Extended meantone notation: Difference between revisions
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In 31edo, sharps can be split in half, so this is solved by semisharps and semiflats, sometimes notated with [[ups and Downs Notation|ups and downs]]. | In 31edo, sharps can be split in half, so this is solved by semisharps and semiflats, sometimes notated with [[ups and Downs Notation|ups and downs]]. | ||
=== Generalizing accidentals === | |||
The meantone circle of fifths, however, has no single semisharp/semiflat. In extended meantone notation, a sharp is split into 2 different parts that can be added to produce a sharp: | The meantone circle of fifths, however, has no single semisharp/semiflat. In extended meantone notation, a sharp is split into 2 different parts that can be added to produce a sharp: | ||
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[[9–odd–limit]] intervals and their notation relative to C: | [[9–odd–limit]] intervals and their notation relative to C: | ||
< | {| class="wikitable center-all" | ||
! Note | |||
| C | |||
| style="border-left: 5px solid black;" | G | |||
| style="border-right: 5px solid black;" | F | |||
| style="border-left: 5px solid black;" | E | |||
| A | |||
| 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♯↑ | |||
12 | | style="border-left: 5px solid black;" | D | ||
10 | | B♭ | ||
| F♭<br>E↑ | |||
| B♭ | |||
| D | |||
| G♯<br>A♭↓ | |||
16 | |- | ||
10 | ! Just interval | ||
14 | | {{sfrac|1|1}} | ||
| style="border-left: 5px solid black;" | {{sfrac|3|2}} | |||
| {{sfrac|4|3}} | |||
| style="border-left: 5px solid black;" | {{sfrac|5|4}} | |||
| {{sfrac|5|3}} | |||
| {{sfrac|6|5}} | |||
| style="border-right: 5px solid black;" | {{sfrac|8|5}} | |||
| style="border-left: 5px solid black;" | {{sfrac|7|4}} | |||
| {{sfrac|7|6}} | |||
| {{sfrac|7|5}} | |||
| {{sfrac|8|7}} | |||
| {{sfrac|12|7}} | |||
| {{sfrac|10|7}} | |||
| style="border-left: 5px solid black;" | {{sfrac|9|8}} | |||
| {{sfrac|9|5}} | |||
| {{sfrac|9|7}} | |||
| {{sfrac|16|9}} | |||
| {{sfrac|10|9}} | |||
| {{sfrac|14|9}} | |||
|} | |||
Two dieses or two kleismas cannot be stacked to produce a chromatic semitone. 11–limit and 13–limit notation can vary (see [[meantone vs meanpop]]). | Two dieses or two kleismas cannot be stacked to produce a chromatic semitone. 11–limit and 13–limit notation can vary (see [[meantone vs meanpop]]). | ||