Vulture family - Revision history

FloraC: Fix categories

2026-10-18T09:15:51Z

Fix categories

← Older revision		Revision as of 09:15, 18 October 2026
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	Badness (Sintel): 1.81		Badness (Sintel): 1.81

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

FloraC: Expand

2026-10-18T09:15:27Z

Expand

← Older revision		Revision as of 09:15, 18 October 2026
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	=== Overview to extensions ===		=== Overview to extensions ===
	~~Temperaments~~ discussed ~~elsewhere include~~ [[Buzzardsmic clan #~~Buzzard\|~~buzzard]]. ~~Considered~~ below ~~are septimal vulture, terture, condor, eagle, and turkey~~.		Strong 7-limit extensions include septimal vulture (53 & 270), which tempers out [[4375/4374]], and buzzard (53 & 58), which tempers out [[1728/1715]].

			Terture adds [[250047/250000]] with a 1/3-octave period. Condor adds [[10976/10935]] and splits the generator in three. Eagle adds [[2401/2400]]. Turkey adds [[4802000/4782969]]. Those split the generator in four.

			Most of these temperaments extend naturally to the 11-limit via tempering out the [[symbiotic comma]] and [[seascape comma]], from 10485760000/10460353203 = (19712/19683)<sup>2</sup>/(160083/160000), and to the 13-limit via identifying the hemitwelfth as [[~]][[26/15]], tempering out the [[island comma]].

			Buzzard is discussed in its own clan (→ [[Buzzardsmic clan #Septimal buzzard]]). The rest are considered below.

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

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:32:59Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

← Older revision		Revision as of 12:32, 24 September 2026
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	Comma list: 4375/4374, 5632/5625, 41503/41472		Comma list: 4375/4374, 5632/5625, 41503/41472

	~~Mapping:~~ {{~~mapping~~\| 1 0 -6 25 -33 \| 0 4 21 -56 92 }}		{{Mapping\|legend=0\| 1 0 -6 25 -33 \| 0 4 21 -56 92 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 676/675, 1001/1000, 4096/4095, 4375/4374		Comma list: 676/675, 1001/1000, 4096/4095, 4375/4374

	~~Mapping:~~ {{~~mapping~~\| 1 0 -6 25 -33 -7 \| 0 4 21 -56 92 27 }}		{{Mapping\|legend=0\| 1 0 -6 25 -33 -7 \| 0 4 21 -56 92 27 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 676/675, 1001/1000, 1216/1215, 1540/1539, 1729/1728		Comma list: 676/675, 1001/1000, 1216/1215, 1540/1539, 1729/1728

	~~Mapping:~~ {{~~mapping~~\| 1 0 -6 25 -33 -7 -12 \| 0 4 21 -56 92 27 41 }}		{{Mapping\|legend=0\| 1 0 -6 25 -33 -7 -12 \| 0 4 21 -56 92 27 41 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 3025/3024, 4375/4374, 33554432/33480783		Comma list: 3025/3024, 4375/4374, 33554432/33480783

	~~Mapping:~~ {{~~mapping~~\| 2 0 -12 50 41 \| 0 4 21 -56 -43 }}		{{Mapping\|legend=0\| 2 0 -12 50 41 \| 0 4 21 -56 -43 }}
	: mapping generators: ~99/70, ~320/243		: mapping generators: ~99/70, ~320/243

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	Comma list: 676/675, 3025/3024, 4096/4095, 4375/4374		Comma list: 676/675, 3025/3024, 4096/4095, 4375/4374

	~~Mapping:~~ {{~~mapping~~\| 2 0 -12 50 41 -14 \| 0 4 21 -56 -43 27 }}		{{Mapping\|legend=0\| 2 0 -12 50 41 -14 \| 0 4 21 -56 -43 27 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 3025/3024, 19712/19683, 102487/102400		Comma list: 3025/3024, 19712/19683, 102487/102400

	~~Mapping:~~ {{~~mapping~~\| 3 0 -18 -32 8 \| 0 4 21 34 2 }}		{{Mapping\|legend=0\| 3 0 -18 -32 8 \| 0 4 21 34 2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 676/675, 1001/1000, 3025/3024, 10985/10976		Comma list: 676/675, 1001/1000, 3025/3024, 10985/10976

	~~Mapping:~~ {{~~mapping~~\| 3 0 -18 -32 8 -21 \| 0 4 21 34 2 27 }}		{{Mapping\|legend=0\| 3 0 -18 -32 8 -21 \| 0 4 21 34 2 27 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 676/675, 715/714, 936/935, 1001/1000, 4928/4913		Comma list: 676/675, 715/714, 936/935, 1001/1000, 4928/4913

	~~Mapping:~~ {{~~mapping~~\| 3 0 -18 -32 8 -21 -2 \| 0 4 21 34 2 27 12 }}		{{Mapping\|legend=0\| 3 0 -18 -32 8 -21 -2 \| 0 4 21 34 2 27 12 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1617/1615		Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1617/1615

	~~Mapping:~~ {{~~mapping~~\| 3 0 -18 -32 8 -21 -2 -36 \| 0 4 21 34 2 27 12 41 }}		{{Mapping\|legend=0\| 3 0 -18 -32 8 -21 -2 -36 \| 0 4 21 34 2 27 12 41 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 460/459, 529/528, 676/675, 715/714, 936/935, 1001/1000, 1216/1215		Comma list: 460/459, 529/528, 676/675, 715/714, 936/935, 1001/1000, 1216/1215

	~~Mapping:~~ {{~~mapping~~\| 3 0 -18 -32 8 -21 -2 -36 10 \| 0 4 21 34 2 27 12 41 3 }}		{{Mapping\|legend=0\| 3 0 -18 -32 8 -21 -2 -36 10 \| 0 4 21 34 2 27 12 41 3 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 441/440, 4000/3993, 10976/10935		Comma list: 441/440, 4000/3993, 10976/10935

	~~Mapping:~~ {{~~mapping~~\| 1 -4 -27 -20 -24 \| 0 12 63 49 59 }}		{{Mapping\|legend=0\| 1 -4 -27 -20 -24 \| 0 12 63 49 59 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 364/363, 441/440, 676/675, 10976/10935		Comma list: 364/363, 441/440, 676/675, 10976/10935

	~~Mapping:~~ {{~~mapping~~\| 1 -4 -27 -20 -24 -34 \| 0 12 63 49 59 81 }}		{{Mapping\|legend=0\| 1 -4 -27 -20 -24 -34 \| 0 12 63 49 59 81 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 364/363, 441/440, 595/594, 676/675, 8624/8619		Comma list: 364/363, 441/440, 595/594, 676/675, 8624/8619

	~~Mapping:~~ {{~~mapping~~\| 1 -4 -27 -20 -24 -34 12 \| 0 12 63 49 59 81 -17 }}		{{Mapping\|legend=0\| 1 -4 -27 -20 -24 -34 12 \| 0 12 63 49 59 81 -17 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 2401/2400, 9801/9800, 19712/19683		Comma list: 2401/2400, 9801/9800, 19712/19683

	~~Mapping:~~ {{~~mapping~~\| 2 4 9 8 12 \| 0 -8 -42 -23 -49 }}		{{Mapping\|legend=0\| 2 4 9 8 12 \| 0 -8 -42 -23 -49 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 676/675, 1001/1000, 1716/1715, 10648/10647		Comma list: 676/675, 1001/1000, 1716/1715, 10648/10647

	~~Mapping:~~ {{~~mapping~~\| 2 4 9 8 12 13 \| 0 -8 -42 -23 -49 -54 }}		{{Mapping\|legend=0\| 2 4 9 8 12 13 \| 0 -8 -42 -23 -49 -54 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 676/675, 1001/1000, 1216/1215, 1331/1330, 1540/1539		Comma list: 676/675, 1001/1000, 1216/1215, 1331/1330, 1540/1539

	~~Mapping:~~ {{~~mapping~~\| 2 4 9 8 12 13 \| 0 -8 -42 -23 -49 -54 -82 }}		{{Mapping\|legend=0\| 2 4 9 8 12 13 \| 0 -8 -42 -23 -49 -54 -82 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 19712/19683, 42875/42768, 160083/160000		Comma list: 19712/19683, 42875/42768, 160083/160000

	~~Mapping:~~ {{~~mapping~~\| 1 -8 -48 7 -87 \| 0 16 84 -7 151 }}		{{Mapping\|legend=0\| 1 -8 -48 7 -87 \| 0 16 84 -7 151 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 676/675, 1001/1000, 19712/19683, 31213/31104		Comma list: 676/675, 1001/1000, 19712/19683, 31213/31104

	~~Mapping:~~ {{~~mapping~~\| 1 -8 -48 7 -87 -61 \| 0 16 84 -7 151 108 }}		{{Mapping\|legend=0\| 1 -8 -48 7 -87 -61 \| 0 16 84 -7 151 108 }}

	Optimal tunings:		Optimal tunings:

FloraC: /* Eagle */ + an obvious add-19 extension

2026-09-01T17:02:17Z

Eagle: + an obvious add-19 extension

← Older revision		Revision as of 17:02, 1 September 2026
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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~~]].		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 edo tunings include [[212edo]], [[270edo]] and [[328edo]] in the 212h, 270 and 328h [[val]]s, respectively.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	Badness (Sintel): 0.673		Badness (Sintel): 0.673

			=== 2.3.5.7.11.13.19 subgroup ===
			Subgroup: 2.3.5.7.11.13.19

			Comma list: 676/675, 1001/1000, 1216/1215, 1331/1330, 1540/1539

			Mapping: {{mapping\| 2 4 9 8 12 13 \| 0 -8 -42 -23 -49 -54 -82 }}

			Optimal tunings:
			* WE: ~99/70 = 599.9810{{c}} ~28/27 = 62.2195{{c}}
			* CWE: ~99/70 = 600.0000{{c}}, ~28/27 = 62.2223{{c}}

			{{Optimal ET sequence\|legend=0\| 58h, 154cefhh, 212h, 270 }}

			Badness (Sintel): 0.609

	== Turkey ==		== Turkey ==

FloraC: Recategorize

2026-08-14T12:25:39Z

Recategorize

← Older revision		Revision as of 12:25, 14 August 2026
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			[[Category:Vulture family\| ]] <!-- main article
	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:~~Vulture family\| ]] <!~~-~~- main article~~		[[Category:Catalogs of rank-2 temperaments]]
	~~[[Category:Rank~~ 2]]

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

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 {{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