31edo: Difference between revisions

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=== Prime harmonics ===

{{Harmonics in equal|31|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 31edo (continued)}}

{{Harmonics in equal|31|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 31edo (continued)}}

=== As a tuning of other temperaments ===

Besides meantone, 31edo can be used as a tuning for [[mohajira]], [[mothra]], or less optimally [[miracle]] and [[valentine]]. These temperaments split 31edo's fifth, at 18 steps, into two, three, six, and nine equal parts. Mohajira and its alternative, called [[migration]], merge in 31edo, and create a near-optimal 11-limit meantone structure in one unified system. In fact, 31edo can be defined as the unique temperament that [[tempering out|tempers out]] [[81/80]], [[99/98]], [[121/120]], and [[126/125]].

31edo also [[support]]s [[orwell]], which splits the [[3/1|perfect twelfth]] into seven equal parts of ~7/6. Another notable temperament it supports is [[myna]], which divides the category of thirds into five different intervals: subminor, minor, neutral, major, and supermajor, representing [[7/6]], [[6/5]], [[11/9~~]][[~~~]][[16/13]], 5/4, and [[9/7]], respectively.

31edo also [[support]]s [[orwell]], which splits the [[3/1|perfect twelfth]] into seven equal parts of ~7/6. Another notable temperament it supports is [[myna]], which divides the category of thirds into five different intervals: subminor, minor, neutral, major, and supermajor, representing [[7/6]], [[6/5]], 11/9~[[16/13]], 5/4, and 9/7, respectively.

=== Subsets and supersets ===

@@ Line 21: / Line 21: @@
 === Prime harmonics ===
-{{Harmonics in equal|31|columns=9}}
+{{Harmonics in equal|31|columns=11}}
-{{Harmonics in equal|31|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 31edo (continued)}}
+{{Harmonics in equal|31|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 31edo (continued)}}
 === As a tuning of other temperaments ===
 Besides meantone, 31edo can be used as a tuning for [[mohajira]], [[mothra]], or less optimally [[miracle]] and [[valentine]]. These temperaments split 31edo's fifth, at 18 steps, into two, three, six, and nine equal parts. Mohajira and its alternative, called [[migration]], merge in 31edo, and create a near-optimal 11-limit meantone structure in one unified system. In fact, 31edo can be defined as the unique temperament that [[tempering out|tempers out]] [[81/80]], [[99/98]], [[121/120]], and [[126/125]].
-edo also [[support]]s [[orwell]], which splits the [[3/1|perfect twelfth]] into seven equal parts of ~7/6. Another notable temperament it supports is [[myna]], which divides the category of thirds into five different intervals: subminor, minor, neutral, major, and supermajor, representing [[7/6]], [[6/5]], [[11/9]][[~]][[16/13]], 5/4, and [[9/7]], respectively.
+edo also [[support]]s [[orwell]], which splits the [[3/1|perfect twelfth]] into seven equal parts of ~7/6. Another notable temperament it supports is [[myna]], which divides the category of thirds into five different intervals: subminor, minor, neutral, major, and supermajor, representing [[7/6]], [[6/5]], 11/9~[[16/13]], 5/4, and 9/7, respectively.
 === Subsets and supersets ===