453edo: Difference between revisions
Cleanup; +prime error table; +subsets and supersets |
m changed EDO intro to ED intro |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
The equal temperament tempers out | The equal temperament [[tempering out|tempers out]] {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| 54 -37 2 }} ([[monzisma]]) in the 5-limit; [[250047/250000]], 589824/588245, and 2460375/2458624 in the 7-limit; [[3025/3024]], [[5632/5625]], 24057/24010, and 102487/102400 in the 11-limit; [[676/675]], [[1001/1000]], [[4096/4095]], [[6656/6655]], and 16848/16807 in the 13-limit, so that it [[support]]s the [[monzismic]] temperament. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 453 factors into {{factorization|453}}, 453edo contains [[3edo]] and [[151edo]] as subsets. | |||
Latest revision as of 17:16, 20 February 2025
| ← 452edo | 453edo | 454edo → |
453 equal divisions of the octave (abbreviated 453edo or 453ed2), also called 453-tone equal temperament (453tet) or 453 equal temperament (453et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 453 equal parts of about 2.65 ¢ each. Each step represents a frequency ratio of 21/453, or the 453rd root of 2.
The equal temperament tempers out [8 14 -13⟩ (parakleisma) and [54 -37 2⟩ (monzisma) in the 5-limit; 250047/250000, 589824/588245, and 2460375/2458624 in the 7-limit; 3025/3024, 5632/5625, 24057/24010, and 102487/102400 in the 11-limit; 676/675, 1001/1000, 4096/4095, 6656/6655, and 16848/16807 in the 13-limit, so that it supports the monzismic temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.03 | +0.44 | +0.71 | -0.32 | -0.79 | +1.00 | -0.82 | -0.46 | +0.89 | -0.66 |
| Relative (%) | +0.0 | +1.2 | +16.7 | +26.8 | -12.3 | -29.9 | +37.9 | -31.1 | -17.4 | +33.5 | -25.1 | |
| Steps (reduced) |
453 (0) |
718 (265) |
1052 (146) |
1272 (366) |
1567 (208) |
1676 (317) |
1852 (40) |
1924 (112) |
2049 (237) |
2201 (389) |
2244 (432) | |
Subsets and supersets
Since 453 factors into 3 × 151, 453edo contains 3edo and 151edo as subsets.