981edo: Difference between revisions

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== Theory ==

981edo is a good 13- and 17-limit system. It tempers out [[2080/2079]], [[2401/2400]], 2431/2430, [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and 4914/4913 in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.

981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. The equal temperament [[Tempering out|tempers out]] [[2080/2079]], [[2401/2400]], 2431/2430, [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and 4914/4913 in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.

=== Prime harmonics ===

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{| class="wikitable center-all left-5"

! Periods<br>per 8ve

! Generator~~<br>(Reduced)~~

! Generator*

! Cents~~<br>(Reduced)~~

! Cents*

! Associated<br>Ratio

! Temperaments

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| [[Ennealimmal]] / ennealimmia

|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct

[[Category:Ennealimmic]]

[[Category:Ennealimmia]]

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 == Theory ==
-edo is a good 13- and 17-limit system. It tempers out [[2080/2079]], [[2401/2400]], 2431/2430, [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and 4914/4913 in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.
+edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. The equal temperament [[Tempering out|tempers out]] [[2080/2079]], [[2401/2400]], 2431/2430, [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and 4914/4913 in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.
 === Prime harmonics ===
@@ Line 68: / Line 68: @@
 {| class="wikitable center-all left-5"
 ! Periods<br>per 8ve
-! Generator<br>(Reduced)
+! Generator*
-! Cents<br>(Reduced)
+! Cents*
 ! Associated<br>Ratio
 ! Temperaments
@@ Line 85: / Line 85: @@
 | [[Ennealimmal]] / ennealimmia
 |}
+<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
 [[Category:Ennealimmic]]
 [[Category:Ennealimmia]]