518edo: Difference between revisions
Tristanbay (talk | contribs) Added page for 518edo Tags: Mobile edit Mobile web edit |
Expand, use information from lower limits not the idiosyncratic 296 & 518 |
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518edo is [[Consistency limit|consistent]] in the [[15-odd-limit]] and is an exceptionally strong 2.3.11 subgroup tuning, where it tempers out the [[frameshift comma]]. | |||
In the 5-limit, it tempers out the [[counterschisma]], {{monzo| -69 45 -1 }}, and is a strong tuning for the [[counterschismic]] temperament hence. In the 7-limit, it tempers out 1959552/1953125, [[235298/234375]], [[420175/419904]] and 5250987/5242880 (mitonisma). In the 11-limit, it tempers out [[5632/5625]], [[9801/9800]], as well as being a tuning for [[loki]]. | |||
In the 13-limit, 518edo tempers out [[1001/1000]], [[4096/4095]], 4496/4495, and it is a strong tuning for the 14th-octave [[silicon]] temperament. | |||
The 518c val, {{val| 518 821 '''1202''' 1454 1792 }}, though less accurate, is of theoretical interest as well because it tunes [[quintilipyth]] and [[compass]]. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|518}} | {{Harmonics in equal|518}} | ||
=== Subsets and supersets === | |||
Since 518 factors as {{Factorization|518}}, 518edo has subsets {{EDOs|1, 2, 7, 14, 37, 74, 259}}. | |||
Revision as of 21:34, 29 July 2026
| ← 517edo | 518edo | 519edo → |
518 equal divisions of the octave (abbreviated 518edo or 518ed2), also called 518-tone equal temperament (518tet) or 518 equal temperament (518et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 518 equal parts of about 2.32 ¢ each. Each step represents a frequency ratio of 21/518, or the 518th root of 2.
518edo is consistent in the 15-odd-limit and is an exceptionally strong 2.3.11 subgroup tuning, where it tempers out the frameshift comma.
In the 5-limit, it tempers out the counterschisma, [-69 45 -1⟩, and is a strong tuning for the counterschismic temperament hence. In the 7-limit, it tempers out 1959552/1953125, 235298/234375, 420175/419904 and 5250987/5242880 (mitonisma). In the 11-limit, it tempers out 5632/5625, 9801/9800, as well as being a tuning for loki.
In the 13-limit, 518edo tempers out 1001/1000, 4096/4095, 4496/4495, and it is a strong tuning for the 14th-octave silicon temperament.
The 518c val, ⟨518 821 1202 1454 1792], though less accurate, is of theoretical interest as well because it tunes quintilipyth and compass.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.02 | +0.56 | -0.49 | +0.03 | +0.40 | -0.71 | -0.99 | -0.48 | -1.01 | -0.63 |
| Relative (%) | +0.0 | -1.1 | +24.1 | -21.0 | +1.4 | +17.2 | -30.6 | -42.6 | -20.5 | -43.4 | -27.4 | |
| Steps (reduced) |
518 (0) |
821 (303) |
1203 (167) |
1454 (418) |
1792 (238) |
1917 (363) |
2117 (45) |
2200 (128) |
2343 (271) |
2516 (444) |
2566 (494) | |
Subsets and supersets
Since 518 factors as 2 × 7 × 37, 518edo has subsets 1, 2, 7, 14, 37, 74, 259.