16edo: Difference between revisions
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'''16-EDO''' is the [[equal division of the octave]] into sixteen narrow chromatic semitones each of 75 [[cent]]s exactly. It is not especially good at representing most low-odd-limit musical intervals, but it has a [[7/4]] which is only six cents sharp, and a [[5/4]] which is only eleven cents flat. Four steps of it gives the 300 cent minor third interval, the same of that 12-EDO, giving it four diminished seventh chords exactly like those of [[12edo|12-EDO]], and a diminished triad on each scale step. | '''16-EDO''' is the [[equal division of the octave]] into sixteen narrow chromatic semitones each of 75 [[cent]]s exactly. It is not especially good at representing most low-odd-limit musical intervals, but it has a [[7/4]] which is only six cents sharp, and a [[5/4]] which is only eleven cents flat. Four steps of it gives the 300 cent minor third interval, the same of that 12-EDO, giving it four diminished seventh chords exactly like those of [[12edo|12-EDO]], and a diminished triad on each scale step. | ||
===Differences between distributionally-even scales and smaller edos=== | |||
{| class="wikitable" | |||
|+ | |||
!N | |||
!L-Nedo | |||
!s-Nedo | |||
|- | |||
|3 | |||
|50¢ | |||
| -25¢ | |||
|- | |||
|5 | |||
|60¢ | |||
| -15¢ | |||
|- | |||
|6 | |||
|25¢ | |||
| -50¢ | |||
|- | |||
|7 | |||
|54.571¢ | |||
| -21.429¢ | |||
|- | |||
|9 | |||
|16.667¢ | |||
| -58.333¢ | |||
|- | |||
|10 | |||
|30¢ | |||
| -45¢ | |||
|- | |||
|11 | |||
|33.909¢ | |||
| -41.091¢ | |||
|- | |||
|12 | |||
|50¢ | |||
| -25¢ | |||
|- | |||
|13 | |||
|57.692¢ | |||
| -17.308¢ | |||
|- | |||
|14 | |||
|64.286¢ | |||
| -10.714¢ | |||
|- | |||
|15 | |||
|70¢ | |||
| -5¢ | |||
|} | |||
==Intervals== | ==Intervals== | ||
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Important MOSes include: | Important MOSes include: | ||
* [[magic]] anti-diatonic 3L4s 1414141 (5\16, 1\1) | * [[magic]] anti-diatonic 3L4s [[Tel:1414141|1414141]] (5\16, 1\1) | ||
* [[magic]] superdiatonic 3L7s 1311311311 (5\16, 1\1) | * [[magic]] superdiatonic 3L7s [[Tel:1311311311|1311311311]] (5\16, 1\1) | ||
* Pathological [[magic]] chromatic 11121121112 3L10s (5\16, 1\1) | * Pathological [[magic]] chromatic [[Tel:11121121112|11121121112]] 3L10s (5\16, 1\1) | ||
* [[mavila]] anti-diatonic 2L5s 2223223 (9\16, 1\1) | * [[mavila]] anti-diatonic 2L5s 2223223 (9\16, 1\1) | ||
* [[mavila]] superdiatonic 7L2s 222212221 (9\16, 1\1) | * [[mavila]] superdiatonic 7L2s 222212221 (9\16, 1\1) | ||