Talk:Kite's thoughts on pergens

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Note to self: "Mids never appear in the perchain." Check that expanding the definition of mid intervals to include the 4th and 5th hasn't changed this. TallKite (talk) 04:46, 30 January 2020 (UTC)

I came across this page yesterday because Jason suggested it as a better approach to the problem TAMNAMS is trying to solve. But I can't get very far before I'm lost. "Both fractions are always of the form 1/N, thus the octave and/or the 3-limit interval is split into N parts. The interval which is split into multiple generators is the multigen. The 3-limit multigen is referred to not by its ratio but by its conventional name, e.g. P5, M6, m7, etc." What is N? And what are these conventional names P5, M6, m7? --Cmloegcmluin (talk) 16:57, 15 April 2021 (UTC)

In (P8, P5/3), N is 3. In (P8/4, P5), N is 4. In (P8/2, M2/4), well, I didn't state that very well, I guess there are two N's, which may or may not be equal. Later I adopt a notation (P8/m, M/n), where M stands for multigen. So for (P8/2, M2/4) we have m=2, n=4.

P stands for perfect, M for major (or multigen if not followed by a number) and m for minor. It's a 3-limit interval, so M2 = major 2nd = 9/8, A4 = aug 4th = 729/512, etc.