95ed5: Difference between revisions

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== Theory ==

95ed5 is related to [[41edo]], but with the ~~5/1~~ rather than the [[2/1]] being just. The octave is about 2.~~5143~~ cents stretched. This tuning has a generally sharp tendency for ~~harmonics~~ up to 12. Unlike 41edo, it is only consistent up to the [[integer limit|12-integer-limit]], with discrepancy for the [[13/1|13th~~]] [[~~harmonic]].

95ed5 is related to [[41edo]], but with the 5th harmonic rather than the [[2/1|octave]] being just. The octave is about 2.51 cents stretched. This tuning has a generally sharp tendency for [[harmonic]]s up to 12. Unlike 41edo, it is only [[consistent]] up to the [[integer limit|12-integer-limit]], with discrepancy for the [[13/1|13th harmonic]].

=== Harmonics ===

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== As a generator ==

95ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.19-subgroup temperament which tempers out 1540/1539, 3025/3024, 6875/6859, and 184877/184320, which is a [[cluster temperament]] with 41 clusters of notes in an octave. While the small chroma interval between adjacent notes in each cluster represents 385/384 ~ 441/440 ~ 1479016/1476225 ~ 194579/194400 ~ 204800/204687 ~ 176000/175959 tempered together, the step interval is very versatile, representing 16807/16500 ~ 19551/19200 ~ 18000/17689 ~ 72900/71687 ~ 273375/268912 ~ 295245/290521 ~ 12100/11907 ~ 64/63 all tempered together. This temperament is supported by [[41edo]], [[491edo]] (491e val), and [[532edo]] (532d val) among others.

== See also ==

* [[24edf]] – relative edf

* [[41edo]] – relative edo

* [[65edt]] – relative edt

* [[106ed6]] – relative ed6

* [[147ed12]] – relative ed12

* [[361ed448]] – close to the zeta-optimized tuning for 41edo

[[Category:41edo]]

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 == Theory ==
-ed5 is related to [[41edo]], but with the 5/1 rather than the [[2/1]] being just. The octave is about 2.5143 cents stretched. This tuning has a generally sharp tendency for harmonics up to 12. Unlike 41edo, it is only consistent up to the [[integer limit|12-integer-limit]], with discrepancy for the [[13/1|13th]] [[harmonic]].
+ed5 is related to [[41edo]], but with the 5th harmonic rather than the [[2/1|octave]] being just. The octave is about 2.51 cents stretched. This tuning has a generally sharp tendency for [[harmonic]]s up to 12. Unlike 41edo, it is only [[consistent]] up to the [[integer limit|12-integer-limit]], with discrepancy for the [[13/1|13th harmonic]].
 === Harmonics ===
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 == As a generator ==
 ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.19-subgroup temperament which tempers out 1540/1539, 3025/3024, 6875/6859, and 184877/184320, which is a [[cluster temperament]] with 41 clusters of notes in an octave. While the small chroma interval between adjacent notes in each cluster represents 385/384 ~ 441/440 ~ 1479016/1476225 ~ 194579/194400 ~ 204800/204687 ~ 176000/175959 tempered together, the step interval is very versatile, representing 16807/16500 ~ 19551/19200 ~ 18000/17689 ~ 72900/71687 ~ 273375/268912 ~ 295245/290521 ~ 12100/11907 ~ 64/63 all tempered together. This temperament is supported by [[41edo]], [[491edo]] (491e val), and [[532edo]] (532d val) among others.
+== See also ==
+* [[24edf]] – relative edf
+* [[41edo]] – relative edo
+* [[65edt]] – relative edt
+* [[106ed6]] – relative ed6
+* [[147ed12]] – relative ed12
+* [[361ed448]] – close to the zeta-optimized tuning for 41edo
+[[Category:41edo]]