Extended meantone notation: Difference between revisions

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! colspan="2" | Symbol

! rowspan="2" | Interval

! rowspan="2" | Number of fifths

! rowspan="2" style="width: 75px;" | Number of fifths

|-

! Raise

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! rowspan="2" style="width: 225px;" | Explanation

|-

! Chromatic~~<br>~~semitone

! style="width: 80px;" | Chromatic semitone

! Diatonic~~<br>~~semitone

! style="width: 80px;" | Diatonic semitone

! Diesis

! Kleisma

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|}

Two dieses or two kleismas cannot be stacked to produce a chromatic semitone~~. 11–limit~~ and ~~13–limit~~ notation can vary (see [[meantone vs meanpop]]).

Two dieses or two kleismas cannot be stacked to produce a chromatic semitone, and notation for 11-limit and 13-limit intervals (intervals involving the 11th and 13th harmonics) can vary (see [[meantone vs meanpop]]).

~~Extended meantone notation was created as a way to notate [[43edo]] with only a base letter with one symbol~~.

== 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 decide that there should only be a single neutral second (i.e. 121/120 should be tempered out, resulting in the small neutral second of 12/11 and large neutral second of 11/10 both being mapped to a single equally-tempered interval), we obtain [[mohajira]], an exceptionally good 11-limit temperament. The neutral third approximates 11/9, and two of them make a perfect fifth. Furthermore, flattening a minor third by a half-flat results in an approximation of 7/6, while sharpening a major third by a half-sharp gives an approximation of 9/7. Mohajira is supported very well by 24edo and [[31edo]].

== Notes ==

[[Category:Meantone]]

[[Category:Notation]]

@@ Line 25: / Line 25: @@
 ! colspan="2" | Symbol
 ! rowspan="2" | Interval
-! rowspan="2" | Number of fifths
+! rowspan="2" style="width: 75px;" | Number of fifths
 |-
 ! Raise
@@ Line 58: / Line 58: @@
 ! rowspan="2" style="width: 225px;" | Explanation
 |-
-! Chromatic<br>semitone
+! style="width: 80px;" | Chromatic semitone
-! Diatonic<br>semitone
+! style="width: 80px;" | Diatonic semitone
 ! Diesis
 ! Kleisma
@@ Line 186: / Line 186: @@
 |}
-Two dieses or two kleismas cannot be stacked to produce a chromatic semitone. 11–limit and 13–limit notation can vary (see [[meantone vs meanpop]]).
+Two dieses or two kleismas cannot be stacked to produce a chromatic semitone, and notation for 11-limit and 13-limit intervals (intervals involving the 11th and 13th harmonics) can vary (see [[meantone vs meanpop]]).
-Extended meantone notation was created as a way to notate [[43edo]] with only a base letter with one symbol.
 == True half-sharps and half-flats ==
@@ Line 196: / Line 194: @@
 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 decide that there should only be a single neutral second (i.e. 121/120 should be tempered out, resulting in the small neutral second of 12/11 and large neutral second of 11/10 both being mapped to a single equally-tempered interval), we obtain [[mohajira]], an exceptionally good 11-limit temperament. The neutral third approximates 11/9, and two of them make a perfect fifth. Furthermore, flattening a minor third by a half-flat results in an approximation of 7/6, while sharpening a major third by a half-sharp gives an approximation of 9/7. Mohajira is supported very well by 24edo and [[31edo]].
+== Notes ==
 [[Category:Meantone]]
 [[Category:Notation]]