848edo: Difference between revisions
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{{Infobox ET}} | |||
{{ | {{ED intro}} | ||
848edo is consistent | 848edo is [[consistent]] to the [[15-odd-limit]] and contains the famous [[53edo]] as a subset. In the 5-limit, it is a very strong system, which [[tempering out|tempers out]] the [[Mercator's comma]]. It also tunes [[kwazy]] and provides the [[optimal patent val]] for the 5-limit [[geb]] temperament. | ||
In higher limits, it is a strong 2.3.5.13.23 [[subgroup]] system, with optional additions of either [[7/1|7]] and [[11/1|11]] or [[17/1|17]] and [[19/1|19]]. It provides the optimal patent val for sextantonic, the rank-4 temperament tempering out [[2601/2600]] in the 2.3.5.13.17 subgroup. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{ | {{Harmonics in equal|848}} | ||
=== Subsets and supersets === | |||
Since 848 factors into {{factorization|848}}, 848edo has subset edos {{EDOs| 2, 4, 8, 16, 53, 106, 212, and 424 }}. | |||
[[Category:Geb]] | |||
Latest revision as of 05:55, 21 February 2025
| ← 847edo | 848edo | 849edo → |
848 equal divisions of the octave (abbreviated 848edo or 848ed2), also called 848-tone equal temperament (848tet) or 848 equal temperament (848et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 848 equal parts of about 1.42 ¢ each. Each step represents a frequency ratio of 21/848, or the 848th root of 2.
848edo is consistent to the 15-odd-limit and contains the famous 53edo as a subset. In the 5-limit, it is a very strong system, which tempers out the Mercator's comma. It also tunes kwazy and provides the optimal patent val for the 5-limit geb temperament.
In higher limits, it is a strong 2.3.5.13.23 subgroup system, with optional additions of either 7 and 11 or 17 and 19. It provides the optimal patent val for sextantonic, the rank-4 temperament tempering out 2601/2600 in the 2.3.5.13.17 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.068 | +0.007 | +0.514 | +0.569 | +0.038 | -0.238 | -0.343 | +0.028 | +0.611 | -0.224 |
| Relative (%) | +0.0 | -4.8 | +0.5 | +36.3 | +40.2 | +2.7 | -16.8 | -24.3 | +1.9 | +43.2 | -15.8 | |
| Steps (reduced) |
848 (0) |
1344 (496) |
1969 (273) |
2381 (685) |
2934 (390) |
3138 (594) |
3466 (74) |
3602 (210) |
3836 (444) |
4120 (728) |
4201 (809) | |
Subsets and supersets
Since 848 factors into 24 × 53, 848edo has subset edos 2, 4, 8, 16, 53, 106, 212, and 424.