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Badness: 0.029741
Badness: 0.029741
== Quintoneum ==
{{See also| 28ed5 #28ed5 as a generator }}
The ''quintoneum'' temperament (12&217) tempers out the hemimean comma (3136/3125) and the garischisma (33554432/33480783) in the 7-limit. In the 2.3.5.7.17.19 subgroup, 256/255 (the difference between 16/15 and 17/16), 289/288 (the difference between 17/16 and 18/17), 324/323 (the difference between 18/17 and 19/18), 361/360 (the difference between 19/18 and 20/19), and 400/399 (the difference between 20/19 and 21/20) are equated together, and 476/475 (the difference between 28/25 and 19/17) is tempered out. Immediate 2.3.5.7.11.17.19 extensions include ''quintoneum'' (12&217, tempering out 441/440), ''quintasandra'' (217&229, equating 385/384 with 400/399), and ''quintasandroid'' (12&229, equating 400/399 with 441/440). The name ''quintoneum'' is so named because the generator is 1/5 of the [[Hemimage temperaments #Cotoneum|cotoneum]] fourth (~4/3, about 497.7 cents).
Subgroup: 2.3.5.7
[[Comma list]]: 3136/3125, 33554432/33480783
[[Mapping]]: [{{val|1 2 0 -3}}, {{val|0 -5 28 70}}]
{{Multival|legend=1|5 -28 -70 -56 -125 -84}}
[[POTE generator]]: ~200/189 = 99.555
{{Val list|legend=1| 12, 217, 229, 446, 675c }}
[[Badness]]: 0.142897
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3136/3125, 7168000/7144929
Mapping: [{{val|1 2 0 -3 -5}}, {{val|0 -5 28 70 102}}]
POTE generator: ~35/33 = 99.539
Vals: {{Val list| 12, 205d, 217 }}
Badness: 0.087157
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 3136/3125, 13720/13689
Mapping: [{{val|1 2 0 -3 -5 -7}}, {{val|0 -5 28 70 102 129}}]
POTE generator: ~35/33 = 99.541
Vals: {{Val list| 12f, 205df, 217 }}
Badness: 0.052361
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 441/440, 595/594, 3136/3125, 3757/3750
Mapping: [{{val|1 2 0 -3 -5 -7 5}}, {{val|0 -5 28 70 102 129 -11}}]
POTE generator: ~18/17 = 99.540
Vals: {{Val list| 12f, 205df, 217 }}
Badness: 0.035653
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 364/363, 441/440, 476/475, 595/594, 1216/1215, 3757/3750
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
Vals: {{Val list| 12f, 205df, 217 }}
Badness: 0.025782
==== Quintoneoid ====
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 1001/1000, 3136/3125, 59150/59049
Mapping: [{{val|1 2 0 -3 -5 11}}, {{val|0 -5 28 70 102 -88}}]
POTE generator: ~35/33 = 99.537
Vals: {{Val list| 12, 205d, 217 }}
Badness: 0.072826
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 441/440, 595/594, 1001/1000, 2601/2600, 3136/3125
Mapping: [{{val|1 2 0 -3 -5 11 5}}, {{val|0 -5 28 70 102 -88 -11}}]
POTE generator: ~18/17 = 99.537
Vals: {{Val list| 12, 205d, 217 }}
Badness: 0.042339
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 441/440, 476/475, 595/594, 1001/1000, 1216/1215, 2601/2600
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
Vals: {{Val list| 12, 205d, 217 }}
Badness: 0.028983
=== Quintasandra ===
Subgroup: 2.3.5.7.11
Comma list: 3136/3125, 19712/19683, 41503/41472
Mapping: [{{val|1 2 0 -3 13}}, {{val|0 -5 28 70 -115}}]
POTE generator: ~200/189 = 99.551
Vals: {{Val list| 12e, 217, 446 }}
Badness: 0.109908
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 3136/3125, 4096/4095, 19712/19683
Mapping: [{{val|1 2 0 -3 13 11}}, {{val|0 -5 28 70 -115 -88}}]
POTE generator: ~55/52 = 99.548
Vals: {{Val list| 12e, 217, 446, 663c }}
Badness: 0.067730
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 936/935, 1156/1155, 1377/1375, 3136/3125, 4096/4095
Mapping: [{{val|1 2 0 -3 13 11 5}}, {{val|0 -5 28 70 -115 -88 -11}}]
POTE generator: ~18/17 = 99.548
Vals: {{Val list| 12e, 217, 446, 663c }}
Badness: 0.038153
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 476/475, 936/935, 1156/1155, 1216/1215, 1377/1375, 1729/1728
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
Vals: {{Val list| 12e, 217, 446, 663ch }}
Badness: 0.026654
=== Quintasandroid ===
Subgroup: 2.3.5.7.11
Comma list: 3136/3125, 8019/8000, 15488/15435
Mapping: [{{val|1 2 0 -3 -6}}, {{val|0 -5 28 70 114}}]
POTE generator: ~200/189 = 99.570
Vals: {{Val list| 12, 217e, 229, 470cd, 699cd }}
Badness: 0.093971
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 2080/2079, 3136/3125, 10648/10647
Mapping: [{{val|1 2 0 -3 -6 -8}}, {{val|0 -5 28 70 114 141}}]
POTE generator: ~55/52 = 99.578
Vals: {{Val list| 12f, 217ef, 229, 241, 470cd, 711ccd }}
Badness: 0.065701
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 442/441, 561/560, 3136/3125, 7744/7735
Mapping: [{{val|1 2 0 -3 -6 -8 5}}, {{val|0 -5 28 70 114 141 -11}}]
POTE generator: ~18/17 = 99.574
Vals: {{Val list| 12f, 217ef, 229, 241, 470cd }}
Badness: 0.046624
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 351/350, 442/441, 476/475, 561/560, 627/625, 6144/6137
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
Vals: {{Val list| 12f, 217ef, 229, 241, 470cd }}
Badness: 0.033145
==== Quintasand ====
Subgroup: 2.3.5.7.11.13
Comma list: 1573/1568, 3136/3125, 4096/4095, 4459/4455
Mapping: [{{val|1 2 0 -3 -6 11}}, {{val|0 -5 28 70 114 -88}}]
POTE generator: ~200/189 = 99.556
Vals: {{Val list| 12, 217e, 229, 446e, 675ceef }}
Badness: 0.100195
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 561/560, 715/714, 1701/1700, 3136/3125, 4096/4095
Mapping: [{{val|1 2 0 -3 -6 11 5}}, {{val|0 -5 28 70 114 -88 -11}}]
POTE generator: ~18/17 = 99.556
Vals: {{Val list| 12, 217e, 229, 446e, 675ceef }}
Badness: 0.057851
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 286/285, 476/475, 561/560, 627/625, 1216/1215, 1729/1728
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
Vals: {{Val list| 12, 217e, 229, 446e, 675ceefh }}
Badness: 0.040410


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
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