518edo: Difference between revisions
Expand, use information from lower limits not the idiosyncratic 296 & 518 |
oops, I meant 4459/4455, not 4496/4495. Thats the right one |
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{{ED intro}} | {{ED intro}} | ||
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]]. | 518edo is [[Consistency limit|consistent]] in the [[15-odd-limit]] and is an exceptionally strong [[2.3.11 subgroup|2.3.11-subgroup]] tuning, where it tempers out the [[frameshift comma]] as well as the [[37-11-comma]]. | ||
In the 5-limit, it tempers out the [[counterschisma]] | 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 [[235298/234375]], [[420175/419904]], 1959552/1953125, 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]], | In the 13-limit, 518edo tempers out [[1001/1000]], [[4096/4095]], [[4459/4455]], 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]]. | 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 === | === Prime harmonics === | ||
{{Harmonics in equal|518}} | {{Harmonics in equal|518}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 518 factors into primes as {{nowrap| 2 × 7 × 37 }}, 518edo has subsets edos {{EDOs| 2, 7, 14, 37, 74, 259 }}. | |||
Since 518 factors as {{ | |||