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 [[ | Most musicians are familiar with the [[circle of fifths]]. This is a way of organizing and showing relationships between pitches of a tuning system, and is applicable to any tuning that is generated by octaves and fifths. More generally, the chain of fifths involves the 7 base note letters of the C major scale, 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 | In some tunings, such as [[24-tone equal temperament]] (quarter tones) and [[31-tone equal temperament]] (extended [[quarter-comma meantone]]), 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 | 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. | ||
The meantone circle of fifths, however, | Using semisharps and semiflats, this can be re-written as: | ||
C – C{{demisharp2}} – C♯ – D♭ – D{{demiflat2}} – D – D{{demisharp2}} – D♯ – E♭ – E{{demiflat2}} – E – E{{demisharp2}} – F{{demiflat2}} – F – F{{demisharp2}} – F♯ – G♭ – G{{demiflat2}} – G – G{{demisharp2}} – G♯ – A♭ – A{{demiflat2}} – A – A{{demisharp2}} – A♯ – B♭ – B{{demiflat2}} – B – B{{demisharp2}} – C{{demiflat2}} – C | |||
The meantone circle of fifths, however, does not have a single semisharp or semiflat. In a general meantone notation, a sharp is split into 2 different parts, the diesis and the kleisma. | |||
== Generalizing accidentals == | == Generalizing accidentals == | ||
Most people are familiar with sharps and | 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). In a general meantone tuning, there are two additional intervals: the diesis, the difference between adjacent accidentals (e.g. C♯–D♭ and D♯–E♭), and the kleisma, which is the amount by which B♯ exceeds C♭ and E♯ exceeds F♭—that is, C♭–B♯ and F♭–E♯. | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
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{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! rowspan="2" style="width: 50px;" | Notes per | ! rowspan="2" style="width: 50px;" | Notes per octave | ||
! rowspan="2" style="width: | ! rowspan="2" style="width: 90px;" | [[Syntonic comma]] fraction | ||
! colspan="4" | Steps | ! colspan="4" | Steps | ||
! rowspan="2" style="width: 225px;" | Explanation | ! rowspan="2" style="width: 225px;" | Explanation | ||