W: Music is Finite!!
me: Hmmmm… Is that a question or a Statement
W: There are just 12 keys and Music is just a permutation of those keys!!
L(a medical student): So you’re telling that after a certain number of melodies or songs they’ll be repeated
W: exactly my point!! My whole gang at work got annoyed when i told them that there are only finite number of songs or melodies that people can produce.
This was part of an interesting conversation of which i only made the opening statement, The rest of the canversation is
extremely stupid where W goes on to explain the following three points to L:
One, Music is made up of notes which are finite. Two, These finite notes when combined together produce sounds which comprise the music we hear.
Three, since there can be only a finite set of combinations of these notes there can be only a finite set of melodies that one can produce.
I was not involved in the rest of the conversation because i actually fell for it. But yesterday, when i was travelling back home from my workplace
(due to the excess delay in the bus) this thought came to me.
There will be finite set of notes that can be played in a finite set of time. ie., if i were playing a song lasting 120 discrete seconds i can play only a finite set of notes/Chords and this is true.
what i mean is i’d be allowed to play only on discerte instants of time lasting 120 seconds. If i played a note at the nth second it would be accepted but a note between n and (n+1)th second would be classified noise and and attributed to the n+1th instant(the process is called quantization)
But time in the realworld is continuous and not discrete. So within the n and n+1th second there are infinite values that time can take. So within these infinite instants of time there can be infinite change of notes.
The previous case was for a finite length of time but time is infinte in length too(theoretically speaking) so you can play a song for an infinite duration even if you consider discrete instants of time and you’ll have infinite number of permutations for a finite set of tones by virtue of time being infinite.
