Smate family: Difference between revisions

Update keys
m Spell 1\1 in decimal; note the badness metric being used; misc. cleanup
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{{Mapping|legend=1| 1 3 2 | 0 -4 1 }}
{{Mapping|legend=1| 1 3 2 | 0 -4 1 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 420.855
: mapping generators: ~2, ~5/4
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~5/4 = 420.855


{{Optimal ET sequence|legend=1| 3, 11, 14, 17c, 20c, 37c }}
{{Optimal ET sequence|legend=1| 3, 11, 14, 17c, 20c, 37c }}


[[Badness]]: 0.178624
[[Badness]] (Smith): 0.178624


== Septimal smate ==
== Septimal smate ==
{{See also| Mint temperaments #Smate }}
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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{{Multival|legend=1| 4 -1 9 -11 3 24 }}
{{Multival|legend=1| 4 -1 9 -11 3 24 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 422.275
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~5/4 = 422.275


{{Optimal ET sequence|legend=1| 3d, 11d, 14, 17c, 37ccdd }}
{{Optimal ET sequence|legend=1| 3d, 11d, 14, 17c, 37ccdd }}


[[Badness]]: 0.077871
[[Badness]] (Smith): 0.077871


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 3 2 6 7 | 0 -4 1 -9 -10 }}
Mapping: {{mapping| 1 3 2 6 7 | 0 -4 1 -9 -10 }}


Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 422.217
Optimal tuning (POTE): ~2 = 1200.000, ~5/4 = 422.217


{{Optimal ET sequence|legend=1| 3de, 14, 17c, 37ccddee }}
{{Optimal ET sequence|legend=0| 3de, 14, 17c, 37ccddee }}


Badness: 0.042518
Badness (Smith): 0.042518


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 3 2 6 7 3 | 0 -4 1 -9 -10 2 }}
Mapping: {{mapping| 1 3 2 6 7 3 | 0 -4 1 -9 -10 2 }}


Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 423.020
Optimal tuning (POTE): ~2 = 1200.000, ~5/4 = 423.020


{{Optimal ET sequence|legend=1| 3de, 14, 17c }}
{{Optimal ET sequence|legend=0| 3de, 14, 17c }}


Badness: 0.036836
Badness (Smith): 0.036836


== Hemismate ==
== Hemismate ==
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{{Multival|legend=1| 8 -2 1 -22 -21 8 }}
{{Multival|legend=1| 8 -2 1 -22 -21 8 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 210.452
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 210.452


{{Optimal ET sequence|legend=1| 6, 11, 17c, 40bcd }}
{{Optimal ET sequence|legend=1| 6, 11, 17c, 40bcd }}


[[Badness]]: 0.154301
[[Badness]] (Smith): 0.154301


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 3 2 3 4 | 0 -8 2 -1 -3 }}
Mapping: {{mapping| 1 3 2 3 4 | 0 -8 2 -1 -3 }}


Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 210.481
Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 210.481


{{Optimal ET sequence|legend=1| 6, 11, 17c, 40bcde }}
{{Optimal ET sequence|legend=0| 6, 11, 17c, 40bcde }}


Badness: 0.065528
Badness (Smith): 0.065528


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 3 2 3 4 3 | 0 -8 2 -1 -3 4 }}
Mapping: {{mapping| 1 3 2 3 4 3 | 0 -8 2 -1 -3 4 }}


Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 210.974
Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 210.974


{{Optimal ET sequence|legend=1| 6, 11, 17c }}
{{Optimal ET sequence|legend=0| 6, 11, 17c }}


Badness: 0.050472
Badness (Smith): 0.050472


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Smate family| ]] <!-- main article -->
[[Category:Smate family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]