Homework Help: math and music

Posted by Gray on Friday, November 19, 2010 at 6:21pm.

How would you go about listing all of the integer ratios? I would like to have the integers listed in ascending order by the product of each integer's numerator and the denominator. This is because in music, more "complex" ratios sound more dissonant.

Every list would exclude ratios that can be simplified (2/4, 3/9).

List A1 would include those ratios with values less than or equal to 1, and List B1 would include those ratios greater than or equal to 1.

Lists A2 and B2 would exclude ratios of 1/n and n/1 where n is a composite number. List A3 would exclude ratios with values less than 1/2. List B3 would exclude ratios with values less than 2/1. Lists A4 and B4 would use both exclusions.

I think this is what I'm aiming for: List A1 = {1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 2/3, 1/7, ...} List A2 = {1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 3/2, ...} and so on.

Finally, is there anyone out there who understands how these lists relate to music theory? Thanks!

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