Quintaleap family - Revision history

Hkm: /* Quintupole */

2026-06-16T17:27:47Z

Quintupole

← Older revision		Revision as of 17:27, 16 June 2026
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	{{Main\| Quintupole }}		{{Main\| Quintupole }}

	The ''quintupole'' temperament tempers out the octagar comma (4000/3969) and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth\|polypyth]] fourth (~4/3, about 495.8 cents)~~. [[User:Xenllium\|Xenllium]] proposes the pronunciation of the word "quintupole" as /'kwɪntʊpəʊl/ or /'kwɪntʊpoʊl/, like as "quin-to-pole"~~.		The ''quintupole'' temperament tempers out the octagar comma (4000/3969) and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth\|polypyth]] fourth (~4/3, about 495.8 cents).

	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

Hkm: /* Quintupole */

2026-06-16T17:27:29Z

Quintupole

← Older revision		Revision as of 17:27, 16 June 2026
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	{{Main\| Quintupole }}		{{Main\| Quintupole }}

	The ''quintupole'' temperament tempers out the octagar comma (4000/3969) and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth\|polypyth]] fourth (~4/3, about 495.8 cents). [[User:Xenllium\|Xenllium]] proposes the pronunciation of the word "quintupole" as /'kwɪntʊpəʊl/ or /'kwɪntʊpoʊl/, like as "quin-to-pole". ~~''Not to be confused with [[#Quintapole\|quint<u>'''a'''</u>pole]] temperament (12&85).''~~		The ''quintupole'' temperament tempers out the octagar comma (4000/3969) and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth\|polypyth]] fourth (~4/3, about 495.8 cents). [[User:Xenllium\|Xenllium]] proposes the pronunciation of the word "quintupole" as /'kwɪntʊpəʊl/ or /'kwɪntʊpoʊl/, like as "quin-to-pole".

	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

Hkm: /* Quintapole */

2026-06-16T02:26:18Z

Quintapole

Show changes

Hkm: /* Subgroup temperament */

2026-06-09T01:15:10Z

Subgroup temperament

← Older revision		Revision as of 01:15, 9 June 2026
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	[[Badness]] (Sintel): 10.427		[[Badness]] (Sintel): 10.427

	~~=== Subgroup temperament ===~~

	The quintaleap temperament works well for the 2.3.5.17.19 subgroup, tempering out 256/255 (equating 16/15 with 17/16), 361/360 (equating 19/18 with 20/19), and 4624/4617. An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and sixteen 18/17s with [[5/2]].		The quintaleap temperament works well for the 2.3.5.17.19 subgroup, tempering out 256/255 (equating 16/15 with 17/16), 361/360 (equating 19/18 with 20/19), and 4624/4617. An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and sixteen 18/17s with [[5/2]].

Xenllium at 23:50, 23 January 2026

2026-01-23T23:50:09Z

Show changes

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:19:37Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:19, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Quintaleap family\| ]] <!-- main article -->		[[Category:Quintaleap family\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Fredg999: Update links

2025-08-07T19:05:08Z

Update links

← Older revision		Revision as of 19:05, 7 August 2025
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	==== Galileic ====		==== Galileic ====
	The name ''galileic'' comes from "~~[[wikipedia:Vincenzo Galilei~~\|Vincenzo Galilei]]", because this temperament is strongly related to [[~~18/17 equal-step tuning\|~~Galilei tuning]].		The name ''galileic'' comes from "{{w\|Vincenzo Galilei}}", because this temperament is strongly related to [[Galilei's tuning]].

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

Lériendil: Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

2025-06-24T00:38:53Z

Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:38, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Quintaleap family\| ]] <!-- main article -->		[[Category:Quintaleap family\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 04:57, 12 June 2025

2025-06-12T04:57:42Z

← Older revision		Revision as of 04:57, 12 June 2025
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	[[Mapping]]: [{{val\| 1 2 1 0 }}, {{val\| 0 -5 16 34 }}]		[[Mapping]]: [{{val\| 1 2 1 0 }}, {{val\| 0 -5 16 34 }}]

	~~{{Multival\|legend=1\| 5 -16 -34 -37 -68 -34 }}~~

	[[POTE generator]]: ~135/128 = 99.175		[[POTE generator]]: ~135/128 = 99.175
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	[[Mapping]]: [{{val\| 1 2 1 1 }}, {{val\| 0 -5 16 22 }}]		[[Mapping]]: [{{val\| 1 2 1 1 }}, {{val\| 0 -5 16 22 }}]

	~~{{Multival\|legend=1\| 5 -16 -22 -37 -49 -6 }}~~

	[[POTE generator]]: ~21/20 = 98.994		[[POTE generator]]: ~21/20 = 98.994
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	[[Mapping]]: [{{val\| 1 2 1 -1 }}, {{val\| 0 -5 16 46 }}]		[[Mapping]]: [{{val\| 1 2 1 -1 }}, {{val\| 0 -5 16 46 }}]

	~~{{Multival\|legend=1\| 5 -16 -46 -37 -87 -62 }}~~

	[[POTE generator]]: ~135/128 = 99.345		[[POTE generator]]: ~135/128 = 99.345
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	[[Mapping]]: [{{val\|1 2 1 5}}, {{val\|0 -10 32 -53}}]		[[Mapping]]: [{{val\|1 2 1 5}}, {{val\|0 -10 32 -53}}]

	~~{{Multival\|legend=1\| 10 -32 53 -74 56 213 }}~~

	[[POTE generator]]: ~36/35 = 49.621		[[POTE generator]]: ~36/35 = 49.621

Lériendil: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:47:51Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:47, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''quintaleap family''' tempers out {{monzo\| 37 -16 -5 }}, equating a stack of two [[Pythagorean comma]]s with a stack of five [[schisma]]s, making it a member of the [[schismic–Pythagorean equivalence continuum]]. It is also the temperament where [[4/3]] is identified by a stack of five [[135/128]]'s.		The '''quintaleap family''' tempers out {{monzo\| 37 -16 -5 }}, equating a stack of two [[Pythagorean comma]]s with a stack of five [[schisma]]s, making it a member of the [[schismic–Pythagorean equivalence continuum]]. It is also the temperament where [[4/3]] is identified by a stack of five [[135/128]]'s.

Quintaleap family - Revision history

Hkm: /* Quintupole */

Hkm: /* Quintupole */

Hkm: /* Quintapole */

Hkm: /* Subgroup temperament */

Xenllium at 23:50, 23 January 2026

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

Fredg999: Update links

Lériendil: Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

VectorGraphics at 04:57, 12 June 2025

Lériendil: Text replacement - "{{Technical data page}}" to "{{Technical data page}}"

Lériendil: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"