27edo: Difference between revisions
→Music: +++ |
→Regular temperament properties: not really "out of tune" for ennealimmal, just not precise enough |
||
| (2 intermediate revisions by the same user not shown) | |||
| Line 539: | Line 539: | ||
|+ style="font-size: 105%;" | Circle of fifths in 27edo | |+ style="font-size: 105%;" | Circle of fifths in 27edo | ||
|- style="white-space: nowrap;" | |- style="white-space: nowrap;" | ||
!Cents | ! Cents | ||
! colspan="2" | Extended<br | ! colspan="2" | Extended<br>Pythagorean<br>notation | ||
! colspan="2" | Quartertone<br | ! colspan="2" | Quartertone<br>notation | ||
|- | |- | ||
| 0.0 | | 0.0 | ||
| Line 671: | Line 671: | ||
Using standard [[chain-of-fifths notation]], a sharp (an augmented unison) raises a note by 4 edosteps, just one edostep beneath the following nominal, and the flat conversely lowers. The sharp is quite wide at about 178¢, sounding like a narrow major 2nd. C to C♯ describes the approximate 10/9 and 11/10 interval. An accidental can be divided in half, and the remaining places can then be filled in with half-sharps, half-flats, sesquisharps, and sesquiflats, reducing the need for double sharps and double flats. The half-sharp is notated as a quartertone, but at about 89¢ it sounds more like a narrow semitone. The gamut from C to D is C, D♭, C{{demisharp2}}, D{{demiflat2}}, C♯, and D, with many ascending intervals appearing to be descending on the staff. | Using standard [[chain-of-fifths notation]], a sharp (an augmented unison) raises a note by 4 edosteps, just one edostep beneath the following nominal, and the flat conversely lowers. The sharp is quite wide at about 178¢, sounding like a narrow major 2nd. C to C♯ describes the approximate 10/9 and 11/10 interval. An accidental can be divided in half, and the remaining places can then be filled in with half-sharps, half-flats, sesquisharps, and sesquiflats, reducing the need for double sharps and double flats. The half-sharp is notated as a quartertone, but at about 89¢ it sounds more like a narrow semitone. The gamut from C to D is C, D♭, C{{demisharp2}}, D{{demiflat2}}, C♯, and D, with many ascending intervals appearing to be descending on the staff. | ||
=== | === Stein–Zimmermann–Gould notation === | ||
27edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat. | [[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows: | ||
{{Sharpness-sharp4-szg}} | |||
=== Kite's ups and downs notation === | |||
27edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat. | |||
{{Ups and downs sharpness}} | {{Ups and downs sharpness}} | ||
=== Sagittal notation === | === Sagittal notation === | ||
| Line 1,022: | Line 1,024: | ||
| 3 | | 3 | ||
| 2\27 | | 2\27 | ||
| [[Augene]] (27e) / | | [[Augene]] (27e) / eugene (27) | ||
| [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]] | | [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]] | ||
|- | |- | ||
| Line 1,032: | Line 1,034: | ||
| 9 | | 9 | ||
| 1\27 | | 1\27 | ||
| [[Niner]] (27e | | [[Niner]] (27e) | ||
| [[9L 9s]] | | [[9L 9s]] | ||
|} | |} | ||
In addition, 27edo can be used as a detempering target for [[ennealimmal]]. | |||
=== Commas === | === Commas === | ||