Major second: Difference between revisions

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|249c ≈ 15/13

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~~== In regular temperaments ==~~

~~The three simplest major second ratios are 10/9, 9/8, and 8/7. The following notable temperaments are generated by them:~~

~~=== Temperaments generated by 8/7 ===~~

* [[Slendric]], where a stack of three 8/7s is equated to 3/2

* [[Semaphore]], where a stack of two 8/7s is equated to 4/3

~~=== Temperaments generated by 9/8 ===~~

~~=== Temperaments generated by 10/9 ===~~

~~=== Other major second temperaments ===~~

* Didacus, where the septimal tritone [[7/5]] is split in three, with 1\3ed7/5 being the generator 28/25 and 2\3ed7/5 being [[5/4]].

~~{{Todo|complete list|inline=1}}~~

== In moment-of-symmetry scales ==

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| [[5L 4s]]

|}

=== Temperament interpretations ===

The three simplest major second ratios are 10/9, 9/8, and 8/7, and these along with other more complex interpretations serve as [[generator]]s for a variety of [[regular temperament]]s.

* The generator of the 7L 1s scale can be interpreted as a [[10/9]] major second that is equated to [[11/10]] and [[12/11]] [[neutral second]]s in [[porcupine]], so that three generators reach [[4/3]]. Its tuning range is therefore somewhat ambiguous between major and neutral second.

* The generator of the 6L 1s and 6L 7s scales can be interpreted as [[didacus]], whose generator represents [[28/25]] and which splits the septimal tritone [[7/5]] in three, with one step making the generator 28/25 and two making [[5/4]]. This generator can also stand in for 10/9 and [[9/8]] in the 2.9.5.7 subgroup, treating it as an index-2 restriction of [[septimal meantone]].

* The generator of the 5L 6s scale can be interpreted as [[8/7]] in [[slendric]] temperament, where three of them are equated to [[3/2]].

* The generator of the 5L 4s scale can be interpreted as [[semaphore]], where 8/7 is equated to the subminor third [[7/6]] so that two generators reach 4/3, or more accurately as [[barbados]] if 8/7 is eschewed in favor of [[15/13]]. Either way, it is tuned as an [[interseptimal interval|interseptimal]] ambiguous between a major second and [[minor third]].

@@ Line 177: / Line 177: @@
 |249c ≈ 15/13
 |}
-== In regular temperaments ==
-The three simplest major second ratios are 10/9, 9/8, and 8/7. The following notable temperaments are generated by them:
-=== Temperaments generated by 8/7 ===
-* [[Slendric]], where a stack of three 8/7s is equated to 3/2
-* [[Semaphore]], where a stack of two 8/7s is equated to 4/3
-=== Temperaments generated by 9/8 ===
-=== Temperaments generated by 10/9 ===
-=== Other major second temperaments ===
-* Didacus, where the septimal tritone [[7/5]] is split in three, with 1\3ed7/5 being the generator 28/25 and 2\3ed7/5 being [[5/4]].
-{{Todo|complete list|inline=1}}
 == In moment-of-symmetry scales ==
@@ Line 228: / Line 211: @@
 | [[5L&nbsp;4s]]
 |}
+=== Temperament interpretations ===
+The three simplest major second ratios are 10/9, 9/8, and 8/7, and these along with other more complex interpretations serve as [[generator]]s for a variety of [[regular temperament]]s.
+* The generator of the 7L 1s scale can be interpreted as a [[10/9]] major second that is equated to [[11/10]] and [[12/11]] [[neutral second]]s in [[porcupine]], so that three generators reach [[4/3]]. Its tuning range is therefore somewhat ambiguous between major and neutral second.
+* The generator of the 6L 1s and 6L 7s scales can be interpreted as [[didacus]], whose generator represents [[28/25]] and which splits the septimal tritone [[7/5]] in three, with one step making the generator 28/25 and two making [[5/4]]. This generator can also stand in for 10/9 and [[9/8]] in the 2.9.5.7 subgroup, treating it as an index-2 restriction of [[septimal meantone]].
+* The generator of the 5L 6s scale can be interpreted as [[8/7]] in [[slendric]] temperament, where three of them are equated to [[3/2]].
+* The generator of the 5L 4s scale can be interpreted as [[semaphore]], where 8/7 is equated to the subminor third [[7/6]] so that two generators reach 4/3, or more accurately as [[barbados]] if 8/7 is eschewed in favor of [[15/13]]. Either way, it is tuned as an [[interseptimal interval|interseptimal]] ambiguous between a major second and [[minor third]].
+{{Todo|complete list|inline=1}}
 {{Navbox intervals}}