Septiennealimmal clan: Difference between revisions

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Ennealimmal extensions discussed elsewhere include [[Compton family #Omicronbeta|omicronbeta]], [[Tritrizo clan #Undecentic|undecentic]], [[Tritrizo clan #Schisennealimmal|schisennealimmal]], and [[Tritrizo clan #Lunennealimmal|lunennealimmal]].

7-limit ennealimmal's S-expression-based comma list is {[[4375/4374|S25/S27]], [[2401/2400|S49]]}. Interestingly, the [[landscape comma]] is equal to [[2401/2400|S49]]/([[4375/4374|S25/S27]]) while the [[wizma]] is equal to [[2401/2400|S49]]*[[4375/4374|S25/S27]].

7-limit ennealimmal's [[S-expression]]-based comma list is {[[4375/4374|S25/S27]], [[2401/2400|S49]]}. Interestingly, the [[landscape comma]] is equal to [[2401/2400|S49]]/([[4375/4374|S25/S27]]) while the [[wizma]] is equal to [[2401/2400|S49]]*[[4375/4374|S25/S27]].

''For the 5-limit temperament, see [[Ennealimma#Ennealimmal]].''

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Hemiennealimmal (72 & 198) has a period of 1/18 octave and tempers out the four smallest superparticular commas of the 11-limit JI, 2401/2400, 3025/3024, 4375/4374, and 9801/9800. Tempering out [[9801/9800]] leads to an octave split into two equal parts. Notably, every one of these commas is part of one or more known infinite comma families; see directly below.

Its S-expression-based comma list is {([[3025/3024|S22/S24 = S55 = S25/S27 * S99]],) [[4375/4374|S25/S27]], [[2401/2400|S49]], [[9801/9800|S33/S35 = S99]]}.

Its [[S-expression]]-based comma list is {([[3025/3024|S22/S24 = S55 = S25/S27 * S99]],) [[4375/4374|S25/S27]], [[2401/2400|S49]], [[9801/9800|S33/S35 = S99]]}.

Subgroup: 2.3.5.7.11

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 Ennealimmal extensions discussed elsewhere include [[Compton family #Omicronbeta|omicronbeta]], [[Tritrizo clan #Undecentic|undecentic]], [[Tritrizo clan #Schisennealimmal|schisennealimmal]], and [[Tritrizo clan #Lunennealimmal|lunennealimmal]].
--limit ennealimmal's S-expression-based comma list is {[[4375/4374|S25/S27]], [[2401/2400|S49]]}. Interestingly, the [[landscape comma]] is equal to [[2401/2400|S49]]/([[4375/4374|S25/S27]]) while the [[wizma]] is equal to [[2401/2400|S49]]*[[4375/4374|S25/S27]].
+-limit ennealimmal's [[S-expression]]-based comma list is {[[4375/4374|S25/S27]], [[2401/2400|S49]]}. Interestingly, the [[landscape comma]] is equal to [[2401/2400|S49]]/([[4375/4374|S25/S27]]) while the [[wizma]] is equal to [[2401/2400|S49]]*[[4375/4374|S25/S27]].
 ''For the 5-limit temperament, see [[Ennealimma#Ennealimmal]].''
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 Hemiennealimmal (72 &amp; 198) has a period of 1/18 octave and tempers out the four smallest superparticular commas of the 11-limit JI, 2401/2400, 3025/3024, 4375/4374, and 9801/9800. Tempering out [[9801/9800]] leads to an octave split into two equal parts. Notably, every one of these commas is part of one or more known infinite comma families; see directly below.
-Its S-expression-based comma list is {([[3025/3024|S22/S24 = S55 = S25/S27 * S99]],) [[4375/4374|S25/S27]], [[2401/2400|S49]], [[9801/9800|S33/S35 = S99]]}.
+Its [[S-expression]]-based comma list is {([[3025/3024|S22/S24 = S55 = S25/S27 * S99]],) [[4375/4374|S25/S27]], [[2401/2400|S49]], [[9801/9800|S33/S35 = S99]]}.
 Subgroup: 2.3.5.7.11