5280edo: Difference between revisions
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5280edo is consistent in the [[7-odd-limit]]. On the patent val, it tempers out the comma {{monzo|-103 -22 0 22 22}}, which associates [[77/48]] to [[22edo|15\22]]. | 5280edo is consistent in the [[7-odd-limit]]. On the patent val, it tempers out the comma {{monzo|-103 -22 0 22 22}}, which associates [[77/48]] to [[22edo|15\22]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{harmonics in equal|5280}} | {{harmonics in equal|5280}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 5280 factors as {{Factorization|5280}}, 5280edo has subset edos {{EDOs|1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 160, 165, 176, 220, 240, 264, 330, 352, 440, 480, 528, 660, 880, 1056, 1320, 1760, 2640}}. | Since 5280 factors as {{Factorization|5280}}, 5280edo has subset edos {{EDOs|1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 160, 165, 176, 220, 240, 264, 330, 352, 440, 480, 528, 660, 880, 1056, 1320, 1760, 2640}}. | ||
Latest revision as of 13:11, 21 February 2025
| ← 5279edo | 5280edo | 5281edo → |
5280 equal divisions of the octave (abbreviated 5280edo or 5280ed2), also called 5280-tone equal temperament (5280tet) or 5280 equal temperament (5280et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5280 equal parts of about 0.227 ¢ each. Each step represents a frequency ratio of 21/5280, or the 5280th root of 2.
5280edo is consistent in the 7-odd-limit. On the patent val, it tempers out the comma [-103 -22 0 22 22⟩, which associates 77/48 to 15\22.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0905 | +0.0499 | +0.0377 | -0.0464 | +0.0457 | -0.0731 | -0.0869 | +0.0446 | -0.0130 | -0.0991 | -0.0925 |
| Relative (%) | +39.8 | +22.0 | +16.6 | -20.4 | +20.1 | -32.2 | -38.2 | +19.6 | -5.7 | -43.6 | -40.7 | |
| Steps (reduced) |
8369 (3089) |
12260 (1700) |
14823 (4263) |
16737 (897) |
18266 (2426) |
19538 (3698) |
20628 (4788) |
21582 (462) |
22429 (1309) |
23191 (2071) |
23884 (2764) | |
Subsets and supersets
Since 5280 factors as 25 × 3 × 5 × 11, 5280edo has subset edos 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 160, 165, 176, 220, 240, 264, 330, 352, 440, 480, 528, 660, 880, 1056, 1320, 1760, 2640.