35th-octave temperaments: Difference between revisions
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Currywurst44 (talk | contribs) →Insanobromismic: remove ~17 as a mapping generator |
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Mapping: [{{val|35 0 0 0 0 0 36}}, {{val|0 1 0 0 0 0 -1}}, {{val|0 0 1 0 0 0 2}}, {{val|0 0 0 1 0 0 0}}, {{val|0 0 0 0 1 0 0}}, {{val|0 0 0 0 0 1 0}}] | Mapping: [{{val|35 0 0 0 0 0 36}}, {{val|0 1 0 0 0 0 -1}}, {{val|0 0 1 0 0 0 2}}, {{val|0 0 0 1 0 0 0}}, {{val|0 0 0 0 1 0 0}}, {{val|0 0 0 0 0 1 0}}] | ||
: mapping generators: ~51/50 = 1\35, ~3, ~5, ~7, ~11, ~13 | : mapping generators: ~51/50 = 1\35, ~3, ~5, ~7, ~11, ~13 | ||
{{Optimal ET sequence|legend=1|35f, 140, 280, 385, 525, 665, 805, 1190, 1330, 2205, 2590, 2730, 3395, 7315, 10045, 10710, 10850, 14420, 16625, 17955, 18480, 20020, 20895, 21875, 24605, 25270, 28000, 31920, ...}} | |||
\* optimal patent val: [[589400edo|589400]] | |||
=== Insanobromic === | === Insanobromic === | ||
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: mapping generators: ~51/50 = 1\35, ~3, ~5, | : mapping generators: ~51/50 = 1\35, ~3, ~5, | ||
[[Support]]ing [[ET]]s: {{EDOs|140, 525, 665, 2730, 3395, 3920, 7980 | [[Support]]ing [[ET]]s: {{EDOs|140, 525, 665, 2730, 3395, 3920, 7980, 16625, 28000}}, ... | ||
== Bromine == | == Bromine == | ||
Bromine is named after the 35th chemical element. | Bromine is named after the 35th chemical element, and is made by combining two notable high-accuracy edos divisible by 35, [[665edo]] and [[3395edo]] - described as the 665 & 3395 temperament. | ||
In the 7-limit, [[1400edo]] is also a tuning. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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[[Mapping]]: [{{val|35 0 -418 653}}, {{val|0 1 9 -10}}] | [[Mapping]]: [{{val|35 0 -418 653}}, {{val|0 1 9 -10}}] | ||
: mapping generators: ~38263752/37515625 = 1\35, ~3 | |||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~38263752/37515625 = 34.286{{c}}, ~3/2 = 701.969{{c}} | |||
: [[error map]]: {{val| -0.006, 0.009, -0.001, 0.002 }} | |||
* [[CWE]]: ~38263752/37515625 = 34.286{{c}}, ~3/2 = 701.973{{c}} | |||
: error map: {{val| -0.000, 0.018, 0.012, 0.018 }} | |||
{{Optimal ET sequence|legend=1|70d, 665, 2065, 2730, 3395, 10850, 14245, 17640}} | |||
Badness: 4.681 | |||
=== 11-limit === | === 11-limit === | ||
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Mapping: [{{val|35 0 -418 653 2451}}, {{val|0 1 9 -10 -42}}] | Mapping: [{{val|35 0 -418 653 2451}}, {{val|0 1 9 -10 -42}}] | ||
: mapping generators: ~1203125/1179648 = 1\35, ~3 | |||
Optimal tuning | [[Optimal tuning]]s: | ||
* [[WE]]: ~1203125/1179648 = 34.286{{c}}, ~3/2 = 701.970{{c}} | |||
: [[error map]]: {{val| -0.007, 0.008, 0.012, -0.020, 0.014 }} | |||
* [[CWE]]: ~1203125/1179648 = 34.286{{c}}, ~3/2 = 701.975{{c}} | |||
: error map: {{val| 0.000, 0.020, 0.029, -0.000, 0.035 }} | |||
{{Optimal ET sequence|legend=1|665, 2730, 3395, 6125, 9520}} | {{Optimal ET sequence|legend=1|665, 2065e, 2730, 3395, 6125, 9520, 12915}} | ||
[[Badness]]: 4.891 | |||
=== 13-limit === | === 13-limit === | ||
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Mapping generators: ~1485/1456 = 1\35, ~3 | Mapping generators: ~1485/1456 = 1\35, ~3 | ||
Optimal tuning | [[Optimal tuning]]s: | ||
* [[WE]]: ~1485/1456 = 34.286{{c}}, ~3/2 = 701.970{{c}} | |||
: [[error map]]: {{val| -0.006, 0.010, 0.013, -0.014, 0.027, -0.035 }} | |||
* [[CWE]]: ~1485/1456 = 34.286{{c}}, ~3/2 = 701.975{{c}} | |||
: error map: {{val| 0.000, 0.019, 0.027, 0.002, 0.043, -0.016 }} | |||
{{Optimal ET sequence|legend=1|665, 2065e, 2730, 3395, 9520, 12915}} | |||
[[Badness]]: 2.328 | |||
=== 17-limit === | === 17-limit === | ||
The period is mapped to ~51/50. | The period is finally mapped to true ~51/50. | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||