9th-octave temperaments: Difference between revisions

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The main 9th-octave temperament of interest is [[ennealimmal]] (temperament data given ~~there~~), notable for being the [[7-limit]] [[microtemperament]] tempering the two smallest [[superparticular interval]]s of the 7-limit, [[2401/2400]] = S49 = ([[49/40]])/([[60/49]]) and [[4375/4374]] = S25/S27 = ([[7/6|28/24]])/([[27/25]])<sup>2</sup>, with the smallest [[patent val]] [[edo]] tunings being [[27edo]] (a sharp [[superpyth]] tuning supporting [[modus]] and [[augene]]) and [[45edo]] (the [[optimal patent val]] of [[flattone]]), which sum to [[72edo]] (the smallest edo tuning that starts to show the accuracy of ennealimmal, with a mild flat tendency) and relatedly [[99edo]] (the second such tuning, with a mild sharp tendency instead).

The main 9th-octave temperament of interest is [[ennealimmal]] (temperament data given at [[Tritrizo clan#Ennealimmal|Tritrizo clan]]), notable for being the [[7-limit]] [[microtemperament]] tempering the two smallest [[superparticular interval]]s of the 7-limit, [[2401/2400]] = S49 = ([[49/40]])/([[60/49]]) and [[4375/4374]] = S25/S27 = ([[7/6|28/24]])/([[27/25]])<sup>2</sup>, with the smallest [[patent val]] [[edo]] tunings being [[27edo]] (a sharp [[superpyth]] tuning supporting [[modus]] and [[augene]]) and [[45edo]] (the [[optimal patent val]] of [[flattone]]), which sum to [[72edo]] (the smallest edo tuning that starts to show the accuracy of ennealimmal, with a mild flat tendency) and relatedly [[99edo]] (the second such tuning, with a mild sharp tendency instead).

It can be thought of as leveraging the most accurate [[JI]] interpretations of [[9edo]], which surprisingly are all 7-limit:

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 {{See also | Ennealimmal}}
-The main 9th-octave temperament of interest is [[ennealimmal]] (temperament data given there), notable for being the [[7-limit]] [[microtemperament]] tempering the two smallest [[superparticular interval]]s of the 7-limit, [[2401/2400]] = S49 = ([[49/40]])/([[60/49]]) and [[4375/4374]] = S25/S27 = ([[7/6|28/24]])/([[27/25]])<sup>2</sup>, with the smallest [[patent val]] [[edo]] tunings being [[27edo]] (a sharp [[superpyth]] tuning supporting [[modus]] and [[augene]]) and [[45edo]] (the [[optimal patent val]] of [[flattone]]), which sum to [[72edo]] (the smallest edo tuning that starts to show the accuracy of ennealimmal, with a mild flat tendency) and relatedly [[99edo]] (the second such tuning, with a mild sharp tendency instead).
+The main 9th-octave temperament of interest is [[ennealimmal]] (temperament data given at [[Tritrizo clan#Ennealimmal|Tritrizo clan]]), notable for being the [[7-limit]] [[microtemperament]] tempering the two smallest [[superparticular interval]]s of the 7-limit, [[2401/2400]] = S49 = ([[49/40]])/([[60/49]]) and [[4375/4374]] = S25/S27 = ([[7/6|28/24]])/([[27/25]])<sup>2</sup>, with the smallest [[patent val]] [[edo]] tunings being [[27edo]] (a sharp [[superpyth]] tuning supporting [[modus]] and [[augene]]) and [[45edo]] (the [[optimal patent val]] of [[flattone]]), which sum to [[72edo]] (the smallest edo tuning that starts to show the accuracy of ennealimmal, with a mild flat tendency) and relatedly [[99edo]] (the second such tuning, with a mild sharp tendency instead).
 It can be thought of as leveraging the most accurate [[JI]] interpretations of [[9edo]], which surprisingly are all 7-limit: