Quote:
Originally Posted by USS
I am a student of math and music, so this was a subject of some masterclass lessons at a university.

I already have my mathematics degree (within which I studied combinatorics) so don't come to me with a holierthanthou attitude, sunshine.
Quite simply, you're making the error that most pure mathematicians make; you are not applying the mathematics to the
real world. Analyse the scenario and the real world in this case is the twelve tones that comprise the basis of western music. This set has a
finite number of arrangements, as already shown.
To show this, try and play more than twelve different notes on your guitar. You can't do it. This is the practical world we need to apply the mathematics to, not the theoretical world which you describe.
Quote:
Originally Posted by USS
For once more: how can I count an infinite collection, except for making a calculation?

I'll do it for you:
C
C#
D
D#
E
F
F#
G
G#
A
A#
B
I think you'll find there are
twelve notes to be arranged there.
On a final note, my calculations are not theory they are mathematical
fact; there is no scope for debate on the number of arrangements of a set with a given number of elements.