Modal UDP notation: Difference between revisions

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== Things to watch out for ==

Requiring the generator to always be bright causes certain issues:

* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5|1 to be Meantone[5] 4|0. But instead it's Meantone[5] 0|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.

* The bright and dark generators may "flip" based on the size of the generator and how many notes are in the corresponding MOS scale.

** The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5|1 to be Meantone[5] 4|0. But instead it's Meantone[5] 0|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.

** Because the MOS type that a temperament's MOS represents is tuning-dependent, the choice of bright generator can be tuning-dependent. For example, assume you are using approximately but not exactly 700¢ for dominant meantone. Then Dominant[12] is either [[7L 5s]] (if generator < 700¢), in which case the bright generator is the fourth, or [[5L 7s]] (if generator > 700¢), meaning that the bright generator is the fifth. As a result, Dominant[12] 7|4 is ambiguous.

* It's impossible to determine the bright generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5|2 is ambiguous.

* Because the MOS type that a temperament's MOS represents is tuning-dependent, the choice of bright generator can be tuning-dependent. For example, assume you are using approximately but not exactly 700¢ for dominant meantone. Then Dominant[12] is either [[7L 5s]] (if generator < 700¢), in which case the bright generator is the fourth, or [[5L 7s]] (if generator > 700¢), meaning that the bright generator is the fifth. As a result, Dominant[12] 7|4 is ambiguous.

== See also ==

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 == Things to watch out for ==
 Requiring the generator to always be bright causes certain issues:
-* The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5|1 to be Meantone[5] 4|0. But instead it's Meantone[5] 0|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.
+* The bright and dark generators may "flip" based on the size of the generator and how many notes are in the corresponding MOS scale.
+** The major pentatonic scale is a subset of the major scale. The genchain is simply shortened on either end. Thus one would expect the major pentatonic scale contained within Meantone[7] 5|1 to be Meantone[5] 4|0. But instead it's Meantone[5] 0|4. This is because changing the size of the MOS scale often changes the generator to its octave inverse. Meantone[5]'s bright generator is the 4th not the 5th.
+** Because the MOS type that a temperament's MOS represents is tuning-dependent, the choice of bright generator can be tuning-dependent. For example, assume you are using approximately but not exactly 700¢ for dominant meantone. Then Dominant[12] is either [[7L 5s]] (if generator < 700¢), in which case the bright generator is the fourth, or [[5L 7s]] (if generator > 700¢), meaning that the bright generator is the fifth. As a result, Dominant[12] 7|4 is ambiguous.
 * It's impossible to determine the bright generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5|2 is ambiguous.
-* Because the MOS type that a temperament's MOS represents is tuning-dependent, the choice of bright generator can be tuning-dependent. For example, assume you are using approximately but not exactly 700¢ for dominant meantone. Then Dominant[12] is either [[7L 5s]] (if generator < 700¢), in which case the bright generator is the fourth, or [[5L 7s]] (if generator > 700¢), meaning that the bright generator is the fifth. As a result, Dominant[12] 7|4 is ambiguous.
 == See also ==