Extended meantone notation: Difference between revisions

... {{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𝄪|s=thin|d=long}} ...

Most musicians are familiar with single and double sharps and flats&mdash;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♯&ndash;D♭ and D♯&ndash;E♭),<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 sharps and flats.</ref> and the kleisma, which is the amount by which B♯ exceeds C♭ and E♯ exceeds F♭ (that is, C♭&#x200A;&ndash;&#x200A;B♯ and F♭&#x200A;&ndash;&#x200A;E♯).

| ♯

| ♭

| ↑

| ↓

! style="width: 90px;" | Chromatic<br>semitone<br>(e.g.&nbsp;C&ndash;C♯)

! style="width: 90px;" | Diatonic<br>semitone<br>(e.g.&nbsp;C&ndash;D♭)

| 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>,<br>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>

* B♯↑ and B𝄪− are equal to C

* C+↑ is equal to C♯ (because the two semisharps add up)

* D𝄫↓ and D♭♭♭− are equal to C

| E♭

| A♭

| style="border-left: 5px solid black;" | A♯<br>B♭↓

| D♯<br>E♭↓

| F♯<br>G♭↓

| E𝄫<br>D↑

| B𝄫<br>A↑

| G♭<br>F♯↑

| colspan="2" | B♭

| F♭<br>E↑

| G♯<br>A♭↓

{{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|s=thin|d=long}}

{{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|s=thin|d=long}}

While real-world Arabic and Persian music often involve many very fine microtonal details (such as the use of multiple unequal neutral intervals) and exhibit significant regional variations, and are very difficult to notate exactly as a result, they are commonly notated using half-sharps and half-flats. If we take these to be exactly equal to one-half of a chromatic semitone, then mathematically, this notation system results in the aforementioned two-dimensional lattice. If notes separated by a diminished second, such as C♯ and D♭, are made enharmonically equivalent, this lattice degenerates further into 24edo, which is often suggested as a simplified framework and tuning system for notating and playing Arabic and Persian music. But the usual written notation typically lets musicians and composers treat adjacent sharps and flats as two distinct entities if it is decided that they should be different.