Parapyth - Revision history

Inthar: /* Supporting temperaments */

2026-04-05T09:03:40Z

Supporting temperaments

← Older revision		Revision as of 09:03, 5 April 2026
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	Todo: Talk about Parapyth diachrome		Todo: Talk about Parapyth diachrome
	== Supporting temperaments ==		== Supporting temperaments ==
	[[Rodan]] (Parapyth + [[Slendric]]) is arguably the most important rank-2 temperament that supports Parapyth (besides the gentle-fifth-generated 2.3.7.11.13 temperament Leapfrog, which see [[Gentle tuning]]).		[[Rodan]] (Parapyth + [[Slendric]]) is arguably the most important rank-2 temperament that supports Parapyth (besides the gentle-fifth-generated 2.3.7.11.13 temperament Leapfrog, which see [[Gentle tuning]]). (As an aside, having Rodan also enables [[penslen]] in a Parapyth tuning.)

	== Extensions ==		== Extensions ==

Inthar at 09:02, 5 April 2026

2026-04-05T09:02:03Z

← Older revision		Revision as of 09:02, 5 April 2026
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	'''Parapyth''' is generally viewed as a no-5 2.3.7.11.13 rank-3 regular temperament {{nowrap\|[[17edo\|17]] & [[41edo\|41]] & [[46edo\|46]],}} sometimes called '''Parapythic'''. (In the strict sense, ''parapyth'' is Margo Schulter's rank-3 tuning construct inspired by medieval European and Middle Eastern music theory, where Schulter imposes commas that are to be ''observed'' as well as commas that are to be tempered out.{{citation needed}})		'''Parapyth''' is generally viewed as a no-5 2.3.7.11.13 rank-3 regular temperament {{nowrap\|[[17edo\|17]] & [[41edo\|41]] & [[46edo\|46]],}} sometimes called '''Parapythic'''. (In the strict sense, ''parapyth'' is Margo Schulter's rank-3 tuning construct inspired by medieval European and Middle Eastern music theory, where Schulter imposes commas that are to be ''observed'' as well as commas that are to be tempered out.{{citation needed}})

	== ~~Theory~~ ==		== Structure ==
	Parapyth has two non-period generators: the fifth (which is tuned in the [[gentle region]], i.e. somewhat sharp of just but flatter than 17edo) and the "spacer" 28/27, which is equated to 33/32. This is equivalent to taking the spacer 64/63, which may be equated with 81/80 (as in [[46edo]] and [[87edo]]) or tempered smaller than 81/80 (mapping [[5120/5103]] negatively, as in [[63edo]] and [[80edo]]) assuming prime 5 is added.		Parapyth has two non-period generators: the fifth (which is tuned in the [[gentle region]], i.e. somewhat sharp of just but flatter than 17edo) and the "spacer" 28/27, which is equated to 33/32. This is equivalent to taking the spacer 64/63, which may be equated with 81/80 (as in [[46edo]] and [[87edo]]) or tempered smaller than 81/80 (mapping [[5120/5103]] negatively, as in [[63edo]] and [[80edo]]) assuming prime 5 is added.
	=== Intervals ===		=== Intervals ===
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	(* Cent values in 2.3.7.11.13 CE tuning. The [[104edo]] tuning (~3/2 = 703.846c, ~28/27 = 57.692c) is close.)		(* Cent values in 2.3.7.11.13 CE tuning. The [[104edo]] tuning (~3/2 = 703.846c, ~28/27 = 57.692c) is close.)

			== Scales ==
			Todo: Talk about Parapyth diachrome
	== Supporting temperaments ==		== Supporting temperaments ==
	[[Rodan]] (Parapyth + [[Slendric]]) is arguably the most important rank-2 temperament that supports Parapyth (besides the gentle-fifth-generated 2.3.7.11.13 temperament Leapfrog, which see [[Gentle tuning]]).		[[Rodan]] (Parapyth + [[Slendric]]) is arguably the most important rank-2 temperament that supports Parapyth (besides the gentle-fifth-generated 2.3.7.11.13 temperament Leapfrog, which see [[Gentle tuning]]).

Inthar: /* Theory */

2026-04-05T08:36:44Z

Theory

← Older revision		Revision as of 08:36, 5 April 2026
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	== Theory ==		== Theory ==
	Parapyth has two non-period generators: the fifth (which is tuned in the [[gentle region]], i.e. somewhat sharp of just but flatter than 17edo) and the "spacer" 28/27, which is equated to 33/32. This is equivalent to taking the spacer 64/63, which may be equated with 81/80 (as in [[46edo]] and [[87edo]]) or tempered smaller than 81/80 (as in [[63edo]] and [[80edo]]) assuming prime 5 is added.		Parapyth has two non-period generators: the fifth (which is tuned in the [[gentle region]], i.e. somewhat sharp of just but flatter than 17edo) and the "spacer" 28/27, which is equated to 33/32. This is equivalent to taking the spacer 64/63, which may be equated with 81/80 (as in [[46edo]] and [[87edo]]) or tempered smaller than 81/80 (mapping [[5120/5103]] negatively, as in [[63edo]] and [[80edo]]) assuming prime 5 is added.
	=== Intervals ===		=== Intervals ===
	{\| class="wikitable"		{\| class="wikitable"

Inthar: /* Extensions */

2026-04-05T08:34:38Z

Extensions

← Older revision		Revision as of 08:34, 5 April 2026
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	== Extensions ==		== Extensions ==
	If prime 5 is added to 2.3.7.11.13 Parapyth via [[Aberschismic]] tempering equating 64/63 to 81/80, the resulting 2.3.5.7.11.13 temperament is called Pele (41 & 46 & 58).		If prime 5 is added to 2.3.7.11.13 Parapyth via [[Aberschismic]] tempering equating 64/63 to 81/80, the resulting 2.3.5.7.11.13 temperament is called Pele (41 & 46 & 58). However, note that there is no canonical 5 extension applying broadly to Parapyth, as 17edo lacks a good prime 5.

	If the diatonic augmented fourth is equated to 23/16, the resulting 2.3.7.11.13.23 temperament is called Skidoo (17 & 24 & 46). [[63edo]] is a particularly good Skidoo tuning.		If the diatonic augmented fourth is equated to 23/16, the resulting 2.3.7.11.13.23 temperament is called Skidoo (17 & 24 & 46). [[63edo]] is a particularly good Skidoo tuning.

Inthar: /* Theory */

2026-04-05T08:31:55Z

Theory

← Older revision		Revision as of 08:31, 5 April 2026
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	== Theory ==		== Theory ==
	Parapyth has two non-period generators: the fifth (which is tuned in the [[gentle region]], i.e. somewhat sharp of just but flatter than 17edo) and the "spacer" 28/27, which is equated to 33/32. This is equivalent to taking the spacer 64/63, which may be equated with 81/80 (as in [[46edo]] and [[87edo]]) or ~~tuned to be even~~ smaller than 81/80 (as in [[63edo]] and [[80edo]]) assuming prime 5 is added.		Parapyth has two non-period generators: the fifth (which is tuned in the [[gentle region]], i.e. somewhat sharp of just but flatter than 17edo) and the "spacer" 28/27, which is equated to 33/32. This is equivalent to taking the spacer 64/63, which may be equated with 81/80 (as in [[46edo]] and [[87edo]]) or tempered smaller than 81/80 (as in [[63edo]] and [[80edo]]) assuming prime 5 is added.
	=== Intervals ===		=== Intervals ===
	{\| class="wikitable"		{\| class="wikitable"

Inthar: /* Intervals */

2026-04-05T07:12:50Z

Intervals

← Older revision		Revision as of 07:12, 5 April 2026
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	\|13/7		\|13/7
	\|1128.4		\|1128.4
	\|26/27		\|52/27
	\|-		\|-
	!-6		!-6
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	!0		!0
	\|1143.8		\|1143.8
	\|27/28, 32/33		\|27/14, 64/33
	\|'''0'''		\|'''0'''
	\|'''1/1'''		\|'''1/1'''
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	\|21/11		\|21/11
	\|1176.1		\|1176.1
	\|63/64		\|63/32
	\|-		\|-
	!6		!6

Inthar: /* Intervals */

2026-04-05T07:11:16Z

Intervals

← Older revision		Revision as of 07:11, 5 April 2026
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	\|24/13		\|24/13
	\|1119.9		\|1119.9
	\|21/22		\|21/11
	\|1176.1		\|1176.1
	\|63/64		\|63/64

Inthar: /* Supporting temperaments */

2026-04-05T06:42:51Z

Supporting temperaments

← Older revision		Revision as of 06:42, 5 April 2026
Line 141:		Line 141:

	== Supporting temperaments ==		== Supporting temperaments ==
	~~41 & 46,~~ [[Rodan]] (Parapyth + [[Slendric]]), is arguably the most important rank-2 temperament that supports Parapyth (besides the gentle-fifth-generated 2.3.7.11.13 temperament Leapfrog, which see [[Gentle tuning]]).		[[Rodan]] (Parapyth + [[Slendric]]) is arguably the most important rank-2 temperament that supports Parapyth (besides the gentle-fifth-generated 2.3.7.11.13 temperament Leapfrog, which see [[Gentle tuning]]).

	== Extensions ==		== Extensions ==

Inthar: /* Supporting temperaments */

2026-04-05T06:21:41Z

Supporting temperaments

← Older revision		Revision as of 06:21, 5 April 2026
Line 141:		Line 141:

	== Supporting temperaments ==		== Supporting temperaments ==
	41 & 46, [[Rodan]] (Parapyth + [[Slendric]]), is arguably the most important rank-2 temperament that supports Parapyth (besides the gentle-fifth-generated 2.3.7.11.13 temperament Leapfrog which see [[Gentle tuning]]).		41 & 46, [[Rodan]] (Parapyth + [[Slendric]]), is arguably the most important rank-2 temperament that supports Parapyth (besides the gentle-fifth-generated 2.3.7.11.13 temperament Leapfrog, which see [[Gentle tuning]]).

	== Extensions ==		== Extensions ==

Inthar: /* Supporting temperaments */

2026-04-05T06:21:34Z

Supporting temperaments

← Older revision		Revision as of 06:21, 5 April 2026
Line 141:		Line 141:

	== Supporting temperaments ==		== Supporting temperaments ==
	41 & 46, [[Rodan]] (Parapyth + [[Slendric]]), is arguably the most important rank-2 temperament that supports Parapyth (besides the gentle-fifth-generated 2.3.7.11.13 temperament Leapfrog).		41 & 46, [[Rodan]] (Parapyth + [[Slendric]]), is arguably the most important rank-2 temperament that supports Parapyth (besides the gentle-fifth-generated 2.3.7.11.13 temperament Leapfrog which see [[Gentle tuning]]).

	== Extensions ==		== Extensions ==