Vulture family - Revision history

Overthink: /* Overview to extensions */ grammar

2026-05-24T17:57:37Z

Overview to extensions: grammar

← Older revision		Revision as of 17:57, 24 May 2026
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	=== Overview to extensions ===		=== Overview to extensions ===
	Temperaments discussed elsewhere include ~~and~~ [[Buzzardsmic clan #Buzzard\|buzzard]]. Considered below are septimal vulture, terture, condor, eagle, and turkey.		Temperaments discussed elsewhere include [[Buzzardsmic clan #Buzzard\|buzzard]]. Considered below are septimal vulture, terture, condor, eagle, and turkey.

	== Septimal vulture ==		== Septimal vulture ==

FloraC: Move terture here

2026-04-24T13:59:58Z

Move terture here

@@ Line 7: / Line 7: @@
 {{Technical data page}}
 The '''vulture family''' of [[temperament]]s [[tempering out|tempers out]] the [[vulture comma]] ({{monzo|legend=1| 24 -21 4 }}, [[ratio]]: 10 485 760 000 / 10 460 353 203), a small [[5-limit]] comma of 4.2 [[cent]]s that is the amount by which a stack of four [[syntonic comma]]s falls short of the [[256/243]] Pythagorean limma. As their defining feature, vulture temperaments split the interval [[3/1]] into four segments (identified in the 5-limit as [[320/243]]).
 == Vulture ==
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 {{Mapping|legend=1| 1 0 -6 | 0 4 21 }}
 : mapping generators: ~2, ~320/243
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 [[Badness]] (Sintel): 0.972
 == Septimal vulture ==
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 Badness (Sintel): 1.47
 == Condor ==

FloraC: Interpretation of generator

2026-04-23T06:36:57Z

Interpretation of generator

← Older revision		Revision as of 06:36, 23 April 2026
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	{{~~interwiki~~		{{Interwiki
			\| en = Vulture family
	\| de = Vulture		\| de = Vulture
	~~\| en = Vulture_family~~
	\| es =		\| es =
	\| ja =		\| ja =
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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1199.9695{{c}}, ~~~320~~/~~243~~ = 475.5451{{c}}		* WE: ~2 = 1199.9695{{c}}, ~154/117 = 475.5451{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~~~320~~/~~243~~ = 475.5571{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~154/117 = 475.5571{{c}}

	{{Optimal ET sequence\|legend=0\| 53, 217, 270 }}		{{Optimal ET sequence\|legend=0\| 53, 217, 270 }}

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

2025-11-27T12:17:31Z

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

← Older revision		Revision as of 12:17, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Vulture family\| ]] <!-- main article		[[Category:Vulture family\| ]] <!-- main article
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: + intro to each entry

2025-10-28T15:00:39Z

+ intro to each entry

← Older revision		Revision as of 15:00, 28 October 2025
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	== Septimal vulture ==		== Septimal vulture ==
	Septimal vulture can be described as the {{nowrap\| 53 & 270 }} microtemperament, tempering out the [[ragisma]], 4375/4374 and the [[garischisma]], 33554432/33480783 ({{monzo\| 25 -14 0 -1 }}) aside from the vulture comma. [[270edo]] is ~~a good~~ tuning for this temperament, with generator 107\270. The harmonic 7 is found at -14 fifths or {{nowrap\| (-14) × 4 {{=}} -56 }} generator steps, so ~~that~~ the smallest [[mos scale]] that includes it is the 58-note one, though for larger scope of harmony, you could try the 111- or 164-note one. For a much simpler mapping of 7 at the cost of higher error, you could try [[Buzzardsmic clan #Septimal buzzard\|buzzard]].		Septimal vulture can be described as the {{nowrap\| 53 & 270 }} microtemperament, tempering out the [[ragisma]], 4375/4374 and the [[garischisma]], 33554432/33480783 ({{monzo\| 25 -14 0 -1 }}) aside from the vulture comma. [[270edo]] is an excellent tuning for this temperament, with generator 107\270. Other compatible tunings include [[217edo]] and [[323edo]]. The harmonic 7 is found at -14 fifths or {{nowrap\| (-14) × 4 {{=}} -56 }} generator steps, so the smallest [[mos scale]] that includes it is the 58-note one, though for larger scope of harmony, you could try the 111- or 164-note one. For a much simpler mapping of 7 at the cost of higher error, you could try [[Buzzardsmic clan #Septimal buzzard\|buzzard]].

	It can be extended to the 11-limit by identifying a stack of four [[5/4]]'s as [[11/9]], tempering out [[5632/5625]], and to the 13-limit by identifying the hemitwelfth as [[26/15]], tempering out [[676/675]]. Furthermore, the generator of vulture is very close to [[25/19]]; a stack of three generator steps octave-reduced thus represents its fifth complement, [[57/50]]. This corresponds to tempering out [[1216/1215]] with the effect of equating the schisma with [[513/512]] and [[361/360]] in addition to many 11- and 13-limit commas. 270edo remains an excellent tuning in all cases.		It can be extended to the 11-limit by identifying a stack of four [[5/4]]'s as [[11/9]], tempering out [[5632/5625]], and to the 13-limit by identifying the hemitwelfth as [[26/15]], tempering out [[676/675]]. Furthermore, the generator of vulture is very close to [[25/19]]; a stack of three generator steps octave-reduced thus represents its fifth complement, [[57/50]]. This corresponds to tempering out [[1216/1215]] with the effect of equating the schisma with [[513/512]] and [[361/360]] in addition to many 11- and 13-limit commas. 270edo remains an excellent tuning in all cases.
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	== Condor ==		== Condor ==
			Condor tempers out [[10976/10935]] and may be described as the {{nowrap\| 58 & 159 }} temperament. The generator represents the [[112/81\|septimal diminished fifth (112/81)]], and three minus an octave make vulture's generator of ~320/243. The ploidacot for this temperament is epsilon-dodecacot. [[217edo]] is an excellent tuning for this temperament.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

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	== Eagle ==		== Eagle ==
			Eagle tempers out [[2401/2400]] and may be described as the {{nowrap\| 58 & 270 }} temperament. It has a semi-octave period and a generator of ~28/27, four of which make a hemifourth which may be identified with 15/13, and two of those make a perfect fourth; its ploidacot thus is diploid wau-octacot. Compatible tunings include [[212edo]], [[270edo]], and [[328edo]].

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

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	== Turkey ==		== Turkey ==
			Named by [[Xenllium]] in 2021, turkey may be described as the {{nowrap\| 212 & 217 }} temperament. It is generated by a fifth sharp of just, close to 3\5 but on the flat side thereof, which can be interpreted as [[50/33]] in the 11-limit. Sixteen generators minus nine octaves make a perfect fifth; its ploidacot is thus theta-16-cot. [[429edo]] may be recommended as a tuning.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: - CTE & POTE tunings

2025-10-28T14:18:11Z

- CTE & POTE tunings

← Older revision		Revision as of 14:18, 28 October 2025
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5396{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5396{{c}}
	: error map: {{val\| 0.000 +0.203 +0.018 }}		: error map: {{val\| 0.000 +0.203 +0.018 }}
	~~<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5351{{c}}~~
	~~: [[error map]]: {{val\| 0.0000 +0.1855 -0.0758 }}~~
	* [[POTE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5426{{c}}
	~~: error map: {{val\| 0.0000 +0.2154 +0.0811 }} -->~~

	{{Optimal ET sequence\|legend=1\| 53, 164, 217, 270, 323, 2531, 2854b, 3177b, …, 4469b }}		{{Optimal ET sequence\|legend=1\| 53, 164, 217, 270, 323, 2531, 2854b, 3177b, …, 4469b }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5515{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5515{{c}}
	: error map: {{val\| 0.000 +0.251 +0.267 +0.292 }}		: error map: {{val\| 0.000 +0.251 +0.267 +0.292 }}
	~~<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5528{{c}}~~
	~~: [[error map]]: {{val\| 0.0000 +0.2561 +0.2945 +0.2188 }}~~
	* [[POTE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5511{{c}}
	~~: error map: {{val\| 0.0000 +0.2495 +0.2601 +0.3106 }} -->~~

	{{Optimal ET sequence\|legend=1\| 53, 164, 217, 270, 593, 863, 1133, 1996d }}		{{Optimal ET sequence\|legend=1\| 53, 164, 217, 270, 593, 863, 1133, 1996d }}
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	* WE: ~2 = 1199.9392{{c}}, ~320/243 = 475.5326{{c}}		* WE: ~2 = 1199.9392{{c}}, ~320/243 = 475.5326{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5655{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5655{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5558{{c}}~~
	* POTE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5567{{c}} -->

	{{Optimal ET sequence\|legend=0\| 53, 217, 270, 2107c, 2377bc }}		{{Optimal ET sequence\|legend=0\| 53, 217, 270, 2107c, 2377bc }}
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	* WE: ~2 = 1199.9695{{c}}, ~320/243 = 475.5451{{c}}		* WE: ~2 = 1199.9695{{c}}, ~320/243 = 475.5451{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5571{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5571{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5566{{c}}~~
	* POTE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5572{{c}} -->

	{{Optimal ET sequence\|legend=0\| 53, 217, 270 }}		{{Optimal ET sequence\|legend=0\| 53, 217, 270 }}
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	* WE: ~2 = 1199.9636{{c}}, ~25/19 = 475.5426{{c}}		* WE: ~2 = 1199.9636{{c}}, ~25/19 = 475.5426{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~25/19 = 475.5569{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~25/19 = 475.5569{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~25/19 = 475.5561{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 53, 217, 270 }}		{{Optimal ET sequence\|legend=0\| 53, 217, 270 }}
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	* WE: ~99/70 = 599.9594{{c}}, ~320/243 = 475.5174{{c}}		* WE: ~99/70 = 599.9594{{c}}, ~320/243 = 475.5174{{c}}
	* CWE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5501{{c}}		* CWE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5501{{c}}
	~~<!-- * CTE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5523{{c}}~~
	* POTE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5496{{c}} -->

	{{Optimal ET sequence\|legend=0\| 106, 164, 270, 916, 1186, 1456 }}		{{Optimal ET sequence\|legend=0\| 106, 164, 270, 916, 1186, 1456 }}
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	* WE: ~99/70 = 599.9859{{c}}, ~320/243 = 475.5423{{c}}		* WE: ~99/70 = 599.9859{{c}}, ~320/243 = 475.5423{{c}}
	* CWE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5536{{c}}		* CWE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5536{{c}}
	~~<!-- * CTE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5540{{c}}~~
	* POTE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.553{{c}} -->

	{{Optimal ET sequence\|legend=0\| 106, 164, 270 }}		{{Optimal ET sequence\|legend=0\| 106, 164, 270 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~112/81 = 558.5212{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~112/81 = 558.5212{{c}}
	: error map: {{val\| 0.000 +0.300 +0.523 -1.287 }}		: error map: {{val\| 0.000 +0.300 +0.523 -1.287 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~112/81 = 558.5209{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 58, 159, 217 }}		{{Optimal ET sequence\|legend=1\| 58, 159, 217 }}
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	* WE: ~2 = 1199.9730{{c}}, ~112/81 = 558.5052{{c}}		* WE: ~2 = 1199.9730{{c}}, ~112/81 = 558.5052{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5173{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5173{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5178{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 58, 101cd, 159, 217, 376d }}		{{Optimal ET sequence\|legend=0\| 58, 101cd, 159, 217, 376d }}
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	* WE: ~2 = 1199.9649{{c}}, ~112/81 = 558.5040{{c}}		* WE: ~2 = 1199.9649{{c}}, ~112/81 = 558.5040{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5197{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5197{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~81/56 = 641.4797{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 58, 159, 217 }}		{{Optimal ET sequence\|legend=0\| 58, 159, 217 }}
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	* WE: ~2 = 1199.9594{{c}}, ~112/81 = 558.5017{{c}}		* WE: ~2 = 1199.9594{{c}}, ~112/81 = 558.5017{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5202{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5202{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5206{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 58, 159, 217 }}		{{Optimal ET sequence\|legend=0\| 58, 159, 217 }}
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	* [[CWE]]: ~177147/125440 = 600.0000{{c}}, ~28/27 = 62.2295{{c}}		* [[CWE]]: ~177147/125440 = 600.0000{{c}}, ~28/27 = 62.2295{{c}}
	: error map: {{val\| 0.000 +0.209 +0.046 -0.105 }}		: error map: {{val\| 0.000 +0.209 +0.046 -0.105 }}
	~~<!-- * [[POTE]]: ~177147/125440 = 600.000{{c}}, ~28/27 = 62.229{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 58, 154c, 212, 270, 752, 1022, 1292, 2854b }}		{{Optimal ET sequence\|legend=1\| 58, 154c, 212, 270, 752, 1022, 1292, 2854b }}
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	* WE: ~99/70 = 599.9796{{c}} ~28/27 = 62.2218{{c}}		* WE: ~99/70 = 599.9796{{c}} ~28/27 = 62.2218{{c}}
	* CWE: ~99/70 = 600.0000{{c}}, ~28/27 = 62.2251{{c}}		* CWE: ~99/70 = 600.0000{{c}}, ~28/27 = 62.2251{{c}}
	~~<!-- * POTE: ~99/70 = 600.000{{c}}, ~28/27 = 62.224{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 58, 154ce, 212, 270 }}		{{Optimal ET sequence\|legend=0\| 58, 154ce, 212, 270 }}
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	* WE: ~99/70 = 599.9763{{c}} ~28/27 = 62.2174{{c}}		* WE: ~99/70 = 599.9763{{c}} ~28/27 = 62.2174{{c}}
	* CWE: ~99/70 = 600.0000{{c}}, ~28/27 = 62.2211{{c}}		* CWE: ~99/70 = 600.0000{{c}}, ~28/27 = 62.2211{{c}}
	~~<!-- * POTE: ~99/70 = 600.000{{c}}, ~28/27 = 62.220{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 58, 154cef, 212, 270 }}		{{Optimal ET sequence\|legend=0\| 58, 154cef, 212, 270 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3592/1715 = 718.8806{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3592/1715 = 718.8806{{c}}
	: error map: {{val\| 0.000 +0.134 -0.345 -0.990 }}		: error map: {{val\| 0.000 +0.134 -0.345 -0.990 }}
	~~<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~1715/1296 = 481.120{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 212, 429, 1070d }}		{{Optimal ET sequence\|legend=1\| 212, 429, 1070d }}
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	* WE: ~2 = 1200.1131{{c}} ~50/33 = 718.9478{{c}}		* WE: ~2 = 1200.1131{{c}} ~50/33 = 718.9478{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~50/33 = 718.8808{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~50/33 = 718.8808{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~50/33 = 728.880{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 212, 429 }}		{{Optimal ET sequence\|legend=0\| 212, 429 }}
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	* WE: ~2 = 1200.1324{{c}} ~50/33 = 718.9608{{c}}		* WE: ~2 = 1200.1324{{c}} ~50/33 = 718.9608{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~50/33 = 718.8825{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~50/33 = 718.8825{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~50/33 = 718.882{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 212, 217, 429 }}		{{Optimal ET sequence\|legend=0\| 212, 217, 429 }}

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

2025-10-28T14:17:19Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus

Show changes

FloraC: - redundant category

2025-10-28T10:46:21Z

- redundant category

← Older revision		Revision as of 10:46, 28 October 2025
Line 264:		Line 264:
	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:Vulture family\| ]] <!-- main article ~~-->~~		[[Category:Vulture family\| ]] <!-- main article
	~~[[Category:Vulture\| ]] <!-- key article -->~~
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Units & misc. cleanup

2025-10-28T10:44:53Z

Units & misc. cleanup

Show changes

Lériendil: /* Septimal vulture */

2025-10-04T15:06:48Z

Septimal vulture

← Older revision		Revision as of 15:06, 4 October 2025
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	== Septimal vulture ==		== Septimal vulture ==
	Septimal vulture can be described as the {{nowrap\| 53 & 270 }} microtemperament, tempering out the [[ragisma]], 4375/4374 and the [[garischisma]], 33554432/33480783 ({{monzo\| 25 -14 0 -1 }}) aside from the vulture comma. [[270edo]] is a good tuning for this temperament, with generator 107\270. The harmonic 7 is found at -14 fifths or {{nowrap\| (-14) × 4 {{=}} -56 }} generator steps, so that the smallest [[mos scale]] that includes it is the 58-note one, though for larger scope of harmony, you could try the 111- or 164-note one. For a much simpler mapping of 7 at the cost of higher error, you could try [[Buzzardsmic clan #~~Buzzard~~\|buzzard]].		Septimal vulture can be described as the {{nowrap\| 53 & 270 }} microtemperament, tempering out the [[ragisma]], 4375/4374 and the [[garischisma]], 33554432/33480783 ({{monzo\| 25 -14 0 -1 }}) aside from the vulture comma. [[270edo]] is a good tuning for this temperament, with generator 107\270. The harmonic 7 is found at -14 fifths or {{nowrap\| (-14) × 4 {{=}} -56 }} generator steps, so that the smallest [[mos scale]] that includes it is the 58-note one, though for larger scope of harmony, you could try the 111- or 164-note one. For a much simpler mapping of 7 at the cost of higher error, you could try [[Buzzardsmic clan #Septimal buzzard\|buzzard]].

	It can be extended to the 11-limit by identifying a stack of four [[5/4]]'s as [[11/9]], tempering out [[5632/5625]], and to the 13-limit by identifying the hemitwelfth as [[26/15]], tempering out [[676/675]]. Furthermore, the generator of vulture is very close to [[25/19]]; a stack of three generator steps octave-reduced thus represents its fifth complement, [[57/50]]. This corresponds to tempering out [[1216/1215]] with the effect of equating the schisma with [[513/512]] and [[361/360]] in addition to many 11- and 13-limit commas. 270edo remains an excellent tuning in all cases.		It can be extended to the 11-limit by identifying a stack of four [[5/4]]'s as [[11/9]], tempering out [[5632/5625]], and to the 13-limit by identifying the hemitwelfth as [[26/15]], tempering out [[676/675]]. Furthermore, the generator of vulture is very close to [[25/19]]; a stack of three generator steps octave-reduced thus represents its fifth complement, [[57/50]]. This corresponds to tempering out [[1216/1215]] with the effect of equating the schisma with [[513/512]] and [[361/360]] in addition to many 11- and 13-limit commas. 270edo remains an excellent tuning in all cases.