Modal UDP notation: Difference between revisions

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Requiring the generator to always be bright causes certain issues:

* 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.

** 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{{c}} for dominant meantone. Then Dominant[12] is either [[7L 5s]] (if generator < 700{{c}}), in which case the bright generator is the fourth, or [[5L 7s]] (if generator > 700{{c}}), meaning that the bright generator is the fifth. As a result, Dominant[12] 7|4 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{{c}} for dominant meantone. Then Dominant[12] is either [[7L 5s]] (if the generator is flatter than 700{{cent}}), in which case the bright generator is the fourth, or [[5L 7s]] (if the generator is sharper than 700{{c}}), 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.

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

Not all notations have these issues (see below).

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 Requiring the generator to always be bright causes certain issues:
 * 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.
+** 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]&nbsp;5|1 to be Meantone[5]&nbsp;4|0. But instead it's Meantone[5]&nbsp;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{{c}} for dominant meantone. Then Dominant[12] is either [[7L 5s]] (if generator < 700{{c}}), in which case the bright generator is the fourth, or [[5L 7s]] (if generator > 700{{c}}), meaning that the bright generator is the fifth. As a result, Dominant[12] 7|4 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{{c}} for dominant meantone. Then Dominant[12] is either [[7L&nbsp;5s]] (if the generator is flatter than 700{{cent}}), in which case the bright generator is the fourth, or [[5L&nbsp;7s]] (if the generator is sharper than 700{{c}}), meaning that the bright generator is the fifth. As a result, "Dominant[12]&nbsp;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.
+* It's impossible to determine the bright generator in a non-MOS scale like Meantone[8], thus Meantone[8]&nbsp;5|2 is ambiguous.
 Not all notations have these issues (see below).