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'''33ed4''' is the [[ed4|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[cent|cent]]s. It takes out every second step of [[33edo|33edo]] and falls between [[16edo|16edo]] and [[17edo|17edo]]. So even degree 16 or degree 17 can play the role of the [[Octave|octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of '''<span style="color: #00cc00;">E</span><span style="color: #00cc00;">quivocal Tuning</span>'''.
'''33ed4''' is the [[ed4|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[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 '''<span style="color: #00cc00;">E</span><span style="color: #00cc00;">quivocal Tuning</span>'''.


It has a [[9/5|9/5]] which is 0.6 cents sharp, a [[7/5|7/5]] which is 0.7 cents flat, and a [[9/7|9/7]] which is 1.3 cents sharp. Therefore it is closely related to [[13edt|13edt]], the [[Bohlen-Pierce|Bohlen-Pierce]] scale, although it has no pure [[3/1|3/1]], which is 11.1 cents flat. The lack of a [[3/2|pure fifth]] makes it also interesting.
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. The lack of a [[3/2|pure fifth]] makes it also interesting.


Furthermore it has some [[11-limit|11-limit]], [[13-limit|13-limit]], [[17-limit|17-limit]] and even [[23-limit|23-limit]] which are very close (most of them under or nearby 1 cent).
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===
== Intervals ==


{| class="wikitable"
{| class="wikitable right-all"
|-
|-
! | degree
! degree
! | in cents
! in cents
! | nearest JI
! nearest JI <br> interval
 
! in cents
interval
! difference <br> in cents
! | in cents
! | difference
 
in cents
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 72,7
| style="text-align:right;" | 24/23
| style="text-align:right;" | 73,7
| style="text-align:right;" | -1,0
|-
|-
| style="text-align:right;" | 2
| 1
| style="text-align:right;" | 145,5
| 72.7
| style="text-align:right;" | 25/23
| 24/23
| style="text-align:right;" | 144,4
| 73.7
| style="text-align:right;" | 1,1
| -1.0
|-
|-
| style="text-align:right;" | 3
| 2
| style="text-align:right;" | 218,2
| 145.5
| style="text-align:right;" | 17/15
| 25/23
| style="text-align:right;" | 216,6
| 144.4
| style="text-align:right;" | 1,6
| 1.1
|-
|-
| style="text-align:right;" | 4
| 3
| style="text-align:right;" | 290,9
| 218.2
| style="text-align:right;" | 13/11
| 17/15
| style="text-align:right;" | 289,2
| 216.6
| style="text-align:right;" | 1,7
| 1.6
|-
|-
| style="text-align:right;" | 5
| 4
| style="text-align:right;" | 363,6
| 290.9
| style="text-align:right;" | 16/13
| 13/11
| style="text-align:right;" | 359,5
| 289.2
| style="text-align:right;" | 4,1
| 1.7
|-
|-
| style="text-align:right;" | '''6'''
| 5
| style="text-align:right;" | '''436,4'''
| 363.6
| style="text-align:right;" | '''9/7'''
| 16/13
| style="text-align:right;" | '''435,1'''
| 359.5
| style="text-align:right;" | '''1,3'''
| 4.1
|- style="font-weight: bold"
| 6
| 436.4
| 9/7
| 435.1
| 1.3
|-
|-
| style="text-align:right;" | 7
| 7
| style="text-align:right;" | 509,1
| 509.1
| style="text-align:right;" | 51/38
| 51/38
| style="text-align:right;" | 509,4
| 509.4
| style="text-align:right;" | -0,3
| -0.3
|- style="font-weight: bold"
| 8
| 581.8
| 7/5
| 582.5
| -0.7
|-
|-
| style="text-align:right;" | '''8'''
| 9
| style="text-align:right;" | '''581,8'''
| 654.5
| style="text-align:right;" | '''7/5'''
| 19/13
| style="text-align:right;" | '''582,5'''
| 657.0
| style="text-align:right;" | '''-0,7'''
| -2.5
|-
|-
| style="text-align:right;" | 9
| 10
| style="text-align:right;" | 654,5
| 727.3
| style="text-align:right;" | 19/13
| 35/23
| style="text-align:right;" | 657,0
| 726.9
| style="text-align:right;" | -2,5
| 0.4
|-
|-
| style="text-align:right;" | 10
| 11
| style="text-align:right;" | 727,3
| 800.0
| style="text-align:right;" | 35/23
| 27/17
| style="text-align:right;" | 726,9
| 800.9
| style="text-align:right;" | 0,4
| -0.9
|-
|-
| style="text-align:right;" | 11
| 12
| style="text-align:right;" | 800,0
| 872.7
| style="text-align:right;" | 27/17
| 53/32
| style="text-align:right;" | 800,9
| 873.5
| style="text-align:right;" | -0,9
| -0.8
|-
|-
| style="text-align:right;" | 12
| 13
| style="text-align:right;" | 872,7
| 945.5
| style="text-align:right;" | 53/32
| 19/11
| style="text-align:right;" | 873,5
| 946.2
| style="text-align:right;" | -0,8
| -0.7
|- style="font-weight: bold"
| 14
| 1018.2
| 9/5
| 1017.6
| 0.6
|-
|-
| style="text-align:right;" | 13
| 15
| style="text-align:right;" | 945,5
| 1090.9
| style="text-align:right;" | 19/11
| 15/8
| style="text-align:right;" | 946,2
| 1088.3
| style="text-align:right;" | -0,7
| 2.6
|- style="font-weight: bold; color: #00cc00;"
| 16
| 1163.6
| 45/23
| 1161.9
| 1.7
|- style="font-weight: bold; color: #00cc00;"
| 17
| 1236.4
| 49/24
| 1235.7
| 0.7
|-
|-
| style="text-align:right;" | '''14'''
| 18
| style="text-align:right;" | '''1018,2'''
| 1309.1
| style="text-align:right;" | '''9/5'''
| 32/15
| style="text-align:right;" | '''1017,6'''
| 1311.7
| style="text-align:right;" | '''0,6'''
| -2.6
|- style="font-weight: bold"
| 19
| 1381.8
| 20/9
| 1382.4
| -0.6
|-
|-
| style="text-align:right;" | 15
| 20
| style="text-align:right;" | 1090,9
| 1454.5
| style="text-align:right;" | 15/8
| 44/19
| style="text-align:right;" | 1088,3
| 1453.8
| style="text-align:right;" | 2,6
| 0.7
|-
|-
| style="text-align:right;" | '''<span style="color: #00cc00;">16</span>'''
| 21
| style="text-align:right;" | '''<span style="color: #00cc00;">1163,6</span>'''
| 1527.3
| style="text-align:right;" | '''<span style="color: #00cc00;">45/23</span>'''
| 29/12
| style="text-align:right;" | '''<span style="color: #00cc00;">1161,9</span>'''
| 1527.6
| style="text-align:right;" | '''<span style="color: #00cc00;">1,7</span>'''
| -0.3
|-
|-
| style="text-align:right;" | '''<span style="color: #00cc00;">17</span>'''
| 22
| style="text-align:right;" | '''<span style="color: #00cc00;">1236,4</span>'''
| 1600.0
| style="text-align:right;" | '''<span style="color: #00cc00;">49/24</span>'''
| 68/27
| style="text-align:right;" | '''<span style="color: #00cc00;">1235,7</span>'''
| 1599.1
| style="text-align:right;" | '''<span style="color: #00cc00;">0,7</span>'''
| 0.9
|-
|-
| style="text-align:right;" | 18
| 23
| style="text-align:right;" | 1309,1
| 1672.7
| style="text-align:right;" | 32/15
| 21/8
| style="text-align:right;" | 1311,7
| 1670.8
| style="text-align:right;" | -2,6
| 1.9
|-
|-
| style="text-align:right;" | '''19'''
| 24
| style="text-align:right;" | '''1381,8'''
| 1745.5
| style="text-align:right;" | '''20/9'''
| 52/19
| style="text-align:right;" | '''1382,4'''
| 1743.0
| style="text-align:right;" | '''-0,6'''
| 2.5
|- style="font-weight: bold"
| 25
| 1818.2
| 20/7
| 1817.5
| 0.7
|-
|-
| style="text-align:right;" | 20
| 26
| style="text-align:right;" | 1454,5
| 1890.9
| style="text-align:right;" | 44/19
| 116/39
| style="text-align:right;" | 1453,8
| 1887.1
| style="text-align:right;" | 0,7
| 3.8
|- style="font-weight: bold"
| 27
| 1963.6
| 28/9
| 1964.9
| -1.3
|-
|-
| style="text-align:right;" | 21
| 28
| style="text-align:right;" | 1527,3
| 2036.4
| style="text-align:right;" | 29/12
| 13/4
| style="text-align:right;" | 1527,6
| 2040.5
| style="text-align:right;" | -0,3
| -4.1
|-
|-
| style="text-align:right;" | 22
| 29
| style="text-align:right;" | 1600,0
| 2109.1
| style="text-align:right;" | 68/27
| 44/13
| style="text-align:right;" | 1599,1
| 2110.8
| style="text-align:right;" | 0,9
| -1.7
|-
|-
| style="text-align:right;" | 23
| 30
| style="text-align:right;" | 1672,7
| 2181.8
| style="text-align:right;" | 21/8
| 60/17
| style="text-align:right;" | 1670,8
| 2183.3
| style="text-align:right;" | 1,9
| -1.5
|-
|-
| style="text-align:right;" | 24
| 31
| style="text-align:right;" | 1745,5
| 2254.5
| style="text-align:right;" | 52/19
| 114/31
| style="text-align:right;" | 1743,0
| 2254.4
| style="text-align:right;" | 2,5
| 0.1
|-
|-
| style="text-align:right;" | '''25'''
| 32
| style="text-align:right;" | '''1818,2'''
| 2327.3
| style="text-align:right;" | '''20/7'''
| 23/6
| style="text-align:right;" | '''1817,5'''
| 2326.3
| style="text-align:right;" | '''0,7'''
| 1.0
|-
|- style="font-weight: bold"
| style="text-align:right;" | 26
| 33
| style="text-align:right;" | 1890,9
| 2400.0
| style="text-align:right;" | 116/39
| 4/1
| style="text-align:right;" | 1887,1
| 2400.0
| style="text-align:right;" | 3,8
| 0.0
|-
| style="text-align:right;" | '''27'''
| style="text-align:right;" | '''1963,6'''
| style="text-align:right;" | '''28/9'''
| style="text-align:right;" | 1964,9
| style="text-align:right;" | '''-1,3'''
|-
| style="text-align:right;" | 28
| style="text-align:right;" | 2036,4
| style="text-align:right;" | 13/4
| style="text-align:right;" | 2040,5
| style="text-align:right;" | -4,1
|-
| style="text-align:right;" | 29
| style="text-align:right;" | 2109,1
| style="text-align:right;" | 44/13
| style="text-align:right;" | 2110,8
| style="text-align:right;" | -1,7
|-
| style="text-align:right;" | 30
| style="text-align:right;" | 2181,8
| style="text-align:right;" | 60/17
| style="text-align:right;" | 2183,3
| style="text-align:right;" | -1,5
|-
| style="text-align:right;" | 31
| style="text-align:right;" | 2254,5
| style="text-align:right;" | 114/31
| style="text-align:right;" | 2254,4
| style="text-align:right;" | 0,1
|-
| style="text-align:right;" | 32
| style="text-align:right;" | 2327,3
| style="text-align:right;" | 23/6
| style="text-align:right;" | 2326,3
| style="text-align:right;" | 1,0
|-
| style="text-align:right;" | '''33'''
| style="text-align:right;" | '''2400,0'''
| style="text-align:right;" | '''4/1'''
| style="text-align:right;" | '''2400,0'''
| style="text-align:right;" | '''0,0'''
|}
|}


===Music===
== Music ==
[http://soundcloud.com/ahornberg/sets/equivocal-tuning-33ed4 Equivocal Tuning] by Ahornberg
 
* [http://soundcloud.com/ahornberg/sets/equivocal-tuning-33ed4 Equivocal Tuning] — Set of compositions by Ahornberg
 
[[Category:31edo]]
[[Category:31edo]]
[[Category:what_is]]
[[Category:wiki]]
Retrieved from "https://en.xen.wiki/w/33ed4"