Extended meantone notation: Difference between revisions
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== Extending the chain of fifths == | Do not read this page while it is under construction of notation. | ||
Meanwhile, you can enjoy the meantone classification of commas between [[superparticular]] ratios: | |||
<pre>Grosstone: | |||
3/2 | |||
9/8 — major second | |||
4/3 | |||
16/15 — minor second | |||
5/4 | |||
25/24 — sharp | |||
6/5 | |||
36/35 — diesis | |||
7/6 | |||
49/48 — kleisma | |||
8/7 | |||
64/63 — diesis | |||
9/8 | |||
81/80 — unison | |||
10/9 | |||
100/99 — diesis | |||
11/10 | |||
121/120 — kleisma, diesis minus | |||
12/11 | |||
144/143 — unison | |||
13/12 | |||
169/168 — two dieses, kleisma minus | |||
14/13 | |||
196/195 — kleisma, diesis minus | |||
15/14 | |||
225/224 — unison | |||
16/15 | |||
Meanpop: | |||
3/2 | |||
9/8 — major second | |||
4/3 | |||
16/15 — minor second | |||
5/4 | |||
25/24 — sharp | |||
6/5 | |||
36/35 — diesis | |||
7/6 | |||
49/48 — kleisma | |||
8/7 | |||
64/63 — diesis | |||
9/8 | |||
81/80 — unison | |||
10/9 | |||
100/99 — kleisma | |||
11/10 | |||
121/120 — diesis, kleisma minus | |||
12/11 | |||
144/143 — unison | |||
13/12 | |||
169/168 — kleisma | |||
14/13 | |||
196/195 — unison | |||
15/14 | |||
225/224 — unison | |||
16/15</pre> | |||
<!-- == Extending the chain of fifths == | |||
Standard meantone [[notation]] uses 7 base note letters, plus sharps and flats. | Standard meantone [[notation]] uses 7 base note letters, plus sharps and flats. | ||
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Two dieses or two kleismas cannot be stacked to produce a chromatic semitone. 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.''' | ||
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Extended meantone notation was created as a way to notate [[43edo]] with only a base letter with one symbol. | Extended meantone notation was created as a way to notate [[43edo]] with only a base letter with one symbol. | ||
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== True half-sharps and half-flats == | == True half-sharps and half-flats == | ||
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The chain-of-neutral thirds tuning system is not a true "temperament," because it is contorted: the neutral third does not have any JI interval mapping to it in the 7-limit. But, if we go to the 11-limit, and add 121/120 to the kernel, we obtain [[Mohajira]], an exceptionally good 11-limit temperament. The neutral third becomes equal to 11/9, and two of them make 3/2. Furthermore, if you take a minor third and ''flatten'' it by a half-flat, you obtain a good representation of 7/6. Conversely if you take a major third ''sharpen'' it by a half-sharp, you obtain a good representation for 9/7. [[31edo]] is a very good tuning for mohajira. | The chain-of-neutral thirds tuning system is not a true "temperament," because it is contorted: the neutral third does not have any JI interval mapping to it in the 7-limit. But, if we go to the 11-limit, and add 121/120 to the kernel, we obtain [[Mohajira]], an exceptionally good 11-limit temperament. The neutral third becomes equal to 11/9, and two of them make 3/2. Furthermore, if you take a minor third and ''flatten'' it by a half-flat, you obtain a good representation of 7/6. Conversely if you take a major third ''sharpen'' it by a half-sharp, you obtain a good representation for 9/7. [[31edo]] is a very good tuning for mohajira. | ||
Although mohajira may not be a great tuning to reflect the way maqam music is played in practice, which often uses multiple unequal neutral thirds and exhibits significant regional variations, it is a highly interesting regular temperament of its own merit, and deserves further study. | Although mohajira may not be a great tuning to reflect the way maqam music is played in practice, which often uses multiple unequal neutral thirds and exhibits significant regional variations, it is a highly interesting regular temperament of its own merit, and deserves further study. --> | ||
[[Category:Stub]] | [[Category:Stub]] | ||
[[Category:Todo:What should the two semisharps and semiflats be called?]] | [[Category:Todo:What should the two semisharps and semiflats be called?]] | ||