873edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
The equal temperament [[ | 873edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]] is quite large. The equal temperament is most notable for [[tempering out]] the [[amity comma]], 1600000/1594323, in the 5-limit, providing the [[optimal patent val]] for it. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 873 factors into | Since 873 factors into {{factorization|873}}, 873edo has subset edos {{EDOs| 3, 9, 97, and 291 }}. | ||
[[Category:Amity]] | [[Category:Amity]] | ||
Latest revision as of 16:30, 20 February 2025
| ← 872edo | 873edo | 874edo → |
873 equal divisions of the octave (abbreviated 873edo or 873ed2), also called 873-tone equal temperament (873tet) or 873 equal temperament (873et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 873 equal parts of about 1.37 ¢ each. Each step represents a frequency ratio of 21/873, or the 873rd root of 2.
873edo is consistent to the 7-odd-limit, but the error of harmonic 3 is quite large. The equal temperament is most notable for tempering out the amity comma, 1600000/1594323, in the 5-limit, providing the optimal patent val for it.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.450 | -0.059 | +0.246 | -0.474 | -0.115 | -0.665 | +0.391 | -0.488 | -0.606 | -0.678 | -0.096 |
| Relative (%) | +32.8 | -4.3 | +17.9 | -34.5 | -8.4 | -48.4 | +28.5 | -35.5 | -44.1 | -49.3 | -7.0 | |
| Steps (reduced) |
1384 (511) |
2027 (281) |
2451 (705) |
2767 (148) |
3020 (401) |
3230 (611) |
3411 (792) |
3568 (76) |
3708 (216) |
3834 (342) |
3949 (457) | |
Subsets and supersets
Since 873 factors into 32 × 97, 873edo has subset edos 3, 9, 97, and 291.