List of 47-odd-limit intervals: Difference between revisions

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Line 1: Line 1:
The 47-limit. Whoa.
The 47-odd-limit. Whoa.


Here is a list of the intervals within the octave belonging to the 47-[[Odd_limit|odd limit]] -- that is, intervals between 1/1 and 2/1 which contain no odd numbers greater than 47. It is organized by [[interval_category|interval category]] according to the Schulter System outlined in [http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum].
Here is a list of the intervals within the octave belonging to the 47-[[Odd_limit|odd limit]] -- that is, intervals between 1/1 and 2/1 which contain no odd numbers greater than 47. It is organized by [[interval_category|interval category]] according to the Schulter System outlined in [http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum].
Line 21: Line 21:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 48/47
| 48/47
| | 36.448
| 36.448
| | 47
| 47
|-
|-
| | 47/46
| 47/46
| | 37.232
| 37.232
| | 47
| 47
|-
|-
| | 46/45
| 46/45
| | 38.051
| 38.051
| | 23
| 23
|-
|-
| | 45/44
| [[45/44]]
| | 38.906
| 38.906
| | 11
| 11
|-
|-
| | 44/43
| 44/43
| | 39.800
| 39.800
| | 43
| 43
|-
|-
| | 43/42
| 43/42
| | 40.737
| 40.737
| | 43
| 43
|-
|-
| | 42/41
| 42/41
| | 41.719
| 41.719
| | 41
| 41
|-
|-
| | 41/40
| 41/40
| | 42.749
| 42.749
| | 41
| 41
|-
|-
| | 40/39
| [[40/39]]
| | 43.831
| 43.831
| | 13
| 13
|-
|-
| | 39/38
| 39/38
| | 44.970
| 44.970
| | 19
| 19
|-
|-
| | 38/37
| 38/37
| | 46/169
| 46/169
| | 37
| 37
|-
|-
| | 37/36
| 37/36
| | 47.434
| 47.434
| | 37
| 37
|-
|-
| | 36/35
| [[36/35]]
| | 48.770
| 48.770
| | 7
| 7
|-
|-
| | 35/34
| 35/34
| | 50.184
| 50.184
| | 17
| 17
|-
|-
| | 34/33
| 34/33
| | 51.682
| 51.682
| | 17
| 17
|-
|-
| | 33/32
| [[33/32]]
| | 53.273
| 53.273
| | 11
| 11
|-
|-
| | 32/31
| [[32/31]]
| | 54.964
| 54.964
| | 31
| 31
|-
|-
| | 31/30
| [[31/30]]
| | 56.767
| 56.767
| | 31
| 31
|-
|-
| | 30/29
| 30/29
| | 58.692
| 58.692
| | 29
| 29
|}
|}


Line 108: Line 108:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 29/28
| 29/28
| | 60.751
| 60.751
| | 29
| 29
|-
|-
| | 28/27
| [[28/27]]
| | 62.961
| 62.961
| | 7
| 7
|-
|-
| | 27/26
| [[27/26]]
| | 65.337
| 65.337
| | 13
| 13
|-
|-
| | 26/25
| [[26/25]]
| | 67.900
| 67.900
| | 13
| 13
|-
|-
| | 25/24
| [[25/24]]
| | 70.672
| 70.672
| | 5
| 5
|-
|-
| | 24/23
| [[24/23]]
| | 73.681
| 73.681
| | 23
| 23
|-
|-
| | 47/45
| 47/45
| | 75.283
| 75.283
| | 47
| 47
|-
|-
| | 23/22
| [[23/22]]
| | 76.956
| 76.956
| | 23
| 23
|-
|-
| | 45/43
| 45/43
| | 78.706
| 78.706
| | 43
| 43
|}
|}


Line 153: Line 153:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 22/21
| [[22/21]]
| | 80.537
| 80.537
| | 11
| 11
|-
|-
| | 43/41
| 43/41
| | 82.455
| 82.455
| | 43
| 43
|-
|-
| | 21/20
| [[21/20]]
| | 84.467
| 84.467
| | 7
| 7
|-
|-
| | 41/39
| 41/39
| | 86.580
| 86.580
| | 41
| 41
|-
|-
| | 20/19
| [[20/19]]
| | 88.801
| 88.801
| | 19
| 19
|-
|-
| | 39/37
| 39/37
| | 91.139
| 91.139
| | 37
| 37
|-
|-
| | 19/18
| [[19/18]]
| | 93.603
| 93.603
| | 19
| 19
|-
|-
| | 37/35
| 37/35
| | 96.204
| 96.204
| | 37
| 37
|-
|-
| | 18/17
| [[18/17]]
| | 98.955
| 98.955
| | 17
| 17
|}
|}


Line 198: Line 198:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 35/33
| 35/33
| | 101.867
| 101.867
| | 11
| 11
|-
|-
| | 17/16
| 17/16
| | 104.955
| 104.955
| | 17
| 17
|-
|-
| | 50/47
| 50/47
| | 107.121
| 107.121
| | 47
| 47
|-
|-
| | 33/31
| 33/31
| | 108.237
| 108.237
| | 31
| 31
|-
|-
| | 16/15 = 48/45
| 16/15 = 48/45
| | 111.731
| 111.731
| | 5
| 5
|-
|-
| | 47/44
| 47/44
| | 114.189
| 114.189
| | 47
| 47
|-
|-
| | 31/29
| 31/29
| | 115.458
| 115.458
| | 31
| 31
|-
|-
| | 46/43
| 46/43
| | 116.757
| 116.757
| | 43
| 43
|-
|-
| | 15/14 = 45/42
| 15/14 = 45/42
| | 119.443
| 119.443
| | 7
| 7
|-
|-
| | 44/41
| 44/41
| | 122.256
| 122.256
| | 41
| 41
|-
|-
| | 29/27
| 29/27
| | 123.712
| 123.712
| | 29
| 29
|}
|}


==Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)==
==Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)==


===Small Central Seconds (125-170 cents)===
===Small Central Seconds (125-135 cents)===


{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 43/40
| 43/40
| | 125.204
| 125.204
| | 43
| 43
|-
|-
| | 14/13 = 42/39
| 14/13 = 42/39
| | 128.298
| 128.298
| | 13
| 13
|-
|-
| | 41/38
| 41/38
| | 131.549
| 131.549
| | 41
| 41
|-
|-
| | 27/25
| 27/25
| | 133.238
| 133.238
| | 5
| 5
|-
|-
| | 40/37
| 40/37
| | 134.970
| 134.970
| | 37
| 37
|}
|}


Line 282: Line 282:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 13/12 = 39/36
| 13/12 = 39/36
| | 138.573
| 138.573
| | 13
| 13
|-
|-
| | 38/35
| 38/35
| | 142.373
| 142.373
| | 19
| 19
|-
|-
| | 25/23
| 25/23
| | 144.353
| 144.353
| | 23
| 23
|-
|-
| | 37/34
| 37/34
| | 146.389
| 146.389
| | 37
| 37
|-
|-
| | 12/11 = 36/33
| 12/11 = 36/33
| | 150.637
| 150.637
| | 11
| 11
|-
|-
| | 47/43
| 47/43
| | 153.989
| 153.989
| | 47
| 47
|-
|-
| | 35/32
| 35/32
| | 155.140
| 155.140
| | 7
| 7
|-
|-
| | 23/21
| 23/21
| | 157.493
| 157.493
| | 23
| 23
|-
|-
| | 34/31
| 34/31
| | 159.920
| 159.920
| | 31
| 31
|}
|}


Line 329: Line 329:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 45/41
| 45/41
| | 161.161
| 161.161
| | 41
| 41
|-
|-
| | 11/10 = 33/30
| 11/10 = 33/30
| | 165.004
| 165.004
| | 11
| 11
|-
|-
| | 43/39
| 43/39
| | 169.035
| 169.035
| | 43
| 43
|}
|}


Line 350: Line 350:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 32/29
| 32/29
| | 170.423
| 170.423
| | 29
| 29
|-
|-
| | 21/19
| 21/19
| | 173.268
| 173.268
| | 19
| 19
|-
|-
| | 52/47
| 52/47
| | 175.021
| 175.021
| | 47
| 47
|-
|-
| | 31/28
| 31/28
| | 176.210
| 176.210
| | 31
| 31
|-
|-
| | 41/37
| 41/37
| | 177.718
| 177.718
| | 41
| 41
|}
|}


Line 383: Line 383:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 10/9 = 30/27 = 50/45
| 10/9 = 30/27 = 50/45
| | 182.404
| 182.404
| | 5
| 5
|-
|-
| | 39/35
| 39/35
| | 187.343
| 187.343
| | 13
| 13
|-
|-
| | 29/26
| 29/26
| | 189.050
| 189.050
| | 29
| 29
|-
|-
| | 19/17
| 19/17
| | 192.558
| 192.558
| | 19
| 19
|-
|-
| | 47/42
| 47/42
| | 194.726
| 194.726
| | 47
| 47
|-
|-
| | 28/25
| 28/25
| | 196.198
| 196.198
| | 7
| 7
|-
|-
| | 37/33
| 37/33
| | 198.071
| 198.071
| | 37
| 37
|-
|-
| | 46/41
| 46/41
| | 199.212
| 199.212
| | 41
| 41
|}
|}


Line 424: Line 424:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 9/8 = 27/24 = 45/40
| 9/8 = 27/24 = 45/40
| | 203.910
| 203.910
| | 3
| 3
|-
|-
| | 44/39
| 44/39
| | 208.835
| 208.835
| | 13
| 13
|-
|-
| | 35/31
| 35/31
| | 210.104
| 210.104
| | 31
| 31
|-
|-
| | 26/23
| 26/23
| | 212.253
| 212.253
| | 23
| 23
|-
|-
| | 43/38
| 43/38
| | 214.005
| 214.005
| | 43
| 43
|-
|-
| | 17/15
| 17/15
| | 216.687
| 216.687
| | 17
| 17
|-
|-
| | 42/37
| 42/37
| | 219.437
| 219.437
| | 37
| 37
|}
|}


Line 461: Line 461:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 25/22
| 25/22
| | 221.309
| 221.309
| | 11
| 11
|-
|-
| | 33/29
| 33/29
| | 223.696
| 223.696
| | 29
| 29
|-
|-
| | 41/36
| 41/36
| | 225.152
| 225.152
| | 41
| 41
|-
|-
| | 8/7 = 24/21 = 40/35
| 8/7 = 24/21 = 40/35
| | 231.174
| 231.174
| | 7
| 7
|-
|-
| | 47/41
| 47/41
| | 236.444
| 236.444
| | 47
| 47
|-
|-
| | 39/34
| 39/34
| | 237.527
| 237.527
| | 17
| 17
|-
|-
| | 31/27
| 31/27
| | 239.171
| 239.171
| | 31
| 31
|}
|}


Line 498: Line 498:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 54/47
| 54/47
| | 240.358
| 240.358
| | 47
| 47
|-
|-
| | 23/20
| 23/20
| | 241.961
| 241.961
| | 23
| 23
|-
|-
| | 38/33
| 38/33
| | 244.240
| 244.240
| | 19
| 19
|-
|-
| | 15/13 = 45/39
| 15/13 = 45/39
| | 247.741
| 247.741
| | 13
| 13
|-
|-
| | 52/45
| 52/45
| | 250.304
| 250.304
| | 13
| 13
|-
|-
| | 37/32
| 37/32
| | 251.344
| 251.344
| | 37
| 37
|-
|-
| | 22/19
| 22/19
| | 253.805
| 253.805
| | 19
| 19
|-
|-
| | 29/25
| 29/25
| | 256.950
| 256.950
| | 29
| 29
|-
|-
| | 36/31
| 36/31
| | 258.874
| 258.874
| | 31
| 31
|}
|}
== ==


==Minor Thirds (260-330 cents)==
==Minor Thirds (260-330 cents)==
Line 547: Line 545:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 43/37
| 43/37
| | 260.174
| 260.174
| | 43
| 43
|-
|-
| | 50/43
| 50/43
| | 261.110
| 261.110
| | 43
| 43
|-
|-
| | 7/6 = 21/18 = 35/30
| 7/6 = 21/18 = 35/30
| | 266.871
| 266.871
| | 7
| 7
|-
|-
| | 48/41
| 48/41
| | 272.893
| 272.893
| | 41
| 41
|-
|-
| | 41/35
| 41/35
| | 273.923
| 273.923
| | 41
| 41
|-
|-
| | 34/29
| 34/29
| | 275.378
| 275.378
| | 29
| 29
|-
|-
| | 27/23
| 27/23
| | 277.591
| 277.591
| | 23
| 23
|-
|-
| | 47/40
| 47/40
| | 279.193
| 279.193
| | 47
| 47
|}
|}


Line 588: Line 586:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 20/17
| 20/17
| | 281.358
| 281.358
| | 17
| 17
|-
|-
| | 33/28
| 33/28
| | 284.447
| 284.447
| | 11
| 11
|-
|-
| | 46/39
| 46/39
| | 285.792
| 285.792
| | 23
| 23
|-
|-
| | 13/11 = 39/33
| 13/11 = 39/33
| | 289.210
| 289.210
| | 13
| 13
|-
|-
| | 45/38
| 45/38
| | 292.711
| 292.711
| | 19
| 19
|-
|-
| | 32/27
| 32/27
| | 294.135
| 294.135
| | 3
| 3
|-
|-
| | 19/16
| 19/16
| | 297.513
| 297.513
| | 19
| 19
|-
|-
| | 44/37
| 44/37
| | 299.974
| 299.974
| | 37
| 37
|}
|}


Line 629: Line 627:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 25/21
| 25/21
| | 301.847
| 301.847
| | 7
| 7
|-
|-
| | 56/47
| 56/47
| | 303.319
| 303.319
| | 47
| 47
|-
|-
| | 31/26
| 31/26
| | 304.508
| 304.508
| | 31
| 31
|-
|-
| | 37/31
| 37/31
| | 306.308
| 306.308
| | 37
| 37
|-
|-
| | 43/36
| 43/36
| | 307.608
| 307.608
| | 43
| 43
|-
|-
| | 6/5 = 18/15 = 30/25 = 42/35 = 54/45
| 6/5 = 18/15 = 30/25 = 42/35 = 54/45
| | 315.641
| 315.641
| | 5
| 5
|-
|-
| | 47/39
| 47/39
| | 323.024
| 323.024
| | 47
| 47
|-
|-
| | 41/34
| 41/34
| | 324.107
| 324.107
| | 41
| 41
|-
|-
| | 35/29
| 35/29
| | 325.562
| 325.562
| | 29
| 29
|-
|-
| | 29/24
| 29/24
| | 327.622
| 327.622
| | 29
| 29
|-
|-
| | 52/43
| 52/43
| | 329.010
| 329.010
| | 43
| 43
|}
|}
== ==


==Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)==
==Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)==
Line 686: Line 682:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 23/19
| 23/19
| | 330.761
| 330.761
| | 23
| 23
|-
|-
| | 40/33
| 40/33
| | 333.041
| 333.041
| | 11
| 11
|-
|-
| | 17/14
| 17/14
| | 336.130
| 336.130
| | 17
| 17
|-
|-
| | 45/37
| 45/37
| | 338.880
| 338.880
| | 37
| 37
|-
|-
| | 28/23
| 28/23
| | 340.552
| 340.552
| | 23
| 23
|}
|}


Line 715: Line 711:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 39/32
| 39/32
| | 342.483
| 342.483
| | 13
| 13
|-
|-
| | 50/41
| 50/41
| | 343.565
| 343.565
| | 41
| 41
|-
|-
| | 11/9 = 33/27
| 11/9 = 33/27
| | 347.408
| 347.408
| | 11
| 11
|-
|-
| | 38/31
| 38/31
| | 352.477
| 352.477
| | 31
| 31
|-
|-
| | 27/22
| 27/22
| | 354.547
| 354.547
| | 11
| 11
|-
|-
| | 43/35
| 43/35
| | 356.378
| 356.378
| | 43
| 43
|-
|-
| | 16/13 = 48/39
| 16/13 = 48/39
| | 359.472
| 359.472
| | 13
| 13
|}
|}


Line 752: Line 748:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 37/30
| 37/30
| | 363.075
| 363.075
| | 37
| 37
|-
|-
| | 58/47
| 58/47
| | 364.071
| 364.071
| | 47
| 47
|-
|-
| | 21/17
| 21/17
| | 365.825
| 365.825
| | 17
| 17
|-
|-
| | 47/38
| 47/38
| | 367.994
| 367.994
| | 47
| 47
|-
|-
| | 26/21
| 26/21
| | 369.747
| 369.747
| | 13
| 13
|}
|}


Line 783: Line 779:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 31/25
| 31/25
| | 372.408
| 372.408
| | 31
| 31
|-
|-
| | 36/29
| 36/29
| | 374.333
| 374.333
| | 29
| 29
|-
|-
| | 41/33
| 41/33
| | 375.789
| 375.789
| | 41
| 41
|-
|-
| | 46/37
| 46/37
| | 376.930
| 376.930
| | 37
| 37
|-
|-
| | 56/45
| 56/45
| | 378.602
| 378.602
| | 7
| 7
|-
|-
| | 5/4 = 15/12 = 25/20 = 35/28 = 45/36
| 5/4 = 15/12 = 25/20 = 35/28 = 45/36
| | 386.314
| 386.314
| | 5
| 5
|-
|-
| | 54/43
| 54/43
| | 394.347
| 394.347
| | 43
| 43
|-
|-
| | 44/35
| 44/35
| | 396.178
| 396.178
| | 11
| 11
|-
|-
| | 39/31
| 39/31
| | 397.447
| 397.447
| | 31
| 31
|-
|-
| | 34/27
| 34/27
| | 399.090
| 399.090
| | 17
| 17
|}
|}


Line 832: Line 828:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 29/23
| 29/23
| | 401.303
| 401.303
| | 29
| 29
|-
|-
| | 24/19
| [[24/19]]
| | 404.442
| 404.442
| | 19
| 19
|-
|-
| | 43/34
| 43/34
| | 406.562
| 406.562
| | 43
| 43
|-
|-
| | 19/15
| [[19/15]]
| | 409.244
| 409.244
| | 19
| 19
|-
|-
| | 52/41
| 52/41
| | 411.465
| 411.465
| | 41
| 41
|-
|-
| | 33/26
| [[33/26]]
| | 412.745
| 412.745
| | 13
| 13
|-
|-
| | 47/37
| [[47/37]]
| | 414.163
| 414.163
| | 47
| 47
|-
|-
| | 14/11 = 42/33
| [[14/11]] = 42/33
| | 417.508
| 417.508
| | 11
| 11
|-
|-
| | 37/29
| [[37/29]]
| | 421.767
| 421.767
| | 37
| 37
|-
|-
| | 60/47
| 60/47
| | 422.762
| 422.762
| | 47
| 47
|}
|}


Line 881: Line 877:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 23/18
| 23/18
| | 424.364
| 424.364
| | 23
| 23
|-
|-
| | 32/25
| 32/25
| | 427.373
| 427.373
| | 5
| 5
|-
|-
| | 41/32
| 41/32
| | 429.062
| 429.062
| | 41
| 41
|-
|-
| | 50/39
| 50/39
| | 430.145
| 430.145
| | 13
| 13
|-
|-
| | 9/7 = 27/21 = 45/35
| 9/7 = 27/21 = 45/35
| | 435.084
| 435.084
| | 7
| 7
|-
|-
| | 58/45
| 58/45
| | 439.353
| 439.353
| | 29
| 29
|}
|}


Line 914: Line 910:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 40/31
| 40/31
| | 441.278
| 441.278
| | 31
| 31
|-
|-
| | 31/24
| 31/24
| | 443.081
| 443.081
| | 31
| 31
|-
|-
| | 22/17
| 22/17
| | 446.363
| 446.363
| | 17
| 17
|-
|-
| | 35/27
| 35/27
| | 449.275
| 449.275
| | 7
| 7
|-
|-
| | 48/37
| 48/37
| | 450.611
| 450.611
| | 37
| 37
|-
|-
| | 13/10 = 39/30
| 13/10 = 39/30
| | 454.214
| 454.214
| | 13
| 13
|-
|-
| | 56/43
| 56/43
| | 457.308
| 457.308
| | 43
| 43
|-
|-
| | 43/33
| 43/33
| | 458.245
| 458.245
| | 43
| 43
|-
|-
| | 30/23
| 30/23
| | 459.994
| 459.994
| | 23
| 23
|-
|-
| | 47/36
| 47/36
| | 461.597
| 461.597
| | 47
| 47
|-
|-
| | 17/13
| 17/13
| | 464.428
| 464.428
| | 17
| 17
|-
|-
| | 38/29
| 38/29
| | 467.936
| 467.936
| | 29
| 29
|}
|}


Line 973: Line 969:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 21/16
| 21/16
| | 470.781
| 470.781
| | 7
| 7
|-
|-
| | 46/35
| 46/35
| | 473.135
| 473.135
| | 23
| 23
|-
|-
| | 25/19
| 25/19
| | 475.114
| 475.114
| | 19
| 19
|-
|-
| | 54/41
| 54/41
| | 476.803
| 476.803
| | 41
| 41
|-
|-
| | 29/22
| 29/22
| | 478.259
| 478.259
| | 29
| 29
|-
|-
| | 62/47
| 62/47
| | 479.529
| 479.529
| | 47
| 47
|-
|-
| | 33/25
| 33/25
| | 480.646
| 480.646
| | 11
| 11
|-
|-
| | 37/28
| 37/28
| | 482.518
| 482.518
| | 37
| 37
|-
|-
| | 41/31
| 41/31
| | 484.027
| 484.027
| | 41
| 41
|-
|-
| | 45/34
| 45/34
| | 485.268
| 485.268
| | 17
| 17
|}
|}


Line 1,022: Line 1,018:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 4/3 = 12/9 = 20/15 = 36/27 = 36/27 = 44/33 = 52/39 = 60/45
| 4/3 = 12/9 = 20/15 = 36/27 = 36/27 = 44/33 = 52/39 = 60/45
| | 498.045
| 498.045
| | 3
| 3
|}
|}


Line 1,035: Line 1,031:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 47/35
| 47/35
| | 510.367
| 510.367
| | 47
| 47
|-
|-
| | 43/32
| 43/32
| | 511.518
| 511.518
| | 43
| 43
|-
|-
| | 39/29
| 39/29
| | 512.905
| 512.905
| | 29
| 29
|-
|-
| | 35/26
| 35/26
| | 514.612
| 514.612
| | 13
| 13
|-
|-
| | 31/23
| 31/23
| | 516.761
| 516.761
| | 31
| 31
|-
|-
| | 58/43
| 58/43
| | 518.059
| 518.059
| | 43
| 43
|-
|-
| | 27/20
| 27/20
| | 519.551
| 519.551
| | 5
| 5
|-
|-
| | 50/37
| 50/37
| | 521.283
| 521.283
| | 37
| 37
|-
|-
| | 23/17
| 23/17
| | 523.319
| 523.319
| | 23
| 23
|-
|-
| | 42/31
| 42/31
| | 525.745
| 525.745
| | 31
| 31
|}
|}


Line 1,084: Line 1,080:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 19/14
| 19/14
| | 528.687
| 528.687
| | 19
| 19
|-
|-
| | 34/25
| 34/25
| | 532.328
| 532.328
| | 17
| 17
|-
|-
| | 64/47
| 64/47
| | 534.493
| 534.493
| | 47
| 47
|-
|-
| | 15/11 = 45/33
| 15/11 = 45/33
| | 536.951
| 536.951
| | 11
| 11
|-
|-
| | 56/41
| 56/41
| | 539.764
| 539.764
| | 41
| 41
|-
|-
| | 41/30
| 41/30
| | 540.794
| 540.794
| | 41
| 41
|-
|-
| | 26/19
| 26/19
| | 543.015
| 543.015
| | 19
| 19
|-
|-
| | 37/27
| 37/27
| | 545.479
| 545.479
| | 37
| 37
|-
|-
| | 48/35
| 48/35
| | 546.815
| 546.815
| | 7
| 7
|-
|-
| | 11/8 = 33/24
| 11/8 = 33/24
| | 551.318
| 551.318
| | 11
| 11
|-
|-
| | 62/45
| 62/45
| | 554.812
| 554.812
| | 31
| 31
|-
|-
| | 40/29
| 40/29
| | 556.737
| 556.737
| | 29
| 29
|-
|-
| | 29/21
| 29/21
| | 558.796
| 558.796
| | 29
| 29
|-
|-
| | 47/34
| 47/34
| | 560.551
| 560.551
| | 47
| 47
|}
|}


Line 1,151: Line 1,147:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 18/13 = 54/39
| 18/13 = 54/39
| | 563.382
| 563.382
| | 13
| 13
|-
|-
| | 43/31
| 43/31
| | 566.382
| 566.382
| | 43
| 43
|-
|-
| | 25/18
| 25/18
| | 568.717
| 568.717
| | 5
| 5
|-
|-
| | 32/23
| 32/23
| | 571.726
| 571.726
| | 23
| 23
|-
|-
| | 39/28
| 39/28
| | 573.657
| 573.657
| | 13
| 13
|-
|-
| | 46/33
| 46/33
| | 575.001
| 575.001
| | 23
| 23
|-
|-
| | 60/43
| 60/43
| | 576.751
| 576.751
| | 43
| 43
|}
|}


Line 1,188: Line 1,184:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 7/5 = 21/15 = 35/25
| 7/5 = 21/15 = 35/25
| | 582.512
| 582.512
| | 7
| 7
|-
|-
| | 66/47
| 66/47
| | 587.766
| 587.766
| | 47
| 47
|-
|-
| | 52/37
| 52/37
| | 589.184
| 589.184
| | 37
| 37
|-
|-
| | 45/32
| 45/32
| | 590.224
| 590.224
| | 5
| 5
|-
|-
| | 38/27
| 38/27
| | 591.648
| 591.648
| | 19
| 19
|-
|-
| | 31/22
| 31/22
| | 593.718
| 593.718
| | 31
| 31
|-
|-
| | 24/17
| 24/17
| | 597.000
| 597.000
| | 17
| 17
|-
|-
| | 41/29
| 41/29
| | 599.485
| 599.485
| | 41
| 41
|-
|-
| | 58/41
| 58/41
| | 600.515
| 600.515
| | 41
| 41
|-
|-
| | 17/12
| 17/12
| | 603.000
| 603.000
| | 17
| 17
|-
|-
| | 44/31
| 44/31
| | 606.282
| 606.282
| | 31
| 31
|-
|-
| | 27/19
| 27/19
| | 608.352
| 608.352
| | 19
| 19
|-
|-
| | 64/45
| 64/45
| | 609.776
| 609.776
| | 5
| 5
|-
|-
| | 37/26
| 37/26
| | 610.816
| 610.816
| | 37
| 37
|-
|-
| | 47/33
| 47/33
| | 612.234
| 612.234
| | 47
| 47
|-
|-
| | 10/7 = 30/21 = 50/35
| 10/7 = 30/21 = 50/35
| | 617.488
| 617.488
| | 7
| 7
|}
|}


Line 1,261: Line 1,257:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | ratio
! ratio
! | cents value
! cents value
! | prime limit
! prime limit
|-
|-
| | 43/30
| 43/30
| | 623.249
| 623.249
| | 43
| 43
|-
|-
| | 33/23
| 33/23
| | 624.999
| 624.999
| | 23
| 23
|-
|-
| | 56/39
| 56/39
| | 626.343
| 626.343
| | 13
| 13
|-
|-
| | 23/16
| 23/16
| | 628.274
| 628.274
| | 23
| 23
|-
|-
| | 36/25
| 36/25
| | 631.283
| 631.283
| | 5
| 5
|-
|-
| | 62/43
| 62/43
| | 633.518
| 633.518
| | 43
| 43
|-
|-
| | 13/9 = 39/27
| 13/9 = 39/27
| | 636.618
| 636.618
| | 13
| 13
|-
|-
| | 68/47
| 68/47
| | 639.449
| 639.449
| | 47
| 47
|}
|}


...to be continued...
...to be continued...
[[Category:limit]]
 
[[Category:odd_limit]]
== See also ==
[[Category:todo:add_examples]]
 
* [[61-limit]]
 
[[Category:47-limit| ]] <!-- main article -->
[[Category:Odd limit]]
 
{{todo| add examples }}
[[Category:Lists of intervals]]

Latest revision as of 05:33, 15 April 2023

The 47-odd-limit. Whoa.

Here is a list of the intervals within the octave belonging to the 47-odd limit -- that is, intervals between 1/1 and 2/1 which contain no odd numbers greater than 47. It is organized by interval category according to the Schulter System outlined in Regions of the Interval Spectrum.

Pure Unison (0 cents)

ratio cents value
1/1 0

Commas (0-30 cents)

None within the 47-odd limit.

Dieses (30-60 cents)

ratio cents value prime limit
48/47 36.448 47
47/46 37.232 47
46/45 38.051 23
45/44 38.906 11
44/43 39.800 43
43/42 40.737 43
42/41 41.719 41
41/40 42.749 41
40/39 43.831 13
39/38 44.970 19
38/37 46/169 37
37/36 47.434 37
36/35 48.770 7
35/34 50.184 17
34/33 51.682 17
33/32 53.273 11
32/31 54.964 31
31/30 56.767 31
30/29 58.692 29

Minor Seconds (60-125 cents)

Small Minor Seconds (60-80 cents)

ratio cents value prime limit
29/28 60.751 29
28/27 62.961 7
27/26 65.337 13
26/25 67.900 13
25/24 70.672 5
24/23 73.681 23
47/45 75.283 47
23/22 76.956 23
45/43 78.706 43

Middle Minor Seconds (80-100 cents)

ratio cents value prime limit
22/21 80.537 11
43/41 82.455 43
21/20 84.467 7
41/39 86.580 41
20/19 88.801 19
39/37 91.139 37
19/18 93.603 19
37/35 96.204 37
18/17 98.955 17

Large Minor Seconds (100-125 cents)

ratio cents value prime limit
35/33 101.867 11
17/16 104.955 17
50/47 107.121 47
33/31 108.237 31
16/15 = 48/45 111.731 5
47/44 114.189 47
31/29 115.458 31
46/43 116.757 43
15/14 = 45/42 119.443 7
44/41 122.256 41
29/27 123.712 29

Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)

Small Central Seconds (125-135 cents)

ratio cents value prime limit
43/40 125.204 43
14/13 = 42/39 128.298 13
41/38 131.549 41
27/25 133.238 5
40/37 134.970 37

Middle Central Seconds (135-160 cents)

ratio cents value prime limit
13/12 = 39/36 138.573 13
38/35 142.373 19
25/23 144.353 23
37/34 146.389 37
12/11 = 36/33 150.637 11
47/43 153.989 47
35/32 155.140 7
23/21 157.493 23
34/31 159.920 31

Large Central Seconds (160-170 cents)

Beginning of Equable Heptatonic Region (160-182 cents)

ratio cents value prime limit
45/41 161.161 41
11/10 = 33/30 165.004 11
43/39 169.035 43

End of Large Central Seconds Region, continuation of Equable Heptatonic Region

ratio cents value prime limit
32/29 170.423 29
21/19 173.268 19
52/47 175.021 47
31/28 176.210 31
41/37 177.718 41

End of Equable Heptatonic Region.

Major Seconds (180-240 cents)

Small Major Seconds (180-200 cents)

ratio cents value prime limit
10/9 = 30/27 = 50/45 182.404 5
39/35 187.343 13
29/26 189.050 29
19/17 192.558 19
47/42 194.726 47
28/25 196.198 7
37/33 198.071 37
46/41 199.212 41

Middle Major Seconds (200-220 cents)

ratio cents value prime limit
9/8 = 27/24 = 45/40 203.910 3
44/39 208.835 13
35/31 210.104 31
26/23 212.253 23
43/38 214.005 43
17/15 216.687 17
42/37 219.437 37

Large Major Seconds (220-240 cents)

ratio cents value prime limit
25/22 221.309 11
33/29 223.696 29
41/36 225.152 41
8/7 = 24/21 = 40/35 231.174 7
47/41 236.444 47
39/34 237.527 17
31/27 239.171 31

Interseptimal Region (M2-m3) (240-260 cents)

ratio cents value prime limit
54/47 240.358 47
23/20 241.961 23
38/33 244.240 19
15/13 = 45/39 247.741 13
52/45 250.304 13
37/32 251.344 37
22/19 253.805 19
29/25 256.950 29
36/31 258.874 31

Minor Thirds (260-330 cents)

Small Minor Thirds (260-280 cents)

ratio cents value prime limit
43/37 260.174 43
50/43 261.110 43
7/6 = 21/18 = 35/30 266.871 7
48/41 272.893 41
41/35 273.923 41
34/29 275.378 29
27/23 277.591 23
47/40 279.193 47

Middle Minor Thirds (280-300 cents)

ratio cents value prime limit
20/17 281.358 17
33/28 284.447 11
46/39 285.792 23
13/11 = 39/33 289.210 13
45/38 292.711 19
32/27 294.135 3
19/16 297.513 19
44/37 299.974 37

Large Minor Thirds (300-330 cents)

ratio cents value prime limit
25/21 301.847 7
56/47 303.319 47
31/26 304.508 31
37/31 306.308 37
43/36 307.608 43
6/5 = 18/15 = 30/25 = 42/35 = 54/45 315.641 5
47/39 323.024 47
41/34 324.107 41
35/29 325.562 29
29/24 327.622 29
52/43 329.010 43

Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)

Small Central Thirds (330-342 cents)

ratio cents value prime limit
23/19 330.761 23
40/33 333.041 11
17/14 336.130 17
45/37 338.880 37
28/23 340.552 23

Middle Central Thirds (342-360 cents)

ratio cents value prime limit
39/32 342.483 13
50/41 343.565 41
11/9 = 33/27 347.408 11
38/31 352.477 31
27/22 354.547 11
43/35 356.378 43
16/13 = 48/39 359.472 13

Large Central Thirds (360-372 cents)

ratio cents value prime limit
37/30 363.075 37
58/47 364.071 47
21/17 365.825 17
47/38 367.994 47
26/21 369.747 13

Major Thirds (372-440 cents)

Small Major Thirds (372-400 cents)

ratio cents value prime limit
31/25 372.408 31
36/29 374.333 29
41/33 375.789 41
46/37 376.930 37
56/45 378.602 7
5/4 = 15/12 = 25/20 = 35/28 = 45/36 386.314 5
54/43 394.347 43
44/35 396.178 11
39/31 397.447 31
34/27 399.090 17

Middle Major Thirds (400-423 cents)

ratio cents value prime limit
29/23 401.303 29
24/19 404.442 19
43/34 406.562 43
19/15 409.244 19
52/41 411.465 41
33/26 412.745 13
47/37 414.163 47
14/11 = 42/33 417.508 11
37/29 421.767 37
60/47 422.762 47

Large Major Thirds (423-440 cents)

ratio cents value prime limit
23/18 424.364 23
32/25 427.373 5
41/32 429.062 41
50/39 430.145 13
9/7 = 27/21 = 45/35 435.084 7
58/45 439.353 29

Interseptimal Region (M3-4) (440-468 cents)

ratio cents value prime limit
40/31 441.278 31
31/24 443.081 31
22/17 446.363 17
35/27 449.275 7
48/37 450.611 37
13/10 = 39/30 454.214 13
56/43 457.308 43
43/33 458.245 43
30/23 459.994 23
47/36 461.597 47
17/13 464.428 17
38/29 467.936 29

Perfect Fourths (468-528 cents)

Small Perfect Fourths (468-491 cents)

ratio cents value prime limit
21/16 470.781 7
46/35 473.135 23
25/19 475.114 19
54/41 476.803 41
29/22 478.259 29
62/47 479.529 47
33/25 480.646 11
37/28 482.518 37
41/31 484.027 41
45/34 485.268 17

Middle Perfect Fourths (491-505 cents)

ratio cents value prime limit
4/3 = 12/9 = 20/15 = 36/27 = 36/27 = 44/33 = 52/39 = 60/45 498.045 3

Large Perfect Fourths (505-528 cents)

ratio cents value prime limit
47/35 510.367 47
43/32 511.518 43
39/29 512.905 29
35/26 514.612 13
31/23 516.761 31
58/43 518.059 43
27/20 519.551 5
50/37 521.283 37
23/17 523.319 23
42/31 525.745 31

Superfourths (528-560 cents)

ratio cents value prime limit
19/14 528.687 19
34/25 532.328 17
64/47 534.493 47
15/11 = 45/33 536.951 11
56/41 539.764 41
41/30 540.794 41
26/19 543.015 19
37/27 545.479 37
48/35 546.815 7
11/8 = 33/24 551.318 11
62/45 554.812 31
40/29 556.737 29
29/21 558.796 29
47/34 560.551 47

Tritonic Region (560-640 cents)

Small Tritones (560-577 cents)

ratio cents value prime limit
18/13 = 54/39 563.382 13
43/31 566.382 43
25/18 568.717 5
32/23 571.726 23
39/28 573.657 13
46/33 575.001 23
60/43 576.751 43

Middle Tritones (577-623 cents)

ratio cents value prime limit
7/5 = 21/15 = 35/25 582.512 7
66/47 587.766 47
52/37 589.184 37
45/32 590.224 5
38/27 591.648 19
31/22 593.718 31
24/17 597.000 17
41/29 599.485 41
58/41 600.515 41
17/12 603.000 17
44/31 606.282 31
27/19 608.352 19
64/45 609.776 5
37/26 610.816 37
47/33 612.234 47
10/7 = 30/21 = 50/35 617.488 7

Large Tritones (623-640 cents)

ratio cents value prime limit
43/30 623.249 43
33/23 624.999 23
56/39 626.343 13
23/16 628.274 23
36/25 631.283 5
62/43 633.518 43
13/9 = 39/27 636.618 13
68/47 639.449 47

...to be continued...

See also

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