4L 5s (3/1-equivalent): Difference between revisions

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This is a very good temperament on the 3.5.7 subgroup, and additionally is supported by many EDT's (and even EDOs!) besides 13-EDT.

Some low-numbered EDOs that support ~~Lambda~~ are 19, 22, 27, 41, and 46, all of which make it possible to play BP music to some reasonable extent. These EDOs contain not only the Lambda BP diatonic scale, but also the 13-note "Lambda chromatic" MOS scale, or Lambda[13], which can be thought of as a "detempered" version of the 13-EDT Bohlen Pierce scale. This scale may be a suitable melodic substitute for the BP chromatic scale, and is basically the same as how 19-EDO and 31-EDO do not contain 12-EDO as a subset, but they do contain the meantone[12] chromatic scale.

Some low-numbered EDOs that support BPS are 19, 22, 27, 41, and 46, and some low-numbered EDTs that support it are 9, 13, 17, and 30, all of which make it possible to play BP music to some reasonable extent. These EDOs contain not only the Lambda BP diatonic scale, but also the 13-note "Lambda chromatic" MOS scale, or Lambda[13], which can be thought of as a "detempered" version of the 13-EDT Bohlen Pierce scale. This scale may be a suitable melodic substitute for the BP chromatic scale, and is basically the same as how 19-EDO and 31-EDO do not contain 12-EDO as a subset, but they do contain the meantone[12] chromatic scale.

When playing this temperament in some EDO, it may be desired to stretch/compress the tuning so that the tritave is pure, rather than the octave being pure - or in general, to minimize the error on the 3.5.7 subgroup while ignoring the error on 2/1.

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 This is a very good temperament on the 3.5.7 subgroup, and additionally is supported by many EDT's (and even EDOs!) besides 13-EDT.
-Some low-numbered EDOs that support Lambda are 19, 22, 27, 41, and 46, all of which make it possible to play BP music to some reasonable extent. These EDOs contain not only the Lambda BP diatonic scale, but also the 13-note "Lambda chromatic" MOS scale, or Lambda[13], which can be thought of as a "detempered" version of the 13-EDT Bohlen Pierce scale. This scale may be a suitable melodic substitute for the BP chromatic scale, and is basically the same as how 19-EDO and 31-EDO do not contain 12-EDO as a subset, but they do contain the meantone[12] chromatic scale.
+Some low-numbered EDOs that support BPS are 19, 22, 27, 41, and 46, and some low-numbered EDTs that support it are 9, 13, 17, and 30, all of which make it possible to play BP music to some reasonable extent. These EDOs contain not only the Lambda BP diatonic scale, but also the 13-note "Lambda chromatic" MOS scale, or Lambda[13], which can be thought of as a "detempered" version of the 13-EDT Bohlen Pierce scale. This scale may be a suitable melodic substitute for the BP chromatic scale, and is basically the same as how 19-EDO and 31-EDO do not contain 12-EDO as a subset, but they do contain the meantone[12] chromatic scale.
 When playing this temperament in some EDO, it may be desired to stretch/compress the tuning so that the tritave is pure, rather than the octave being pure - or in general, to minimize the error on the 3.5.7 subgroup while ignoring the error on 2/1.