Xenharmonic Wiki

Mint temperaments: Difference between revisions

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m →Penta: update the link
m Spell 1\1 in decimal, note the badness metric being used, and misc. cleanup
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{{Multival|legend=1| 5 3 7 -7 -3 8 }}
{{Multival|legend=1| 5 3 7 -7 -3 8 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 140.927
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~15/14 = 140.927


{{Optimal ET sequence|legend=1| 8d, 9, 17c }}
{{Optimal ET sequence|legend=1| 8d, 9, 17c }}


[[Badness]]: 0.048356
[[Badness]] (Smith): 0.048356


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 1 2 2 3 | 0 5 3 7 4 }}
Mapping: {{mapping| 1 1 2 2 3 | 0 5 3 7 4 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 140.747
Optimal tunings:
* POTE: ~2 = 1200.000, ~12/11 = 140.747


{{Optimal ET sequence|legend=1| 8d, 9, 17c }}
{{Optimal ET sequence|legend=0| 8d, 9, 17c }}


Badness: 0.026050
Badness (Smith): 0.026050


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 1 2 2 3 3 | 0 5 3 7 4 6 }}
Mapping: {{mapping| 1 1 2 2 3 3 | 0 5 3 7 4 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.751
Optimal tunings:
* POTE: ~2 = 1200.000, ~13/12 = 140.751


{{Optimal ET sequence|legend=1| 8d, 9, 17c }}
{{Optimal ET sequence|legend=0| 8d, 9, 17c }}


Badness: 0.018158
Badness (Smith): 0.018158


=== 17-limit ===
=== 17-limit ===
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Mapping: {{mapping| 1 1 2 2 3 3 4 | 0 5 3 7 4 6 1 }}
Mapping: {{mapping| 1 1 2 2 3 3 4 | 0 5 3 7 4 6 1 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 141.404
Optimal tunings:
* POTE: ~2 = 1200.000, ~13/12 = 141.404


{{Optimal ET sequence|legend=1| 8d, 9, 17cg }}
{{Optimal ET sequence|legend=0| 8d, 9, 17cg }}


Badness: 0.016743
Badness (Smith): 0.016743


=== 19-limit ===
=== 19-limit ===
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Mapping: {{mapping| 1 1 2 2 3 3 4 4 | 0 5 3 7 4 6 1 2 }}
Mapping: {{mapping| 1 1 2 2 3 3 4 4 | 0 5 3 7 4 6 1 2 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.479
Optimal tunings:
* POTE: ~2 = 1200.000, ~13/12 = 140.479


{{Optimal ET sequence|legend=1| 8d, 9, 17cg }}
{{Optimal ET sequence|legend=0| 8d, 9, 17cg }}


Badness: 0.016841
Badness (Smith): 0.016841


== Subklei ==
== Subklei ==
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{{Multival|legend=1| 6 7 5 -3 -9 -8 }}
{{Multival|legend=1| 6 7 5 -3 -9 -8 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 284.219
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~6/5 = 284.219


{{Optimal ET sequence|legend=1| 4, 17c, 21, 38c }}
{{Optimal ET sequence|legend=1| 4, 17c, 21, 38c }}


[[Badness]]: 0.061101
[[Badness]] (Smith): 0.061101


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 3 4 4 7 | 0 -6 -7 -5 -15 }}
Mapping: {{mapping| 1 3 4 4 7 | 0 -6 -7 -5 -15 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 283.253
Optimal tunings:
* POTE: ~2 = 1200.000, ~6/5 = 283.253


{{Optimal ET sequence|legend=1| 17c, 55ccd }}
{{Optimal ET sequence|legend=0| 17c, 55ccd }}


Badness: 0.044651
Badness (Smith): 0.044651


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 3 4 4 7 7 | 0 -6 -7 -5 -15 -14 }}
Mapping: {{mapping| 1 3 4 4 7 7 | 0 -6 -7 -5 -15 -14 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 282.856
Optimal tunings:
* POTE: ~2 = 1200.000, ~6/5 = 282.856


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


Badness: 0.032324
Badness (Smith): 0.032324


=== Subkla ===
=== Subkla ===
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Mapping: {{mapping| 1 3 4 4 3 | 0 -6 -7 -5 2 }}
Mapping: {{mapping| 1 3 4 4 3 | 0 -6 -7 -5 2 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 283.822
Optimal tunings:
* POTE: ~2 = 1200.000, ~6/5 = 283.822


{{Optimal ET sequence|legend=1| 4, 17c, 21, 38ce, 55ccde }}
{{Optimal ET sequence|legend=0| 4, 17c, 21, 38ce, 55ccde }}


Badness: 0.047247
Badness (Smith): 0.047247


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 3 4 4 3 3 | 0 -6 -7 -5 2 3 }}
Mapping: {{mapping| 1 3 4 4 3 3 | 0 -6 -7 -5 2 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 283.882
Optimal tunings:
* POTE: ~2 = 1200.000, ~6/5 = 283.882


{{Optimal ET sequence|legend=1| 4, 17c, 21, 38ce, 55ccde }}
{{Optimal ET sequence|legend=0| 4, 17c, 21, 38ce, 55ccde }}


Badness: 0.036701
Badness (Smith): 0.036701


== Slurpee ==
== Slurpee ==
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{{Multival|legend=1| 7 11 3 1 -15 -24 }}
{{Multival|legend=1| 7 11 3 1 -15 -24 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 72.303
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~21/20 = 72.303


{{Optimal ET sequence|legend=1| 16, 17c, 33, 50cd, 83bccd }}
{{Optimal ET sequence|legend=1| 16, 17c, 33, 50cd, 83bccd }}


[[Badness]]: 0.114869
[[Badness]] (Smith): 0.114869


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


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 72.297
Optimal tunings:
* POTE: ~2 = 1200.000, ~21/20 = 72.297


{{Optimal ET sequence|legend=1| 16, 17c, 33, 50cd, 83bccd }}
{{Optimal ET sequence|legend=0| 16, 17c, 33, 50cd, 83bccd }}


Badness: 0.050514
Badness (Smith): 0.050514


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 2 3 3 4 4 | 0 -7 -11 -3 -9 -5 }}
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -7 -11 -3 -9 -5 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 72.409
Optimal tunings:
* POTE: ~2 = 1200.000, ~21/20 = 72.409


{{Optimal ET sequence|legend=1| 16, 17c, 33, 83bccd }}
{{Optimal ET sequence|legend=0| 16, 17c, 33, 83bccd }}


Badness: 0.033102
Badness (Smith): 0.033102


== Penta ==
== Penta ==
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{{Multival|legend=1| 3 2 4 -4 -2 4 }}
{{Multival|legend=1| 3 2 4 -4 -2 4 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 239.977
[[Optimal tuning]]s:
* [[POTE]]: ~2 = 1200.000, ~6/5 = 239.977


{{Optimal ET sequence|legend=1| 1bd, 5 }}
{{Optimal ET sequence|legend=1| 1bd, 5 }}


[[Badness]]: 0.046882
[[Badness]] (Smith): 0.046882


== Shallowtone ==
== Shallowtone ==
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[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 681.2780
* [[CTE]]: ~2 = 1200.000, ~3/2 = 681.2780
* [[CWE]]: ~2 = 1\1, ~3/2 = 681.2447
* [[CWE]]: ~2 = 1200.000, ~3/2 = 681.2447


{{Optimal ET sequence|legend=1| 7, 30b, 37b }}
{{Optimal ET sequence|legend=1| 7, 30b, 37b }}


[[Badness]]: 0.308
[[Badness]] (Smith): 0.308


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 681.2538
* CTE: ~2 = 1200.000, ~3/2 = 681.2538
* CWE: ~2 = 1\1, ~3/2 = 681.3267
* CWE: ~2 = 1200.000, ~3/2 = 681.3267


Optimal ET sequence: {{Optimal ET sequence| 7, 30b, 37b }}
{{Optimal ET sequence|legend=0| 7, 30b, 37b }}


Badness: 0.130
Badness (Smith): 0.130


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 681.2374
* CTE: ~2 = 1200.000, ~3/2 = 681.2374
* CWE: ~2 = 1\1, ~3/2 = 681.2669
* CWE: ~2 = 1200.000, ~3/2 = 681.2669


Optimal ET sequence: {{Optimal ET sequence| 7, 30b, 37b }}
{{Optimal ET sequence|legend=0| 7, 30b, 37b }}


Badness: 0.0773
Badness (Smith): 0.0773


== Notes ==
== Notes ==
Retrieved from "https://en.xen.wiki/w/Mint_temperaments"