101ed7: Difference between revisions

(11 intermediate revisions by 3 users not shown)

Line 1:

'''101 divisions of the seventh harmonic''' ('''101ed7''') is related to [[36edo]] (sixth-tone tuning), but with the 7/1 rather than the 2/1 being just. The octave is about 1.2347 [[cent]]s stretched and the step size is about 33.3547 cents. It is consistent to the [[7-odd-limit|8-integer-limit]]. This tuning tempers out the [[syntonic comma]].

~~Lookalikes:~~ [[~~21edf~~]], [[~~36edo~~]], [[~~57edt~~]], [[~~93ed6~~]]

== Theory ==

101ed7 is closely related to [[36edo]] (sixth-tone tuning), but with the 7th harmonic rather than the [[2/1|octave]] being just. The octave is stretched by about 0.770 [[cent]]s (almost identical to [[93ed6]], where the octave is stretched by about 0.757 cents). Like 36edo, 101ed7 is [[consistent]] to the [[integer limit|8-integer-limit]].

~~== Harmonics ==~~

Compared to 36edo, 101ed7 is pretty well optimized for the 2.3.7.13.17 [[subgroup]], with slightly better [[3/1|3]], [[7/1|7]], [[13/1|13]] and [[17/1|17]], and a slightly worse 2 versus 36edo. Using the [[patent val]], the [[5/1|5]] is also less accurate. Overall this means 36edo is still better in the [[5-limit]], but 101ed7 is better in the [[13-limit|13-]] and [[17-limit]], especially when treating it as a dual-5 dual-11 tuning.

~~{{Harmonics in equal~~|~~101~~|7|1}}

=== Harmonics ===

{{Harmonics in equal|101|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 101ed7 (continued)}}

=== Subsets and supersets ===

[[Category:~~Edonoi~~]]

101ed7 is the 26th [[prime equal division|prime ed7]], so it does not contain any nontrivial subset ed7's.

== Intervals ==

== See also ==

* [[21edf]] – relative edf

* [[36edo]] – relative edo

* [[57edt]] – relative edt

* [[93ed6]] – relative ed6

* [[129ed12]] – relative ed12, close to the zeta-optimized tuning for 36edo

[[Category:36edo]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''101 divisions of the seventh harmonic''' ('''101ed7''') is related to [[36edo]] (sixth-tone tuning), but with the 7/1 rather than the 2/1 being just. The octave is about 1.2347 [[cent]]s stretched and the step size is about 33.3547 cents. It is consistent to the [[7-odd-limit|8-integer-limit]]. This tuning tempers out the [[syntonic comma]].
+{{ED intro}}
-Lookalikes: [[21edf]], [[36edo]], [[57edt]], [[93ed6]]
+== Theory ==
+ed7 is closely related to [[36edo]] (sixth-tone tuning), but with the 7th harmonic rather than the [[2/1|octave]] being just. The octave is stretched by about 0.770 [[cent]]s (almost identical to [[93ed6]], where the octave is stretched by about 0.757 cents). Like 36edo, 101ed7 is [[consistent]] to the [[integer limit|8-integer-limit]].
-== Harmonics ==
+Compared to 36edo, 101ed7 is pretty well optimized for the 2.3.7.13.17 [[subgroup]], with slightly better [[3/1|3]], [[7/1|7]], [[13/1|13]] and [[17/1|17]], and a slightly worse 2 versus 36edo. Using the [[patent val]], the [[5/1|5]] is also less accurate. Overall this means 36edo is still better in the [[5-limit]], but 101ed7 is better in the [[13-limit|13-]] and [[17-limit]], especially when treating it as a dual-5 dual-11 tuning.
-{{Harmonics in equal|101|7|1}}
+=== Harmonics ===
+{{Harmonics in equal|101|7|1|intervals=integer|columns=11}}
+{{Harmonics in equal|101|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 101ed7 (continued)}}
-{{todo|expand}}
+=== Subsets and supersets ===
-[[Category:Edonoi]]
+ed7 is the 26th [[prime equal division|prime ed7]], so it does not contain any nontrivial subset ed7's.
+== Intervals ==
+{{Interval table}}
+== See also ==
+* [[21edf]] – relative edf
+* [[36edo]] – relative edo
+* [[57edt]] – relative edt
+* [[93ed6]] – relative ed6
+* [[129ed12]] – relative ed12, close to the zeta-optimized tuning for 36edo
+[[Category:36edo]]