Major second: Difference between revisions

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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 7L 1s scale can be interpreted as a [[10/9]] major second, that is equated to [[11/10]] and [[12/11]] [[neutral second]]s by [[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 6L 1s and 6L 7s scales can be interpreted in terms of [[2.5.7 subgroup|2.5.7]] [[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 6s scale can be interpreted as [[8/7]] in [[2.3.7 subgroup|2.3.7]] [[slendric]], 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]].

* The generator of the 5L 4s scale can be interpreted in terms of 2.3.7 [[semaphore]], where 8/7 is equated to the subminor third [[7/6]] so that two generators reach 4/3, or more accurately as 2.3.13/5 [[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]].

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 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 7L 1s scale can be interpreted as a [[10/9]] major second, that is equated to [[11/10]] and [[12/11]] [[neutral second]]s by [[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 6L 1s and 6L 7s scales can be interpreted in terms of [[2.5.7 subgroup|2.5.7]] [[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 6s scale can be interpreted as [[8/7]] in [[2.3.7 subgroup|2.3.7]] [[slendric]], 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]].
+* The generator of the 5L 4s scale can be interpreted in terms of 2.3.7 [[semaphore]], where 8/7 is equated to the subminor third [[7/6]] so that two generators reach 4/3, or more accurately as 2.3.13/5 [[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]].
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 {{Navbox intervals}}