Talk:Kite's thoughts on pergens - Revision history

TallKite: /* Pergens for no-3 temperaments? */

2026-05-14T10:26:50Z

Pergens for no-3 temperaments?

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	==Pergens for no-3 temperaments?==		==Pergens for no-3 temperaments?==
	Hey TallKite, I was just wondering if you could explain how to use pergens to describe no-3 temperaments. Also, how do I determine tunings such as 3/7-comma mintaka? Thanks! [[User:MisterShafXen\|MisterShafXen]] ([[User talk:MisterShafXen\|talk]]) 11:57, 10 May 2026 (UTC)		Hey TallKite, I was just wondering if you could explain how to use pergens to describe no-3 temperaments. Also, how do I determine tunings such as 3/7-comma mintaka? Thanks! [[User:MisterShafXen\|MisterShafXen]] ([[User talk:MisterShafXen\|talk]]) 11:57, 10 May 2026 (UTC)
			: Glad to help! For no-3 temps, see https://en.xen.wiki/w/Kite%27s_thoughts_on_pergens#Notating_non-8ve_and_no-5ths_pergens. Analogous to imperfect 2.3 pergens like (P8/2, M2/4), there are imperfect 2.5 pergens that would use A5, defined as 25/16. And likewise d4, A7, etc.
			: For mintaka, the period is P12 = 3/1 and the generator is 11/7. The 3.7.11 mapping is [(1 3 3)(0 -3 -2)]. Thus prime 7 equals 3 periods minus 3 generators. Thus the multigen is 27/7. The pergen is #9 in the 3.7 column (P12, cM7/3), where cM7 means P12 = 3/1 plus a M3 = 9/7.
			: 3/7-comma mintaka means the multigen 27/7 is sharpened or flattened by 3/7 of a comma, 4.473¢. The mintaka comma has 7 in the denominator, so tempering it out implies sharpening prime 7. Thus prime 7 is sharpened by 4.473¢, and the multigen 27/7 is flattened by 4.473¢. (We're assuming a just prime 3.)
			: If you're into temps that don't use 2 and/or 3, you might find pergen squares useful, since they apply to all JI subgroups.
			: --[[User:TallKite\|TallKite]] ([[User talk:TallKite\|talk]]) 10:26, 14 May 2026 (UTC)

MisterShafXen at 11:57, 10 May 2026

2026-05-10T11:57:39Z

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	== Updated terminology ==		== Updated terminology ==
	Ups and downs are collectively called arrows. Lifts and drops are collectively called slants. Arrows and slants are collectively called inflections. Thus a better term for "bare" enharmonic is uninflected enharmonic. The article has been edited to correct this. Also, the term "E" for enharmonic interval has been replaced with EI. --[[User:TallKite\|TallKite]] ([[User talk:TallKite\|talk]]) 02:19, 17 December 2023 (UTC)		Ups and downs are collectively called arrows. Lifts and drops are collectively called slants. Arrows and slants are collectively called inflections. Thus a better term for "bare" enharmonic is uninflected enharmonic. The article has been edited to correct this. Also, the term "E" for enharmonic interval has been replaced with EI. --[[User:TallKite\|TallKite]] ([[User talk:TallKite\|talk]]) 02:19, 17 December 2023 (UTC)

			==Pergens for no-3 temperaments?==
			Hey TallKite, I was just wondering if you could explain how to use pergens to describe no-3 temperaments. Also, how do I determine tunings such as 3/7-comma mintaka? Thanks! [[User:MisterShafXen\|MisterShafXen]] ([[User talk:MisterShafXen\|talk]]) 11:57, 10 May 2026 (UTC)

TallKite: TallKite moved page Talk:Pergen to Talk:Kite's thoughts on pergens: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me.

2025-08-20T01:20:44Z

TallKite moved page Talk:Pergen to Talk:Kite's thoughts on pergens: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me.

← Older revision	Revision as of 01:20, 20 August 2025
(No difference)

TallKite: updated terminology explained (bare and EI)

2023-12-17T02:19:17Z

updated terminology explained (bare and EI)

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			== Updated terminology ==
			Ups and downs are collectively called arrows. Lifts and drops are collectively called slants. Arrows and slants are collectively called inflections. Thus a better term for "bare" enharmonic is uninflected enharmonic. The article has been edited to correct this. Also, the term "E" for enharmonic interval has been replaced with EI. --[[User:TallKite\|TallKite]] ([[User talk:TallKite\|talk]]) 02:19, 17 December 2023 (UTC)

TallKite: Wrote down some insights on using pergens to find canonical mappings

2022-02-01T07:12:24Z

Wrote down some insights on using pergens to find canonical mappings

Show changes

TallKite at 05:39, 16 April 2021

2021-04-16T05:39:56Z

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	:: 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. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 23:04, 15 April 2021 (UTC)		:: 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. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk: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. --[[User:TallKite\|TallKite]] ([[User talk:TallKite\|talk]]) 05:39, 16 April 2021 (UTC)

Cmloegcmluin at 23:04, 15 April 2021

2021-04-15T23:04:11Z

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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. [[User:TallKite\|TallKite]] ([[User talk:TallKite\|talk]]) 04:46, 30 January 2020 (UTC)		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. [[User:TallKite\|TallKite]] ([[User talk: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? --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 16:57, 15 April 2021 (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? --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 16:57, 15 April 2021 (UTC)
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	: 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.		: 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. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 23:04, 15 April 2021 (UTC)

TallKite at 22:24, 15 April 2021

2021-04-15T22:24:17Z

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	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? --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 16:57, 15 April 2021 (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? --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk: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.

Cmloegcmluin at 16:57, 15 April 2021

2021-04-15T16:57:52Z

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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. [[User:TallKite\|TallKite]] ([[User talk:TallKite\|talk]]) 04:46, 30 January 2020 (UTC)		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. [[User:TallKite\|TallKite]] ([[User talk: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? --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 16:57, 15 April 2021 (UTC)

TallKite at 04:46, 30 January 2020

2020-01-30T04:46:33Z

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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. [[User:TallKite\|TallKite]] ([[User talk:TallKite\|talk]]) 04:46, 30 January 2020 (UTC)