52nd-octave temperaments: Difference between revisions
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{{ | {{Technical data page}} | ||
{{Infobox fractional-octave|52}} | |||
See [[52edo]]. | See [[52edo]]. | ||
== 52-31/29-commatic == | == 52-31/29-commatic == | ||
This temperament establishes the mapping of [[31/29]] to 5\52. | This temperament establishes the mapping of [[31/29]] to 5\52. | ||
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[[Support]]ing [[ET]]s: {{EDOs|52, 260, 416, 624, 676, 988, 1092, 1352, 1768}},... | [[Support]]ing [[ET]]s: {{EDOs|52, 260, 416, 624, 676, 988, 1092, 1352, 1768}},... | ||
== French deck == | == French deck == | ||
A period-52 temperament described as the 988 & 2444 temperament for the 2.5.11.13.19.29.31 subgroup, and tempers out the comma 2.29.31 {{monzo|-5 -52 52}}, which means 5 periods are equal to 31/29. Called so because there's 52 playing cards in the traditional deck. 1789edo does not support it as 1789 is a prime number, and therefore is not divisible by 52. | A period-52 temperament described as the 988 & 2444 temperament for the 2.5.11.13.19.29.31 subgroup, and tempers out the comma 2.29.31 {{monzo|-5 -52 52}}, which means 5 periods are equal to 31/29. Called so because there's 52 playing cards in the traditional deck. 1789edo does not support it as 1789 is a prime number, and therefore is not divisible by 52. | ||
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{{Optimal ET sequence|legend=1|988, 1456, 2444}}, ... | {{Optimal ET sequence|legend=1|988, 1456, 2444}}, ... | ||
== Tellurium == | |||
Tellurium preserves [[26edo]]'s accurate mappings of [[8/7]] and [[13/12]]; it brings in mappings of [[11/9]] and [[51/49]] from 52edo. | |||
Subgroup: 2.3.7.11.13.17 | |||
[[Comma list]]: 8624/8619, 22528/22491, 34969/34944, 41503/41472 | |||
[[Mapping]]: [{{val| 52 52 146 119 162 243 }}, {{val| 0 1 0 2 1 -1 }}] | |||
Mapping generators: ~78/77, ~3/2 | |||
Optimal tuning ([[CTE]]): ~3/2 = 702.261 | |||
{{Optimal ET sequence|legend=1| 104, 260, 364, 832, 1196, 2028bdefg }} | |||
[[Badness]] (Sintel): 1.501 | |||
{{Navbox fractional-octave}} | |||
{{todo|inline=1|improve synopsis}} | |||
Latest revision as of 16:39, 6 June 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
See 52edo.
52-31/29-commatic
This temperament establishes the mapping of 31/29 to 5\52.
Subgroup: 2.29.31
Comma list: 2.29.31 [-5 -52 52⟩
Subgroup-val mapping: [⟨52 0 5], ⟨0 1 1]]
- sval mapping generators: ~2.29.31 [2 -21 21⟩ = 1\52, ~29
Optimal tuning (CTE): ~29/16 = 1029.613
Supporting ETs: 52, 260, 416, 624, 676, 988, 1092, 1352, 1768,...
French deck
A period-52 temperament described as the 988 & 2444 temperament for the 2.5.11.13.19.29.31 subgroup, and tempers out the comma 2.29.31 [-5 -52 52⟩, which means 5 periods are equal to 31/29. Called so because there's 52 playing cards in the traditional deck. 1789edo does not support it as 1789 is a prime number, and therefore is not divisible by 52.
Subgroup: 2.5.11.13.19.29.31
Comma list: 6656/6655, 600704/600625, 1308736/1308625, 35934301/35932160, 17179869184/17174157715
Sval mapping: [⟨52 1 197 124 238 475 480], ⟨0 7 -1 4 -1 -13 13]]
- sval mapping generators: ~1460875/1441792, ~1045/832
Optimal tuning (CTE): ~134560000/107132311 = 394.757
Optimal ET sequence: 988, 1456, 2444, ...
Tellurium
Tellurium preserves 26edo's accurate mappings of 8/7 and 13/12; it brings in mappings of 11/9 and 51/49 from 52edo.
Subgroup: 2.3.7.11.13.17
Comma list: 8624/8619, 22528/22491, 34969/34944, 41503/41472
Mapping: [⟨52 52 146 119 162 243], ⟨0 1 0 2 1 -1]]
Mapping generators: ~78/77, ~3/2
Optimal tuning (CTE): ~3/2 = 702.261
Optimal ET sequence: 104, 260, 364, 832, 1196, 2028bdefg
Badness (Sintel): 1.501
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Todo: improve synopsis |