathematics. Many of us
still work on the basis of just noodling about and 'ooo, that sounds
nice' without the slightest thought of relationships etc.
Ok but the fact that people used mathematical relationships without being fully aware of them (e.g. I IV V I progression) doesn't mean the relationships don't exist or aren't important. The whole 'western' tonal system is heavily dependent on this 'maths' we like it or not :)
The only time I ever think about chords, progressions, is when I've
more-or-less finished a composition and/or want to collaborate with
someone else.

When I was a child, I put together a construction of timber and waxed
string. To this day I don't have the faintest idea what the string
tunings were. I just know it produced some lovely sound combinations.

Group/orchestral instrument&  synth makers are no doubt deeply involved
in the mathematics of their designs, but the players don't necessarily
have any concept of this.

A friend of mine is a member of a local choral group. He can't read
music, just uses the dots as a vague reminder of when bits go up, down
speed up or slow down. He seems quite happy like that.

There may be incredible mathematical 'truths' in music, but I think it
will be a very sad day when people concentrate on these rather than
just having fun.
Being (as I said) a musician and not a mathematician I have to say that I don't like much this kind of maths=boring=kills the fun etc. When I started studying electronic music and also some of the physics and maths behind it I was clearly fascinated to learn some of the things behind music, and I still have great fun making it.. but of course that's me :)

Lorenzo
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