Extended meantone notation: Difference between revisions

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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]].

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]], 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]].

An octave is made of 19 dieses and 12 kleismas. Unlike semisharps and semiflats, the diesis and kleisma 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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! rowspan="2" | Comma fraction

! colspan="4" | Steps

! rowspan="2" | Explanation

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

|-

! Chromatic semitone

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| 1

| −1

| Chromatic semitone is tempered out, ~~ ~~diesis is positive, and kleisma is negative

| Chromatic semitone is tempered out, diesis is positive, and kleisma is negative

|-

| [[12edo|12]]

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| 0

| 1

| Chromatic semitone is equal to kleisma,~~ ~~diesis is tempered out

| Chromatic semitone is equal to kleisma, diesis is tempered out

|-

| [[19edo|19]]

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| 1

| 0

| Chromatic semitone is equal to diesis,~~ ~~kleisma is tempered out

| Chromatic semitone is equal to diesis, kleisma is tempered out

|-

| [[26edo|26]]

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| 2

| −1

| rowspan="2" | Diesis is larger than chromatic semitone,~~ ~~kleisma is negative

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

|-

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

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 |}
-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]].
+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]], 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]].
-An octave is made of 19 dieses and 12 kleismas. Unlike semisharps and semiflats, the diesis and kleisma 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 50: / Line 52: @@
 ! rowspan="2" | Comma<br>fraction
 ! colspan="4" | Steps
-! rowspan="2" | Explanation
+! rowspan="2" style="width: 225px;" | Explanation
 |-
 ! Chromatic<br>semitone
@@ Line 63: / Line 65: @@
 | 1
 | &minus;1
-| Chromatic semitone is tempered out, <br>diesis is positive, and kleisma is negative
+| Chromatic semitone is tempered out, diesis is positive, and kleisma is negative
 |-
 | [[12edo|12]]
@@ Line 71: / Line 73: @@
 | 0
 | 1
-| Chromatic semitone is equal to kleisma,<br>diesis is tempered out
+| Chromatic semitone is equal to kleisma, diesis is tempered out
 |-
 | [[19edo|19]]
@@ Line 79: / Line 81: @@
 | 1
 | 0
-| Chromatic semitone is equal to diesis,<br>kleisma is tempered out
+| Chromatic semitone is equal to diesis, kleisma is tempered out
 |-
 | [[26edo|26]]
@@ Line 87: / Line 89: @@
 | 2
 | &minus;1
-| rowspan="2" | Diesis is larger than chromatic semitone,<br>kleisma is negative
+| rowspan="2" | Diesis is larger than chromatic semitone, kleisma is negative
 |-
 | [[33edo#Theory|33c]]