600edo: Difference between revisions

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== Theory ==

The equal temperament [[tempering out|tempers out]] the [[tricot comma]], {{monzo| 39 -29 3 }}, and the [[mutt comma]], {{monzo| -44 -3 21 }} in the 5-limit, [[65625/65536]], [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the 7-limit, [[support]]ing septimal [[mutt]]. The [[patent val]] is also a tuning for [[atomic]], whereas the 600e [[val]] is a tuning for atomic in the 11-limit. In addition, 600e val is a tuning for 20th-octave temperament [[soviet ferris wheel]] as high as the 19-limit.

600edo has good approximations to [[harmonic]]s [[3/1|3]], [[5/1|5]], [[13/1|13]], and [[23/1|23]], on top of which we may consider adding [[7/1|7]] or [[19/1|19]]. The equal temperament [[tempering out|tempers out]] the [[tricot comma]], {{monzo| 39 -29 3 }}, and the [[mutt comma]], {{monzo| -44 -3 21 }} in the 5-limit, [[65625/65536]], [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the 7-limit, [[support]]ing septimal [[mutt]]. The [[patent val]] is also a tuning for [[atomic]], whereas the 600e [[val]] is a tuning for atomic in the 11-limit. In addition, 600e val is a tuning for 20th-octave temperament [[soviet ferris wheel]] as high as the 19-limit.

=== Prime harmonics ===

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=== Subsets and supersets ===

Since 600 factors into ~~2<sup>3</sup> × 3 × 5<sup>2</sup>~~, it has subset edos {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 25, 30, 40, 60, 100, 200, and 300 }}. Since 600 = 6 × 100, one step of 600edo is named ''centitone'', being a relative cent of [[6edo]], otherwise known as the whole tone scale. In addition, because the step size is 2 cents, it is the smallest edo where every possible interval is tuned within 1 cent of error using direct approximation.

Since 600 factors into {{factorization|600}}, 600edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 25, 30, 40, 60, 100, 200, and 300 }}. Since 600 = 6 × 100, one step of 600edo is named a ''centitone'', being a relative cent of [[6edo]], otherwise known as the whole tone scale. In addition, because the step size is 2 cents, it is the smallest edo where every possible interval is tuned within 1 cent of error using direct approximation.

== Regular temperament properties ==

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 == Theory ==
-The equal temperament [[tempering out|tempers out]] the [[tricot comma]], {{monzo| 39 -29 3 }}, and the [[mutt comma]], {{monzo| -44 -3 21 }} in the 5-limit, [[65625/65536]], [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the 7-limit, [[support]]ing septimal [[mutt]]. The [[patent val]] is also a tuning for [[atomic]], whereas the 600e [[val]] is a tuning for atomic in the 11-limit. In addition, 600e val is a tuning for 20th-octave temperament [[soviet ferris wheel]] as high as the 19-limit.
+edo has good approximations to [[harmonic]]s [[3/1|3]], [[5/1|5]], [[13/1|13]], and [[23/1|23]], on top of which we may consider adding [[7/1|7]] or [[19/1|19]]. The equal temperament [[tempering out|tempers out]] the [[tricot comma]], {{monzo| 39 -29 3 }}, and the [[mutt comma]], {{monzo| -44 -3 21 }} in the 5-limit, [[65625/65536]], [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the 7-limit, [[support]]ing septimal [[mutt]]. The [[patent val]] is also a tuning for [[atomic]], whereas the 600e [[val]] is a tuning for atomic in the 11-limit. In addition, 600e val is a tuning for 20th-octave temperament [[soviet ferris wheel]] as high as the 19-limit.
 === Prime harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-Since 600 factors into 2<sup>3</sup> × 3 × 5<sup>2</sup>, it has subset edos {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 25, 30, 40, 60, 100, 200, and 300 }}. Since 600 = 6 × 100, one step of 600edo is named ''centitone'', being a relative cent of [[6edo]], otherwise known as the whole tone scale. In addition, because the step size is 2 cents, it is the smallest edo where every possible interval is tuned within 1 cent of error using direct approximation.
+Since 600 factors into {{factorization|600}}, 600edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 25, 30, 40, 60, 100, 200, and 300 }}. Since 600 = 6 × 100, one step of 600edo is named a ''centitone'', being a relative cent of [[6edo]], otherwise known as the whole tone scale. In addition, because the step size is 2 cents, it is the smallest edo where every possible interval is tuned within 1 cent of error using direct approximation.
 == Regular temperament properties ==