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Extended meantone notation: Difference between revisions

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:''This page is currently reworked at [[User:PiotrGrochowski/Extended meantone notation]], see also [[{{TALKPAGENAME}} #under construction|Talk:Extended meantone notation #under construction]]''.
:''This page is currently reworked at [[User:PiotrGrochowski/Extended meantone notation]], see also [[{{TALKPAGENAME}} #under construction|Talk:Extended meantone notation #under construction]]''.


Most musicians are familiar with the [[Circle-of-fifths notation|circle of fifths]]. In general, notes use 7 base note letters, along with sharps, double-sharps, flats, and double-flats (and beyond):
Most musicians are familiar with the [[Chain-of-fifths notation|circle of fifths]]. The general chain of fifths involves 7 base note letters, along with sharps, double-sharps, flats, and double-flats (and beyond):


... F𝄫 – C𝄫 – G𝄫 – D𝄫 – A𝄫 – E𝄫 – B𝄫 – F♭ – C♭ – G♭ – D♭ – A♭ – E♭ – B♭ – F – C – G – D – A – E – B – F♯ – C♯ – G♯ – D♯ – A♯ – E♯ – B♯ – F𝄪 – C𝄪 – G𝄪 – D𝄪 – A𝄪 – E𝄪 – B𝄪 ...
... F𝄫 – C𝄫 – G𝄫 – D𝄫 – A𝄫 – E𝄫 – B𝄫 – F♭ – C♭ – G♭ – D♭ – A♭ – E♭ – B♭ – F – C – G – D – A – E – B – F♯ – C♯ – G♯ – D♯ – A♯ – E♯ – B♯ – F𝄪 – C𝄪 – G𝄪 – D𝄪 – A𝄪 – E𝄪 – B𝄪 ...


In some tunings (such as 24edo and 31edo), sharps can be split in half. Thus, some notes can be notated using semisharps and semiflats or with [[ups and Downs Notation|ups and downs]].
In some tunings (such as 24edo and 31edo), sharps can be split in half. Thus, some notes can be notated using semisharps and semiflats, or with [[ups and Downs Notation|ups and downs]].


For example, in 31edo, the chromatic scale becomes:
For example, in [[31-tone equal temperament]], the chromatic scale becomes:


C – D𝄫 – C♯ – D♭ – C𝄪 – D – E𝄫 – D♯ – E♭ – D𝄪 – E – F♭ – E♯ – F – G𝄫 – F♯ – G♭ – F𝄪 – G – A𝄫 – G♯ – A♭ – G𝄪 – A – B𝄫 – A♯ – B♭ – A𝄪 – B – C♭ – B♯ – C
C – D𝄫 – C♯ – D♭ – C𝄪 – D – E𝄫 – D♯ – E♭ – D𝄪 – E – F♭ – E♯ – F – G𝄫 – F♯ – G♭ – F𝄪 – G – A𝄫 – G♯ – A♭ – G𝄪 – A – B𝄫 – A♯ – B♭ – A𝄪 – B – C♭ – B♯ – C
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== Generalizing accidentals ==
== Generalizing accidentals ==
Sharps and flats denote raising and lowering by a given number of chromatic semitones. The diesis is the difference between adjacent accidentals (e.g. C♯–D♭ and D♯–E♭), while the kleisma is the amount by which B♯ exceeds C♭ and E♯ exceeds F♭.
Most people are familiar with sharps and flats—these denote raising and lowering, respectively, by a chromatic semitone (note that in most tunings, the chromatic semitone and diatonic semitone are different sizes). The diesis is the difference between adjacent accidentals (e.g. C♯–D♭ and D♯–E♭), while the kleisma is the amount by which B♯ exceeds C♭ and E♯ exceeds F♭.


{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="2" | Symbol
! colspan="2" | Symbol
! rowspan="2" | Interval
! rowspan="2" | Interval
! rowspan="2" | Number of fifths<br>(move up to raise,<br>move down to lower)
! rowspan="2" | Number of fifths
|-
|-
! Raise
! Raise
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{| class="wikitable center-all"
{| class="wikitable center-all"
! rowspan="2" | EDO
! rowspan="2" style="width: 50px;" | Notes per<br>octave
! rowspan="2" | Comma<br>fraction
! rowspan="2" style="width: 75px;" | Syntonic comma fraction
! colspan="4" | Steps
! colspan="4" | Steps
! rowspan="2" style="width: 220px;" | Explanation
! rowspan="2" style="width: 200px;" | Explanation
|-
|-
! Chromatic<br>semitone
! Chromatic<br>semitone
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! Kleisma
! Kleisma
|-
|-
| [[7edo|7]]
| [[7edo]]
|  
|  
| 0
| 0
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| 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]]
| [[12edo]] (standard tuning)
| {{frac|11}} comma
| {{frac|11}} comma
| 1
| 1
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| Chromatic semitone is equal to kleisma, diesis is tempered out
| Chromatic semitone is equal to kleisma, diesis is tempered out
|-
|-
| [[19edo|19]]
| [[19edo]]
| {{frac|3}} comma
| {{frac|3}} comma
| 1
| 1
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| Chromatic semitone is equal to diesis, kleisma is tempered out
| Chromatic semitone is equal to diesis, kleisma is tempered out
|-
|-
| [[26edo|26]]
| [[26edo]]
|  
|  
| 1
| 1
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| 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]]
| [[33edo]] (c&nbsp;mapping)
| {{frac|2}} comma
| {{frac|2}} comma
| 1
| 1
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| &minus;2
| &minus;2
|-
|-
| [[31edo|31]]
| [[31edo]]
| {{frac|4}} comma
| {{frac|4}} comma
| 2
| 2
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| Diesis is equal to kleisma
| Diesis is equal to kleisma
|-
|-
| [[43edo|43]]
| [[43edo]]
| {{frac|5}} comma
| {{frac|5}} comma
| 3
| 3
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| rowspan="2" | Diesis is smaller than kleisma
| rowspan="2" | Diesis is smaller than kleisma
|-
|-
| [[55edo|55]]
| [[55edo]]
| {{frac|6}} comma
| {{frac|6}} comma
| 4
| 4
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| 3
| 3
|-
|-
| [[50edo|50]]
| [[50edo]]
| {{frac|2|7}} comma
| {{frac|2|7}} comma
| 3
| 3
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