Extended meantone notation: Difference between revisions

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Added diesis vs kleisma
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The meantone circle of fifths however, has no single semisharp/semiflat. In extended meantone notation, a sharp is split into 2 different parts that can be added to produce a sharp.
The meantone circle of fifths however, has no single semisharp/semiflat. In extended meantone notation, a sharp is split into 2 different parts that can be added to produce a sharp.


<pre># — sharp, 7 fifths up
<pre># — sharpen by meantone chromatic semitone, 7 fifths up
b — flat, 7 fifths down
b — flatten by meantone chromatic semitone, 7 fifths down
Y — semisharp 1, 12 fifths down
Y — sharpen by meantone diesis, 12 fifths down
Z — semiflat 1, 12 fifths up
Z — flatten by meantone diesis, 12 fifths up
y — semisharp 2, 19 fifths up
y — sharpen by meantone kleisma, 19 fifths up
z — semiflat 2, 19 fifths down</pre>
z — flatten by meantone kleisma, 19 fifths down</pre>


Unlike a single semisharp/semiflat, this can be generalized to other meantone tunings:
Unlike a single semisharp/semiflat, this can be generalized to other meantone tunings:


*[[7edo]] (sharp is tempered out, semisharp 1 is positive and semisharp 2 is negative)
*[[7edo]] (chromatic semitone is tempered out, diesis is positive and kleisma is negative)
*[[12edo]] (sharp is equal to semisharp 2, semisharp 1 is tempered out)
*[[12edo]] (chromatic semitone is tempered equal to kleisma, diesis is tempered out)
*[[19edo]] (sharp is equal to semisharp 1, semisharp 2 is tempered out)
*[[19edo]] (chromatic semitone is tempered equal to diesis, kleisma is tempered out)
*[[26edo]] (semisharp 1 is greater than sharp, and semisharp 2 is negative)
*[[26edo]] (diesis is larger than chromatic semitone, kleisma is negative)
*[[31edo]] (semisharp 1 is equal to semisharp 2)
*[[31edo]] (kleisma is tempered equal to diesis)
*[[43edo]] (semisharp 1 is smaller than semisharp 2)
*[[43edo]] (diesis is smaller than kleisma)
*[[50edo]] (semisharp 1 is greater than semisharp 2)
*[[50edo]] (diesis is larger than kleisma)


There are of course notational equivalences.
There are of course notational equivalences.
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*DbbZ and Dbbby are equal to C
*DbbZ and Dbbby are equal to C


Semisharp 1 can be considered to be [[36/35]], [[50/49]] or [[64/63]], while semisharp 2 is [[49/48]], assuming [[septimal meantone]].
The meantone diesis can be considered to be [[36/35]], [[50/49]] [[64/63]], or [[128/125]], while the meantone kleisma is [[49/48]] or [[15625/15552]] assuming [[septimal meantone]].
 
[[9–odd–limit]] intervals and their notation relative to C:
[[9–odd–limit]] intervals and their notation relative to C:


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14/9 — G#, or AbZ</pre>
14/9 — G#, or AbZ</pre>


Two semisharp 1 or two semisharp 2 cannot be stacked to produce a sharp. 11–limit and 13–limit notation can [[Meantone vs meanpop|vary]].
Two dieses or two kleismas cannot be stacked to produce a chromatic semitone. 11–limit and 13–limit notation can [[Meantone vs meanpop|vary]].


'''Y, Z, y and z is placeholder notation and should be replaced with better notation. It should be in ASCII, so that it can be easily written on a keyboard, like # and b are.'''
'''Y, Z, y and z is placeholder notation and should be replaced with better notation. It should be in ASCII, so that it can be easily written on a keyboard, like # and b are.'''


[[Category:Stub]]
[[Category:Stub]]
[[Category:Todo:What should the two semisharps and semiflats be called?]]