107ed11: Difference between revisions

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== Theory ==

107ed11 is related to [[31edo]], but with the 7/1 rather than the [[2/1]] being just. The octave is ~~slightly~~ stretched ~~(about~~ 2.~~7182~~{{c}}, which is almost exactly {{w|e (mathematical constant)|''e''}} cents). Like 31edo, 107ed11 is [[consistent]] through the [[integer limit|12-integer-limit]].

107ed11 is related to [[31edo]], but with the 11/1 rather than the [[2/1]] being just. The octave is stretched by 2.718{{c}}, which is interesting in that it is almost exactly {{w|e (mathematical constant)|''e''}} cents. Like 31edo, 107ed11 is [[consistent]] through the [[integer limit|12-integer-limit]], but unlike 31edo it has a discrepancy for the 13th harmonic.

=== Harmonics ===

{{Harmonics in equal|87|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~87ed7~~ (continued)}}

{{Harmonics in equal|107|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 107ed11 (continued)}}

~~=== Subsets and supersets ===~~

~~Since 87 factors into primes as {{nowrap| 3 × 29 }}, 87ed7 contains [[3ed7]] and [[29ed7]] as subset ed7's.~~

== Intervals ==

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* [[72ed5]] – relative ed5

* [[80ed6]] – relative ed6

* [[87ed7]] – relative ~~ed17~~

* [[87ed7]] – relative ed7

* [[111ed12]] – relative ed12

* [[138ed22]] – relative ed22

* [[204ed96]] – close to the zeta-optimized tuning for 31edo

* [[39cET]]

[[Category:31edo]]

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 == Theory ==
-ed11 is related to [[31edo]], but with the 7/1 rather than the [[2/1]] being just. The octave is slightly stretched (about 2.7182{{c}}, which is almost exactly {{w|e (mathematical constant)|''e''}} cents). Like 31edo, 107ed11 is [[consistent]] through the [[integer limit|12-integer-limit]].
+ed11 is related to [[31edo]], but with the 11/1 rather than the [[2/1]] being just. The octave is stretched by 2.718{{c}}, which is interesting in that it is almost exactly {{w|e (mathematical constant)|''e''}} cents. Like 31edo, 107ed11 is [[consistent]] through the [[integer limit|12-integer-limit]], but unlike 31edo it has a discrepancy for the 13th harmonic.
 === Harmonics ===
-{{Harmonics in equal|87|7|1|intervals=integer|columns=11}}
+{{Harmonics in equal|107|11|1|intervals=integer|columns=11}}
-{{Harmonics in equal|87|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 87ed7 (continued)}}
+{{Harmonics in equal|107|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 107ed11 (continued)}}
-=== Subsets and supersets ===
-Since 87 factors into primes as {{nowrap| 3 × 29 }}, 87ed7 contains [[3ed7]] and [[29ed7]] as subset ed7's.
 == Intervals ==
@@ Line 21: / Line 18: @@
 * [[72ed5]] – relative ed5
 * [[80ed6]] – relative ed6
-* [[87ed7]] – relative ed17
+* [[87ed7]] – relative ed7
 * [[111ed12]] – relative ed12
+* [[138ed22]] – relative ed22
+* [[204ed96]] – close to the zeta-optimized tuning for 31edo
 * [[39cET]]
+[[Category:31edo]]