33ed4
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author jauernig and made on 2015-01-09 18:20:44 UTC.
- The original revision id was 536805560.
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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
33ed4 is the Equal Divisions of the Double Octave into 33 narrow chromatic semitones each of 72.727 [[xenharmonic/cent|cent]]s. It takes out every second step of 33edo and falls between 16edo and 17edo. So even degree 16 or degree 17 can play the role of the octave, depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of equivocal tuning. It has a 9/5 which is 0.6 cents sharp, a 7/5 which is 0.7 cents flat, and a 9/7 which is 1.3 cents sharp. Therefore it is closely related to 13edt, the Bohlen-Pierce scale, although it has no pure 3/1, which is 11.1 cents flat. Furthermore it has some 11-limit, 13-limit, 17-limit and even 23-limit which are very close (most of them under or nearby 1 cent). Intervals degree cents nearest JI interval in cent diff 1 72,7 24/23 73,7 -1,0 2 145,5 25/23 144,4 1,1 3 218,2 17/15 216,6 1,6 4 290,9 13/11 289,2 1,7 5 363,6 16/13 359,5 4,1 6 436,4 9/ 7 435,1 1,3 7 509,1 51/38 509,4 -0,3 8 581,8 7/ 5 582,5 -0,7 9 654,5 19/13 657,0 -2,5 10 727,3 35/23 726,9 0,4 11 800,0 27/17 800,9 -0,9 12 872,7 53/32 873,5 -0,8 13 945,5 19/11 946,2 -0,7 14 1018,2 9/ 5 1017,6 0,6 15 1090,9 15/ 8 1088,3 2,6 16 1163,6 45/23 1161,9 1,7 17 1236,4 49/24 1235,7 0,7 18 1309,1 32/15 1311,7 -2,6 19 1381,8 20/ 9 1382,4 -0,6 20 1454,5 44/19 1453,8 0,7 21 1527,3 29/12 1527,6 -0,3 22 1600,0 68/27 1599,1 0,9 23 1672,7 21/8 1670,8 1,9 24 1745,5 52/19 1743,0 2,5 25 1818,2 20/ 7 1817,5 0,7 26 1890,9 116/39 1887,1 3,8 27 1963,6 28/ 9 1964,9 -1,3 28 2036,4 13/ 4 2040,5 -4,1 29 2109,1 44/13 2110,8 -1,7 30 2181,8 60/17 2183,3 -1,5 31 2254,5 114/31 2254,4 0,1 32 2327,3 23/ 6 2326,3 1,0 33 2400,0 4/ 1 2400,0 0,0
Original HTML content:
<html><head><title>33ed4</title></head><body>33ed4 is the Equal Divisions of the Double Octave into 33 narrow chromatic semitones each of 72.727 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s. It takes out every second step of 33edo and falls between 16edo and 17edo. So even degree 16 or degree 17 can play the role of the octave, depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of equivocal tuning.<br /> <br /> It has a 9/5 which is 0.6 cents sharp, a 7/5 which is 0.7 cents flat, and a 9/7 which is 1.3 cents sharp. Therefore it is closely related to 13edt, the Bohlen-Pierce scale, although it has no pure 3/1, which is 11.1 cents flat.<br /> <br /> Furthermore it has some 11-limit, 13-limit, 17-limit and even 23-limit which are very close (most of them under or nearby 1 cent).<br /> <br /> Intervals<br /> <br /> degree cents nearest JI interval in cent diff<br /> 1 72,7 24/23 73,7 -1,0<br /> 2 145,5 25/23 144,4 1,1<br /> 3 218,2 17/15 216,6 1,6<br /> 4 290,9 13/11 289,2 1,7<br /> 5 363,6 16/13 359,5 4,1<br /> 6 436,4 9/ 7 435,1 1,3<br /> 7 509,1 51/38 509,4 -0,3<br /> 8 581,8 7/ 5 582,5 -0,7<br /> 9 654,5 19/13 657,0 -2,5<br /> 10 727,3 35/23 726,9 0,4<br /> 11 800,0 27/17 800,9 -0,9<br /> 12 872,7 53/32 873,5 -0,8<br /> 13 945,5 19/11 946,2 -0,7<br /> 14 1018,2 9/ 5 1017,6 0,6<br /> 15 1090,9 15/ 8 1088,3 2,6<br /> 16 1163,6 45/23 1161,9 1,7<br /> 17 1236,4 49/24 1235,7 0,7<br /> 18 1309,1 32/15 1311,7 -2,6<br /> 19 1381,8 20/ 9 1382,4 -0,6<br /> 20 1454,5 44/19 1453,8 0,7<br /> 21 1527,3 29/12 1527,6 -0,3<br /> 22 1600,0 68/27 1599,1 0,9<br /> 23 1672,7 21/8 1670,8 1,9<br /> 24 1745,5 52/19 1743,0 2,5<br /> 25 1818,2 20/ 7 1817,5 0,7<br /> 26 1890,9 116/39 1887,1 3,8<br /> 27 1963,6 28/ 9 1964,9 -1,3<br /> 28 2036,4 13/ 4 2040,5 -4,1<br /> 29 2109,1 44/13 2110,8 -1,7<br /> 30 2181,8 60/17 2183,3 -1,5<br /> 31 2254,5 114/31 2254,4 0,1<br /> 32 2327,3 23/ 6 2326,3 1,0<br /> 33 2400,0 4/ 1 2400,0 0,0</body></html>