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The Archipelago: Difference between revisions

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→Taylor: +extension involving 37, by request
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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 20: Line 20:
{{val| 0 0 0 0 1 0 }}
{{val| 0 0 0 0 1 0 }}


{{Val list|legend=1| 5, 9, 10, 14cf, 15, 19, 24, 29, 34d, 43, 49f, 53, 58, 72, 87, 111, 121, 130, 183, 198, 270, 940, 1210f }}
{{Optimal ET sequence|legend=1| 5, 9, 10, 14cf, 15, 19, 24, 29, 34d, 43, 49f, 53, 58, 72, 87, 111, 121, 130, 183, 198, 270, 940, 1210f }}


[[Optimal patent val]]: [[940edo|940]]
[[Optimal patent val]]: [[940edo|940]]
Line 32: Line 32:
[[Mapping]]: [{{val| 1 0 0 0 4 -1 }}, {{val| 0 2 0 0 -3 3 }}, {{val| 0 0 1 0 2 1 }}, {{val| 0 0 0 1 -1 0 }}]
[[Mapping]]: [{{val| 1 0 0 0 4 -1 }}, {{val| 0 2 0 0 -3 3 }}, {{val| 0 0 1 0 2 1 }}, {{val| 0 0 0 1 -1 0 }}]


{{Val list|legend=1| 14cf, 15, 19, 29, 39df, 43, 53, 58, 72, 87, 111, 130, 183, 198, 270, 940, 1210f }}
{{Optimal ET sequence|legend=1| 14cf, 15, 19, 29, 39df, 43, 53, 58, 72, 87, 111, 130, 183, 198, 270, 940, 1210f }}


=== 49/48 ===
=== 49/48 ===
Line 41: Line 41:
[[Mapping]]: [{{val| 1 0 0 2 0 -1 }}, {{val| 0 2 0 1 0 3 }}, {{val| 0 0 1 0 0 1 }}, {{val| 0 0 0 0 1 0 }}]
[[Mapping]]: [{{val| 1 0 0 2 0 -1 }}, {{val| 0 2 0 1 0 3 }}, {{val| 0 0 1 0 0 1 }}, {{val| 0 0 0 0 1 0 }}]


{{Val list|legend=1| 5, 9, 10, 14cf, 15, 19, 24, 29, 38df, 53d, 67cddef, 105cdddeefff }}
{{Optimal ET sequence|legend=1| 5, 9, 10, 14cf, 15, 19, 24, 29, 38df, 53d, 67cddef, 105cdddeefff }}


=== 1716/1715 ===
=== 1716/1715 ===
Line 50: Line 50:
[[Mapping]]: [{{val| 1 0 0 0 -1 -1 }}, {{val| 0 2 0 0 -5 3 }}, {{val| 0 0 1 0 0 1 }}, {{val| 0 0 0 1 3 0 }}]
[[Mapping]]: [{{val| 1 0 0 0 -1 -1 }}, {{val| 0 2 0 0 -5 3 }}, {{val| 0 0 1 0 0 1 }}, {{val| 0 0 0 1 3 0 }}]


{{Val list|legend=1| 58, 72, 121, 130, 193, 198, 270, 940, 1210f }}
{{Optimal ET sequence|legend=1| 58, 72, 121, 130, 193, 198, 270, 940, 1210f }}


=== 364/363 ===
=== 364/363 ===
Line 59: Line 59:
[[Mapping]]: [{{val| 1 0 0 -1 0 -1 }}, {{val| 0 2 0 1 1 3 }}, {{val| 0 0 1 1 1 1 }}, {{val| 0 0 0 2 1 0 }}]
[[Mapping]]: [{{val| 1 0 0 -1 0 -1 }}, {{val| 0 2 0 1 1 3 }}, {{val| 0 0 1 1 1 1 }}, {{val| 0 0 0 2 1 0 }}]


{{Val list|legend=1| 14cf, 15, 23deff, 24, 29, 34d, 43, 49f, 58, 72, 87, 121, 130, 193, 217, 289, 338e, 410e }}
{{Optimal ET sequence|legend=1| 14cf, 15, 23deff, 24, 29, 34d, 43, 49f, 58, 72, 87, 121, 130, 193, 217, 289, 338e, 410e }}


=== 351/350 ===
=== 351/350 ===
Line 68: Line 68:
[[Mapping]]: [{{val| 1 0 0 -2 0 -1 }}, {{val| 0 2 0 9 0 3 }}, {{val| 0 0 1 -1 0 1 }}, {{val| 0 0 0 0 1 0 }}]
[[Mapping]]: [{{val| 1 0 0 -2 0 -1 }}, {{val| 0 2 0 9 0 3 }}, {{val| 0 0 1 -1 0 1 }}, {{val| 0 0 0 0 1 0 }}]


{{Val list|legend=1| 14cf, 19, 24, 34d, 53, 58, 72, 111, 130, 183, 313, 462f }}
{{Optimal ET sequence|legend=1| 14cf, 19, 24, 34d, 53, 58, 72, 111, 130, 183, 313, 462f }}


=== 352/351 ===
=== 352/351 ===
Line 77: Line 77:
[[Mapping]]: [{{val| 1 0 0 0 -6 -1 }}, {{val| 0 2 0 0 9 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 1 0 0 }}]
[[Mapping]]: [{{val| 1 0 0 0 -6 -1 }}, {{val| 0 2 0 0 9 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 1 0 0 }}]


{{Val list|legend=1| 10, 19e, 24, 29, 34d, 53, 58, 87, 111, 121, 140, 198, 459b, 517bcdf, 657bdf }}
{{Optimal ET sequence|legend=1| 10, 19e, 24, 29, 34d, 53, 58, 87, 111, 121, 140, 198, 459b, 517bcdf, 657bdf }}


=== 540/539 ===
=== 540/539 ===
Line 86: Line 86:
[[Mapping]]: [{{val| 1 0 0 0 2 -1 }}, {{val| 0 2 0 0 6 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 1 -2 0 }}]
[[Mapping]]: [{{val| 1 0 0 0 2 -1 }}, {{val| 0 2 0 0 6 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 1 -2 0 }}]


{{Val list|legend=1| 9, 10, 14cf, 19, 33cdff, 39df, 48c, 49f, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de }}
{{Optimal ET sequence|legend=1| 9, 10, 14cf, 19, 33cdff, 39df, 48c, 49f, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de }}


=== 847/845 ===
=== 847/845 ===
Line 95: Line 95:
[[Mapping]]: [{{val| 1 0 0 0 -1 -1 }}, {{val| 0 2 0 0 3 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 2 -1 0 }}]
[[Mapping]]: [{{val| 1 0 0 0 -1 -1 }}, {{val| 0 2 0 0 3 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 2 -1 0 }}]


{{Val list|legend=1| 24d, 29, 38df, 49f, 53, 58, 87, 111, 140, 198, 347, 487e, 545c }}
{{Optimal ET sequence|legend=1| 24d, 29, 38df, 49f, 53, 58, 87, 111, 140, 198, 347, 487e, 545c }}


== Rank-3 temperaments ==
== Rank-3 temperaments ==
Line 131: Line 131:
[[POTE generator]]: ~15/13 = 248.917
[[POTE generator]]: ~15/13 = 248.917


{{Val list|legend=1| 130, 270, 940, 1210f }}
{{Optimal ET sequence|legend=1| 130, 270, 940, 1210f }}


[[Badness]]: 0.013475
[[Badness]]: 0.013475
Line 146: Line 146:
[[POTE generator]]: ~13/12 = 137.777
[[POTE generator]]: ~13/12 = 137.777


{{Val list|legend=1| 87, 183, 270 }}
{{Optimal ET sequence|legend=1| 87, 183, 270 }}


[[Badness]]: 0.015557
[[Badness]]: 0.015557
Line 161: Line 161:
[[POTE generator]]: ~14/13 = 128.8902
[[POTE generator]]: ~14/13 = 128.8902


{{Val list|legend=1| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }}
{{Optimal ET sequence|legend=1| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }}


[[Badness]]: 0.019494
[[Badness]]: 0.019494
Line 174: Line 174:
POTE generator: ~14/13 = 128.8912
POTE generator: ~14/13 = 128.8912


Vals: {{Val list| 121, 149, 270 }}
{{Optimal ET sequence|legend=1| 121, 149, 270 }}


Badness: 0.019107
Badness: 0.019107
Line 190: Line 190:
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621


{{Val list|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}


[[Badness]]: 0.002335
[[Badness]]: 0.002335
Line 210: Line 210:
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.868
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.868


{{Val list|legend=1| 5, 24, 29, 53, 82, 111, 135 }}
{{Optimal ET sequence|legend=1| 5, 24, 29, 53, 82, 111, 135 }}


[[Badness]]: ?
[[Badness]]: ?
Line 231: Line 231:
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 249.312
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 249.312


{{Val list|legend=1| 10, 14, 24, 58, 82, 130 }}
{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}


[[Tp tuning#T2 tuning|RMS error]]: 0.3533 cents
[[Tp tuning#T2 tuning|RMS error]]: 0.3533 cents
Line 249: Line 249:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 317.076
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 317.076


{{Val list|legend=1| 15, 19, 34, 53, 87, 140, 193, 246 }}
{{Optimal ET sequence|legend=1| 15, 19, 34, 53, 87, 140, 193, 246 }}


[[Badness]]: 0.394
[[Badness]]: 0.394
Line 264: Line 264:
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~26/15 = 950.8331
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~26/15 = 950.8331


{{Val list|legend=1| 24, 53, 130, 183, 236, 525f, 761ff }}
{{Optimal ET sequence|legend=1| 24, 53, 130, 183, 236, 525f, 761ff }}


[[Badness]]: 0.0100
[[Badness]]: 0.0100
Line 277: Line 277:
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~26/15 = 950.8199
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~26/15 = 950.8199


{{Val list|legend=1| 24, 29, 53, 130, 183, 236h, 289h }}
{{Optimal ET sequence|legend=1| 24, 29, 53, 130, 183, 236h, 289h }}


[[Badness]]: 0.00575
[[Badness]]: 0.00575
Line 290: Line 290:
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~26/15 = 950.8187
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~26/15 = 950.8187


{{Val list|legend=1| 24, 29, 53, 183, 236h, 289hl, 631fhhll }}
{{Optimal ET sequence|legend=1| 24, 29, 53, 183, 236h, 289hl, 631fhhll }}


[[Badness]]: 0.00357
[[Badness]]: 0.00357
Line 303: Line 303:
[[Sval]] [[mapping]]: [{{val| 1 0 0 -1 }}, {{val| 0 2 0 3 }}, {{val| 0 0 1 1 }}]
[[Sval]] [[mapping]]: [{{val| 1 0 0 -1 }}, {{val| 0 2 0 3 }}, {{val| 0 0 1 1 }}]


{{Val list|legend=1| 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270 }}
{{Optimal ET sequence|legend=1| 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270 }}


[[Badness]]: 0.00811 × 10<sup>-3</sup>
[[Badness]]: 0.00811 × 10<sup>-3</sup>
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