Xenharmonic Wiki

Vulture family: Difference between revisions

← Older edit
VisualWikitext
Overthink (talk | contribs)
autopatrolled
2,676 edits
 
(2 intermediate revisions by one other user not shown)
Line 1: Line 1:
{{interwiki
{{Interwiki
| en = Vulture family
| de = Vulture
| de = Vulture
| en = Vulture_family
| es =  
| es =  
| ja =  
| ja =  
Line 7: Line 7:
{{Technical data page}}
{{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]]).
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]]).
Temperaments discussed elsewhere include [[Landscape microtemperaments #Terture|terture]] and [[Buzzardsmic clan #Buzzard|buzzard]]. Considered below are septimal vulture, condor, eagle, and turkey.


== Vulture ==
== Vulture ==
Line 18: Line 16:


{{Mapping|legend=1| 1 0 -6 | 0 4 21 }}
{{Mapping|legend=1| 1 0 -6 | 0 4 21 }}
: mapping generators: ~2, ~320/243
: mapping generators: ~2, ~320/243


Line 30: Line 27:


[[Badness]] (Sintel): 0.972
[[Badness]] (Sintel): 0.972
=== Overview to extensions ===
Temperaments discussed elsewhere include [[Buzzardsmic clan #Buzzard|buzzard]]. Considered below are septimal vulture, terture, condor, eagle, and turkey.


== Septimal vulture ==
== Septimal vulture ==
Line 75: Line 75:


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 }}
Line 127: Line 127:


Badness (Sintel): 1.47
Badness (Sintel): 1.47
== Terture ==
Named by [[Xenllium]] in 2021, terture tempers out 250047/250000, the [[landscape comma]], and may be described as the {{nowrap| 111 & 159 }} temperament, with a [[ploidacot]] signature of triploid gamma-tetracot.
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 250047/250000, 359661568/358722675
{{Mapping|legend=1| 3 0 -18 -32 | 0 4 21 34 }}
: mapping generators: ~63/50, ~320/243
[[Optimal tuning]]s:
* [[WE]]: ~63/50 = 399.9723{{c}}, ~320/243 = 475.5221{{c}} (~392/375 = 75.5499{{c}})
: [[error map]]: {{val| -0.083 +0.134 +0.151 -0.185 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~320/243 = 475.5519{{c}} (~392/375 = 75.5519{{c}})
: error map: {{val| 0.000 +0.253 +0.276 -0.061 }}
{{Optimal ET sequence|legend=1| 111, 159, 270 }}
[[Badness]] (Sintel): 2.21
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 19712/19683, 102487/102400
Mapping: {{mapping| 3 0 -18 -32 8 | 0 4 21 34 2 }}
Optimal tunings:
* WE: ~63/50 = 399.9902{{c}}, ~320/243 = 475.5383{{c}} (~392/375 = 75.5481{{c}})
* CWE: ~63/50 = 400.0000{{c}}, ~320/243 = 475.5490{{c}} (~392/375 = 75.5490{{c}})
{{Optimal ET sequence|legend=0| 111, 159, 270, 1239, 1509, 1779, 2049, 2319 }}
Badness (Sintel): 0.969
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 3025/3024, 10985/10976
Mapping: {{mapping| 3 0 -18 -32 8 -21 | 0 4 21 34 2 27 }}
Optimal tunings:
* WE: ~63/50 = 399.9958{{c}}, ~154/117 = 475.5485{{c}} (~117/112 = 75.5527{{c}})
* CWE: ~63/50 = 400.0000{{c}}, ~154/117 = 475.5531{{c}} (~117/112 = 75.5531{{c}})
{{Optimal ET sequence|legend=0| 111, 159, 270 }}
Badness (Sintel): 0.771
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
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 }}
Optimal tunings:
* WE: ~34/27 = 399.9664{{c}}, ~112/85 = 475.5198{{c}} (~117/112 = 75.5534{{c}})
* CWE: ~34/27 = 400.0000{{c}}, ~112/85 = 475.5568{{c}} (~117/112 = 75.5568{{c}})
{{Optimal ET sequence|legend=0| 111, 159, 270 }}
Badness (Sintel): 0.953
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
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 }}
Optimal tunings:
* WE: ~34/27 = 399.9665{{c}}, ~112/85 = 475.5198{{c}} (~95/91 = 75.5533{{c}})
* CWE: ~34/27 = 400.0000{{c}}, ~112/85 = 475.5568{{c}} (~95/91 = 75.5568{{c}})
{{Optimal ET sequence|legend=0| 111, 159, 270 }}
Badness (Sintel): 0.846
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
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 }}
Optimal tunings:
* WE: ~34/27 = 400.0026{{c}}, ~112/85 = 475.5510{{c}} (~24/23 = 75.5485{{c}})
* CWE: ~34/27 = 400.0000{{c}}, ~112/85 = 475.5482{{c}} (~24/23 = 75.5482{{c}})
{{Optimal ET sequence|legend=0| 111, 159, 270 }}
Badness (Sintel): 1.07


== Condor ==
== Condor ==
Retrieved from "https://en.xen.wiki/w/Vulture_family"