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

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The 47-odd-limit. Whoa.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
 
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2013-10-22 21:15:16 UTC</tt>.<br>
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].
: The original revision id was <tt>462226426</tt>.<br>
 
: The revision comment was: <tt></tt><br>
==Pure Unison (0 cents)==
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 
<h4>Original Wikitext content:</h4>
{| class="wikitable"
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The 47-limit. Whoa.</pre></div>
|-
<h4>Original HTML content:</h4>
! | ratio
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;47-limit&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 47-limit. Whoa.&lt;/body&gt;&lt;/html&gt;</pre></div>
! | cents value
|-
| | 1/1
| | 0
|}
 
==Commas (0-30 cents)==
None within the 47-odd limit.
 
==Dieses (30-60 cents)==
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)====
 
{| class="wikitable"
|-
! 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====
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)==
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)==
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)==
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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)===
 
{| class="wikitable"
|-
! 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 ==
 
* [[61-limit]]
 
[[Category:47-limit| ]] <!-- main article -->
[[Category:Odd limit]]
 
{{todo| add examples }}
[[Category:Lists of intervals]]
Retrieved from "https://en.xen.wiki/w/List_of_47-odd-limit_intervals"