Canopus: Difference between revisions

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''For technical information see [[~~Mirkwai clan~~#Canopus]]''

''For technical information see [[No-twos subgroup temperaments#Canopus]]''

'''Canopus''' is the [[Rank-2 temperament|rank two]] [[~~No-twos subgroup temperaments|~~3.5.7]] temperament [[Temper out|tempering]] out [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of ~[[7/5|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)|1L 2s]] ~~(triad)~~, [[3L 1s (3/1-equivalent)|3L 1s]] ~~(tetrad)~~, [[3L 4s (3/1-equivalent)|3L 4s]] ~~("neutral" [[diatonic]])~~ and [[3L 7s (3/1-equivalent)|3L 7s]] (~~augmented neutral decatonic~~)~~. On either side the greater region where it appears~~, ~~there appear~~ the ~~most important, though as yet unnamed,~~ [[~~tritave~~]]~~-equivalent temperaments which retain twos~~, ~~they being important for using a~~ (~~smeary~~) ~~~4:3 or 3:~~2 ~~as a generator~~.

'''Canopus''' is the [[Rank-2 temperament|rank two]] [[3.5.7 subgroup]] temperament [[Temper out|tempering]] out [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)|1L 2s]], [[3L 1s (3/1-equivalent)|3L 1s]], [[3L 4s (3/1-equivalent)|3L 4s]], and [[3L 7s (3/1-equivalent)|3L 7s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27.

== Relationship between MOS with P4 generator and MOS with P5 generator ==

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-''For technical information see [[Mirkwai clan#Canopus]]''
+''For technical information see [[No-twos subgroup temperaments#Canopus]]''
-'''Canopus''' is the [[Rank-2 temperament|rank two]] [[No-twos subgroup temperaments|3.5.7]] temperament [[Temper out|tempering]] out [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of ~[[7/5|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)|1L 2s]] (triad), [[3L 1s (3/1-equivalent)|3L 1s]] (tetrad), [[3L 4s (3/1-equivalent)|3L 4s]] ("neutral" [[diatonic]]) and [[3L 7s (3/1-equivalent)|3L 7s]] (augmented neutral decatonic). On either side the greater region where it appears, there appear the most important, though as yet unnamed, [[tritave]]-equivalent temperaments which retain twos, they being important for using a (smeary) ~4:3 or 3:2 as a generator.
+'''Canopus''' is the [[Rank-2 temperament|rank two]] [[3.5.7 subgroup]] temperament [[Temper out|tempering]] out [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)|1L 2s]], [[3L 1s (3/1-equivalent)|3L 1s]], [[3L 4s (3/1-equivalent)|3L 4s]], and [[3L 7s (3/1-equivalent)|3L 7s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27.
 == Relationship between MOS with P4 generator and MOS with P5 generator ==

Canopus: Difference between revisions

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