245edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
[[ | == Theory == | ||
245edo is only [[consistent]] to the [[5-odd-limit]]. The equal temperament [[tempering out|tempers out]] {{monzo| -17 21 -7 }} and {{monzo| 19 10 -15 }} in the 5-limit; [[6144/6125]] and [[16875/16807]] in the 7-limit; [[441/440]], [[4000/3993]], 6912/6875, 14700/14641, 30375/30184 and 54675/54208 in the 11-limit. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|245}} | |||
=== Subsets and supersets === | |||
Since 245 factors into {{factorization|245}}, 245edo has subset edos {{EDOs| 5, 7, 35, and 49 }}. | |||
{{todo|expand}} | |||
Latest revision as of 17:17, 20 February 2025
| ← 244edo | 245edo | 246edo → |
245 equal divisions of the octave (abbreviated 245edo or 245ed2), also called 245-tone equal temperament (245tet) or 245 equal temperament (245et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 245 equal parts of about 4.9 ¢ each. Each step represents a frequency ratio of 21/245, or the 245th root of 2.
Theory
245edo is only consistent to the 5-odd-limit. The equal temperament tempers out [-17 21 -7⟩ and [19 10 -15⟩ in the 5-limit; 6144/6125 and 16875/16807 in the 7-limit; 441/440, 4000/3993, 6912/6875, 14700/14641, 30375/30184 and 54675/54208 in the 11-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.55 | +0.63 | +0.97 | +1.80 | +2.15 | +1.92 | -0.92 | -2.10 | +1.26 | -0.58 | -1.34 |
| Relative (%) | -31.6 | +12.8 | +19.8 | +36.8 | +43.9 | +39.2 | -18.8 | -42.8 | +25.8 | -11.8 | -27.3 | |
| Steps (reduced) |
388 (143) |
569 (79) |
688 (198) |
777 (42) |
848 (113) |
907 (172) |
957 (222) |
1001 (21) |
1041 (61) |
1076 (96) |
1108 (128) | |
Subsets and supersets
Since 245 factors into 5 × 72, 245edo has subset edos 5, 7, 35, and 49.