1889edo: Difference between revisions
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The '''1889 division''' divides the octave into 1889 equal parts of 0.6353 cents each. It is strong in the 23-limit, though [[1578edo|1578]], which among other things has a lower 23-limit | The '''1889 division''' divides the octave into 1889 equal parts of 0.6353 cents each. It is strong in the 23-limit, though [[1578edo|1578]], which among other things has a lower 23-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], rather puts it in the shade. It is distinctly [[consistent]] through the 27-odd-limit, but not, unlike 1578, to the 29-odd-limit. Even so, it should be noted that it supplies the [[optimal patent val]] for the 7-limit [[monzismic]] temperament. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|1889|columns=11}} | |||
=== Miscellaneous properties === | |||
1889edo is the 290th [[prime edo]]. | |||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | ||
[[Category:Prime EDO]] | |||
[[Category:Monzismic]] | |||
Revision as of 15:45, 2 November 2022
| ← 1888edo | 1889edo | 1890edo → |
The 1889 division divides the octave into 1889 equal parts of 0.6353 cents each. It is strong in the 23-limit, though 1578, which among other things has a lower 23-limit relative error, rather puts it in the shade. It is distinctly consistent through the 27-odd-limit, but not, unlike 1578, to the 29-odd-limit. Even so, it should be noted that it supplies the optimal patent val for the 7-limit monzismic temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.004 | -0.078 | -0.059 | +0.085 | -0.083 | -0.138 | -0.213 | -0.005 | +0.174 | -0.303 |
| Relative (%) | +0.0 | +0.6 | -12.2 | -9.3 | +13.4 | -13.1 | -21.7 | -33.5 | -0.9 | +27.4 | -47.7 | |
| Steps (reduced) |
1889 (0) |
2994 (1105) |
4386 (608) |
5303 (1525) |
6535 (868) |
6990 (1323) |
7721 (165) |
8024 (468) |
8545 (989) |
9177 (1621) |
9358 (1802) | |
Miscellaneous properties
1889edo is the 290th prime edo.