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I know this is not to the usual caliber of your questions but I can't figure out this simple question:

A Cmaj is made out of 3 notes, C E G. If those notes can appear in 9 octaves, how many ways of making a Cmaj are there?

Bear in mind that you must select exactly 1 of each note in each appearance.

UPDATE: It is $9^3$ you can treat the problem as counting all possible 3 bit base-9 numbers

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So you mean taking in account inversions as well? Like E G C? –  Raskolnikov May 1 '11 at 10:55
    
no, interesting point though. C4 E4 G4 is the same as G4 C4 E4 so order has no importance –  Chimoo May 1 '11 at 10:57
    
Actually, the inversion of C4 E4 G4 is G4 C4 E5. But I guess that makes your answer $9^3$ correct. Why don't you put it as an answer yourself. –  Raskolnikov May 1 '11 at 11:23
    
Simple modification of the above problem: If you play piano, you might add some constraint, like only use notes from two successive octaves. (If your hand is big enough to play C1 and G2 at the same time. Probably C1-E2 range would be more realistic.) –  Martin Sleziak May 1 '11 at 11:37
    
A simple modification but a much more difficult problem...any ideas? –  Chimoo May 1 '11 at 11:43

1 Answer 1

up vote 1 down vote accepted

It is $9^3$ you can treat the problem as counting all possible 3 bit base-9 numbers

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