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)

Cmloegcmluin's clarification questions

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.

Okay, thanks. If there's a place where that terminology is explained, that might be great to link to (people like me who never formally studied music and are unfamiliar with those abbreviations might benefit.

And re: N, what I meant was more like: what does it mean? Does the letter N stand for something? Or does that value represent something I would be familiar with? Or is it just some abstract number to work with? It's probably obvious to some readers (esp. given the way you matter-of-factly present it) but I have no idea myself. Thanks for indulging my questions. Hopefully I can at least help improve the accessibility of the ideas for others. --Cmloegcmluin (talk) 23:04, 15 April 2021 (UTC)

Explanation of M2, m7, etc.: https://en.wikipedia.org/wiki/Interval_(music)#Main_intervals. Knowing these terms really helps with chord names like CM6 and Dm7.

N doesn't stand for anything. It's like x or y in algebra. But N isn't really important. The important thing is the pergen. I only wrote "Both fractions are always of the form 1/N" because I wanted to make clear that there is no "two-thirds-of-a-fifth" pergen. IOW the fraction always has a numerator of 1. If N still confuses you, I suggest you just ignore it. --TallKite (talk) 05:39, 16 April 2021 (UTC)