283edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
283edo is in[[consistent]] to the [[5-odd-limit]] and the [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise it is good in approximating harmonics [[5/1|5]], [[9/1|9]], [[11/1|11]], [[13/1|13]], [[17/1|17]], [[19/1|19]], [[21/1|21]], and [[23/1|23]], making it suitable for a 2.9.5.21.11.13.17.19.23 [[subgroup]] interpretation. | |||
Using the [[patent val]] nonetheless, the equal temperament is closely associated with the [[245/243|sensamagic comma (245/243)]], defining the [[optimal patent val]] for the sensamagic [[7-limit]] [[planar temperament]] as well as [[escaped]], which tempers out both 245/243 and [[65625/65536]] in the 7-limit, [[385/384]] and [[4000/3993]] in the [[11-limit]], and [[352/351]] and [[625/624]] in the [[13-limit]]. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|283}} | |||
=== Subsets and supersets === | |||
283edo is the 61st [[prime edo]]. | |||
[[Category:Sensamagic]] | |||
[[Category:Escaped]] | |||
Latest revision as of 14:28, 20 February 2025
| ← 282edo | 283edo | 284edo → |
283 equal divisions of the octave (abbreviated 283edo or 283ed2), also called 283-tone equal temperament (283tet) or 283 equal temperament (283et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 283 equal parts of about 4.24 ¢ each. Each step represents a frequency ratio of 21/283, or the 283rd root of 2.
283edo is inconsistent to the 5-odd-limit and the harmonic 3 is about halfway between its steps. Otherwise it is good in approximating harmonics 5, 9, 11, 13, 17, 19, 21, and 23, making it suitable for a 2.9.5.21.11.13.17.19.23 subgroup interpretation.
Using the patent val nonetheless, the equal temperament is closely associated with the sensamagic comma (245/243), defining the optimal patent val for the sensamagic 7-limit planar temperament as well as escaped, which tempers out both 245/243 and 65625/65536 in the 7-limit, 385/384 and 4000/3993 in the 11-limit, and 352/351 and 625/624 in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.93 | -0.45 | -2.04 | -0.38 | -0.08 | -0.95 | +1.48 | +1.05 | -0.69 | -0.11 | -0.71 |
| Relative (%) | +45.6 | -10.6 | -48.1 | -8.9 | -1.9 | -22.4 | +35.0 | +24.8 | -16.3 | -2.6 | -16.8 | |
| Steps (reduced) |
449 (166) |
657 (91) |
794 (228) |
897 (48) |
979 (130) |
1047 (198) |
1106 (257) |
1157 (25) |
1202 (70) |
1243 (111) |
1280 (148) | |
Subsets and supersets
283edo is the 61st prime edo.