Extended meantone notation: Difference between revisions
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== Generalizing accidentals == | == Generalizing accidentals == | ||
Most | Most musicians are familiar with single and double sharps and flats—these denote raising and lowering by one or two chromatic semitones, respectively. In a general meantone tuning, there are two additional intervals: the diesis, which is the difference between adjacent accidentals (e.g. C♯–D♭ and D♯–E♭),<ref group="note" name="diesis_note" /> and the kleisma, which is the amount by which B♯ exceeds C♭ and E♯ exceeds F♭ (that is, C♭–B♯ and F♭–E♯). | ||
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| Chromatic semitone is tempered out<ref group="note" name="chroma_note">In 7-tone equal temperament, the tempering out of the chromatic semitone means that sharps and flats cannot alter the pitch.</ref>, diesis is positive, and kleisma is negative<ref group="note" name="kleisma_note">A negative kleisma means that B♯ is lower in pitch than C♭ and E♯ is lower in pitch than F♭.</ref> | | Chromatic semitone is tempered out<ref group="note" name="chroma_note">In 7-tone equal temperament, the tempering out of the chromatic semitone means that sharps and flats are redundant (in the sense that they cannot alter the pitch).</ref>, diesis is positive, and kleisma is negative<ref group="note" name="kleisma_note">A negative kleisma means that B♯ is lower in pitch than C♭ and E♯ is lower in pitch than F♭. Conversely, a positive kleisma means B♯ sits higher than C♭ and E♯ sits higher than F♭. In 19-tone equal temperament, the tempering out of the kleisma means that B♯ = C♭ and E♯ = F♭.</ref> | ||
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| Chromatic semitone is equal to kleisma, diesis is tempered out<ref group="note" name="diesis_note">Having C♯ and D♭ be enharmonically equivalent is what most musicians | | Chromatic semitone is equal to kleisma, diesis is tempered out<ref group="note" name="diesis_note">Having C♯ and D♭ be enharmonically equivalent is what most musicians would expect, but this is only true in equal temperament tunings where the number of notes is a multiple of 12. In most tuning systems, there are no enharmonic equivalents involving only single sharps and flats.</ref> | ||
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| [[19edo|19]] | | [[19edo|19]] | ||