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Extended meantone notation: Difference between revisions

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Most musicians are familiar with the [[circle of fifths]]. This is a way of organizing and showing relationships between pitches as a sequence of [[3/2|fifths]], and applies to any tuning system that can be generated by fifths and octaves. The generalized 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):
Most musicians are familiar with the [[circle of fifths]]. This is a way of organizing and showing relationships between pitches as a sequence of [[3/2|fifths]], and applies to any tuning system that can be generated by fifths and octaves. The generalized 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𝄪 ...
... {{dash|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𝄪|spaces=thin|sep=mdash}} ...


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]].
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]].
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For example, in 31edo, the chromatic scale becomes:
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
{{dash|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|spaces=thin|sep=mdash}}


Note that the base note letters alternate.
Note that the base note letters alternate.
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Using semisharps and semiflats, this can be re-written as:
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
{{dash|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|spaces=thin|sep=mdash}}


The generalized chain of fifths, however, does not have a single semisharp or semiflat. In a general meantone tuning, a sharp is split into 2 different parts, the diesis and the kleisma.
The generalized chain of fifths, however, does not have a single semisharp or semiflat. In a general meantone tuning, a sharp is split into 2 different parts, the diesis and the kleisma.
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