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Quindromeda family: Difference between revisions

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[[Badness]] (Sintel): 9.380
[[Badness]] (Sintel): 9.380
=== Subgroup temperament ===


The quindromeda temperament works well for the 2.3.5.17.19 subgroup, tempering out the [[1216/1215|password comma]] (1216/1215), [[1445/1444|aureusma]] (1445/1444), and [[6144/6137|langwisma]] (6144/6137). An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and twenty-eight 18/17s with the [[5/1|fifth harmonic]].
The quindromeda temperament works well for the 2.3.5.17.19 subgroup, tempering out the [[1216/1215|password comma]] (1216/1215), [[1445/1444|aureusma]] (1445/1444), and [[6144/6137|langwisma]] (6144/6137). An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and twenty-eight 18/17s with the [[5/1|fifth harmonic]].
Line 102: Line 100:
Mapping: [{{val| 1 2 0 -3 -5 -7 }}, {{val| 0 -5 28 70 102 129 }}]
Mapping: [{{val| 1 2 0 -3 -5 -7 }}, {{val| 0 -5 28 70 102 129 }}]


POTE generator: ~35/33 = 99.541
Optimal tunings:
* WE: ~2 = 1199.855¢, ~35/33 = 99.529¢
* CWE: ~2 = 1200.000¢, ~35/33 = 99.540¢


{{Optimal ET sequence|legend=0| 12f, 205df, 217 }}
{{Optimal ET sequence|legend=0| 12f, 205df, 217 }}


Badness: 0.052361
Badness (Sintel): 2.164


===== 17-limit =====
===== 17-limit =====
Line 115: Line 115:
Mapping: [{{val| 1 2 0 -3 -5 -7 5 }}, {{val| 0 -5 28 70 102 129 -11 }}]
Mapping: [{{val| 1 2 0 -3 -5 -7 5 }}, {{val| 0 -5 28 70 102 129 -11 }}]


POTE generator: ~18/17 = 99.540
Optimal tunings:
* WE: ~2 = 1199.890¢, ~18/17 = 99.531¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.539¢


{{Optimal ET sequence|legend=0| 12f, 205df, 217 }}
{{Optimal ET sequence|legend=0| 12f, 205df, 217 }}


Badness: 0.035653
Badness (Sintel): 1.816


===== 19-limit =====
===== 19-limit =====
Line 128: Line 130:
Mapping: [{{val| 1 2 0 -3 -5 -7 5 4 }}, {{val| 0 -5 28 70 102 129 -11 3 }}]
Mapping: [{{val| 1 2 0 -3 -5 -7 5 4 }}, {{val| 0 -5 28 70 102 129 -11 3 }}]


POTE generator: ~18/17 = 99.541
Optimal tunings:
* WE: ~2 = 1199.859¢, ~18/17 = 99.529¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.540¢


{{Optimal ET sequence|legend=0| 12f, 205df, 217 }}
{{Optimal ET sequence|legend=0| 12f, 205df, 217 }}


Badness: 0.025782
Badness (Sintel): 1.569


==== Quintoneoid ====
==== Quintoneoid ====
Line 141: Line 145:
Mapping: [{{val| 1 2 0 -3 -5 11 }}, {{val| 0 -5 28 70 102 -88 }}]
Mapping: [{{val| 1 2 0 -3 -5 11 }}, {{val| 0 -5 28 70 102 -88 }}]


POTE generator: ~35/33 = 99.537
Optimal tunings:
* WE: ~2 = 1199.901¢, ~35/33 = 99.529¢
* CWE: ~2 = 1200.000¢, ~35/33 = 99.537¢


{{Optimal ET sequence|legend=0| 12, 205d, 217 }}
{{Optimal ET sequence|legend=0| 12, 205d, 217 }}


Badness: 0.072826
Badness (Sintel): 3.009


===== 17-limit =====
===== 17-limit =====
Line 154: Line 160:
Mapping: [{{val| 1 2 0 -3 -5 11 5 }}, {{val| 0 -5 28 70 102 -88 -11 }}]
Mapping: [{{val| 1 2 0 -3 -5 11 5 }}, {{val| 0 -5 28 70 102 -88 -11 }}]


POTE generator: ~18/17 = 99.537
Optimal tunings:
* WE: ~2 = 1199.912¢, ~18/17 = 99.530¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.537¢


{{Optimal ET sequence|legend=0| 12, 205d, 217 }}
{{Optimal ET sequence|legend=0| 12, 205d, 217 }}


Badness: 0.042339
Badness (Sintel): 2.157


===== 19-limit =====
===== 19-limit =====
Line 167: Line 175:
Mapping: [{{val| 1 2 0 -3 -5 11 5 4 }}, {{val| 0 -5 28 70 102 -88 -11 3 }}]
Mapping: [{{val| 1 2 0 -3 -5 11 5 4 }}, {{val| 0 -5 28 70 102 -88 -11 3 }}]


POTE generator: ~18/17 = 99.537
Optimal tunings:
* WE: ~2 = 1199.889¢, ~18/17 = 99.528¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.537¢


{{Optimal ET sequence|legend=0| 12, 205d, 217 }}
{{Optimal ET sequence|legend=0| 12, 205d, 217 }}


Badness: 0.028983
Badness (Sintel): 1.763


=== Quinsandra ===
=== Quinsandra ===
Line 197: Line 207:
Mapping: [{{val| 1 2 0 -3 13 11 }}, {{val| 0 -5 28 70 -115 -88 }}]
Mapping: [{{val| 1 2 0 -3 13 11 }}, {{val| 0 -5 28 70 -115 -88 }}]


POTE generator: ~55/52 = 99.548
Optimal tunings:
* WE: ~2 = 1199.922¢, ~55/52 = 99.541¢
* CWE: ~2 = 1200.000¢, ~55/52 = 99.548¢


{{Optimal ET sequence|legend=0| 12e, 217, 446, 663c }}
{{Optimal ET sequence|legend=0| 12e, 217, 446, 663c }}


Badness: 0.067730
Badness (Sintel): 2.799


==== 17-limit ====
==== 17-limit ====
Line 210: Line 222:
Mapping: [{{val| 1 2 0 -3 13 11 5 }}, {{val| 0 -5 28 70 -115 -88 -11 }}]
Mapping: [{{val| 1 2 0 -3 13 11 5 }}, {{val| 0 -5 28 70 -115 -88 -11 }}]


POTE generator: ~18/17 = 99.548
Optimal tunings:
* WE: ~2 = 1199.932¢, ~18/17 = 99.542¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.548¢


{{Optimal ET sequence|legend=0| 12e, 217, 446, 663c }}
{{Optimal ET sequence|legend=0| 12e, 217, 446, 663c }}


Badness: 0.038153
Badness (Sintel): 1.944


==== 19-limit ====
==== 19-limit ====
Line 223: Line 237:
Mapping: [{{val| 1 2 0 -3 13 11 5 4 }}, {{val| 0 -5 28 70 -115 -88 -11 3 }}]
Mapping: [{{val| 1 2 0 -3 13 11 5 4 }}, {{val| 0 -5 28 70 -115 -88 -11 3 }}]


POTE generator: ~18/17 = 99.547
Optimal tunings:
* WE: ~2 = 1199.907¢, ~18/17 = 99.540¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.547¢


{{Optimal ET sequence|legend=0| 12e, 217, 446, 663ch }}
{{Optimal ET sequence|legend=0| 12e, 217, 446, 663ch }}


Badness: 0.026654
Badness (Sintel): 1.621


=== Quinsandric ===
=== Quinsandric ===
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Mapping: [{{val| 1 2 0 -3 -6 -8 }}, {{val| 0 -5 28 70 114 141 }}]
Mapping: [{{val| 1 2 0 -3 -6 -8 }}, {{val| 0 -5 28 70 114 141 }}]


POTE generator: ~55/52 = 99.578
Optimal tunings:
* WE: ~2 = 1199.730¢, ~55/52 = 99.555¢
* CWE: ~2 = 1200.000¢, ~55/52 = 99.575¢


{{Optimal ET sequence|legend=0| 12f, 217ef, 229, 241, 470cd, 711ccd }}
{{Optimal ET sequence|legend=0| 12f, 217ef, 229, 241, 470cd, 711ccd }}


Badness: 0.065701
Badness (Sintel): 2.715


===== 17-limit =====
===== 17-limit =====
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Mapping: [{{val| 1 2 0 -3 -6 -8 5 }}, {{val| 0 -5 28 70 114 141 -11 }}]
Mapping: [{{val| 1 2 0 -3 -6 -8 5 }}, {{val| 0 -5 28 70 114 141 -11 }}]


POTE generator: ~18/17 = 99.574
Optimal tunings:
* WE: ~2 = 1199.827¢, ~18/17 = 99.560¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.573¢


{{Optimal ET sequence|legend=0| 12f, 217ef, 229, 241, 470cd }}
{{Optimal ET sequence|legend=0| 12f, 217ef, 229, 241, 470cd }}


Badness: 0.046624
Badness (Sintel): 2.375


===== 19-limit =====
===== 19-limit =====
Line 277: Line 297:
Mapping: [{{val| 1 2 0 -3 -6 -8 5 4 }}, {{val| 0 -5 28 70 114 141 -11 3 }}]
Mapping: [{{val| 1 2 0 -3 -6 -8 5 4 }}, {{val| 0 -5 28 70 114 141 -11 3 }}]


POTE generator: ~18/17 = 99.575
Optimal tunings:
* WE: ~2 = 1199.804¢, ~18/17 = 99.559¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.574¢


{{Optimal ET sequence|legend=0| 12f, 217ef, 229, 241, 470cd }}
{{Optimal ET sequence|legend=0| 12f, 217ef, 229, 241, 470cd }}


Badness: 0.033145
Badness (Sintel): 2.016


==== Quinsandro ====
==== Quinsandro ====
Line 290: Line 312:
Mapping: [{{val| 1 2 0 -3 -6 11 }}, {{val| 0 -5 28 70 114 -88 }}]
Mapping: [{{val| 1 2 0 -3 -6 11 }}, {{val| 0 -5 28 70 114 -88 }}]


Optimal tunings:
* WE: ~2 = 1200.032¢, ~200/189 = 99.559¢
* CWE: ~2 = 1200.000¢, ~200/189 = 99.556¢
POTE generator: ~200/189 = 99.556
POTE generator: ~200/189 = 99.556


{{Optimal ET sequence|legend=0| 12, 217e, 229, 446e, 675ceef }}
{{Optimal ET sequence|legend=0| 12, 217e, 229, 446e, 675ceef }}


Badness: 0.100195
Badness (Sintel): 4.140


===== 17-limit =====
===== 17-limit =====
Line 303: Line 328:
Mapping: [{{val| 1 2 0 -3 -6 11 5 }}, {{val| 0 -5 28 70 114 -88 -11 }}]
Mapping: [{{val| 1 2 0 -3 -6 11 5 }}, {{val| 0 -5 28 70 114 -88 -11 }}]


POTE generator: ~18/17 = 99.556
Optimal tunings:
* WE: ~2 = 1200.030¢, ~18/17 = 99.559¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.556¢


{{Optimal ET sequence|legend=0| 12, 217e, 229, 446e, 675ceef }}
{{Optimal ET sequence|legend=0| 12, 217e, 229, 446e, 675ceef }}


Badness: 0.057851
Badness (Sintel): 2.947


===== 19-limit =====
===== 19-limit =====
Line 316: Line 343:
Mapping: [{{val| 1 2 0 -3 -6 11 5 4 }}, {{val| 0 -5 28 70 114 -88 -11 3 }}]
Mapping: [{{val| 1 2 0 -3 -6 11 5 4 }}, {{val| 0 -5 28 70 114 -88 -11 3 }}]


POTE generator: ~18/17 = 99.557
Optimal tunings:
* WE: ~2 = 1199.989¢, ~18/17 = 99.556¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.557¢


{{Optimal ET sequence|legend=0| 12, 217e, 229, 446e, 675ceefh }}
{{Optimal ET sequence|legend=0| 12, 217e, 229, 446e, 675ceefh }}


Badness: 0.040410
Badness (Sintel): 2.458


== Quintakwai ==
== Quintakwai ==
Line 567: Line 596:


== Hemiquindromeda ==
== Hemiquindromeda ==
The ''hemiquindromeda'' temperament (193&217) splits the fourth in ten, and tempers out the [[canousma]] (4802000/4782969) and the decovulture comma (67108864/66976875) in the 7-limit.
The ''hemiquindromeda'' temperament (193&217) splits the fourth in ten, and tempers out the [[canousma]] (4802000/4782969) and the [[decovulture comma]] (67108864/66976875) in the 7-limit.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Retrieved from "https://en.xen.wiki/w/Quindromeda_family"