Septiennealimmal clan: Difference between revisions
| Line 35: | Line 35: | ||
== Ennealimmal == | == Ennealimmal == | ||
{{Main| Ennealimmal }} | {{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. | ||