432edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| 685 -432 }} | | {{monzo| 685 -432 }} | ||
| {{mapping| 432 685 }} | | {{mapping| 432 685 }} | ||
| | | −0.2596 | ||
| 0.2595 | | 0.2595 | ||
| 9.34 | | 9.34 | ||
| Line 33: | Line 24: | ||
| {{monzo| 41 -20 -4 }}, {{monzo| -3 -23 17 }} | | {{monzo| 41 -20 -4 }}, {{monzo| -3 -23 17 }} | ||
| {{mapping| 432 685 1003 }} | | {{mapping| 432 685 1003 }} | ||
| | | −0.1440 | ||
| 0.2676 | | 0.2676 | ||
| 9.63 | | 9.63 | ||
| Line 40: | Line 31: | ||
| 5120/5103, 703125/702464, 6565234375/6530347008 | | 5120/5103, 703125/702464, 6565234375/6530347008 | ||
| {{mapping| 432 685 1003 1213 }} | | {{mapping| 432 685 1003 1213 }} | ||
| | | −0.1631 | ||
| 0.2341 | | 0.2341 | ||
| 8.43 | | 8.43 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 66: | Line 50: | ||
| 4/3 | | 4/3 | ||
| [[Undim]] | | [[Undim]] | ||
{{rank-2 end}} | |||
{{orf}} | {{orf}} | ||
Revision as of 01:45, 16 November 2024
| ← 431edo | 432edo | 433edo → |
Theory
432edo has a reasonable approximation to the 7-limit, where the equal temperament tempers out 5120/5103, 703125/702464, 40353607/40310784, 102760448/102515625, and 283115520/282475249. It supports and provides a good tuning for the 5-limit maja temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.82 | -0.20 | +0.62 | -1.13 | -1.32 | +1.14 | +0.62 | +0.60 | -0.29 | -1.34 | -0.50 |
| Relative (%) | +29.6 | -7.3 | +22.3 | -40.8 | -47.4 | +41.0 | +22.3 | +21.6 | -10.5 | -48.1 | -17.9 | |
| Steps (reduced) |
685 (253) |
1003 (139) |
1213 (349) |
1369 (73) |
1494 (198) |
1599 (303) |
1688 (392) |
1766 (38) |
1835 (107) |
1897 (169) |
1954 (226) | |
Subsets and supersets
432 is a highly factorable number, factoring into 24 × 33, so 432edo has subset edos 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, and 216.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [685 -432⟩ | [⟨432 685]] | −0.2596 | 0.2595 | 9.34 |- | 2.3.5 | [41 -20 -4⟩, [-3 -23 17⟩ | [⟨432 685 1003]] | −0.1440 | 0.2676 | 9.63 |- | 2.3.5.7 | 5120/5103, 703125/702464, 6565234375/6530347008 | [⟨432 685 1003 1213]] | −0.1631 | 0.2341 | 8.43 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 163\432
| 452.78
| 125/96
| Maja
|-
| 4
| 179\432
(37\432)
| 497.22
(102.78)
| 4/3
| Undim
Template:Rank-2 end
Template:Orf