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{| class="wikitable"
{| class="wikitable"
|+ Common Diasem Tunings
|+ Common Diasem Tunings
! rowspan="2" |Tuning
! rowspan="2" |L:m:s
! rowspan="2" |Good Just Approximations
! rowspan="2" |other comments
! colspan="8" |Degrees
|-
|-
! Tuning !! L:m:s !! Good Just Approximations !! Degrees !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9
!1!!2!!3!!4!!5 !!6 !! 7!!8
|-
|-
| || || || 1/1 || 9/8 || 7/6 || 21/16 || 4/3 || 3/2 || 14/9 || 7/4 || 16/9 || 2/1
| || ||
| || 9/8||7/6||21/16||4/3||3/2|| 14/9 ||7/4 ||16/9
|-
|-
| JI || 7.479:2.309:1 || Just 7/6, 8/7, and 3/2 || 0.000 || 203.910 || 266.871 || 470.781 || 498.045 || 701.955 || 764.916 || 968.826 || 996.090 || 1200.000
|JI||7.479:2.309:1||Just 7/6, 8/7, and 3/2
| || 203.910||266.871||470.781 ||498.045||701.955 || 764.916||968.826||996.090
|-
|-
| 26edo || 4:2:1 || Neogothic thirds and 8/7 || 0.000 || 184.615 || 276.923 || 461.538 || 507.692 || 692.308 || 784.615 || 969.231 || 1015.385 || 1200.000
| 21edo
|3:2:1
|
|
|171.429
|285.714
|457.143
| 514.286
|685.714
|800
|971.429
|1028.571
|-
|-
| 31edo || 5:2:1 || Pental thirds and 7/5 || 0.000 || 193.548 || 270.968  || 464.516 || 503.226 || 696.774 || 774.194 || 967.742 || 1006.452 || 1200.000
|26edo||4:2:1 ||Neogothic thirds and 8/7
| ||184.615||276.923 ||461.538 ||507.692 ||692.308||784.615|| 969.231||1015.385
|-
|-
| 36edo || 6:2:1 || Septimal thirds and 3/2 || 0.000 || 200.000 || 266.667 || 466.667 || 500.000 || 700.000 || 766.667 || 966.667 || 1000.000 || 1200.000
| 28edo
|4:3:1
|Pental thirds
|
| 171.429
|300
| 471.429
|514.286
|685.714
|771.429
|985.714
|1028.571
|-
|30edo
| 4:3:2
|
| cross between Mavila and Semaphore
|160
|280
|440
|520
| 680
|800
|960
|1040
|-
|31edo||5:2:1||Pental thirds and 7/5
| ||193.548||270.968||464.516||503.226||696.774|| 774.194||967.742||1006.452
|-
|33edo
|5:3:1
|Septimal and Neogothic thirds and 10/9
|
| 181.818
|290.909
|472.727
| 509.091
|690.909
|763.636
| 981.818
|1018.182
|-
|35edo
| 5:3:2
5:4:1
|
|Uses 21/16 as inconsistent 4/3
|171.429
|274.286
308.571
|445.714
480
|514.286
|685.714
|788.571
822.857
|960
994.286
|1028.571
|-
|36edo||6:2:1||Septimal thirds and 3/2
| ||200.000||266.667|| 466.667|| 500.000|| 700.000||766.667||966.667||1000.000
|-
|37edo
|5:4:2
|35/32
|cross between Mavila and Semaphore
|162.162
|291.892
|454.054
|518.919
|681.081
|810.811
|972.973
|1037.838
|-
|38edo
|6:3:1
|
|
|189.474
|284.2105
|473.684
|505.263
| 694.737
| 789.474
| 978.947
|1010.526
|-
|39edo
|5:4:3
|
| cross between Mavila and Semaphore
|153.846
|276.923
|430.769
|523.077
|676.923
|800
|953.846
| 1046.154
|-
|40edo
|6:3:2
6:4:1
|
|Uses 21/16 as inconsistent 4/3
| 180
| 270
300
|450
480
| 510
|690
| 780
810
|960
990
|1020
|-
|41edo
|7:2:1
|
|
|204.878
|263.415
|468.293
|497.561
|702.439
|760.976
| 965.854
|995.122
|-
| 42edo
|6:5:1
|
|Uses 21/16 as inconsistent 4/3
|171.429
| 314.286
|485.714
|514.286
|685.714
|828.571
|1000
|1028.571
|-
|43edo
|7:3:1
|
|
|195.349
|279.07
|474.419
|502.326
|697.674
|781.395
|976.744
|1004.651
|-
|44edo
|6:4:3
6:5:2
|11/10 (and 9/7)
|cross between Mavila and Semaphore
|163.636
|272.727
300
|436.364
463.636
|518.182
|681.818
|790.909
818.182
|954.5455
981.818
|1036.364
|-
|45edo
|7:3:2
7:4:1
|
|
|186.667
|266.667
293.333
|453.333
480
|506.667
|693.333
|773.333
800
|960
986.667
|1013.333
|-
|46edo
|6:5:3
8:2:1
|Neogothic thirds
|cross between Mavila and Semaphore
Gentle fifth
|156.522
208.696
|286.9565
260.87
|443.478
469.565
|521.739
495.652
|678.231
704.348
|808.696
756.522
|965.218
|1043.418
991.314
|-
|47edo
|7:4:2
7:5:1
|
|Uses 21/16 as inconsistent 4/3
|178.723
|280.851
306.383
|459.578
485.106
|510.638
|689.362
|791.489
817.021
|970.212
995.744
|1021.27h
|-
|48edo
|6:5:4
8:3:1
|
|cross between Mavila and Semaphore
|150
200
|275
|425
475
|525
500
|675
700
|800
775
|950
975
|1050
1000
|-
|49edo
|7:4:3
7:5:2
 
7:6:1
|
|Uses 21/16 as inconsistent 4/3
|171.429
|269.388
293.878
 
318.367
|440.817
465.756
 
489.796
|514.286
|685.714
|783.6735
808.163
 
832.653
|955.102
979.592
 
1004.082
|1028.571
|-
|50edo
|8:3:2
8:4:1
|
|
|192
|264
288
|456
480
|504
|696
|768
792
|960
984
|1008
|-
|51edo
|7:5:3
7:6:2
|
|cross between Mavila and Semaphore
|164.706
|282.353
305.882
|447.059
470.588
|517.647
|682.353
|800
823.529
|964.706
988.235
|1035.294
|-
|52edo
|8:5:1
|
|Uses 21/16 as inconsistent 4/3
|184.615
|300
|484.615
|507.692
|692.308
|807.692
|992.308
|1015.385
|-
|53edo
|7:5:4
7:6:3
|27/20
|cross between Mavila and Semaphore
|158.491
|271.698
294.34
|429.189
452.831
|520.755
|679.245
|792.453
815.094
|950.944
973.585
|1041.509
|-
|54edo
|8:4:3
8:5:2
 
8:6:1
|Septimal thirds
Neogothic thirds
|Uses 21/16 as inconsistent 4/3
|177.778
|266.667
288.889
 
311.111
|444.444
466.667
 
488.889
|511.111
|688.889
|777.778
800
 
822.222
|955.556
977.778
 
1000
|1022.222
|-
|55edo
|7:6:4
|
|cross between Mavila and Semaphore
|152.727
|283.636
|436.364
|523.636
|676.364
|807.273
|960
|1047.273
|-
|56edo
|8:5:3
8:7:1
|
|Golden tuning
Uses 21/16 as inconsistent 4/3
|171.429
|278.571
321.429
|450
492.857
|514.286
|685.714
|792.857
814.286
|964.286
985.714
|1028.571
|-
|57edo
|7:6:5
|
|cross between Mavila and Semaphore
|147.368
|273.684
|421.053
|526.316
|673.684
|800
|947.368
|1052.684
|-
|58edo
|8:5:4
8:6:3
 
8:7:2
|(Septimal and) Neogothic thirds
|cross between Mavila and Semaphore
|165.517
|268.9655
290.394
 
311.084
|435.222
455.911
 
476.601
|517.98
|682.02
|786.946
807.6355
 
828.325
|952.463
973.153
 
993.842
|1034.483
|-
|60edo
|8:7:3
|
|cross between Mavila and Semaphore
|160
|300
|460
|520
|680
|820
|980
|1040
|-
|62edo
|8:7:4
|Neogothic thirds
|cross between Mavila and Semaphore
|154.839
|290.323
|445.161
|522.581
|677.419
|812.903
|967.742
|1045.161
|-
|64edo
|8:7:5
|
|cross between Mavila and Semaphore
|150
|281.25
|431.25
|525
|675
|806.25
|956.25
|1050
|-
|66edo
|8:7:6
|Neogothic thirds
|cross between Mavila and Semaphore
|145.4545
|272.727
|418.182
|527.273
|672.727
|800
|945.4545
|1054.5455
|}
|}


Like [[superpyth]], diasem is great for diatonic melodies in the 2.3.7 subgroup; however, it does not temper 64/63, adding two diesis-sized steps to what would normally be a diatonic scale. Not tempering 64/63 is actually quite useful, because it's the difference between only two 4/3 and a 7/4, so the error is spread over just two perfect fourths, unlike the syntonic comma where the error is spread out over four perfect fifths. As a result, the results of tempering out [[81/80]] are not as bad, because each fifth only needs to be bent by about half as much to achieve the same optimization for the 5-limit. So in the case of 2.3.7, it may actually be worth it to accept the addition of small step sizes in order to improve tuning accuracy. Another advantage of detempering the septimal comma is that it allows one to use both 9/8 and 8/7, as well as 21/16 and 4/3, in the same scale. Semaphore in a sense does the opposite of what superpyth does, exaggerating 64/63 to the point that 21/16 is no longer recognizable, and the small steps of diasem become equal to the medium steps.
Like [[superpyth]], diasem is great for diatonic melodies in the 2.3.7 subgroup; however, it does not temper 64/63, adding two diesis-sized steps to what would normally be a diatonic scale. Not tempering 64/63 is actually quite useful, because it's the difference between only two 4/3 and a 7/4, so the error is spread over just two perfect fourths, unlike the syntonic comma where the error is spread out over four perfect fifths. As a result, the results of tempering out [[81/80]] are not as bad, because each fifth only needs to be bent by about half as much to achieve the same optimization for the 5-limit. So in the case of 2.3.7, it may actually be worth it to accept the addition of small step sizes in order to improve tuning accuracy. Another advantage of detempering the septimal comma is that it allows one to use both 9/8 and 8/7, as well as 21/16 and 4/3, in the same scale. Semaphore in a sense does the opposite of what superpyth does, exaggerating 64/63 to the point that 21/16 is no longer recognizable, and the small steps of diasem become equal to the medium steps.


== Links ==
==Links==
* [https://sevish.com/scaleworkshop/?name=JI%20Diasem&data=9%2F8%0A7%2F6%0A21%2F16%0A4%2F3%0A3%2F2%0A14%2F9%0A7%2F4%0A16%2F9%0A2%2F1&freq=440&midi=69&vert=5&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white%20white%20black%20white%20black&waveform=square&ampenv=organ Play JI diasem] - Sevish Scale Workshop
*[https://sevish.com/scaleworkshop/?name=JI%20Diasem&data=9%2F8%0A7%2F6%0A21%2F16%0A4%2F3%0A3%2F2%0A14%2F9%0A7%2F4%0A16%2F9%0A2%2F1&freq=440&midi=69&vert=5&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white%20white%20black%20white%20black&waveform=square&ampenv=organ Play JI diasem] - Sevish Scale Workshop
* [https://sevish.com/scaleworkshop/?name=Diasem%2026edo&data=46.15384615384615%0A92.3076923076923%0A138.46153846153845%0A184.6153846153846%0A230.76923076923077%0A276.9230769230769%0A323.0769230769231%0A369.2307692307692%0A415.38461538461536%0A461.53846153846155%0A507.6923076923077%0A553.8461538461538%0A600.%0A646.1538461538462%0A692.3076923076923%0A738.4615384615385%0A784.6153846153846%0A830.7692307692307%0A876.9230769230769%0A923.0769230769231%0A969.2307692307692%0A1015.3846153846154%0A1061.5384615384614%0A1107.6923076923076%0A1153.8461538461538%0A1200.&freq=440&midi=69&vert=9&horiz=1&colors=white%20black%20grey%20black%20white%20black%20white%20black%20grey%20black%20white%20white%20black%20grey%20black%20white%20black%20white%20black%20grey%20black%20white%20white%20black%20grey%20black&waveform=square&ampenv=organ Play 26edo diasem] - Sevish Scale Workshop
*[https://sevish.com/scaleworkshop/?name=Diasem%2026edo&data=46.15384615384615%0A92.3076923076923%0A138.46153846153845%0A184.6153846153846%0A230.76923076923077%0A276.9230769230769%0A323.0769230769231%0A369.2307692307692%0A415.38461538461536%0A461.53846153846155%0A507.6923076923077%0A553.8461538461538%0A600.%0A646.1538461538462%0A692.3076923076923%0A738.4615384615385%0A784.6153846153846%0A830.7692307692307%0A876.9230769230769%0A923.0769230769231%0A969.2307692307692%0A1015.3846153846154%0A1061.5384615384614%0A1107.6923076923076%0A1153.8461538461538%0A1200.&freq=440&midi=69&vert=9&horiz=1&colors=white%20black%20grey%20black%20white%20black%20white%20black%20grey%20black%20white%20white%20black%20grey%20black%20white%20black%20white%20black%20grey%20black%20white%20white%20black%20grey%20black&waveform=square&ampenv=organ Play 26edo diasem] - Sevish Scale Workshop


[[Category:Scale]]
[[Category:Scale]]
Retrieved from "https://en.xen.wiki/w/Diasem"