Extended meantone notation: Difference between revisions

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A meantone chromatic semitone ~~is equivalent to a~~ diesis ~~added to a~~ kleisma. Note that in most meantone tunings, the diesis and kleisma are roughly a quarter tone.

A meantone chromatic semitone consists of one diesis and one kleisma. Note that in most meantone tunings, the diesis and kleisma are roughly a quarter tone. The diesis represents the [[just intonation|just]] intervals [[128/125]] and [[648/625]], while the meantone kleisma represents [[15625/15552]] or [[3125/3072]]. In [[septimal meantone]] (meantone temperaments where 7/4 is an augmented sixth), the diesis also represents [[36/35]], [[50/49]], and [[64/63]], while the kleisma also represents [[49/48]] and [[245/243]].

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

An octave is made of 19 dieses and 12 kleismas. Unlike semisharps and semiflats, the diesis and kleisma can be generalized to other tunings:

{| class="wikitable center-all"

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| 2

| −1

| Diesis is larger than chromatic semitone,<br>kleisma is negative

| rowspan="2" | Diesis is larger than chromatic semitone,<br>kleisma is negative

|-

| [[33edo#Theory|33c]]

| {{frac|2}} comma

| 1

| 4

| 3

| −2

|-

| [[31edo|31]]

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*C+↑ is equal to C♯ (because the two semisharps add up)

*D𝄫↓ and D♭♭♭− are equal to C

Assuming [[septimal meantone]], the meantone diesis can be considered to be [[36/35]], [[50/49]], [[64/63]], [[128/125]], or [[648/625]], while the meantone kleisma is [[49/48]], [[245/243]], [[3125/3072]], or [[15625/15552]]. An octave is made of 19 dieses and 12 kleismas.

[[9–odd–limit]] intervals and their notation relative to C:

@@ Line 42: / Line 42: @@
 |}
-A meantone chromatic semitone is equivalent to a diesis added to a kleisma. Note that in most meantone tunings, the diesis and kleisma are roughly a quarter tone.
+A meantone chromatic semitone consists of one diesis and one kleisma. Note that in most meantone tunings, the diesis and kleisma are roughly a quarter tone. The diesis represents the [[just intonation|just]] intervals [[128/125]] and [[648/625]], while the meantone kleisma represents [[15625/15552]] or [[3125/3072]]. In [[septimal meantone]] (meantone temperaments where 7/4 is an augmented sixth), the diesis also represents [[36/35]], [[50/49]], and [[64/63]], while the kleisma also represents [[49/48]] and [[245/243]].
-Unlike a single semisharp/semiflat, this can be generalized to other tunings:
+An octave is made of 19 dieses and 12 kleismas. Unlike semisharps and semiflats, the diesis and kleisma can be generalized to other tunings:
 {| class="wikitable center-all"
@@ Line 87: / Line 87: @@
 | 2
 | &minus;1
-| Diesis is larger than chromatic semitone,<br>kleisma is negative
+| rowspan="2" | Diesis is larger than chromatic semitone,<br>kleisma is negative
+|-
+| [[33edo#Theory|33c]]
+| {{frac|2}} comma
+| 1
+| 4
+| 3
+| &minus;2
 |-
 | [[31edo|31]]
@@ Line 126: / Line 133: @@
 *C+↑ is equal to C♯ (because the two semisharps add up)
 *D𝄫↓ and D♭♭♭− are equal to C
-Assuming [[septimal meantone]], the meantone diesis can be considered to be [[36/35]], [[50/49]], [[64/63]], [[128/125]], or [[648/625]], while the meantone kleisma is [[49/48]], [[245/243]], [[3125/3072]], or [[15625/15552]]. An octave is made of 19 dieses and 12 kleismas.
 [[9–odd–limit]] intervals and their notation relative to C: