Ragismic microtemperaments: Difference between revisions

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Ennealimmal tempers out the two smallest 7-limit [[superparticular]] commas, 2401/2400 and 4375/4374, leading to a temperament of unusual efficiency. It also tempers out the [[ennealimma]], {{monzo| 1 -27 18 }}, which leads to the identification of (27/25)<sup>9</sup> with the [[octave]], and gives ennealimmal a [[period]] of 1/9 octave. Its [[pergen]] is (P8/9, P5/2). While 27/25 is a 5-limit interval, a stack of two periods equates to 7/6 because of identification by 4375/4374, and this represents 7/6 with such accuracy (a fifth of a cent flat) that there is no realistic possibility of treating ennealimmal as anything other than 7-limit.

Ennealimmal tempers out the two smallest 7-limit [[superparticular]] commas, 2401/2400 and 4375/4374, leading to a temperament of unusual [[efficiency]]. It also tempers out the [[ennealimma]], {{monzo| 1 -27 18 }}, which leads to the identification of (27/25)<sup>9</sup> with the [[octave]], and gives ennealimmal a [[period]] of 1/9 octave. Its [[pergen]] is (P8/9, P5/2). While 27/25 is a 5-limit interval, a stack of two periods equates to 7/6 because of identification by 4375/4374, and this represents 7/6 with such accuracy (a fifth of a cent flat) that there is no realistic possibility of treating ennealimmal as anything other than 7-limit.

Aside from 10/9 which has already been mentioned, possible generators include 36/35, 21/20, 6/5, 7/5 and the neutral thirds pair 49/40~60/49, all of which have their own interesting advantages. Possible tunings are 441-, 612-, or 3600edo, though its hardly likely anyone could tell the difference.

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 {{Main| Ennealimmal }}
-Ennealimmal tempers out the two smallest 7-limit [[superparticular]] commas, 2401/2400 and 4375/4374, leading to a temperament of unusual efficiency. It also tempers out the [[ennealimma]], {{monzo| 1 -27 18 }}, which leads to the identification of (27/25)<sup>9</sup> with the [[octave]], and gives ennealimmal a [[period]] of 1/9 octave. Its [[pergen]] is (P8/9, P5/2). While 27/25 is a 5-limit interval, a stack of two periods equates to 7/6 because of identification by 4375/4374, and this represents 7/6 with such accuracy (a fifth of a cent flat) that there is no realistic possibility of treating ennealimmal as anything other than 7-limit.
+Ennealimmal tempers out the two smallest 7-limit [[superparticular]] commas, 2401/2400 and 4375/4374, leading to a temperament of unusual [[efficiency]]. It also tempers out the [[ennealimma]], {{monzo| 1 -27 18 }}, which leads to the identification of (27/25)<sup>9</sup> with the [[octave]], and gives ennealimmal a [[period]] of 1/9 octave. Its [[pergen]] is (P8/9, P5/2). While 27/25 is a 5-limit interval, a stack of two periods equates to 7/6 because of identification by 4375/4374, and this represents 7/6 with such accuracy (a fifth of a cent flat) that there is no realistic possibility of treating ennealimmal as anything other than 7-limit.
 Aside from 10/9 which has already been mentioned, possible generators include 36/35, 21/20, 6/5, 7/5 and the neutral thirds pair 49/40~60/49, all of which have their own interesting advantages. Possible tunings are 441-, 612-, or 3600edo, though its hardly likely anyone could tell the difference.