Extended meantone notation: Difference between revisions
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... 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]]. For example, in 31edo, 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. | ||
The meantone circle of fifths, however, has no single semisharp or semiflat. In extended meantone notation, a sharp is split into 2 different parts | The meantone circle of fifths, however, has no single semisharp or semiflat. In extended meantone notation, a sharp is split into 2 different parts, the diesis and the kleisma. | ||
=== Generalizing accidentals === | === Generalizing accidentals === | ||
Sharps and flats | 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♭. | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
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|} | |} | ||
A diesis | A meantone chromatic semitone is equivalent to a diesis added to a kleisma. Note that in most meantone tunings, the diesis and kleisma are roughly a quarter tone. | ||
Unlike a single semisharp/semiflat, this can be generalized to other | Unlike a single semisharp/semiflat, this can be generalized to other tunings: | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
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| 1 | | 1 | ||
| 1 | | 1 | ||
| | | 0 | ||
| 1 | | 1 | ||
| Chromatic semitone is equal to kleisma,<br>diesis is tempered out | | Chromatic semitone is equal to kleisma,<br>diesis is tempered out | ||
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|} | |} | ||
There are of course notational equivalences | There are of course notational equivalences: | ||
*B♯↑ and B𝄪− are equal to C | *B♯↑ and B𝄪− are equal to C | ||
*C+↑ is equal to C♯ (because the two semisharps add up) | *C+↑ is equal to C♯ (because the two semisharps add up) | ||
* | *D𝄫↓ and D♭♭♭− are equal to C | ||
Assuming [[septimal meantone]], the meantone diesis can be considered to be [[36/35]], [[50/49]], [[64/63]], [[128/125]], or [[648/625]], while the meantone kleisma is [[49/48]], [[245/243]], [[3125/3072]], or [[15625/15552]]. An octave is made of 19 dieses and 12 | Assuming [[septimal meantone]], the meantone diesis can be considered to be [[36/35]], [[50/49]], [[64/63]], [[128/125]], or [[648/625]], while the meantone kleisma is [[49/48]], [[245/243]], [[3125/3072]], or [[15625/15552]]. An octave is made of 19 dieses and 12 kleismas. | ||
[[9–odd–limit]] intervals and their notation relative to C: | [[9–odd–limit]] intervals and their notation relative to C: | ||