34ed7: Difference between revisions

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== Theory ==
== Theory ==
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 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 ===
=== Harmonics ===
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| [[7/1]]
| [[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 ==
== See also ==