UDP: Difference between revisions

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* Melodic minor is 5|1(1) b3, abbreviated 5|1 b3 for short, but could also be 3|3(1) #7, abbreviated 3|3 #7 for short.

* Paul Erlich's standard pentachordal major for Pajara[10] is 4|4(2) #8, or alternatively 6|2(2) b3.

== Issues ==

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.

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

* The choice of generator can be tuning-dependent. For example, Dominant meantone's generator is approximately 700¢. Dominant[12]'s bright generator is either the 4th or the 5th, depending on the exact tuning. As a result, Dominant[12] 7|4 is ambiguous.

== Other Notations ==

* [[Kite%27s_Method_of_Naming_Rank-2_Scales_using_Mode_Numbers|Kite Giedraitis' notation]] numbers each mode by its position on the genchain: 1st Meantone[7] = Lydian, 2nd Meantone[7] = Ionian, 3rd Meantone[7] = Mixolydian, etc.

* [[Kite%27s_Method_of_Naming_Rank-2_Scales_using_Mode_Numbers|Kite Giedraitis' notation]] numbers each mode by its position on the genchain: 1st Meantone[7] = Lydian, 2nd Meantone[7] = Ionian, 3rd Meantone[7] = Mixolydian, etc. The generator is not always bright: 1st Meantone[5] = major pentatonic.

* [[Naming_Rank-2_Scales#Jake Freivald method|Jake Freivald's notation]] numbers each mode by its position in the scale: 1st Meantone[7] = Ionian, 2nd Meantone[7] = Dorian, 3rd Meantone[7] = Phrygian, etc.

@@ Line 150: / Line 150: @@
 * Melodic minor is 5|1(1) b3, abbreviated 5|1 b3 for short, but could also be 3|3(1) #7, abbreviated 3|3 #7 for short.
 * Paul Erlich's standard pentachordal major for Pajara[10] is 4|4(2) #8, or alternatively 6|2(2) b3.
+== Issues ==
+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.
+* It's impossible to determine the bright generator in a non-MOS scale like Meantone[8], thus Meantone[8] 5|2 is ambiguous.
+* The choice of generator can be tuning-dependent. For example, Dominant meantone's generator is approximately 700¢. Dominant[12]'s bright generator is either the 4th or the 5th, depending on the exact tuning. As a result, Dominant[12] 7|4 is ambiguous.
 == Other Notations ==
-* [[Kite%27s_Method_of_Naming_Rank-2_Scales_using_Mode_Numbers|Kite Giedraitis' notation]] numbers each mode by its position on the genchain: 1st Meantone[7] = Lydian, 2nd Meantone[7] = Ionian, 3rd Meantone[7] = Mixolydian, etc.
+* [[Kite%27s_Method_of_Naming_Rank-2_Scales_using_Mode_Numbers|Kite Giedraitis' notation]] numbers each mode by its position on the genchain: 1st Meantone[7] = Lydian, 2nd Meantone[7] = Ionian, 3rd Meantone[7] = Mixolydian, etc. The generator is not always bright: 1st Meantone[5] = major pentatonic.
 * [[Naming_Rank-2_Scales#Jake Freivald method|Jake Freivald's notation]] numbers each mode by its position in the scale: 1st Meantone[7] = Ionian, 2nd Meantone[7] = Dorian, 3rd Meantone[7] = Phrygian, etc.