518edo: Difference between revisions

Line 2:

~~This tuning may be of interest to those who compose in larger edos as it~~ is [[Consistency limit|consistent]] in the [[15-odd-limit]] and ~~supports~~ the [[~~Rank~~-~~2 temperament~~|~~rank~~-2]] [[~~74th-octave temperaments|74th-octave~~]] [[~~296edo|296~~]] ~~& 518 temperament~~. ~~This means~~ it tempers out ~~commas including~~ [[9801/9800]] ~~and 5250987~~/~~5242880~~, the [[~~Mitonisma~~|~~mitonisma~~]].

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 ===

=== Subsets and supersets ===

Since 518 factors as {{Factorization|518}}, 518edo has subsets {{EDOs|1, 2, 7, 14, 37, 74, 259}}.

@@ Line 2: / Line 2: @@
 {{ED intro}}
-This tuning may be of interest to those who compose in larger edos as it is [[Consistency limit|consistent]] in the [[15-odd-limit]] and supports the [[Rank-2 temperament|rank-2]] [[74th-octave temperaments|74th-octave]] [[296edo|296]] & 518 temperament. This means it tempers out commas including [[9801/9800]] and 5250987/5242880, the [[Mitonisma|mitonisma]].
+edo 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}}
+=== Subsets and supersets ===
+Since 518 factors as {{Factorization|518}}, 518edo has subsets {{EDOs|1, 2, 7, 14, 37, 74, 259}}.