Jinn: Difference between revisions

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The ''jinn'' is a unit of interval size which is defined as 1/16808 of an [[Octave|octave]], the step size of [[16808edo|16808edo]]. 16808edo is consistent and distinct though the 35 limit, and is a very strong system for intervals less than the 37 prime limit, which includes most of what people find of interest.
The '''jinn''' is a [[interval size unit|unit of interval size]] which is defined as 1/16808 of an [[octave]], the step size of [[16808edo]]. 16808edo is consistent and distinct though the 35 limit, and is a very strong system for intervals less than the 37 prime limit, which includes most of what people find of interest.


Below the intervals of the [[35-limit|35-limit]] [[Tonality_diamond|tonality diamond]] are tabulated, with the sizes listed in both [[cent|cent]]s and jinns. The worst error occurs for 33/25 and 50/33, which is less than 1/4 of a jinn off.
Below the intervals of the [[35-limit]] [[tonality diamond]] are tabulated, with the sizes listed in both [[cent]]s and jinns. The worst error occurs for 33/25 and 50/33, which is less than 1/4 of a jinn off.


{| class="wikitable"
{| class="wikitable"
! interval
! size in cents
! size in jinns
|-
|-
! | interval
| 36/35
! | size in cents
| 48.7700
! | size in jinns
| 683.110
|-
|-
| | 36/35
| 35/34
| | 48.7700
| 50.1840
| | 683.110
| 702.914
|-
|-
| | 35/34
| 34/33
| | 50.1840
| 51.6820
| | 702.914
| 723.899
|-
|-
| | 34/33
| 33/32
| | 51.6820
| 53.273
| | 723.899
| 746.176
|-
|-
| | 33/32
| 32/31
| | 53.273
| 54.964
| | 746.176
| 769.868
|-
|-
| | 32/31
| 31/30
| | 54.964
| 56.767
| | 769.868
| 795.114
|-
|-
| | 31/30
| 30/29
| | 56.767
| 58.692
| | 795.114
| 822.073
|-
|-
| | 30/29
| 29/28
| | 58.692
| 60.751
| | 822.073
| 850.923
|-
|-
| | 29/28
| 28/27
| | 60.751
| 62.961
| | 850.923
| 881.872
|-
|-
| | 28/27
| 27/26
| | 62.961
| 65.337
| | 881.872
| 915.158
|-
|-
| | 27/26
| 26/25
| | 65.337
| 67.900
| | 915.158
| 951.056
|-
|-
| | 26/25
| 25/24
| | 67.900
| 70.672
| | 951.056
| 989.885
|-
|-
| | 25/24
| 24/23
| | 70.672
| 73.681
| | 989.885
| 1032.020
|-
|-
| | 24/23
| 23/22
| | 73.681
| 76.956
| | 1032.020
| 1077.903
|-
|-
| | 23/22
| 22/21
| | 76.956
| 80.537
| | 1077.903
| 1128.055
|-
|-
| | 22/21
| 21/20
| | 80.537
| 84.467
| | 1128.055
| 1183.104
|-
|-
| | 21/20
| 20/19
| | 84.467
| 88.801
| | 1183.104
| 1243.802
|-
|-
| | 20/19
| 19/18
| | 88.801
| 93.603
| | 1243.802
| 1311.066
|-
|-
| | 19/18
| 18/17
| | 93.603
| 98.955
| | 1311.066
| 1386.024
|-
|-
| | 18/17
| 35/33
| | 98.955
| 101.867
| | 1386.024
| 1426.813
|-
|-
| | 35/33
| 17/16
| | 101.867
| 104.955
| | 1426.813
| 1470.075
|-
|-
| | 17/16
| 33/31
| | 104.955
| 108.237
| | 1470.075
| 1516.045
|-
|-
| | 33/31
| 16/15
| | 108.237
| 111.731
| | 1516.045
| 1564.983
|-
|-
| | 16/15
| 31/29
| | 111.731
| 115.458
| | 1564.983
| 1617.187
|-
|-
| | 31/29
| 15/14
| | 115.458
| 119.443
| | 1617.187
| 1672.996
|-
|-
| | 15/14
| 29/27
| | 119.443
| 123.712
| | 1672.996
| 1732.795
|-
|-
| | 29/27
| 14/13
| | 123.712
| 128.298
| | 1732.795
| 1797.031
|-
|-
| | 14/13
| 27/25
| | 128.298
| 133.238
| | 1797.031
| 1866.214
|-
|-
| | 27/25
| 13/12
| | 133.238
| 138.573
| | 1866.214
| 1940.941
|-
|-
| | 13/12
| 38/35
| | 138.573
| 142.373
| | 1940.941
| 1994.177
|-
|-
| | 38/35
| 25/23
| | 142.373
| 144.353
| | 1994.177
| 2021.905
|-
|-
| | 25/23
| 12/11
| | 144.353
| 150.637
| | 2021.905
| 2109.923
|-
|-
| | 12/11
| 35/32
| | 150.637
| 155.140
| | 2109.923
| 2172.989
|-
|-
| | 35/32
| 23/21
| | 155.140
| 157.493
| | 2172.989
| 2205.958
|-
|-
| | 23/21
| 34/31
| | 157.493
| 159.920
| | 2205.958
| 2239.944
|-
|-
| | 34/31
| 11/10
| | 159.920
| 165.004
| | 2239.944
| 2311.159
|-
|-
| | 11/10
| 32/29
| | 165.004
| 170.423
| | 2311.159
| 2387.055
|-
|-
| | 32/29
| 21/19
| | 170.423
| 173.268
| | 2387.055
| 2426.906
|-
|-
| | 21/19
| 31/28
| | 173.268
| 176.210
| | 2426.906
| 2468.110
|-
|-
| | 31/28
| 10/9
| | 176.210
| 182.404
| | 2468.110
| 2554.868
|-
|-
| | 10/9
| 29/26
| | 182.404
| 189.050
| | 2554.868
| 2647.954
|-
|-
| | 29/26
| 19/17
| | 189.050
| 192.558
| | 2647.954
| 2697.090
|-
|-
| | 19/17
| 28/25
| | 192.558
| 196.198
| | 2697.090
| 2748.087
|-
|-
| | 28/25
| 9/8
| | 196.198
| 203.910
| | 2748.087
| 2856.099
|-
|-
| | 9/8
| 35/31
| | 203.910
| 210.104
| | 2856.099
| 2942.857
|-
|-
| | 35/31
| 26/23
| | 210.104
| 212.253
| | 2942.857
| 2972.961
|-
|-
| | 26/23
| 17/15
| | 212.253
| 216.687
| | 2972.961
| 3035.058
|-
|-
| | 17/15
| 25/22
| | 216.687
| 221.309
| | 3035.058
| 3099.808
|-
|-
| | 25/22
| 33/29
| | 221.309
| 223.696
| | 3099.808
| 3133.232
|-
|-
| | 33/29
| 8/7
| | 223.696
| 231.174
| | 3133.232
| 3237.978
|-
|-
| | 8/7
| 31/27
| | 231.174
| 239.171
| | 3237.978
| 3349.982
|-
|-
| | 31/27
| 23/20
| | 239.171
| 241.961
| | 3349.982
| 3389.062
|-
|-
| | 23/20
| 38/33
| | 241.961
| 244.240
| | 3389.062
| 3420.989
|-
|-
| | 38/33
| 15/13
| | 244.240
| 247.741
| | 3420.989
| 3470.026
|-
|-
| | 15/13
| 22/19
| | 247.741
| 253.805
| | 3470.026
| 3554.961
|-
|-
| | 22/19
| 29/25
| | 253.805
| 256.950
| | 3554.961
| 3599.010
|-
|-
| | 29/25
| 36/31
| | 256.950
| 258.874
| | 3599.010
| 3625.968
|-
|-
| | 36/31
| 7/6
| | 258.874
| 266.871
| | 3625.968
| 3737.972
|-
|-
| | 7/6
| 34/29
| | 266.871
| 275.378
| | 3737.972
| 3857.131
|-
|-
| | 34/29
| 27/23
| | 275.378
| 277.591
| | 3857.131
| 3888.120
|-
|-
| | 27/23
| 20/17
| | 277.591
| 281.358
| | 3888.120
| 3940.892
|-
|-
| | 20/17
| 33/28
| | 281.358
| 284.447
| | 3940.892
| 3984.155
|-
|-
| | 33/28
| 13/11
| | 284.447
| 289.210
| | 3984.155
| 4050.864
|-
|-
| | 13/11
| 32/27
| | 289.210
| 294.135
| | 4050.864
| 4119.851
|-
|-
| | 32/27
| 19/16
| | 294.135
| 297.513
| | 4119.851
| 4167.166
|-
|-
| | 19/16
| 25/21
| | 297.513
| 301.847
| | 4167.166
| 4227.864
|-
|-
| | 25/21
| 31/26
| | 301.847
| 304.508
| | 4227.864
| 4265.141
|-
|-
| | 31/26
| 6/5
| | 304.508
| 315.641
| | 4265.141
| 4421.082
|-
|-
| | 6/5
| 35/29
| | 315.641
| 325.562
| | 4421.082
| 4560.044
|-
|-
| | 35/29
| 29/24
| | 325.562
| 327.622
| | 4560.044
| 4588.895
|-
|-
| | 29/24
| 23/19
| | 327.622
| 330.761
| | 4588.895
| 4632.864
|-
|-
| | 23/19
| 40/33
| | 330.761
| 333.041
| | 4632.864
| 4664.791
|-
|-
| | 40/33
| 17/14
| | 333.041
| 336.130
| | 4664.791
| 4708.054
|-
|-
| | 17/14
| 28/23
| | 336.130
| 340.552
| | 4708.054
| 4769.992
|-
|-
| | 28/23
| 11/9
| | 340.552
| 347.408
| | 4769.992
| 4866.027
|-
|-
| | 11/9
| 38/31
| | 347.408
| 352.477
| | 4866.027
| 4937.034
|-
|-
| | 38/31
| 27/22
| | 352.477
| 354.547
| | 4937.034
| 4966.022
|-
|-
| | 27/22
| 16/13
| | 354.547
| 359.472
| | 4966.022
| 5035.009
|-
|-
| | 16/13
| 21/17
| | 359.472
| 365.825
| | 5035.009
| 5123.996
|-
|-
| | 21/17
| 26/21
| | 365.825
| 369.747
| | 5123.996
| 5178.920
|-
|-
| | 26/21
| 31/25
| | 369.747
| 372.408
| | 5178.920
| 5216.197
|-
|-
| | 31/25
| 36/29
| | 372.408
| 374.333
| | 5216.197
| 5243.155
|-
|-
| | 36/29
| 5/4
| | 374.333
| 386.314
| | 5243.155
| 5410.967
|-
|-
| | 5/4
| 44/35
| | 386.314
| 396.178
| | 5410.967
| 5549.138
|-
|-
| | 44/35
| 34/27
| | 396.178
| 399.090
| | 5549.138
| 5589.926
|-
|-
| | 34/27
| 29/23
| | 399.090
| 401.303
| | 5589.926
| 5620.915
|-
|-
| | 29/23
| 24/19
| | 401.303
| 404.442
| | 5620.915
| 5664.884
|-
|-
| | 24/19
| 19/15
| | 404.442
| 409.244
| | 5664.884
| 5732.149
|-
|-
| | 19/15
| 33/26
| | 409.244
| 412.745
| | 5732.149
| 5781.186
|-
|-
| | 33/26
| 14/11
| | 412.745
| 417.508
| | 5781.186
| 5847.895
|-
|-
| | 14/11
| 23/18
| | 417.508
| 424.364
| | 5847.895
| 5943.930
|-
|-
| | 23/18
| 32/25
| | 424.364
| 427.373
| | 5943.930
| 5986.065
|-
|-
| | 32/25
| 9/7
| | 427.373
| 435.084
| | 5986.065
| 6094.078
|-
|-
| | 9/7
| 40/31
| | 435.084
| 441.278
| | 6094.078
| 6180.836
|-
|-
| | 40/31
| 31/24
| | 441.278
| 443.081
| | 6180.836
| 6206.082
|-
|-
| | 31/24
| 22/17
| | 443.081
| 446.363
| | 6206.082
| 6252.051
|-
|-
| | 22/17
| 35/27
| | 446.363
| 449.275
| | 6252.051
| 6292.840
|-
|-
| | 35/27
| 13/10
| | 449.275
| 454.214
| | 6292.840
| 6362.023
|-
|-
| | 13/10
| 30/23
| | 454.214
| 459.994
| | 6362.023
| 6442.988
|-
|-
| | 30/23
| 17/13
| | 459.994
| 464.428
| | 6442.988
| 6505.085
|-
|-
| | 17/13
| 38/29
| | 464.428
| 467.936
| | 6505.085
| 6554.221
|-
|-
| | 38/29
| 21/16
| | 467.936
| 470.781
| | 6554.221
| 6594.071
|-
|-
| | 21/16
| 46/35
| | 470.781
| 473.135
| | 6594.071
| 6627.040
|-
|-
| | 46/35
| 25/19
| | 473.135
| 475.114
| | 6627.040
| 6654.769
|-
|-
| | 25/19
| 29/22
| | 475.114
| 478.259
| | 6654.769
| 6698.818
|-
|-
| | 29/22
| 33/25
| | 478.259
| 480.646
| | 6698.818
| 6732.242
|-
|-
| | 33/25
| 4/3
| | 480.646
| 498.045
| | 6732.242
| 6975.950
|-
|-
| | 4/3
| 35/26
| | 498.045
| 514.612
| | 6975.950
| 7207.998
|-
|-
| | 35/26
| 31/23
| | 514.612
| 516.761
| | 7207.998
| 7238.102
|-
|-
| | 31/23
| 27/20
| | 516.761
| 519.551
| | 7238.102
| 7277.182
|-
|-
| | 27/20
| 23/17
| | 519.551
| 523.319
| | 7277.182
| 7329.954
|-
|-
| | 23/17
| 42/31
| | 523.319
| 525.745
| | 7329.954
| 7363.940
|-
|-
| | 42/31
| 19/14
| | 525.745
| 528.687
| | 7363.940
| 7405.144
|-
|-
| | 19/14
| 34/25
| | 528.687
| 532.328
| | 7405.144
| 7456.141
|-
|-
| | 34/25
| 15/11
| | 532.328
| 536.951
| | 7456.141
| 7520.890
|-
|-
| | 15/11
| 26/19
| | 536.951
| 543.015
| | 7520.890
| 7605.825
|-
|-
| | 26/19
| 48/35
| | 543.015
| 546.815
| | 7605.825
| 7659.061
|-
|-
| | 48/35
| 11/8
| | 546.815
| 551.318
| | 7659.061
| 7722.127
|-
|-
| | 11/8
| 40/29
| | 551.318
| 556.737
| | 7722.127
| 7798.023
|-
|-
| | 40/29
| 29/21
| | 556.737
| 558.796
| | 7798.023
| 7826.873
|-
|-
| | 29/21
| 18/13
| | 558.796
| 563.382
| | 7826.873
| 7891.109
|-
|-
| | 18/13
| 25/18
| | 563.382
| 568.717
| | 7891.109
| 7965.835
|-
|-
| | 25/18
| 32/23
| | 568.717
| 571.726
| | 7965.835
| 8007.971
|-
|-
| | 32/23
| 46/33
| | 571.726
| 575.001
| | 8007.971
| 8053.853
|-
|-
| | 46/33
| 7/5
| | 575.001
| 582.512
| | 8053.853
| 8159.054
|-
|-
| | 7/5
| 38/27
| | 582.512
| 591.648
| | 8159.054
| 8287.017
|-
|-
| | 38/27
| 31/22
| | 591.648
| 593.718
| | 8287.017
| 8316.005
|-
|-
| | 31/22
| 24/17
| | 593.718
| 597.000
| | 8316.005
| 8361.974
|-
|-
| | 24/17
| 17/12
| | 597.000
| 603.000
| | 8361.974
| 8446.026
|-
|-
| | 17/12
| 44/31
| | 603.000
| 606.282
| | 8446.026
| 8491.995
|-
|-
| | 44/31
| 27/19
| | 606.282
| 608.352
| | 8491.995
| 8520.983
|-
|-
| | 27/19
| 10/7
| | 608.352
| 617.488
| | 8520.983
| 8648.946
|-
|-
| | 10/7
| 33/23
| | 617.488
| 624.999
| | 8648.946
| 8754.147
|-
|-
| | 33/23
| 23/16
| | 624.999
| 628.274
| | 8754.147
| 8800.029
|-
|-
| | 23/16
| 36/25
| | 628.274
| 631.283
| | 8800.029
| 8842.165
|-
|-
| | 36/25
| 13/9
| | 631.283
| 636.618
| | 8842.165
| 8916.891
|-
|-
| | 13/9
| 42/29
| | 636.618
| 641.204
| | 8916.891
| 8981.127
|-
|-
| | 42/29
| 29/20
| | 641.204
| 643.263
| | 8981.127
| 9009.977
|-
|-
| | 29/20
| 16/11
| | 643.263
| 648.682
| | 9009.977
| 9085.873
|-
|-
| | 16/11
| 35/24
| | 648.682
| 653.185
| | 9085.873
| 9148.939
|-
|-
| | 35/24
| 19/13
| | 653.185
| 656.985
| | 9148.939
| 9202.175
|-
|-
| | 19/13
| 22/15
| | 656.985
| 663.049
| | 9202.175
| 9287.110
|-
|-
| | 22/15
| 25/17
| | 663.049
| 667.672
| | 9287.110
| 9351.859
|-
|-
| | 25/17
| 28/19
| | 667.672
| 671.313
| | 9351.859
| 9402.856
|-
|-
| | 28/19
| 31/21
| | 671.313
| 674.255
| | 9402.856
| 9444.060
|-
|-
| | 31/21
| 34/23
| | 674.255
| 676.681
| | 9444.060
| 9478.046
|-
|-
| | 34/23
| 40/27
| | 676.681
| 680.449
| | 9478.046
| 9530.818
|-
|-
| | 40/27
| 46/31
| | 680.449
| 683.239
| | 9530.818
| 9569.898
|-
|-
| | 46/31
| 52/35
| | 683.239
| 685.388
| | 9569.898
| 9600.002
|-
|-
| | 52/35
| 3/2
| | 685.388
| 701.955
| | 9600.002
| 9832.050
|-
|-
| | 3/2
| 50/33
| | 701.955
| 719.354
| | 9832.050
| 10075.758
|-
|-
| | 50/33
| 44/29
| | 719.354
| 721.741
| | 10075.758
| 10109.182
|-
|-
| | 44/29
| 38/25
| | 721.741
| 724.886
| | 10109.182
| 10153.231
|-
|-
| | 38/25
| 35/23
| | 724.886
| 726.865
| | 10153.231
| 10180.96
|-
|-
| | 35/23
| 32/21
| | 726.865
| 729.219
| | 10180.96
| 10213.929
|-
|-
| | 32/21
| 29/19
| | 729.219
| 732.064
| | 10213.929
| 10253.779
|-
|-
| | 29/19
| 26/17
| | 732.064
| 735.572
| | 10253.779
| 10302.915
|-
|-
| | 26/17
| 23/15
| | 735.572
| 740.006
| | 10302.915
| 10365.012
|-
|-
| | 23/15
| 20/13
| | 740.006
| 745.786
| | 10365.012
| 10445.977
|-
|-
| | 20/13
| 54/35
| | 745.786
| 750.725
| | 10445.977
| 10515.160
|-
|-
| | 54/35
| 17/11
| | 750.725
| 753.637
| | 10515.160
| 10555.949
|-
|-
| | 17/11
| 48/31
| | 753.637
| 756.919
| | 10555.949
| 10601.918
|-
|-
| | 48/31
| 31/20
| | 756.919
| 758.722
| | 10601.918
| 10627.164
|-
|-
| | 31/20
| 14/9
| | 758.722
| 764.916
| | 10627.164
| 10713.922
|-
|-
| | 14/9
| 25/16
| | 764.916
| 772.627
| | 10713.922
| 10821.935
|-
|-
| | 25/16
| 36/23
| | 772.627
| 775.636
| | 10821.935
| 10864.070
|-
|-
| | 36/23
| 11/7
| | 775.636
| 782.492
| | 10864.070
| 10960.105
|-
|-
| | 11/7
| 52/33
| | 782.492
| 787.255
| | 10960.105
| 11026.814
|-
|-
| | 52/33
| 30/19
| | 787.255
| 790.756
| | 11026.814
| 11075.851
|-
|-
| | 30/19
| 19/12
| | 790.756
| 795.558
| | 11075.851
| 11143.116
|-
|-
| | 19/12
| 46/29
| | 795.558
| 798.697
| | 11143.116
| 11187.085
|-
|-
| | 46/29
| 27/17
| | 798.697
| 800.910
| | 11187.085
| 11218.074
|-
|-
| | 27/17
| 35/22
| | 800.910
| 803.822
| | 11218.074
| 11258.862
|-
|-
| | 35/22
| 8/5
| | 803.822
| 813.686
| | 11258.862
| 11397.033
|-
|-
| | 8/5
| 29/18
| | 813.686
| 825.667
| | 11397.033
| 11564.845
|-
|-
| | 29/18
| 50/31
| | 825.667
| 827.592
| | 11564.845
| 11591.803
|-
|-
| | 50/31
| 21/13
| | 827.592
| 830.253
| | 11591.803
| 11629.080
|-
|-
| | 21/13
| 34/21
| | 830.253
| 834.175
| | 11629.080
| 11684.004
|-
|-
| | 34/21
| 13/8
| | 834.175
| 840.528
| | 11684.004
| 11772.991
|-
|-
| | 13/8
| 44/27
| | 840.528
| 845.453
| | 11772.991
| 11841.978
|-
|-
| | 44/27
| 31/19
| | 845.453
| 847.523
| | 11841.978
| 11870.966
|-
|-
| | 31/19
| 18/11
| | 847.523
| 852.592
| | 11870.966
| 11941.973
|-
|-
| | 18/11
| 23/14
| | 852.592
| 859.448
| | 11941.973
| 12038.008
|-
|-
| | 23/14
| 28/17
| | 859.448
| 863.870
| | 12038.008
| 12099.946
|-
|-
| | 28/17
| 33/20
| | 863.870
| 866.959
| | 12099.946
| 12143.209
|-
|-
| | 33/20
| 38/23
| | 866.959
| 869.239
| | 12143.209
| 12175.136
|-
|-
| | 38/23
| 48/29
| | 869.239
| 872.378
| | 12175.136
| 12219.105
|-
|-
| | 48/29
| 58/35
| | 872.378
| 874.438
| | 12219.105
| 12247.956
|-
|-
| | 58/35
| 5/3
| | 874.438
| 884.359
| | 12247.956
| 12386.918
|-
|-
| | 5/3
| 52/31
| | 884.359
| 895.492
| | 12386.918
| 12542.859
|-
|-
| | 52/31
| 42/25
| | 895.492
| 898.153
| | 12542.859
| 12580.136
|-
|-
| | 42/25
| 32/19
| | 898.153
| 902.487
| | 12580.136
| 12640.834
|-
|-
| | 32/19
| 27/16
| | 902.487
| 905.865
| | 12640.834
| 12688.149
|-
|-
| | 27/16
| 22/13
| | 905.865
| 910.790
| | 12688.149
| 12757.136
|-
|-
| | 22/13
| 56/33
| | 910.790
| 915.553
| | 12757.136
| 12823.845
|-
|-
| | 56/33
| 17/10
| | 915.553
| 918.642
| | 12823.845
| 12867.108
|-
|-
| | 17/10
| 46/27
| | 918.642
| 922.409
| | 12867.108
| 12919.880
|-
|-
| | 46/27
| 29/17
| | 922.409
| 924.622
| | 12919.880
| 12950.869
|-
|-
| | 29/17
| 12/7
| | 924.622
| 933.129
| | 12950.869
| 13070.028
|-
|-
| | 12/7
| 31/18
| | 933.129
| 941.126
| | 13070.028
| 13182.032
|-
|-
| | 31/18
| 50/29
| | 941.126
| 943.050
| | 13182.032
| 13208.990
|-
|-
| | 50/29
| 19/11
| | 943.050
| 946.195
| | 13208.990
| 13253.039
|-
|-
| | 19/11
| 26/15
| | 946.195
| 952.259
| | 13253.039
| 13337.974
|-
|-
| | 26/15
| 33/19
| | 952.259
| 955.760
| | 13337.974
| 13387.011
|-
|-
| | 33/19
| 40/23
| | 955.760
| 958.039
| | 13387.011
| 13418.938
|-
|-
| | 40/23
| 54/31
| | 958.039
| 960.829
| | 13418.938
| 13458.018
|-
|-
| | 54/31
| 7/4
| | 960.829
| 968.826
| | 13458.018
| 13570.022
|-
|-
| | 7/4
| 58/33
| | 968.826
| 976.304
| | 13570.022
| 13674.768
|-
|-
| | 58/33
| 44/25
| | 976.304
| 978.691
| | 13674.768
| 13708.192
|-
|-
| | 44/25
| 30/17
| | 978.691
| 983.313
| | 13708.192
| 13772.942
|-
|-
| | 30/17
| 23/13
| | 983.313
| 987.747
| | 13772.942
| 13835.039
|-
|-
| | 23/13
| 62/35
| | 987.747
| 989.896
| | 13835.039
| 13865.143
|-
|-
| | 62/35
| 16/9
| | 989.896
| 996.090
| | 13865.143
| 13951.901
|-
|-
| | 16/9
| 25/14
| | 996.090
| 1003.802
| | 13951.901
| 14059.913
|-
|-
| | 25/14
| 34/19
| | 1003.802
| 1007.442
| | 14059.913
| 14110.910
|-
|-
| | 34/19
| 52/29
| | 1007.442
| 1010.950
| | 14110.910
| 14160.046
|-
|-
| | 52/29
| 9/5
| | 1010.950
| 1017.596
| | 14160.046
| 14253.132
|-
|-
| | 9/5
| 56/31
| | 1017.596
| 1023.790
| | 14253.132
| 14339.890
|-
|-
| | 56/31
| 38/21
| | 1023.790
| 1026.732
| | 14339.890
| 14381.094
|-
|-
| | 38/21
| 29/16
| | 1026.732
| 1029.577
| | 14381.094
| 14420.945
|-
|-
| | 29/16
| 20/11
| | 1029.577
| 1034.996
| | 14420.945
| 14496.841
|-
|-
| | 20/11
| 31/17
| | 1034.996
| 1040.080
| | 14496.841
| 14568.056
|-
|-
| | 31/17
| 42/23
| | 1040.080
| 1042.507
| | 14568.056
| 14602.042
|-
|-
| | 42/23
| 64/35
| | 1042.507
| 1044.860
| | 14602.042
| 14635.011
|-
|-
| | 64/35
| 11/6
| | 1044.860
| 1049.363
| | 14635.011
| 14698.077
|-
|-
| | 11/6
| 46/25
| | 1049.363
| 1055.647
| | 14698.077
| 14786.095
|-
|-
| | 46/25
| 35/19
| | 1055.647
| 1057.627
| | 14786.095
| 14813.823
|-
|-
| | 35/19
| 24/13
| | 1057.627
| 1061.427
| | 14813.823
| 14867.059
|-
|-
| | 24/13
| 50/27
| | 1061.427
| 1066.762
| | 14867.059
| 14941.786
|-
|-
| | 50/27
| 13/7
| | 1066.762
| 1071.702
| | 14941.786
| 15010.969
|-
|-
| | 13/7
| 54/29
| | 1071.702
| 1076.288
| | 15010.969
| 15075.205
|-
|-
| | 54/29
| 28/15
| | 1076.288
| 1080.557
| | 15075.205
| 15135.004
|-
|-
| | 28/15
| 58/31
| | 1080.557
| 1084.542
| | 15135.004
| 15190.813
|-
|-
| | 58/31
| 15/8
| | 1084.542
| 1088.269
| | 15190.813
| 15243.017
|-
|-
| | 15/8
| 62/33
| | 1088.269
| 1091.763
| | 15243.017
| 15291.955
|-
|-
| | 62/33
| 32/17
| | 1091.763
| 1095.045
| | 15291.955
| 15337.925
|-
|-
| | 32/17
| 66/35
| | 1095.045
| 1098.133
| | 15337.925
| 15381.187
|-
|-
| | 66/35
| 17/9
| | 1098.133
| 1101.045
| | 15381.187
| 15421.976
|-
|-
| | 17/9
| 36/19
| | 1101.045
| 1106.397
| | 15421.976
| 15496.934
|-
|-
| | 36/19
| 19/10
| | 1106.397
| 1111.199
| | 15496.934
| 15564.198
|-
|-
| | 19/10
| 40/21
| | 1111.199
| 1115.533
| | 15564.198
| 15624.896
|-
|-
| | 40/21
| 21/11
| | 1115.533
| 1119.463
| | 15624.896
| 15679.945
|-
|-
| | 21/11
| 44/23
| | 1119.463
| 1123.044
| | 15679.945
| 15730.097
|-
|-
| | 44/23
| 23/12
| | 1123.044
| 1126.319
| | 15730.097
| 15775.980
|-
|-
| | 23/12
| 48/25
| | 1126.319
| 1129.328
| | 15775.980
| 15818.115
|-
|-
| | 48/25
| 25/13
| | 1129.328
| 1132.100
| | 15818.115
| 15856.944
|-
|-
| | 25/13
| 52/27
| | 1132.100
| 1134.663
| | 15856.944
| 15892.842
|-
|-
| | 52/27
| 27/14
| | 1134.663
| 1137.039
| | 15892.842
| 15926.128
|-
|-
| | 27/14
| 56/29
| | 1137.039
| 1139.249
| | 15926.128
| 15957.077
|-
|-
| | 56/29
| 29/15
| | 1139.249
| 1141.308
| | 15957.077
| 15985.927
|-
|-
| | 29/15
| 60/31
| | 1141.308
| 1143.233
| | 15985.927
| 16012.886
|-
|-
| | 60/31
| 31/16
| | 1143.233
| 1145.036
| | 16012.886
| 16038.132
|-
|-
| | 31/16
| 64/33
| | 1145.036
| 1146.727
| | 16038.132
| 16061.824
|-
|-
| | 64/33
| 33/17
| | 1146.727
| 1148.318
| | 16061.824
| 16084.101
|-
|-
| | 33/17
| 68/35
| | 1148.318
| 1149.816
| | 16084.101
| 16105.086
|-
|-
| | 68/35
| 35/18
| | 1149.816
| 1151.230
| | 16105.086
| 16124.890
|-
|-
| | 35/18
| 2
| | 1151.230
| 1200.000
| | 16124.890
| 16808.000
|-
| | 2
| | 1200.000
| | 16808.000
|}
|}


[[Category:Interval size measure]]
[[Category:Interval size measure]]
[[Category:Unit]]
[[Category:Unit]]

Revision as of 14:19, 9 June 2020

The jinn is a unit of interval size which is defined as 1/16808 of an octave, the step size of 16808edo. 16808edo is consistent and distinct though the 35 limit, and is a very strong system for intervals less than the 37 prime limit, which includes most of what people find of interest.

Below the intervals of the 35-limit tonality diamond are tabulated, with the sizes listed in both cents and jinns. The worst error occurs for 33/25 and 50/33, which is less than 1/4 of a jinn off.

interval size in cents size in jinns
36/35 48.7700 683.110
35/34 50.1840 702.914
34/33 51.6820 723.899
33/32 53.273 746.176
32/31 54.964 769.868
31/30 56.767 795.114
30/29 58.692 822.073
29/28 60.751 850.923
28/27 62.961 881.872
27/26 65.337 915.158
26/25 67.900 951.056
25/24 70.672 989.885
24/23 73.681 1032.020
23/22 76.956 1077.903
22/21 80.537 1128.055
21/20 84.467 1183.104
20/19 88.801 1243.802
19/18 93.603 1311.066
18/17 98.955 1386.024
35/33 101.867 1426.813
17/16 104.955 1470.075
33/31 108.237 1516.045
16/15 111.731 1564.983
31/29 115.458 1617.187
15/14 119.443 1672.996
29/27 123.712 1732.795
14/13 128.298 1797.031
27/25 133.238 1866.214
13/12 138.573 1940.941
38/35 142.373 1994.177
25/23 144.353 2021.905
12/11 150.637 2109.923
35/32 155.140 2172.989
23/21 157.493 2205.958
34/31 159.920 2239.944
11/10 165.004 2311.159
32/29 170.423 2387.055
21/19 173.268 2426.906
31/28 176.210 2468.110
10/9 182.404 2554.868
29/26 189.050 2647.954
19/17 192.558 2697.090
28/25 196.198 2748.087
9/8 203.910 2856.099
35/31 210.104 2942.857
26/23 212.253 2972.961
17/15 216.687 3035.058
25/22 221.309 3099.808
33/29 223.696 3133.232
8/7 231.174 3237.978
31/27 239.171 3349.982
23/20 241.961 3389.062
38/33 244.240 3420.989
15/13 247.741 3470.026
22/19 253.805 3554.961
29/25 256.950 3599.010
36/31 258.874 3625.968
7/6 266.871 3737.972
34/29 275.378 3857.131
27/23 277.591 3888.120
20/17 281.358 3940.892
33/28 284.447 3984.155
13/11 289.210 4050.864
32/27 294.135 4119.851
19/16 297.513 4167.166
25/21 301.847 4227.864
31/26 304.508 4265.141
6/5 315.641 4421.082
35/29 325.562 4560.044
29/24 327.622 4588.895
23/19 330.761 4632.864
40/33 333.041 4664.791
17/14 336.130 4708.054
28/23 340.552 4769.992
11/9 347.408 4866.027
38/31 352.477 4937.034
27/22 354.547 4966.022
16/13 359.472 5035.009
21/17 365.825 5123.996
26/21 369.747 5178.920
31/25 372.408 5216.197
36/29 374.333 5243.155
5/4 386.314 5410.967
44/35 396.178 5549.138
34/27 399.090 5589.926
29/23 401.303 5620.915
24/19 404.442 5664.884
19/15 409.244 5732.149
33/26 412.745 5781.186
14/11 417.508 5847.895
23/18 424.364 5943.930
32/25 427.373 5986.065
9/7 435.084 6094.078
40/31 441.278 6180.836
31/24 443.081 6206.082
22/17 446.363 6252.051
35/27 449.275 6292.840
13/10 454.214 6362.023
30/23 459.994 6442.988
17/13 464.428 6505.085
38/29 467.936 6554.221
21/16 470.781 6594.071
46/35 473.135 6627.040
25/19 475.114 6654.769
29/22 478.259 6698.818
33/25 480.646 6732.242
4/3 498.045 6975.950
35/26 514.612 7207.998
31/23 516.761 7238.102
27/20 519.551 7277.182
23/17 523.319 7329.954
42/31 525.745 7363.940
19/14 528.687 7405.144
34/25 532.328 7456.141
15/11 536.951 7520.890
26/19 543.015 7605.825
48/35 546.815 7659.061
11/8 551.318 7722.127
40/29 556.737 7798.023
29/21 558.796 7826.873
18/13 563.382 7891.109
25/18 568.717 7965.835
32/23 571.726 8007.971
46/33 575.001 8053.853
7/5 582.512 8159.054
38/27 591.648 8287.017
31/22 593.718 8316.005
24/17 597.000 8361.974
17/12 603.000 8446.026
44/31 606.282 8491.995
27/19 608.352 8520.983
10/7 617.488 8648.946
33/23 624.999 8754.147
23/16 628.274 8800.029
36/25 631.283 8842.165
13/9 636.618 8916.891
42/29 641.204 8981.127
29/20 643.263 9009.977
16/11 648.682 9085.873
35/24 653.185 9148.939
19/13 656.985 9202.175
22/15 663.049 9287.110
25/17 667.672 9351.859
28/19 671.313 9402.856
31/21 674.255 9444.060
34/23 676.681 9478.046
40/27 680.449 9530.818
46/31 683.239 9569.898
52/35 685.388 9600.002
3/2 701.955 9832.050
50/33 719.354 10075.758
44/29 721.741 10109.182
38/25 724.886 10153.231
35/23 726.865 10180.96
32/21 729.219 10213.929
29/19 732.064 10253.779
26/17 735.572 10302.915
23/15 740.006 10365.012
20/13 745.786 10445.977
54/35 750.725 10515.160
17/11 753.637 10555.949
48/31 756.919 10601.918
31/20 758.722 10627.164
14/9 764.916 10713.922
25/16 772.627 10821.935
36/23 775.636 10864.070
11/7 782.492 10960.105
52/33 787.255 11026.814
30/19 790.756 11075.851
19/12 795.558 11143.116
46/29 798.697 11187.085
27/17 800.910 11218.074
35/22 803.822 11258.862
8/5 813.686 11397.033
29/18 825.667 11564.845
50/31 827.592 11591.803
21/13 830.253 11629.080
34/21 834.175 11684.004
13/8 840.528 11772.991
44/27 845.453 11841.978
31/19 847.523 11870.966
18/11 852.592 11941.973
23/14 859.448 12038.008
28/17 863.870 12099.946
33/20 866.959 12143.209
38/23 869.239 12175.136
48/29 872.378 12219.105
58/35 874.438 12247.956
5/3 884.359 12386.918
52/31 895.492 12542.859
42/25 898.153 12580.136
32/19 902.487 12640.834
27/16 905.865 12688.149
22/13 910.790 12757.136
56/33 915.553 12823.845
17/10 918.642 12867.108
46/27 922.409 12919.880
29/17 924.622 12950.869
12/7 933.129 13070.028
31/18 941.126 13182.032
50/29 943.050 13208.990
19/11 946.195 13253.039
26/15 952.259 13337.974
33/19 955.760 13387.011
40/23 958.039 13418.938
54/31 960.829 13458.018
7/4 968.826 13570.022
58/33 976.304 13674.768
44/25 978.691 13708.192
30/17 983.313 13772.942
23/13 987.747 13835.039
62/35 989.896 13865.143
16/9 996.090 13951.901
25/14 1003.802 14059.913
34/19 1007.442 14110.910
52/29 1010.950 14160.046
9/5 1017.596 14253.132
56/31 1023.790 14339.890
38/21 1026.732 14381.094
29/16 1029.577 14420.945
20/11 1034.996 14496.841
31/17 1040.080 14568.056
42/23 1042.507 14602.042
64/35 1044.860 14635.011
11/6 1049.363 14698.077
46/25 1055.647 14786.095
35/19 1057.627 14813.823
24/13 1061.427 14867.059
50/27 1066.762 14941.786
13/7 1071.702 15010.969
54/29 1076.288 15075.205
28/15 1080.557 15135.004
58/31 1084.542 15190.813
15/8 1088.269 15243.017
62/33 1091.763 15291.955
32/17 1095.045 15337.925
66/35 1098.133 15381.187
17/9 1101.045 15421.976
36/19 1106.397 15496.934
19/10 1111.199 15564.198
40/21 1115.533 15624.896
21/11 1119.463 15679.945
44/23 1123.044 15730.097
23/12 1126.319 15775.980
48/25 1129.328 15818.115
25/13 1132.100 15856.944
52/27 1134.663 15892.842
27/14 1137.039 15926.128
56/29 1139.249 15957.077
29/15 1141.308 15985.927
60/31 1143.233 16012.886
31/16 1145.036 16038.132
64/33 1146.727 16061.824
33/17 1148.318 16084.101
68/35 1149.816 16105.086
35/18 1151.230 16124.890
2 1200.000 16808.000
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