281edo: Difference between revisions
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The | {{Infobox ET}} | ||
{{ED intro}} | |||
The equal temperament [[tempering out|tempers out]] [[225/224]] in the 7-limit, and [[243/242]] and [[4000/3993]] in the 11-limit, so that it [[support]]s [[marvo]] and provides the [[optimal patent val]]; it also gives the optimal patent val for the rank-3 [[spectacle]] temperament. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|281}} | |||
=== Subsets and supersets === | |||
281edo is the 60th [[prime edo]]. | |||
[[Category:Spectacle]] | |||
[[Category:Marvo]] | |||
Latest revision as of 06:55, 20 February 2025
| ← 280edo | 281edo | 282edo → |
281 equal divisions of the octave (abbreviated 281edo or 281ed2), also called 281-tone equal temperament (281tet) or 281 equal temperament (281et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 281 equal parts of about 4.27 ¢ each. Each step represents a frequency ratio of 21/281, or the 281st root of 2.
The equal temperament tempers out 225/224 in the 7-limit, and 243/242 and 4000/3993 in the 11-limit, so that it supports marvo and provides the optimal patent val; it also gives the optimal patent val for the rank-3 spectacle temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.60 | -1.97 | +0.57 | +1.07 | -0.43 | +0.75 | +0.70 | +1.81 | +1.42 | -1.03 | -0.52 |
| Relative (%) | -37.4 | -46.2 | +13.3 | +25.1 | -10.0 | +17.6 | +16.4 | +42.3 | +33.2 | -24.1 | -12.1 | |
| Steps (reduced) |
445 (164) |
652 (90) |
789 (227) |
891 (48) |
972 (129) |
1040 (197) |
1098 (255) |
1149 (25) |
1194 (70) |
1234 (110) |
1271 (147) | |
Subsets and supersets
281edo is the 60th prime edo.