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Subgroup temperaments: Difference between revisions

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Comment out temperament data with naming conflict
Cmloegcmluin (talk | contribs)
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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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[[Optimal tuning]] ([[POTE]]): ~531441/524288 = 23.4763
[[Optimal tuning]] ([[POTE]]): ~531441/524288 = 23.4763


{{Val list|legend=1| 460, 1329, 1789 }}
{{Optimal ET sequence|legend=1| 460, 1329, 1789 }}


==== 2.9.5.7.11 ====
==== 2.9.5.7.11 ====
Line 97: Line 97:
[[Optimal tuning]] ([[POTE]]): ~8/7 = 214.384
[[Optimal tuning]] ([[POTE]]): ~8/7 = 214.384


{{Val list|legend=1| 5, 6, 11, 17, 28 }}
{{Optimal ET sequence|legend=1| 5, 6, 11, 17, 28 }}


[[Tp tuning #T2 tuning|RMS error]]: 1.977 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.977 cents
Line 114: Line 114:
[[Optimal tuning]] ([[POTE]]): ~9/7 = 438.465
[[Optimal tuning]] ([[POTE]]): ~9/7 = 438.465


{{Val list|legend=1| 8, 11, 30, 41, 52 }}
{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents
Line 131: Line 131:
[[Optimal tuning]] ([[POTE]]): ~77/72 = 115.570
[[Optimal tuning]] ([[POTE]]): ~77/72 = 115.570


{{Val list|legend=1| 10, 21, 31, 52, 83, 135, 353, 488, 623 }}
{{Optimal ET sequence|legend=1| 10, 21, 31, 52, 83, 135, 353, 488, 623 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.0673 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.0673 cents
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[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~9/7 = 439.296
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~9/7 = 439.296


{{Val list|legend=1| 8, 11, 30, 41, 71, 93, 112c, 134c, 175c }}
{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 71, 93, 112c, 134c, 175c }}


[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
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Optimal tuning (subgroup POTE): ~9/7 = 438.977
Optimal tuning (subgroup POTE): ~9/7 = 438.977


Optimal GPV sequence: {{Val list| 11, 30, 41, 153cdef, 194cdef, 235cdef }}
{{Optimal ET sequence|legend=1| 11, 30, 41, 153cdef, 194cdef, 235cdef }}


RMS error: 1.540 cents
RMS error: 1.540 cents
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[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/16 = 467.375
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/16 = 467.375


{{Val list|legend=1| 5, 13, 18, 41, 59, 77, 95 }}
{{Optimal ET sequence|legend=1| 5, 13, 18, 41, 59, 77, 95 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
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Optimal tuning (subgroup POTE): ~21/16 = 463.956
Optimal tuning (subgroup POTE): ~21/16 = 463.956


Optimal GPV sequence: {{Val list| 5, 13, 31}}
{{Optimal ET sequence|legend=1| 5, 13, 31}}


== Fractional subgroup temperaments ==
== Fractional subgroup temperaments ==
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[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016


{{Val list|legend=1| 14, 29, 72, 101, 130, 159 }}
{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
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[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518


{{Val list|legend=1| 17, 36, 118e, 125e, 161e, 197e }}
{{Optimal ET sequence|legend=1| 17, 36, 118e, 125e, 161e, 197e }}


[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
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[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910


{{Val list|legend=1| 5, 22, 27, 32, 37 }}
{{Optimal ET sequence|legend=1| 5, 22, 27, 32, 37 }}


[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
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[[Sval]] [[mapping]]: [{{val| 1 2 1 }}, {{val| 0 1 -2 }}]
[[Sval]] [[mapping]]: [{{val| 1 2 1 }}, {{val| 0 1 -2 }}]


{{Val list|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc }}
{{Optimal ET sequence|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc }}


[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
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[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 386.558
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 386.558


{{Val list|legend=1| 3, …, 22, 25, 28, 31, 59 }}
{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}


[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
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[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966


{{Val list|legend=1|?}}
{{Optimal ET sequence|legend=1|?}}


[[Tp tuning #T2 tuning|RMS error]]: ?
[[Tp tuning #T2 tuning|RMS error]]: ?
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[[Optimal tuning]] ([[POL2]]): ~7/6 = 262.1728
[[Optimal tuning]] ([[POL2]]): ~7/6 = 262.1728


[[Optimal GPV sequence]]: [[3edf]], [[5edf]], [[8edf]]
[[Optimal ET sequence]]: [[3edf]], [[5edf]], [[8edf]]


==== Semilupine ====
==== Semilupine ====
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[[POL2]] generator: ~7/6 = 264.3771
[[POL2]] generator: ~7/6 = 264.3771


[[Optimal GPV sequence]]: [[8edf]], [[13edf]]
[[Optimal ET sequence]]: [[8edf]], [[13edf]]


==== Hemilycan ====
==== Hemilycan ====
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[[Optimal tuning]] ([[POL2]]): ~7/6 = 261.5939
[[Optimal tuning]] ([[POL2]]): ~7/6 = 261.5939


[[Optimal GPV sequence]]: [[8edf]], [[11edf]]
[[Optimal ET sequence]]: [[8edf]], [[11edf]]


=== Greeley ===
=== Greeley ===
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