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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]]''.


== Extending the chain of fifths ==
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):
[[Circle-of-fifths notation|Standard meantone notation]] uses 7 base note letters, plus sharps and flats.


... 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𝄪 ...


However, when transferred into a 31edo scale, the chromatic scale becomes:
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:


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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Note that the base note letters alternate.
Note that the base note letters alternate.


In 31edo, sharps can be split in half, so this is solved by semisharps and semiflats, sometimes notated with [[ups and Downs Notation|ups and downs]].
The meantone circle of fifths, however, has no single semisharp or semiflat. In extended meantone notation, a sharp is split into 2 different parts that can be added to produce a sharp:


=== Generalizing accidentals ===
=== Generalizing accidentals ===
The meantone circle of fifths, however, has no single semisharp/semiflat. In extended meantone notation, a sharp is split into 2 different parts that can be added to produce a sharp:
Sharps and flats, which denote raising and lowering by a given number of chromatic semitones. However, in a generalized meantone system, there are two other intervals, the diesis and kleisma. The the diesis is the difference between adjacent accidentals (e.g. C♯–D♭ and D♯–E♭), while the kleisma is the difference between B♯ and C♭ and between E♯ and F♭.


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