34ed7: Difference between revisions

(3 intermediate revisions by one other user not shown)

Line 3:

== Theory ==

34ed7 is related to [[12edo]], but with the 7/1 rather than the 2/1 being just. ~~The~~ octave ~~is about~~ 11.0026 ~~cents compressed and the step size is about 99.0831 cents~~. It is consistent to the [[integer limit|11-integer-limit]], but not to the 12-integer-limit. In comparison, 12edo is only consistent up to the 10-integer-limit.

34ed7 is related to [[12edo]], but with the 7/1 rather than the 2/1 being just. This compresses the octave by 11.0026{{c}}, a small but significant deviation. It is consistent to the [[integer limit|11-integer-limit]], but not to the 12-integer-limit. In comparison, 12edo is only consistent up to the 10-integer-limit.

34ed7 can also be thought of as a [[generator]] chain of the 11-limit [[quintupole]] temperament, which tempers out 896/891, 1375/1372, and 4375/4356 and is a [[cluster temperament]] with 12 clusters of notes in an octave. This temperament is supported by [[12edo]], [[109edo]], and [[121edo]] among others.

=== Harmonics ===

Line 14:

Line 16:

== Intervals ==

{| class="wikitable center-1 right-2"

|+ Intervals of 34ed7

|+ style="font-size: 105%;" | Intervals of 34ed7

|-

! #

Line 160:

Line 162:

| [[7/1]]

|}

~~== Regular temperaments ==~~

~~{{See also| Quintaleap family }}~~

34ed7 can also be thought of as a [[generator]] of the 11-limit temperament which tempers out 896/891, 1375/1372, and 4375/4356, which is a [[cluster temperament]] with 12 clusters of notes in an octave ([[quintupole]] temperament). This temperament is supported by [[12edo]], [[109edo]], and [[121edo]] among others.

== See also ==

Line 173:

Line 170:

* [[40ed10]] – relative ed10

* [[42ed11]] – relative ed11

* [[76ed80]] – close to the zeta-optimized tuning for 12edo

* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]

[[Category:12edo]]

@@ Line 3: / Line 3: @@
 == Theory ==
-ed7 is related to [[12edo]], but with the 7/1 rather than the 2/1 being just. The octave is about 11.0026 cents compressed and the step size is about 99.0831 cents. It is consistent to the [[integer limit|11-integer-limit]], but not to the 12-integer-limit. In comparison, 12edo is only consistent up to the 10-integer-limit.
+ed7 is related to [[12edo]], but with the 7/1 rather than the 2/1 being just. This compresses the octave by 11.0026{{c}}, a small but significant deviation. It is consistent to the [[integer limit|11-integer-limit]], but not to the 12-integer-limit. In comparison, 12edo is only consistent up to the 10-integer-limit.
+ed7 can also be thought of as a [[generator]] chain of the 11-limit [[quintupole]] temperament, which tempers out 896/891, 1375/1372, and 4375/4356 and is a [[cluster temperament]] with 12 clusters of notes in an octave. This temperament is supported by [[12edo]], [[109edo]], and [[121edo]] among others.
 === Harmonics ===
@@ Line 14: / Line 16: @@
 == Intervals ==
 {| class="wikitable center-1 right-2"
-|+ Intervals of 34ed7
+|+ style="font-size: 105%;" | Intervals of 34ed7
 |-
 ! #
@@ Line 160: / Line 162: @@
 | [[7/1]]
 |}
-== Regular temperaments ==
-{{See also| Quintaleap family }}
-ed7 can also be thought of as a [[generator]] of the 11-limit temperament which tempers out 896/891, 1375/1372, and 4375/4356, which is a [[cluster temperament]] with 12 clusters of notes in an octave ([[quintupole]] temperament). This temperament is supported by [[12edo]], [[109edo]], and [[121edo]] among others.
 == See also ==
@@ Line 173: / Line 170: @@
 * [[40ed10]] – relative ed10
 * [[42ed11]] – relative ed11
+* [[76ed80]] – close to the zeta-optimized tuning for 12edo
 * [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]
+[[Category:12edo]]

34ed7: Difference between revisions

FloraC (talk | contribs)