446edo: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 299288018 - Original comment: ** |
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{{Infobox ET}} | |||
{{ED intro}} | |||
446edo is only [[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[5/1|5]] is quite large. The equal temperament [[tempering out|tempers out]] [[3136/3125]] and 420175/419904 in the 7-limit, and provides the [[optimal patent val]] for the [[hemimean]] temperament tempering out 3136/3125, and [[sengagen]], the {{nowrap|99 & 347}} temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 198 & 248 temperament. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|446}} | |||
=== Subsets and supersets === | |||
Since 446 factors into {{factorization|446}}, 446edo contains [[2edo]] and [[223edo]] as subsets. | |||
[[Category:Hemimean]] | |||
[[Category:Sengagen]] | |||
Latest revision as of 14:57, 20 February 2025
| ← 445edo | 446edo | 447edo → |
446 equal divisions of the octave (abbreviated 446edo or 446ed2), also called 446-tone equal temperament (446tet) or 446 equal temperament (446et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 446 equal parts of about 2.69 ¢ each. Each step represents a frequency ratio of 21/446, or the 446th root of 2.
446edo is only consistent to the 5-odd-limit and the error of harmonic 5 is quite large. The equal temperament tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the optimal patent val for the hemimean temperament tempering out 3136/3125, and sengagen, the 99 & 347 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 198 & 248 temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.29 | +1.13 | -0.22 | +0.57 | +0.25 | -1.07 | -1.27 | -0.02 | +1.14 | +0.07 | +1.32 |
| Relative (%) | +10.7 | +42.0 | -8.0 | +21.3 | +9.3 | -39.6 | -47.3 | -0.8 | +42.4 | +2.6 | +49.1 | |
| Steps (reduced) |
707 (261) |
1036 (144) |
1252 (360) |
1414 (76) |
1543 (205) |
1650 (312) |
1742 (404) |
1823 (39) |
1895 (111) |
1959 (175) |
2018 (234) | |
Subsets and supersets
Since 446 factors into 2 × 223, 446edo contains 2edo and 223edo as subsets.