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The number of possible musical notes using an n-key instrument 2015-05-04
From Farihin:
Lets say that i have keys, and each key is for notes of a musical instrument, So i wanted to find out the number of notes i can get for a certain number keys, of course in the form of an equation. Notes can use as many keys, it can use 1, or 2, or 3, or even 100.
Notes in real life is not as such, but ignore reality. I tried doing this but i can't seem to find a formula for it. For example, i have 4 keys, say A, B, C, and D. so, for notes that uses one key are 4, which is A, B, C, and D themselves. for notes that uses two keys are 6,
AB, AC, AD, BC, BD and CD.
for notes that uses three keys are 4,
lastly for notes that uses all four keys is 1, ABCD.
So, the total will be 4+6+4+1=15#

The nth term for the first equation is n, the second is [(n^2)-n]/2 the third and the fourth, i don't know but the final answer should be like,
n + [(n^2)-n]/2 + [3rd] + [4th]

Sorry for the long question though...

Answered by Penny Nom.





