Fifive family - Revision history

FloraC: /* Subgroup extensions */

2026-08-27T02:49:30Z

Subgroup extensions

← Older revision		Revision as of 02:49, 27 August 2026
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	Comma list: 325/324, 20000/19773		Comma list: 325/324, 20000/19773

	~~Mapping~~: {{mapping\| 2 2 3 6 \| 0 5 7 6 }}		Subgroup-val mapping: {{mapping\| 2 2 3 6 \| 0 5 7 6 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 170/169, 289/288, 325/324		Comma list: 170/169, 289/288, 325/324

	~~Mapping~~: {{mapping\| 2 2 3 6 7 \| 0 5 7 6 5 }}		Subgroup-val mapping: {{mapping\| 2 2 3 6 7 \| 0 5 7 6 5 }}

	Optimal tunings:		Optimal tunings:

FloraC: + intro to fifive and its add-13 add-17 extension

2026-08-25T04:21:19Z

+ intro to fifive and its add-13 add-17 extension

← Older revision		Revision as of 04:21, 25 August 2026
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	The '''fifive family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[fifive comma]] ({{monzo\|legend=1\| -1 -14 10 }}, [[ratio]]: 9765625/9565938).		The '''fifive family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[fifive comma]] ({{monzo\|legend=1\| -1 -14 10 }}, [[ratio]]: 9765625/9565938).

	The name ''fifive'' was given by [[Petr Pařízek]] in 2011 for it splits the ~~[[3/2\|~~perfect fifth]] in five.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>		== Fifive ==
			The head of this family is fifive, which splits the [[3/2\|perfect fifth]] into five [[27/25]]'s, and [[5/4]] is found as seven generators minus a half-octave period. Its [[ploidacot]] is diploid pentacot, and it is a member of the [[diaschismic–gothmic equivalence continuum]] with equivalence number ''n'' = 5/2.

			The name ''fifive'' was given by [[Petr Pařízek]] in 2011 for it splits the perfect fifth in five.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>

	~~== Fifive ==~~
	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

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	The second comma in the comma list defines which 7-limit family member we are looking at. Crepuscular (26 & 34d) adds [[50/49]]. Fifives (26 & 34) adds [[875/864]]. Both use the same generators as fifive. The weak extension fourfives (60 & 68) adds [[245/243]]. All are considered below.		The second comma in the comma list defines which 7-limit family member we are looking at. Crepuscular (26 & 34d) adds [[50/49]]. Fifives (26 & 34) adds [[875/864]]. Both use the same generators as fifive. The weak extension fourfives (60 & 68) adds [[245/243]]. All are considered below.

	The fifive family boasts a very remarkable extension to the 2.3.5.13 subgroup, which has further extensions with higher primes. These are listed at the bottom of this page, in [[#Subgroup extensions]].		The fifive family boasts a very remarkable extension to the [[2.3.5.13 subgroup]], which has further extensions with higher primes. These are listed at the bottom of this page, in [[#Subgroup extensions]].

	== Crepuscular ==		== Crepuscular ==
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	== Subgroup extensions ==		== Subgroup extensions ==
	=== Fifive (2.3.5.13) ===		=== Fifive (2.3.5.13) ===
			As the [[~]][[27/25]] generator of fifive is so close to [[13/12]], one may temper out their difference, [[325/324]], to obtain this extension in the 2.3.5.13 subgroup. It is also not unreasonable to equate both [[17/12]] and [[24/17]] with the semi-octave period given its overall level of precision, tempering out [[289/288]] and leading to a 2.3.5.13.17-subgroup temperament.

	Subgroup: 2.3.5.13		Subgroup: 2.3.5.13

FloraC: Re-organize

2026-08-25T04:05:08Z

Re-organize

@@ Line 3: / Line 3: @@
 The name ''fifive'' was given by [[Petr Pařízek]] in 2011 for it splits the [[3/2|perfect fifth]] in five.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>
 == Fifive ==
@@ Line 24: / Line 22: @@
 [[Badness]] (Sintel): 4.83
-=== 2.3.5.13 subgroup ===
+=== Overview to extensions ===
-Subgroup: 2.3.5.13
+The second comma in the comma list defines which 7-limit family member we are looking at. Crepuscular (26 & 34d) adds [[50/49]]. Fifives (26 & 34) adds [[875/864]]. Both use the same generators as fifive. The weak extension fourfives (60 & 68) adds [[245/243]]. All are considered below.
-{{Optimal ET sequence|legend=0| 8, 18bcfg, 26, 34, 94, 128 }}
+The fifive family boasts a very remarkable extension to the 2.3.5.13 subgroup, which has further extensions with higher primes. These are listed at the bottom of this page, in [[#Subgroup extensions]].
 == Crepuscular ==
@@ Line 276: / Line 249: @@
 Badness (Sintel): 1.26
 == References ==

FloraC: Oops

2026-08-25T03:59:49Z

Oops

← Older revision		Revision as of 03:59, 25 August 2026
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	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~17/12 = 599.9773{{c}}, ~13/12 = 140.6075{{c}}		* WE: ~17/12 = 599.9773{{c}}, ~13/12 = 140.6075{{c}}
	* CWE: ~17/12 = 600.0000{{c}}, ~13/12 = 140.6057{{c}}		* CWE: ~17/12 = 600.0000{{c}}, ~13/12 = 140.6057{{c}}

FloraC: Switch to Sintel's badness, WE & CWE tunings

2026-08-25T03:48:20Z

Switch to Sintel's badness, WE & CWE tunings

Show changes

FloraC: Units & misc. cleanup

2026-08-25T03:29:47Z

Units & misc. cleanup

Show changes

FloraC: Notes -> references; recategorize

2026-08-14T11:57:47Z

Notes -> references; recategorize

← Older revision		Revision as of 11:57, 14 August 2026
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	Badness: 0.024796		Badness: 0.024796

	== ~~Notes~~ ==		== References ==

	~~[[Category:Temperament families]]~~
	[[Category:Fifive family\| ]] <!-- main article -->		[[Category:Fifive family\| ]] <!-- main article -->
	[[Category:Fifive\| ]] <!-- key article -->		[[Category:Fifive\| ]] <!-- key article -->
	[[Category:~~Rank~~ 2]]		[[Category:Temperament families]]
			[[Category:Catalogs of rank-2 temperaments]]

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

2025-11-27T12:24:56Z

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

← Older revision		Revision as of 12:24, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Fifive family\| ]] <!-- main article -->		[[Category:Fifive family\| ]] <!-- main article -->
	[[Category:Fifive\| ]] <!-- key article -->		[[Category:Fifive\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

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

2025-06-24T00:27:18Z

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

← Older revision		Revision as of 00:27, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Fifive family\| ]] <!-- main article -->		[[Category:Fifive family\| ]] <!-- main article -->
	[[Category:Fifive\| ]] <!-- key article -->		[[Category:Fifive\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 05:20, 12 June 2025

2025-06-12T05:20:26Z

← Older revision		Revision as of 05:20, 12 June 2025
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	{{Mapping\|legend=1\| 2 2 3 4 \| 0 5 7 7 }}		{{Mapping\|legend=1\| 2 2 3 4 \| 0 5 7 7 }}

	~~{{Multival\|legend=1\| 10 14 14 -1 -6 -7 }}~~

	[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349		[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349