305edo: Difference between revisions
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[[ | 305edo has a flat tendency, with the [[3/1|3]], [[5/1|5]], [[7/1|7]] and [[11/1|11]] of the [[patent val]] all flat, and the equal temperament [[tempering out|tempers out]] 2109375/2097152, the [[semicomma|semicomma (orson comma)]] in the 5-limit, [[2401/2400]] in the 7-limit, and [[243/242]], [[441/440]], and [[540/539]] in the 11-limit. It provides the [[optimal patent val]] for 7- and 11-limit [[breedsmic temperaments #Neominor|neominor temperament]]. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|305}} | |||
=== Subsets and supersets === | |||
Since 305 factors into 5 × 61, 305edo has [[5edo]] and [[61edo]] as its subsets. | |||
[[Category:Neominor]] | |||
Latest revision as of 14:33, 20 February 2025
| ← 304edo | 305edo | 306edo → |
305 equal divisions of the octave (abbreviated 305edo or 305ed2), also called 305-tone equal temperament (305tet) or 305 equal temperament (305et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 305 equal parts of about 3.93 ¢ each. Each step represents a frequency ratio of 21/305, or the 305th root of 2.
305edo has a flat tendency, with the 3, 5, 7 and 11 of the patent val all flat, and the equal temperament tempers out 2109375/2097152, the semicomma (orson comma) in the 5-limit, 2401/2400 in the 7-limit, and 243/242, 441/440, and 540/539 in the 11-limit. It provides the optimal patent val for 7- and 11-limit neominor temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.63 | -0.74 | -0.96 | +0.68 | -0.50 | +1.44 | +1.57 | +1.27 | +1.50 | +1.35 | +1.23 |
| Relative (%) | -41.4 | -18.8 | -24.3 | +17.3 | -12.7 | +36.6 | +39.8 | +32.4 | +38.2 | +34.3 | +31.4 | |
| Steps (reduced) |
483 (178) |
708 (98) |
856 (246) |
967 (52) |
1055 (140) |
1129 (214) |
1192 (277) |
1247 (27) |
1296 (76) |
1340 (120) |
1380 (160) | |
Subsets and supersets
Since 305 factors into 5 × 61, 305edo has 5edo and 61edo as its subsets.