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># — | <pre># — sharpen by meantone chromatic semitone, 7 fifths up | ||
b — | b — flatten by meantone chromatic semitone, 7 fifths down | ||
Y — | Y — sharpen by meantone diesis, 12 fifths down | ||
Z — | Z — flatten by meantone diesis, 12 fifths up | ||
y — | y — sharpen by meantone kleisma, 19 fifths up | ||
z — | 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]] ( | *[[7edo]] (chromatic semitone is tempered out, diesis is positive and kleisma is negative) | ||
*[[12edo]] ( | *[[12edo]] (chromatic semitone is tempered equal to kleisma, diesis is tempered out) | ||
*[[19edo]] ( | *[[19edo]] (chromatic semitone is tempered equal to diesis, kleisma is tempered out) | ||
*[[26edo]] ( | *[[26edo]] (diesis is larger than chromatic semitone, kleisma is negative) | ||
*[[31edo]] ( | *[[31edo]] (kleisma is tempered equal to diesis) | ||
*[[43edo]] ( | *[[43edo]] (diesis is smaller than kleisma) | ||
*[[50edo]] ( | *[[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 | ||
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 | 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]] | ||