5040edo: Difference between revisions
m Moving from Category:Highly melodic to Category:Highly composite using Cat-a-lot |
added contorsion for harmonics upwards to 67th, for now just the "tempered commas" section since I can't fill in the whole table |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|5040}} | |||
== Theory == | == Theory == | ||
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There's an interesting property that arises in a stricter subgroup, 2.7.13.17.29.31.41.47.61.67. In this subgroup, it makes a rank two temperament with 1111edo (1111 & 5040), which brings two notable number classes together - a repunit and a highly composite number. | There's an interesting property that arises in a stricter subgroup, 2.7.13.17.29.31.41.47.61.67. In this subgroup, it makes a rank two temperament with 1111edo (1111 & 5040), which brings two notable number classes together - a repunit and a highly composite number. | ||
Using the patent val, 5040edo tempers out [[9801/9800]] in the 11-limit. | |||
=== Contorsion table === | === Contorsion table === | ||
| Line 62: | Line 64: | ||
|4 | |4 | ||
|1260edo | |1260edo | ||
|- | |||
|31 | |||
|21 | |||
|[[240edo]] | |||
|- | |||
|37 | |||
|48 | |||
|[[105edo]] | |||
|- | |||
|41 | |||
|2 | |||
|[[2520edo]] | |||
|- | |||
|43 | |||
|12 | |||
|[[420edo]] | |||
|- | |||
|47 | |||
|5 | |||
|[[1008edo]] | |||
|- | |||
|53 | |||
|3 | |||
|[[1680edo]] | |||
|- | |||
|59 | |||
|3 | |||
|[[1680edo]] | |||
|- | |||
|61 | |||
|1 | |||
|5040edo (maps to a coprime step) | |||
|- | |||
|67 | |||
|9 | |||
|[[560edo]] | |||
|} | |} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Tempered commas === | |||
2.3.7 subgroup: {{Monzo|81 41 -52}}, {{Monzo|-110 119 -28}} | |||
2.3.7.13 subgroup: {{monzo|8 15 -10 -1}}, {{monzo|-41 34 2 -5}}, {{monzo|-52 6 -2 13}} | |||
2.3.7.13.17 subgroup: [[5832/5831]], [[31213/31212]], {{monzo|-44 28 5 -5 1}}, {{monzo|-50 9 -6 12 2}}. | |||
2.3.7.13.17.23 subgroup: 5832/5831, 213003/212992, 279888/279841, {{Monzo|-25 -3 -9 14 3 -2}}, {{Monzo|-27 -6 -5 15 1 -2}} | |||
2.3.7.13.17.23.29 subgroup: 4914/4913, 5832/5831, 107406/107387, 116928/116909, 3234573/3233984, 2871098559212689/2870492063072256 | |||
== Scales == | == Scales == | ||