600edo: Difference between revisions

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== Theory ==

~~600edo~~ 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, ~~supporting~~ septimal [[mutt]].

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's patent val is a tuning for the [[atomic]] temperament in the 5- and 7-limit and the 600e val is a tuning 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 ===

=== Subsets and supersets ===

Since 600 factors into 23 × 3 × 52, 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 factors into 23 × 3 × 52, 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 = 6 x 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.

== Regular temperament properties ==

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|+Table of rank-2 temperaments by generator

! Periods per 8ve

! Generator~~ (Reduced)~~

! Generator*

! Cents~~ (Reduced)~~

! Cents*

! Associated Ratio

! Associated Ratio*

! Temperaments

|-

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| 566.00 (26.00)

| 238/165 (?)

| [[Soviet ~~Ferris~~ wheel]] (600e)

| [[Soviet ferris wheel]] (600e)

|-

| 60

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| [[Minutes]] (600e)

|}

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

@@ Line 3: / Line 3: @@
 == Theory ==
-edo 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, supporting septimal [[mutt]].
+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's patent val is a tuning for the [[atomic]] temperament in the 5- and 7-limit and the 600e val is a tuning 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 ===
 {{Harmonics in equal|600}}
 === 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 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 = 6 x 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.
 == Regular temperament properties ==
@@ Line 18: / Line 16: @@
 |+Table of rank-2 temperaments by generator
 ! Periods<br>per 8ve
-! Generator<br>(Reduced)
+! Generator*
-! Cents<br>(Reduced)
+! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-
@@ Line 45: / Line 43: @@
 | 566.00<br>(26.00)
 | 238/165<br>(?)
-| [[Soviet Ferris wheel]] (600e)
+| [[Soviet ferris wheel]] (600e)
 |-
 | 60
@@ Line 53: / Line 51: @@
 | [[Minutes]] (600e)
 |}
+<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct