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Stearnsmic clan: Difference between revisions

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Line 13: Line 13:
{{Mapping|legend=3| 2 1 0 2 | 0 3 0 5 }}
{{Mapping|legend=3| 2 1 0 2 | 0 3 0 5 }}


[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~9/7 = 433.888
[[Optimal tuning]]s:
* [[WE]]: ~343/243 = 599.994¢, ~9/7 = 433.884¢
* [[CWE]]: ~343/243 = 600.000¢, ~9/7 = 433.885¢


{{Optimal ET sequence|legend=1| 14, 22, 36, 94, 130, 224, 354, 484, 838 }}
{{Optimal ET sequence|legend=1| 14, 22, 36, 94, 130, 224, 354, 484, 838 }}
[[Badness]] (Sintel): 0.382


=== Overview to extensions ===
=== Overview to extensions ===
Line 31: Line 35:


== Pogo ==
== Pogo ==
{{See also| Schismatic family #Pogo }}
{{See also| Schismatic family }}


The pogo temperament (94 & 130) tempers out the [[schisma]], whose amount of tempering of the fifth is just about right for the stearnsma and vice versa. It is also the temperament that reconciles the difference between [[tertiaschis]] and [[countertertiaschis]], using its semi-octave period.  
The pogo temperament (94 & 130) tempers out the [[schisma]], whose amount of tempering of the fifth is just about right for the stearnsma and vice versa. It is also the temperament that reconciles the difference between [[tertiaschis]] and [[countertertiaschis]], using its semi-octave period.  
Line 42: Line 46:
: mapping generators: ~343/243, ~9/7
: mapping generators: ~343/243, ~9/7


[[Optimal tuning]] ([[POTE]]): ~343/243 = 600.000{{c}}, ~9/7 = 433.901{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~343/243 = 599.986¢, ~9/7 = 433.890¢
* [[CWE]]: ~343/243 = 600.000¢, ~9/7 = 433.901¢


{{Optimal ET sequence|legend=1| 36, 94, 130, 224, 354 }}
{{Optimal ET sequence|legend=1| 36, 94, 130, 224, 354 }}


[[Badness]] (Smith): 0.079635
[[Badness]] (Sintel): 2.015


=== 11-limit ===
=== 11-limit ===
Line 81: Line 87:
{{Mapping|legend=1| 2 1 -12 2 | 0 3 23 5 }}
{{Mapping|legend=1| 2 1 -12 2 | 0 3 23 5 }}


[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~9/7 = 434.218
[[Optimal tuning]]s:
* [[WE]]: ~343/243 = 599.806¢, ~9/7 = 434.078¢
* [[CWE]]: ~343/243 = 600.000¢, ~9/7 = 434.203¢


{{Optimal ET sequence|legend=1| 58, 94, 152 }}
{{Optimal ET sequence|legend=1| 58, 94, 152 }}


[[Badness]]: 0.092748
[[Badness]] (Sintel): 2.347


=== 11-limit ===
=== 11-limit ===
Line 96: Line 104:
Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 434.217
Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 434.217


{{Optimal ET sequence|legend=1| 58, 94, 152 }}
{{Optimal ET sequence|legend=0| 58, 94, 152 }}


Badness: 0.028240
Badness: 0.028240
Line 109: Line 117:
Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 434.221
Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 434.221


{{Optimal ET sequence|legend=1| 58, 94, 152f }}
{{Optimal ET sequence|legend=0| 58, 94, 152f }}


Badness: 0.021645
Badness: 0.021645
Line 122: Line 130:
Optimal tuning (POTE): ~17/12 = 1\2, ~9/7 = 434.181
Optimal tuning (POTE): ~17/12 = 1\2, ~9/7 = 434.181


{{Optimal ET sequence|legend=1| 58, 94, 152f }}
{{Optimal ET sequence|legend=0| 58, 94, 152f }}


Badness: 0.021316
Badness: 0.021316
Line 135: Line 143:
: mapping generators: ~2450/2187, ~567/500
: mapping generators: ~2450/2187, ~567/500


[[Optimal tuning]] ([[CTE]]): ~2450/2187 = 1\6, ~567/500 = 216.9394 (~245/243 = 16.9394)
[[Optimal tuning]]s:
* [[WE]]: ~2450/2187 = 199.998¢, ~567/500 = 216.940¢
* [[CWE]]: ~2450/2187 = 200.000¢, ~567/500 = 216.941¢


{{Optimal ET sequence|legend=1| 72, 210, 282, 354 }}
{{Optimal ET sequence|legend=1| 72, 210, 282, 354 }}


[[Badness]]: 0.090467
[[Badness]] (Sintel): 2.289


=== 11-limit ===
=== 11-limit ===
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Optimal tuning (CTE): ~55/49 = 1\6, ~567/500 = 216.9242 (~100/99 = 16.9242)
Optimal tuning (CTE): ~55/49 = 1\6, ~567/500 = 216.9242 (~100/99 = 16.9242)


{{Optimal ET sequence|legend=1| 72, 210e, 282, 354 }}
{{Optimal ET sequence|legend=0| 72, 210e, 282, 354 }}


Badness: 0.032096
Badness: 0.032096
Line 163: Line 173:
Optimal tuning (CTE): ~55/49 = 1\6, ~312/275 = 216.9332 (~105/104 = 16.9332)
Optimal tuning (CTE): ~55/49 = 1\6, ~312/275 = 216.9332 (~105/104 = 16.9332)


{{Optimal ET sequence|legend=1| 72, 210ef, 282, 354 }}
{{Optimal ET sequence|legend=0| 72, 210ef, 282, 354 }}


Badness: 0.0258
Badness: 0.0258
Line 176: Line 186:
Optimal tuning (CTE): ~55/49 = 1\6, ~17/15 = 216.9345 (~105/104 = 16.9345)
Optimal tuning (CTE): ~55/49 = 1\6, ~17/15 = 216.9345 (~105/104 = 16.9345)


{{Optimal ET sequence|legend=1| 72, 210efg, 282, 354 }}
{{Optimal ET sequence|legend=0| 72, 210efg, 282, 354 }}


Badness: 0.0154
Badness: 0.0154
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{{Mapping|legend=1| 94 149 0 264 | 0 0 1 0 }}
{{Mapping|legend=1| 94 149 0 264 | 0 0 1 0 }}


[[Optimal tuning]] ([[POTE]]): ~1029/1024 = 1\94, ~5/4 = 386.7805
: mapping generators: ~1029/1024, ~5
 
[[Optimal tuning]]s:
* [[CTE]]: ~1029/1024 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.3137¢
* [[CWE]]: ~1029/1024 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.6637¢


{{Optimal ET sequence|legend=1| 94, 282, 658d, 940dd }}
{{Optimal ET sequence|legend=1| 94, 282, 658d, 940dd }}


[[Badness]]: 0.307043
[[Badness]] (Sintel): 7.770


=== 11-limit ===
=== 11-limit ===
Line 202: Line 216:
Mapping: {{mapping| 94 149 0 264 107 | 0 0 1 0 1 }}
Mapping: {{mapping| 94 149 0 264 107 | 0 0 1 0 1 }}


Optimal tuning (POTE): ~1029/1024 = 1\94, ~5/4 = 386.5968
Optimal tunings:
* CTE: ~1029/1024 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.0177¢
* CWE: ~1029/1024 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.4545¢


{{Optimal ET sequence|legend=1| 94, 282, 376, 658de }}
{{Optimal ET sequence|legend=0| 94, 282, 376, 658de }}


Badness: 0.082255
Badness (Sintel): 2.719


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 94 149 0 264 107 348 | 0 0 1 0 1 0 }}
Mapping: {{mapping| 94 149 0 264 107 348 | 0 0 1 0 1 0 }}


Optimal tuning (POTE): ~169/168 = 1\94, ~5/4 = 386.8141
Optimal tunings:
* CTE: ~169/168 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.0177¢
* CWE: ~169/168 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.6570¢


{{Optimal ET sequence|legend=1| 94, 282 }}
{{Optimal ET sequence|legend=0| 94, 282 }}


Badness: 0.045941
Badness (Sintel): 1.898


=== 17-limit ===
=== 17-limit ===
Line 228: Line 246:
Mapping: {{mapping| 94 149 0 264 107 348 166 | 0 0 1 0 1 0 1 }}
Mapping: {{mapping| 94 149 0 264 107 348 166 | 0 0 1 0 1 0 1 }}


Optimal tuning (POTE): ~169/168 = 1\94, ~5/4 = 386.8420
Optimal tunings:
* CTE: ~169/168 = 12.7660¢ (1 ⧵ 94), ~5/4 = 385.9792¢
* CWE: ~169/168 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.6751¢


{{Optimal ET sequence|legend=1| 94, 282 }}
{{Optimal ET sequence|legend=0| 94, 282 }}


Badness: 0.027608
Badness (Sintel): 1.406


== Decistearn ==
== Decistearn ==
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: mapping generators: ~15/14, ~135/98
: mapping generators: ~15/14, ~135/98


[[Optimal tuning]] ([[CTE]]): ~15/14 = 1\10, ~135/98 = 553.810 (~36/35 = 46.190)
[[Optimal tuning]]s:
* [[WE]]: ~15/14 = 119.975¢, ~135/98 = 553.845¢
* [[CWE]]: ~15/14 = 120.000¢, ~135/98 = 553.893¢


{{Optimal ET sequence|legend=1| 50, 80, 130, 470cd, 600cd, 730cd, 860ccd }}
{{Optimal ET sequence|legend=1| 50, 80, 130, 470cd, 600cd, 730cd, 860ccd }}


[[Badness]]: 0.095543
[[Badness]] (Sintel): 2.418


=== 11-limit ===
=== 11-limit ===
Line 260: Line 282:
Mapping: {{mapping| 10 2 14 5 30 | 0 3 2 5 1 }}
Mapping: {{mapping| 10 2 14 5 30 | 0 3 2 5 1 }}


Optimal tuning (CTE): ~15/14 = 1\10, ~11/8 = 553.783 (~36/35 = 46.217)
Optimal tunings:
* WE: ~15/14 = 119.953¢, ~11/8 = 553.864¢
* CWE: ~15/14 = 120.000¢, ~11/8 = 553.978¢


{{Optimal ET sequence|legend=1| 50, 80, 130, 210e, 340ce }}
{{Optimal ET sequence|legend=0| 50, 80, 130, 210e, 340ce }}


Badness: 0.038556
Badness (Sintel): 1.275


=== 13-limit ===
=== 13-limit ===
Line 273: Line 297:
Mapping: {{mapping| 10 2 14 5 30 37 | 0 3 2 5 1 0 }}
Mapping: {{mapping| 10 2 14 5 30 37 | 0 3 2 5 1 0 }}


Optimal tuning (CTE): ~15/14 = 1\10, ~11/8 = 553.783 (~36/35 = 46.217)
Optimal tunings:
* WE: ~15/14 = 119.974¢, ~11/8 = 553.827¢
* CWE: ~15/14 = 120.000¢, ~11/8 = 553.905¢


{{Optimal ET sequence|legend=1| 50, 80, 130 }}
{{Optimal ET sequence|legend=0| 50, 80, 130 }}


Badness: 0.026895
Badness (Sintel): 1.111


=== 17-limit ===
=== 17-limit ===
Line 286: Line 312:
Mapping: {{mapping| 10 2 14 5 30 37 27 | 0 3 2 5 1 0 3 }}
Mapping: {{mapping| 10 2 14 5 30 37 27 | 0 3 2 5 1 0 3 }}


Optimal tuning (CTE): ~15/14 = 1\10, ~11/8 = 553.862 (~36/35 = 46.138)
Optimal tunings:
* WE: ~15/14 = 119.990¢, ~11/8 = 553.884¢
* CWE: ~15/14 = 120.000¢, ~11/8 = 553.914¢


{{Optimal ET sequence|legend=1| 50, 80, 130 }}
{{Optimal ET sequence|legend=0| 50, 80, 130 }}


Badness: 0.024234
Badness (Sintel): 1.235


=== 19-limit ===
=== 19-limit ===
Line 299: Line 327:
Mapping: {{mapping| 10 2 14 5 30 37 27 24 | 0 3 2 5 1 0 3 4 }}
Mapping: {{mapping| 10 2 14 5 30 37 27 24 | 0 3 2 5 1 0 3 4 }}


Optimal tuning (CTE): ~15/14 = 1\10, ~11/8 = 553.913 (~36/35 = 46.087)
Optimal tunings:
* WE: ~15/14 = 119.995¢, ~11/8 = 553.925¢
* CWE: ~15/14 = 120.000¢, ~11/8 = 553.940¢


{{Optimal ET sequence|legend=1| 50, 80, 130 }}
{{Optimal ET sequence|legend=0| 50, 80, 130 }}


Badness: 0.018232
Badness (Sintel): 1.109


=== 23-limit ===
=== 23-limit ===
Line 314: Line 344:
Mapping: {{mapping| 10 2 14 5 30 37 27 24 36 | 0 3 2 5 1 0 3 4 2 }}
Mapping: {{mapping| 10 2 14 5 30 37 27 24 36 | 0 3 2 5 1 0 3 4 2 }}


Optimal tuning (CTE): ~161/150 = 1\10, ~11/8 = 553.918 (~36/35 = 46.082)
Optimal tunings:
* WE: ~15/14 = 119.997¢, ~11/8 = 553.925¢
* CWE: ~15/14 = 120.000¢, ~11/8 = 553.933¢


{{Optimal ET sequence|legend=1| 30dh, 50, 80, 130 }}
{{Optimal ET sequence|legend=0| 30dh, 50, 80, 130 }}


Badness: 0.016719
Badness (Sintel): 1.017


[[Category:Temperament clans]]
[[Category:Temperament clans]]
Retrieved from "https://en.xen.wiki/w/Stearnsmic_clan"