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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
''Fudging'', or virtual tempering, is the use of one [[Just_intonation|just intonation]] interval to approximate another. Below are listed fudging intervals ("fudgers") which are all ratios between two 15-limit [[Tonality_diamond|tonality diamond]] intervals (listed in the fifth column) which come within a comma of less than eight cents (listed in the fourth column) of a 15-limit tonality diamond interval (listed in the third column). If the comma is less than 1, the fudger is flat of the interval it approximates; if greater than 1, sharp of it.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-03 15:57:35 UTC</tt>.<br>
: The original revision id was <tt>598266736</tt>.<br>
: The revision comment was: <tt></tt><br>
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>
<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">//Fudging//, or virtual tempering, is the use of one [[just intonation]] interval to approximate another. Below are listed fudging intervals ("fudgers") which are all ratios between two 15-limit [[tonality diamond]] intervals (listed in the fifth column) which come within a comma of less than eight cents (listed in the fourth column) of a 15-limit tonality diamond interval (listed in the third column). If the comma is less than 1, the fudger is flat of the interval it approximates; if greater than 1, sharp of it.


A limit-raising fudger is a p prime limit interval which approximates to a q prime limit consonance, with p&lt;q. An example is 100/77, which is 1001/1000 (1.7 cents) flat of [[13_10|13/10]], and which arises in 11-limit scales as the interval between 11/10 and 10/7, giving 13-limit harmony "for free", so to speak. A limit-lowering fudger is an interval such as the marvelous fourth, 75/56, which is 225/224 (7.7 cents) sharp of 4/3, and which arises very often in 7-limit JI scales as the interval between 16/15 and 10/7, 7/5 and 15/8, 8/5 and 15/7, and 28/15 and 5/2, giving a 3-limit interval approximated in the 7-limit.
A limit-raising fudger is a p prime limit interval which approximates to a q prime limit consonance, with p&lt;q. An example is 100/77, which is 1001/1000 (1.7 cents) flat of [[13/10|13/10]], and which arises in 11-limit scales as the interval between 11/10 and 10/7, giving 13-limit harmony "for free", so to speak. A limit-lowering fudger is an interval such as the marvelous fourth, 75/56, which is 225/224 (7.7 cents) sharp of 4/3, and which arises very often in 7-limit JI scales as the interval between 16/15 and 10/7, 7/5 and 15/8, 8/5 and 15/7, and 28/15 and 5/2, giving a 3-limit interval approximated in the 7-limit.


By tempering out the fudging commas, the error in the fudging may be distributed evenly. Since 225/224, 385/384 and 540/539 occur so commonly as fudging commas, marvel tempering in particular is often an excellent means to introduce smooth 7- and 11-limit harmonies into 5- or 7- limit scales. Adding 441/440 to that list results in miracle tempering, another excellent smoothing option. However, indiscriminate tempering can lead to problems. For example, 112/75, 121/81, 338/225, 182/121 and 176/117 are all fudged fifths, with commas 676/675, 364/363, 352/351, 243/242 and 225/224. Tempering them all out leads to 34d tempering, a rather crude system by comparison.
By tempering out the fudging commas, the error in the fudging may be distributed evenly. Since 225/224, 385/384 and 540/539 occur so commonly as fudging commas, marvel tempering in particular is often an excellent means to introduce smooth 7- and 11-limit harmonies into 5- or 7- limit scales. Adding 441/440 to that list results in miracle tempering, another excellent smoothing option. However, indiscriminate tempering can lead to problems. For example, 112/75, 121/81, 338/225, 182/121 and 176/117 are all fudged fifths, with commas 676/675, 364/363, 352/351, 243/242 and 225/224. Tempering them all out leads to 34d tempering, a rather crude system by comparison.


==Fudging Intervals==  
==Fudging Intervals==
===Up-fudge===
|| fudger || cents || approximately || comma(s) || (example) intervals || name ||
|| 242/225 || 126.098 || 15/14, 14/13 || 3388/3375, 1573/1575 || [15/11 22/15] ||  ||
|| [[xenharmonic/27_25|27/25]] || 133.238 || 14/13, 13/12 || 351/350, 324/325 || [10/9 6/5] || large limma ||
|| 121/112 || 133.810 || 14/13, 13/12 || 1573/1568, 363/364 || [14/11 11/8] ||  ||
|| 225/208 || 136.010 || 14/13, 13/12 || 225/224, 675/676 || [16/15 15/13] ||  ||
|| [[xenharmonic/49_45|49/45]] || 147.428 || 12/11 || 539/540 || [15/14 7/6] || swetismic neutral second ||
|| [[xenharmonic/35_32|35/32]] || 155.140 || 12/11 || 385/384 || [16/15 7/6] || septimal neutral second ||
|| [[xenharmonic/54_49|54/49]] || 168.213 || 11/10 || 540/539 || [7/6 9/7] || Zalzal's mujannab ||
|| 121/105 || 245.541 || 15/13 || 1573/1575 || [14/11 22/15] ||  ||
|| 140/121 || 252.504 || 15/13 || 364/363 || [11/10 14/11] ||  ||
|| 81/70 || 252.680 || 15/13 || 351/350 || [10/9 9/7] ||  ||
|| 75/64 || 274.582 || 7/6 || 225/224 || [16/15 5/4] ||  ||
|| 33/28 || 284.447 || 13/11 || 363/364 || [12/11 9/7] ||  ||
|| 32/27 || 294.135 || 13/11 || 352/351 || [9/8 4/3] ||  ||
|| 128/105 || 342.905 || 11/9 || 384/385 || [7/4 32/15] ||  ||
|| 60/49 || 350.617 || 11/9 || 540/539 || [7/6 10/7] ||  ||
|| 49/40 || 351.338 || 11/9 || 441/440 || [8/7 7/5] ||  ||
|| 100/81 || 364.807 || 16/13 || 325/324 || [9/5 20/9] ||  ||
|| 121/98 || 364.984 || 16/13 || 1573/1568 || [14/11 11/7] ||  ||
|| 80/63 || 413.578 || 14/11 || 440/441 || [9/8 10/7] ||  ||
|| 32/25 || 427.373 || 9/7 || 224/225 || [5/4 8/5] ||  ||
|| 35/27 || 449.275 || 13/10 || 350/351 || [6/5 14/9] ||  ||
|| 100/77 || 452.484 || 13/10 || 1000/1001 || [11/10 10/7] ||  ||
|| 49/36 || 533.742 || 15/11 || 539/540 || [8/7 14/9] ||  ||
|| 308/225 || 543.606 || 15/11, 11/8 || 3388/3375, 224/225 || [15/14 22/15] ||  ||
|| 48/35 || 546.815 || 11/8 || 384/385 || [7/6 8/5] ||  ||
|| 112/81 || 561.006 || 18/13 || 728/729 || [9/8 14/9] ||  ||
|| 168/121 || 568.145 || 18/13 || 364/363 || [11/7 24/11] ||  ||
|| 25/18 || 568.717 || 18/13 || 325/324 || [6/5 5/3] ||  ||
|| 36/25 || 631.283 || 13/9 || 324/325 || [10/9 8/5] ||  ||
|| 121/84 || 631.855 || 13/9 || 363/364 || [12/11 11/7] ||  ||
|| 81/56 || 638.994 || 13/9 || 729/728 || [14/9 9/4] ||  ||
|| 35/24 || 653.185 || 16/11 || 385/384 || [16/15 14/9] ||  ||
|| 143/98 || 654.194 || 16/11 || 1573/1568 || [14/13 11/7] ||  ||
|| 225/154 || 656.394 || 16/11, 22/15 || 225/224, 3375/3388 || [22/15 15/7] ||  ||
|| 77/50 || 747.516 || 20/13 || 1001/1000 || [10/7 11/5] ||  ||
|| 54/35 || 750.725 || 20/13 || 351/350 || [10/9 12/7] ||  ||
|| 25/16 || 772.627 || 14/9 || 225/224 || [16/15 5/3] ||  ||
|| 63/40 || 786.422 || 11/7 || 441/440 || [10/9 7/4] ||  ||
|| 196/121 || 835.016 || 13/8 || 1568/1573 || [11/7 28/11] ||  ||
|| 81/50 || 835.193 || 13/8 || 324/325 || [10/9 9/5] ||  ||
|| 80/49 || 848.662 || 18/11 || 440/441 || [7/5 16/7] ||  ||
|| 49/30 || 849.383 || 18/11 || 539/540 || [15/14 7/4] ||  ||
|| 105/64 || 857.095 || 18/11 || 385/384 || [16/15 7/4] ] ||  ||
|| 27/16 || 905.865 || 22/13 || 351/352 || [16/15 9/5] ||  ||
|| 56/33 || 915.553 || 22/13 || 364/363 || [15/14 20/11] ||  ||
|| 128/75 || 925.418 || 12/7 || 224/225 || [5/4 32/15] ||  ||
|| 140/81 || 947.320 || 26/15 || 350/351 || [9/7 20/9] ||  ||
|| 121/70 || 947.496 || 26/15 || 363/364 || [14/11 11/5] ||  ||
|| 210/121 || 954.459 || 26/15 || 1575/1573 || [22/15 28/11] ||  ||
|| 49/27 || 1031.787 || 20/11 || 539/540 || [9/7 7/3] ||  ||
|| 64/35 || 1044.86 || 11/6 || 384/385 || [7/6 32/15] ||  ||
|| 90/49 || 1052.572 || 11/6 || 540/539 || [7/6 15/7] ||  ||
|| 416/225 || 1063.99 || 24/13, 13/7 || 676/675, 224/225 || [15/13 32/15] ||  ||
|| 224/121 || 1066.19 || 24/13, 13/7 || 364/363, 1568/1573 || [11/8 28/11] ||  ||
|| 50/27 || 1066.762 || 24/13, 13/7 || 325/324, 350/351 || [6/5 20/9] ||  ||
|| 117/110 || 106.806 || 16/15 || 351/352 || [10/9 13/11] ||  ||
|| 180/169 || 109.168 || 16/15 || 675/676 || [13/12 15/13] ||  ||
|| [[xenharmonic/77_72|77/72]] || 116.234 || 16/15, 15/14 || 385/384, 539/540 || [12/11 7/6] || undecimal secor ||
|| 28/25 || 196.198 || 9/8 || 224/225 || [15/14 6/5] ||  ||
|| 224/195 || 240.030 || 15/13 || 224/225 || [15/14 16/13] ||  ||
|| 52/45 || 250.304 || 15/13 || 676/675 || [9/8 13/10] ||  ||
|| 77/60 || 431.875 || 9/7 || 539/540 || [15/14 11/8] ||  ||
|| 110/81 || 529.812 || 15/11 || 242/243 || [18/11 20/9] ||  ||
|| 160/117 || 541.876 || 15/11 || 352/351 || [9/8 20/13] ||  ||
|| 117/80 || 658.124 || 22/15 || 351/352 || [10/9 13/8] ||  ||
|| 81/55 || 670.188 || 22/15 || 243/242 || [10/9 18/11] ||  ||
|| 120/77 || 768.125 || 14/9 || 540/539 || [11/10 12/7] ||  ||
|| 45/26 || 949.696 || 26/15 || 675/676 || [16/15 24/13] ||  ||
|| 195/112 || 959.970 || 26/15 || 225/224 || [16/15 13/7] ||  ||
|| 25/14 || 1003.802 || 16/9 || 225/224 || [6/5 15/7] ||  ||
|| 144/77 || 1083.766 || 28/15, 15/8 || 540/539, 384/385 || [7/6 24/11] ||  ||
|| 169/90 || 1090.832 || 15/8 || 676/675 || [15/13 13/6] ||  ||
|| 220/117 || 1093.194 || 15/8 || 352/351 || [13/11 20/9] ||  ||
===Neutral/ambiguous===
|| fudger || cents || approximately || comma(s) || (example) intervals || names ||
|| 130/121 || 124.205 || 15/14, 14/13 || 364/363, 845/847 || [11/10 13/11] ||  ||
|| [[xenharmonic/88_81|88/81]] || 143.498 || 13/12, 12/11 || 352/351, 242/243 || [9/8 11/9] || undecimal subtone ||
|| 99/91 || 145.874 || 13/12, 12/11 || 1188/1183, 363/364 || [13/11 9/7] ||  ||
|| 256/225 || 223.463 || 8/7 || 224/225 || [15/8 32/15] ||  ||
|| 225/196 || 238.886 || 8/7 || 225/224 || [28/15 15/7] ||  ||
|| 200/169 || 291.572 || 13/11 || 2200/2197 || [13/10 20/13] ||  ||
|| 77/65 || 293.302 || 13/11 || 847/845 || [13/11 7/5] ||  ||
|| 108/91 || 296.511 || 13/11 || 1188/1183 || [13/12 9/7] ||  ||
|| 27/22 || 354.547 || 11/9, 16/13 || 243/242, 351/352 || [10/9 15/11] ||  ||
|| 225/182 || 367.184 || 16/13 || 225/224 || [26/15 15/7] ||  ||
|| 286/225 || 415.308 || 14/11 || 1573/1575 || [15/13 22/15] ||  ||
|| 225/176 || 425.219 || 14/11 || 225/224 || [16/15 15/11] ||  ||
|| 135/104 || 451.651 || 13/10 || 675/676 || [16/15 18/13] ||  ||
|| 220/169 || 456.576 || 13/10 || 2200/2197 || [13/11 20/13] ||  ||
|| 176/135 || 459.139 || 13/10 || 352/351 || [9/8 22/15] ||  ||
|| 224/165 || 529.239 || 15/11 || 224/225 || [15/14 16/11] ||  ||
|| 143/105 || 534.751 || 15/11 || 1573/1575 || [14/13 22/15] ||  ||
|| 91/66 || 556.081 || 11/8, 18/13 || 364/363, 1183/1188 || [11/7 13/6] ||  ||
|| 135/98 || 554.527 || 11/8 || 540/539 || [14/9 15/7] ||  ||
|| 104/75 || 565.945 || 18/13 || 676/675 || [15/13 8/5] ||  ||
|| 45/32 || 590.224 || 7/5 || 225/224 || [16/15 3/2] ||  ||
|| 64/45 || 609.776 || 10/7 || 224/225 || [9/8 8/5] ||  ||
|| 75/52 || 634.055 || 675/676 || 13/9 || [16/15 20/13] ||  ||
|| 132/91 || 643.919 || 13/9, 16/11 || 1188/1183, 363/364 || [13/12 11/7] ||  ||
|| 196/135 || 645.473 || 16/11 || 539/540 || [15/14 14/9] ||  ||
|| 210/143 || 665.249 || 22/15 || 1575/1573 || [22/15 28/13] ||  ||
|| 165/112 || 670.761 || 22/15 || 225/224 || [16/15 11/7] ||  ||
|| 135/88 || 740.861 || 20/13 || 351/352 || [16/15 18/11] ||  ||
|| 169/110 || 743.424 || 20/13 || 2197/2200 || [20/13 26/11] ||  ||
|| 208/135 || 748.349 || 20/13 || 676/675 || [9/8 26/15] ||  ||
|| 352/225 || 774.781 || 11/7 || 224/225 || [15/11 32/15] ||  ||
|| 225/143 || 784.692 || 11/7 || 1575/1573 || [22/15 30/13] ||  ||
|| 364/225 || 832.816 || 13/8 || 224/225 || [15/14 26/15] ||  ||
|| 44/27 || 845.453 || 13/8, 18/11 || 352/351, 242/243 || [12/11 16/9] ||  ||
|| 91/54 || 903.489 || 22/13 || 1183/1188 || [9/7 13/6] ||  ||
|| 130/77 || 906.698 || 22/13 || 845/847 || [14/13 20/11] ||  ||
|| 169/100 || 908.428 || 22/13 || 2197/2200 || [20/13 13/5] ||  ||
|| 392/225 || 961.114 || 7/4 || 224/225 || [15/14 28/15] ||  ||
|| 225/128 || 976.537 || 7/4 || 225/224 || [16/15 15/8] ||  ||
|| 81/44 || 1056.502 || 11/6, 24/13 || 243/242, 351/352 || [11/9 9/4] ||  ||
|| 225/121 || 1073.902 || 13/7, 28/15 || 1575/1573, 3375/3388 || [22/15 30/11] ||  ||
|| 121/65 || 1075.795 || 13/7, 28/15 || 847/845, 363/364 || [13/11 11/5] ||  ||
===Down-fudge===
|| fudger || cents || approximately || commas || (example) intervals ||
|| 128/117 || 155.562 || 12/11 || 352/351 || [9/8 16/13] ||
|| 169/154 || 160.911 || 11/10 || 845/847 || [14/13 13/11] ||
|| 100/91 || 163.274 || 11/10 || 1000/1001 || [13/10 10/7] ||
|| 182/165 || 169.767 || 11/10 || 364/363 || [15/14 13/11] ||
|| 72/65 || 177.069 || 10/9 || 324/325 || [13/12 6/5] ||
|| 195/176 || 177.478 || 10/9 || 351/352 || [16/15 13/11] ||
|| 49/44 || 186.334 || 10/9 || 441/440 || [8/7 14/11] ||
|| 39/35 || 187.343 || 10/9 || 351/350 || [14/13 6/5] ||
|| 135/121 || 189.543 || 10/9 || 243/242 || [11/9 15/11] ||
|| 121/108 || 196.771 || 9/8 || 242/243 || [12/11 11/9] ||
|| 55/49 || 199.980 || 9/8 || 440/441 || [14/11 10/7] ||
|| 91/81 || 201.534 || 9/8 || 728/729 || [9/7 13/9] ||
|| 169/150 || 206.473 || 9/8 || 676/675 || [15/13 13/10] ||
|| 44/39 || 208.835 || 9/8 || 352/351 || [13/12 11/9] ||
|| 154/135 || 227.965 || 8/7 || 539/540 || [15/14 11/9] ||
|| 63/55 || 235.104 || 8/7 || 441/440 || [10/9 14/11] ||
|| 55/48 || 235.677 || 8/7 || 385/384 || [16/15 11/9] ||
|| 121/104 || 262.108 || 7/6 || 363/364 || [13/11 11/8] ||
|| 64/55 || 262.368 || 7/6 || 384/385 || [5/4 16/11] ||
|| 90/77 || 270.080 || 7/6 || 540/539 || [11/10 9/7] ||
|| 117/100 || 271.810 || 7/6 || 351/350 || [10/9 13/10] ||
|| 198/169 || 274.173 || 7/6 || 1188/1183 || [13/11 18/13] ||
|| 140/117 || 310.702 || 6/5 || 350/351 || [9/7 20/13] ||
|| 77/64 || 320.144 || 6/5 || 385/384 || [8/7 11/8] ||
|| 65/54 || 320.976 || 6/5 || 325/324 || [6/5 13/9] ||
|| 135/112 || 323.353 || 6/5 || 225/224 || [16/15 9/7] ||
|| 39/32 || 342.483 || 11/9 || 351/352 || [16/15 13/10] ||
|| 56/45 || 378.602 || 5/4 || 224/225 || [15/14 4/3] ||
|| 81/65 || 380.979 || 5/4 || 324/325 || [10/9 18/13] ||
|| 96/77 || 381.811 || 5/4 || 384/385 || [7/6 16/11] ||
|| 169/135 || 388.877 || 5/4 || 676/675 || [15/13 13/9] ||
|| 33/26 || 412.745 || 14/11 || 363/364 || [13/12 11/8] ||
|| 143/112 || 423.020 || 14/11 || 1573/1568 || [14/13 11/8] ||
|| 216/169 || 424.810 || 14/11 || 1188/1183 || [13/12 18/13] ||
|| 169/132 || 427.782 || 9/7 || 1183/1188 || [22/13 13/6] ||
|| 50/39 || 430.145 || 9/7 || 350/351 || [6/5 20/13] ||
|| 104/81 || 432.708 || 9/7 || 728/729 || [9/8 13/9] ||
|| 165/128 || 439.587 || 9/7 || 385/384 || [16/15 11/8] ||
|| 156/121 || 439.847 || 9/7 || 364/363 || [22/13 24/11] ||
|| 117/88 || 493.120 || 4/3 || 351/352 || [11/9 13/8] ||
|| 121/91 || 493.282 || 4/3 || 363/364 || [13/11 11/7] ||
|| 225/169 || 495.482 || 4/3 || 675/676 || [26/15 30/13] ||
|| 162/121 || 505.184 || 4/3 || 243/242 || [11/9 18/11] ||
|| 75/56 || 505.757 || 4/3 || 225/224 || [16/15 10/7] ||
|| 196/143 || 545.806 || 11/8 || 1568/1573 || [11/7 28/13] ||
|| 169/121 || 578.419 || 7/5 || 845/847 || [22/13 26/11] ||
|| 88/63 || 578.582 || 7/5 || 440/441 || [9/8 11/7] ||
|| 200/143 || 580.782 || 7/5 || 1000/1001 || [11/10 20/13] ||
|| 108/77 || 585.721 || 7/5 || 540/539 || [7/6 18/11] ||
|| 77/54 || 614.279 || 10/7 || 539/540 || [12/11 14/9] ||
|| 143/100 || 619.218 || 10/7 || 1001/1000 || [20/13 11/5] ||
|| 63/44 || 621.418 || 10/7 || 441/440 || [8/7 18/11] ||
|| 242/169 || 621.581 || 10/7 || 847/845 || [13/11 22/13] ||
|| 72/49 || 666.258 || 22/15 || 540/539 || [7/6 12/7] ||
|| 112/75 || 694.243 || 3/2 || 224/225 || [15/14 8/5] ||
|| 121/81 || 694.816 || 3/2 || 242/243 || [18/11 22/9] ||
|| 338/225 || 704.518 || 3/2 || 676/675 || [15/13 26/15] ||
|| 182/121 || 706.718 || 3/2 || 364/363 || [11/7 26/11] ||
|| 176/117 || 706.880 || 3/2 || 352/351 || [9/8 22/13] ||
|| 121/78 || 760.153 || 14/9 || 363/364 || [12/11 22/13] ||
|| 256/165 || 760.413 || 14/9 || 384/385 || [11/8 32/15] ||
|| 81/52 || 767.292 || 14/9 || 729/728 || [13/9 9/4] ||
|| 39/25 || 769.855 || 14/9 || 351/350 || [10/9 26/15] ||
|| 264/169 || 772.218 || 14/9 || 1188/1183 || [13/12 22/13] ||
|| 169/108 || 775.190 || 11/7 || 1183/1188 || [18/13 13/6] ||
|| 224/143 || 776.980 || 11/7 || 1568/1573 || [11/8 28/13] ||
|| 52/33 || 787.255 || 11/7 || 364/363 || [11/10 26/15] ||
|| 270/169 || 811.123 || 8/5 || 675/676 || [13/9 30/13] ||
|| 77/48 || 818.189 || 8/5 || 385/384 || [12/11 7/4] ||
|| 130/81 || 819.021 || 8/5 || 325/324 || [18/13 20/9] ||
|| 45/28 || 821.398 || 8/5 || 225/224 || [16/15 12/7] ||
|| 64/39 || 857.517 || 18/11 || 352/351 || [13/12 16/9] ||
|| 224/135 || 876.647 || 5/3 || 224/225 || [15/14 16/9] ||
|| 108/65 || 879.024 || 5/3 || 324/325 || [13/12 9/5] ||
|| 128/77 || 879.856 || 5/3 || 384/385 || [11/8 16/7] ||
|| 117/70 || 889.298 || 5/3 || 351/350 || [14/13 9/5] ||
|| 169/99 || 925.827 || 12/7 || 1183/1188 || [18/13 26/11] ||
|| 200/117 || 928.190 || 12/7 || 350/351 || [13/10 20/9] ||
|| 77/45 || 929.920 || 12/7 || 539/540 || [15/14 11/6] ||
|| 55/32 || 937.632 || 12/7 || 385/384 || [16/15 11/6] ||
|| 208/121 || 937.892 || 12/7 || 364/363 || [11/8 26/11] ||
|| 96/55 || 964.323 || 7/4 || 384/385 || [11/9 32/15] ||
|| 110/63 || 964.896 || 7/4 || 440/441 || [14/11 20/9] ||
|| 135/77 || 972.035 || 7/4 || 540/539 || [11/9 15/7] ||
|| 39/22 || 991.165 || 16/9 || 351/352 || [11/9 13/6] ||
|| 300/169 || 993.527 || 16/9 || 675/676 || [13/10 30/13] ||
|| 162/91 || 998.466 || 16/9 || 729/728 || [13/9 18/7] ||
|| 98/55 || 1000.02 || 16/9 || 441/440 || [10/7 28/11] ||
|| 216/121 || 1003.229 || 16/9 || 243/242 || [11/9 24/11] ||
|| 242/135 || 1010.457 || 9/5 || 242/243 || [15/11 22/9] ||
|| 70/39 || 1012.657 || 9/5 || 350/351 || [6/5 28/13] ||
|| 88/49 || 1013.666 || 9/5 || 440/441 || [14/11 16/7] ||
|| 352/195 || 1022.522 || 9/5 || 352/351 || [13/11 32/15] ||
|| 65/36 || 1022.931 || 9/5 || 325/324 || [6/5 13/6] ||
|| 165/91 || 1030.233 || 20/11 || 363/364 || [13/11 15/7] ||
|| 91/50 || 1036.726 || 20/11 || 1001/1000 || [10/7 13/5] ||
|| 308/169 || 1039.089 || 20/11 || 847/845 || [13/11 28/13] ||
|| 117/64 || 1044.438 || 11/6 || 351/352 || [16/13 9/4] ||
|| 182/99 || 1054.126 || 11/6, 24/13 || 364/363, 1183/1188 || [9/7 26/11] ||</pre></div>
<h4>Original HTML content:</h4>
<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;Fudging&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;Fudging&lt;/em&gt;, or virtual tempering, is the use of one &lt;a class="wiki_link" href="/just%20intonation"&gt;just intonation&lt;/a&gt; interval to approximate another. Below are listed fudging intervals (&amp;quot;fudgers&amp;quot;) which are all ratios between two 15-limit &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; intervals (listed in the fifth column) which come within a comma of less than eight cents (listed in the fourth column) of a 15-limit tonality diamond interval (listed in the third column). If the comma is less than 1, the fudger is flat of the interval it approximates; if greater than 1, sharp of it.&lt;br /&gt;
&lt;br /&gt;
A limit-raising fudger is a p prime limit interval which approximates to a q prime limit consonance, with p&amp;lt;q. An example is 100/77, which is 1001/1000 (1.7 cents) flat of &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt;, and which arises in 11-limit scales as the interval between 11/10 and 10/7, giving 13-limit harmony &amp;quot;for free&amp;quot;, so to speak. A limit-lowering fudger is an interval such as the marvelous fourth, 75/56, which is 225/224 (7.7 cents) sharp of 4/3, and which arises very often in 7-limit JI scales as the interval between 16/15 and 10/7, 7/5 and 15/8, 8/5 and 15/7, and 28/15 and 5/2, giving a 3-limit interval approximated in the 7-limit.&lt;br /&gt;
&lt;br /&gt;
By tempering out the fudging commas, the error in the fudging may be distributed evenly. Since 225/224, 385/384 and 540/539 occur so commonly as fudging commas, marvel tempering in particular is often an excellent means to introduce smooth 7- and 11-limit harmonies into 5- or 7- limit scales. Adding 441/440 to that list results in miracle tempering, another excellent smoothing option. However, indiscriminate tempering can lead to problems. For example, 112/75, 121/81, 338/225, 182/121 and 176/117 are all fudged fifths, with commas 676/675, 364/363, 352/351, 243/242 and 225/224. Tempering them all out leads to 34d tempering, a rather crude system by comparison.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Fudging Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Fudging Intervals&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Fudging Intervals-Up-fudge"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Up-fudge&lt;/h3&gt;


&lt;table class="wiki_table"&gt;
===Up-fudge===
    &lt;tr&gt;
        &lt;td&gt;fudger&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;cents&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;approximately&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;comma(s)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(example) intervals&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;name&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;242/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;126.098&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/14, 14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3388/3375, 1573/1575&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/11 22/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/27_25"&gt;27/25&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;133.238&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/13, 13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/350, 324/325&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 6/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;large limma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121/112&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;133.810&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/13, 13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1573/1568, 363/364&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/11 11/8]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;225/208&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;136.010&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/13, 13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224, 675/676&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 15/13]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/49_45"&gt;49/45&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;147.428&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;539/540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 7/6]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic neutral second&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/35_32"&gt;35/32&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;155.140&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 7/6]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;septimal neutral second&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/54_49"&gt;54/49&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;168.213&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540/539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7/6 9/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Zalzal's mujannab&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121/105&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;245.541&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1573/1575&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/11 22/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;140/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;252.504&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364/363&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/10 14/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81/70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;252.680&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/350&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 9/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;75/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;274.582&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 5/4]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;284.447&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;363/364&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[12/11 9/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;294.135&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;352/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 4/3]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;128/105&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;342.905&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384/385&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7/4 32/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;60/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;350.617&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540/539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7/6 10/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49/40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351.338&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;441/440&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[8/7 7/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;100/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364.807&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;325/324&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/5 20/9]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121/98&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364.984&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1573/1568&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/11 11/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;80/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;413.578&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;440/441&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 10/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;427.373&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[5/4 8/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;449.275&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;350/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[6/5 14/9]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;100/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;452.484&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1000/1001&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/10 10/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49/36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;533.742&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;539/540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[8/7 14/9]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;308/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;543.606&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/11, 11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3388/3375, 224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 22/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;48/35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;546.815&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384/385&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7/6 8/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;112/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;561.006&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;728/729&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 14/9]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;168/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;568.145&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364/363&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/7 24/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25/18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;568.717&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;325/324&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[6/5 5/3]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;36/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;631.283&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;324/325&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 8/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121/84&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;631.855&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;363/364&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[12/11 11/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81/56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;638.994&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;729/728&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/9 9/4]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35/24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;653.185&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 14/9]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;143/98&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;654.194&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1573/1568&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/13 11/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;225/154&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;656.394&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/11, 22/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224, 3375/3388&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[22/15 15/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;77/50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;747.516&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1001/1000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/7 11/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;54/35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;750.725&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/350&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 12/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;772.627&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 5/3]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;63/40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;786.422&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;441/440&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 7/4]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;196/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;835.016&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1568/1573&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/7 28/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81/50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;835.193&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;324/325&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 9/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;80/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;848.662&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;440/441&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7/5 16/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49/30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;849.383&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;539/540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 7/4]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;105/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;857.095&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 7/4] ]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;905.865&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 9/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;56/33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;915.553&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364/363&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 20/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;128/75&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;925.418&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[5/4 32/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;140/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;947.320&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;350/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/7 20/9]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121/70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;947.496&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;363/364&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/11 11/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;210/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;954.459&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1575/1573&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[22/15 28/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1031.787&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;539/540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/7 7/3]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;64/35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1044.86&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384/385&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7/6 32/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;90/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1052.572&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540/539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7/6 15/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;416/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1063.99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;24/13, 13/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;676/675, 224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/13 32/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;224/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1066.19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;24/13, 13/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364/363, 1568/1573&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/8 28/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;50/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1066.762&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;24/13, 13/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;325/324, 350/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[6/5 20/9]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;117/110&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;106.806&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 13/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;180/169&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;109.168&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;675/676&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/12 15/13]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/77_72"&gt;77/72&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.234&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/15, 15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;385/384, 539/540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[12/11 7/6]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;undecimal secor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;196.198&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 6/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;224/195&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;240.030&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 16/13]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;52/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;250.304&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;676/675&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 13/10]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;77/60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;431.875&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;539/540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 11/8]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;110/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;529.812&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;242/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[18/11 20/9]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;160/117&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;541.876&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;352/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 20/13]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;117/80&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;658.124&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 13/8]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81/55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;670.188&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;243/242&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 18/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;120/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;768.125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540/539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/10 12/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;45/26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;949.696&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;675/676&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 24/13]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;195/112&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;959.970&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 13/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1003.802&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[6/5 15/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;144/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1083.766&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;28/15, 15/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540/539, 384/385&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7/6 24/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;169/90&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1090.832&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;676/675&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/13 13/6]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;220/117&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1093.194&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;352/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/11 20/9]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Fudging Intervals-Neutral/ambiguous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Neutral/ambiguous&lt;/h3&gt;
{| class="wikitable"
|-
| | fudger
| | cents
| | approximately
| | comma(s)
| | (example) intervals
| | name
|-
| | 242/225
| | 126.098
| | 15/14, 14/13
| | 3388/3375, 1573/1575
| | [15/11 22/15]
| |
|-
| | [[27/25|27/25]]
| | 133.238
| | 14/13, 13/12
| | 351/350, 324/325
| | [10/9 6/5]
| | large limma
|-
| | 121/112
| | 133.810
| | 14/13, 13/12
| | 1573/1568, 363/364
| | [14/11 11/8]
| |
|-
| | 225/208
| | 136.010
| | 14/13, 13/12
| | 225/224, 675/676
| | [16/15 15/13]
| |
|-
| | [[49/45|49/45]]
| | 147.428
| | 12/11
| | 539/540
| | [15/14 7/6]
| | swetismic neutral second
|-
| | [[35/32|35/32]]
| | 155.140
| | 12/11
| | 385/384
| | [16/15 7/6]
| | septimal neutral second
|-
| | [[54/49|54/49]]
| | 168.213
| | 11/10
| | 540/539
| | [7/6 9/7]
| | Zalzal's mujannab
|-
| | 121/105
| | 245.541
| | 15/13
| | 1573/1575
| | [14/11 22/15]
| |
|-
| | 140/121
| | 252.504
| | 15/13
| | 364/363
| | [11/10 14/11]
| |
|-
| | 81/70
| | 252.680
| | 15/13
| | 351/350
| | [10/9 9/7]
| |
|-
| | 75/64
| | 274.582
| | 7/6
| | 225/224
| | [16/15 5/4]
| |
|-
| | 33/28
| | 284.447
| | 13/11
| | 363/364
| | [12/11 9/7]
| |
|-
| | 32/27
| | 294.135
| | 13/11
| | 352/351
| | [9/8 4/3]
| |
|-
| | 128/105
| | 342.905
| | 11/9
| | 384/385
| | [7/4 32/15]
| |
|-
| | 60/49
| | 350.617
| | 11/9
| | 540/539
| | [7/6 10/7]
| |
|-
| | 49/40
| | 351.338
| | 11/9
| | 441/440
| | [8/7 7/5]
| |
|-
| | 100/81
| | 364.807
| | 16/13
| | 325/324
| | [9/5 20/9]
| |
|-
| | 121/98
| | 364.984
| | 16/13
| | 1573/1568
| | [14/11 11/7]
| |
|-
| | 80/63
| | 413.578
| | 14/11
| | 440/441
| | [9/8 10/7]
| |
|-
| | 32/25
| | 427.373
| | 9/7
| | 224/225
| | [5/4 8/5]
| |
|-
| | 35/27
| | 449.275
| | 13/10
| | 350/351
| | [6/5 14/9]
| |
|-
| | 100/77
| | 452.484
| | 13/10
| | 1000/1001
| | [11/10 10/7]
| |
|-
| | 49/36
| | 533.742
| | 15/11
| | 539/540
| | [8/7 14/9]
| |
|-
| | 308/225
| | 543.606
| | 15/11, 11/8
| | 3388/3375, 224/225
| | [15/14 22/15]
| |
|-
| | 48/35
| | 546.815
| | 11/8
| | 384/385
| | [7/6 8/5]
| |
|-
| | 112/81
| | 561.006
| | 18/13
| | 728/729
| | [9/8 14/9]
| |
|-
| | 168/121
| | 568.145
| | 18/13
| | 364/363
| | [11/7 24/11]
| |
|-
| | 25/18
| | 568.717
| | 18/13
| | 325/324
| | [6/5 5/3]
| |
|-
| | 36/25
| | 631.283
| | 13/9
| | 324/325
| | [10/9 8/5]
| |
|-
| | 121/84
| | 631.855
| | 13/9
| | 363/364
| | [12/11 11/7]
| |
|-
| | 81/56
| | 638.994
| | 13/9
| | 729/728
| | [14/9 9/4]
| |
|-
| | 35/24
| | 653.185
| | 16/11
| | 385/384
| | [16/15 14/9]
| |
|-
| | 143/98
| | 654.194
| | 16/11
| | 1573/1568
| | [14/13 11/7]
| |
|-
| | 225/154
| | 656.394
| | 16/11, 22/15
| | 225/224, 3375/3388
| | [22/15 15/7]
| |
|-
| | 77/50
| | 747.516
| | 20/13
| | 1001/1000
| | [10/7 11/5]
| |
|-
| | 54/35
| | 750.725
| | 20/13
| | 351/350
| | [10/9 12/7]
| |
|-
| | 25/16
| | 772.627
| | 14/9
| | 225/224
| | [16/15 5/3]
| |
|-
| | 63/40
| | 786.422
| | 11/7
| | 441/440
| | [10/9 7/4]
| |
|-
| | 196/121
| | 835.016
| | 13/8
| | 1568/1573
| | [11/7 28/11]
| |
|-
| | 81/50
| | 835.193
| | 13/8
| | 324/325
| | [10/9 9/5]
| |
|-
| | 80/49
| | 848.662
| | 18/11
| | 440/441
| | [7/5 16/7]
| |
|-
| | 49/30
| | 849.383
| | 18/11
| | 539/540
| | [15/14 7/4]
| |
|-
| | 105/64
| | 857.095
| | 18/11
| | 385/384
| | [16/15 7/4] ]
| |
|-
| | 27/16
| | 905.865
| | 22/13
| | 351/352
| | [16/15 9/5]
| |
|-
| | 56/33
| | 915.553
| | 22/13
| | 364/363
| | [15/14 20/11]
| |
|-
| | 128/75
| | 925.418
| | 12/7
| | 224/225
| | [5/4 32/15]
| |
|-
| | 140/81
| | 947.320
| | 26/15
| | 350/351
| | [9/7 20/9]
| |
|-
| | 121/70
| | 947.496
| | 26/15
| | 363/364
| | [14/11 11/5]
| |
|-
| | 210/121
| | 954.459
| | 26/15
| | 1575/1573
| | [22/15 28/11]
| |
|-
| | 49/27
| | 1031.787
| | 20/11
| | 539/540
| | [9/7 7/3]
| |
|-
| | 64/35
| | 1044.86
| | 11/6
| | 384/385
| | [7/6 32/15]
| |
|-
| | 90/49
| | 1052.572
| | 11/6
| | 540/539
| | [7/6 15/7]
| |
|-
| | 416/225
| | 1063.99
| | 24/13, 13/7
| | 676/675, 224/225
| | [15/13 32/15]
| |
|-
| | 224/121
| | 1066.19
| | 24/13, 13/7
| | 364/363, 1568/1573
| | [11/8 28/11]
| |
|-
| | 50/27
| | 1066.762
| | 24/13, 13/7
| | 325/324, 350/351
| | [6/5 20/9]
| |
|-
| | 117/110
| | 106.806
| | 16/15
| | 351/352
| | [10/9 13/11]
| |
|-
| | 180/169
| | 109.168
| | 16/15
| | 675/676
| | [13/12 15/13]
| |
|-
| | [[77/72|77/72]]
| | 116.234
| | 16/15, 15/14
| | 385/384, 539/540
| | [12/11 7/6]
| | undecimal secor
|-
| | 28/25
| | 196.198
| | 9/8
| | 224/225
| | [15/14 6/5]
| |
|-
| | 224/195
| | 240.030
| | 15/13
| | 224/225
| | [15/14 16/13]
| |
|-
| | 52/45
| | 250.304
| | 15/13
| | 676/675
| | [9/8 13/10]
| |
|-
| | 77/60
| | 431.875
| | 9/7
| | 539/540
| | [15/14 11/8]
| |
|-
| | 110/81
| | 529.812
| | 15/11
| | 242/243
| | [18/11 20/9]
| |
|-
| | 160/117
| | 541.876
| | 15/11
| | 352/351
| | [9/8 20/13]
| |
|-
| | 117/80
| | 658.124
| | 22/15
| | 351/352
| | [10/9 13/8]
| |
|-
| | 81/55
| | 670.188
| | 22/15
| | 243/242
| | [10/9 18/11]
| |
|-
| | 120/77
| | 768.125
| | 14/9
| | 540/539
| | [11/10 12/7]
| |
|-
| | 45/26
| | 949.696
| | 26/15
| | 675/676
| | [16/15 24/13]
| |
|-
| | 195/112
| | 959.970
| | 26/15
| | 225/224
| | [16/15 13/7]
| |
|-
| | 25/14
| | 1003.802
| | 16/9
| | 225/224
| | [6/5 15/7]
| |
|-
| | 144/77
| | 1083.766
| | 28/15, 15/8
| | 540/539, 384/385
| | [7/6 24/11]
| |
|-
| | 169/90
| | 1090.832
| | 15/8
| | 676/675
| | [15/13 13/6]
| |
|-
| | 220/117
| | 1093.194
| | 15/8
| | 352/351
| | [13/11 20/9]
| |
|}


&lt;table class="wiki_table"&gt;
===Neutral/ambiguous===
    &lt;tr&gt;
        &lt;td&gt;fudger&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;cents&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;approximately&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;comma(s)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(example) intervals&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;names&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;130/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;124.205&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/14, 14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364/363, 845/847&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/10 13/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/88_81"&gt;88/81&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;143.498&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/12, 12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;352/351, 242/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 11/9]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;undecimal subtone&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;99/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;145.874&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/12, 12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1188/1183, 363/364&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/11 9/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;256/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;223.463&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/8 32/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;225/196&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;238.886&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[28/15 15/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;200/169&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;291.572&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2200/2197&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/10 20/13]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;77/65&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;293.302&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;847/845&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/11 7/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;108/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;296.511&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1188/1183&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/12 9/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27/22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;354.547&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9, 16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;243/242, 351/352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 15/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;225/182&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;367.184&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[26/15 15/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;286/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;415.308&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1573/1575&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/13 22/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;225/176&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;425.219&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 15/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;135/104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;451.651&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;675/676&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 18/13]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;220/169&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;456.576&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2200/2197&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/11 20/13]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;176/135&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;459.139&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;352/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 22/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;224/165&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;529.239&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 16/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;143/105&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;534.751&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1573/1575&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/13 22/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;91/66&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;556.081&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8, 18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364/363, 1183/1188&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/7 13/6]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;135/98&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;554.527&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540/539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/9 15/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;104/75&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;565.945&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;676/675&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/13 8/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;45/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;590.224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 3/2]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;64/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;609.776&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 8/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;75/52&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;634.055&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;675/676&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 20/13]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;132/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;643.919&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/9, 16/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1188/1183, 363/364&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/12 11/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;196/135&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;645.473&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;539/540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 14/9]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;210/143&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;665.249&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1575/1573&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[22/15 28/13]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;165/112&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;670.761&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 11/7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;135/88&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;740.861&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 18/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;169/110&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;743.424&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2197/2200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[20/13 26/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;208/135&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;748.349&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;676/675&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 26/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;352/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;774.781&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/11 32/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;225/143&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;784.692&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1575/1573&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[22/15 30/13]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;364/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;832.816&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 26/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;44/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;845.453&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/8, 18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;352/351, 242/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[12/11 16/9]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;91/54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;903.489&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1183/1188&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/7 13/6]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;130/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;906.698&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;845/847&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/13 20/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;169/100&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;908.428&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2197/2200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[20/13 13/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;392/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;961.114&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 28/15]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;225/128&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;976.537&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 15/8]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81/44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1056.502&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/6, 24/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;243/242, 351/352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/9 9/4]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;225/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1073.902&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/7, 28/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1575/1573, 3375/3388&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[22/15 30/11]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121/65&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1075.795&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/7, 28/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;847/845, 363/364&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/11 11/5]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Fudging Intervals-Down-fudge"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Down-fudge&lt;/h3&gt;
{| class="wikitable"
|-
| | fudger
| | cents
| | approximately
| | comma(s)
| | (example) intervals
| | names
|-
| | 130/121
| | 124.205
| | 15/14, 14/13
| | 364/363, 845/847
| | [11/10 13/11]
| |
|-
| | [[88/81|88/81]]
| | 143.498
| | 13/12, 12/11
| | 352/351, 242/243
| | [9/8 11/9]
| | undecimal subtone
|-
| | 99/91
| | 145.874
| | 13/12, 12/11
| | 1188/1183, 363/364
| | [13/11 9/7]
| |
|-
| | 256/225
| | 223.463
| | 8/7
| | 224/225
| | [15/8 32/15]
| |
|-
| | 225/196
| | 238.886
| | 8/7
| | 225/224
| | [28/15 15/7]
| |
|-
| | 200/169
| | 291.572
| | 13/11
| | 2200/2197
| | [13/10 20/13]
| |
|-
| | 77/65
| | 293.302
| | 13/11
| | 847/845
| | [13/11 7/5]
| |
|-
| | 108/91
| | 296.511
| | 13/11
| | 1188/1183
| | [13/12 9/7]
| |
|-
| | 27/22
| | 354.547
| | 11/9, 16/13
| | 243/242, 351/352
| | [10/9 15/11]
| |
|-
| | 225/182
| | 367.184
| | 16/13
| | 225/224
| | [26/15 15/7]
| |
|-
| | 286/225
| | 415.308
| | 14/11
| | 1573/1575
| | [15/13 22/15]
| |
|-
| | 225/176
| | 425.219
| | 14/11
| | 225/224
| | [16/15 15/11]
| |
|-
| | 135/104
| | 451.651
| | 13/10
| | 675/676
| | [16/15 18/13]
| |
|-
| | 220/169
| | 456.576
| | 13/10
| | 2200/2197
| | [13/11 20/13]
| |
|-
| | 176/135
| | 459.139
| | 13/10
| | 352/351
| | [9/8 22/15]
| |
|-
| | 224/165
| | 529.239
| | 15/11
| | 224/225
| | [15/14 16/11]
| |
|-
| | 143/105
| | 534.751
| | 15/11
| | 1573/1575
| | [14/13 22/15]
| |
|-
| | 91/66
| | 556.081
| | 11/8, 18/13
| | 364/363, 1183/1188
| | [11/7 13/6]
| |
|-
| | 135/98
| | 554.527
| | 11/8
| | 540/539
| | [14/9 15/7]
| |
|-
| | 104/75
| | 565.945
| | 18/13
| | 676/675
| | [15/13 8/5]
| |
|-
| | 45/32
| | 590.224
| | 7/5
| | 225/224
| | [16/15 3/2]
| |
|-
| | 64/45
| | 609.776
| | 10/7
| | 224/225
| | [9/8 8/5]
| |
|-
| | 75/52
| | 634.055
| | 675/676
| | 13/9
| | [16/15 20/13]
| |
|-
| | 132/91
| | 643.919
| | 13/9, 16/11
| | 1188/1183, 363/364
| | [13/12 11/7]
| |
|-
| | 196/135
| | 645.473
| | 16/11
| | 539/540
| | [15/14 14/9]
| |
|-
| | 210/143
| | 665.249
| | 22/15
| | 1575/1573
| | [22/15 28/13]
| |
|-
| | 165/112
| | 670.761
| | 22/15
| | 225/224
| | [16/15 11/7]
| |
|-
| | 135/88
| | 740.861
| | 20/13
| | 351/352
| | [16/15 18/11]
| |
|-
| | 169/110
| | 743.424
| | 20/13
| | 2197/2200
| | [20/13 26/11]
| |
|-
| | 208/135
| | 748.349
| | 20/13
| | 676/675
| | [9/8 26/15]
| |
|-
| | 352/225
| | 774.781
| | 11/7
| | 224/225
| | [15/11 32/15]
| |
|-
| | 225/143
| | 784.692
| | 11/7
| | 1575/1573
| | [22/15 30/13]
| |
|-
| | 364/225
| | 832.816
| | 13/8
| | 224/225
| | [15/14 26/15]
| |
|-
| | 44/27
| | 845.453
| | 13/8, 18/11
| | 352/351, 242/243
| | [12/11 16/9]
| |
|-
| | 91/54
| | 903.489
| | 22/13
| | 1183/1188
| | [9/7 13/6]
| |
|-
| | 130/77
| | 906.698
| | 22/13
| | 845/847
| | [14/13 20/11]
| |
|-
| | 169/100
| | 908.428
| | 22/13
| | 2197/2200
| | [20/13 13/5]
| |
|-
| | 392/225
| | 961.114
| | 7/4
| | 224/225
| | [15/14 28/15]
| |
|-
| | 225/128
| | 976.537
| | 7/4
| | 225/224
| | [16/15 15/8]
| |
|-
| | 81/44
| | 1056.502
| | 11/6, 24/13
| | 243/242, 351/352
| | [11/9 9/4]
| |
|-
| | 225/121
| | 1073.902
| | 13/7, 28/15
| | 1575/1573, 3375/3388
| | [22/15 30/11]
| |
|-
| | 121/65
| | 1075.795
| | 13/7, 28/15
| | 847/845, 363/364
| | [13/11 11/5]
| |
|}


&lt;table class="wiki_table"&gt;
===Down-fudge===
    &lt;tr&gt;
        &lt;td&gt;fudger&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;cents&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;approximately&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;commas&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(example) intervals&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;128/117&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;155.562&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;352/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 16/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;169/154&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;160.911&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;845/847&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/13 13/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;100/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;163.274&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1000/1001&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/10 10/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;182/165&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;169.767&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364/363&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 13/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;72/65&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;177.069&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;324/325&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/12 6/5]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;195/176&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;177.478&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 13/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49/44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;186.334&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;441/440&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[8/7 14/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39/35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;187.343&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/350&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/13 6/5]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;135/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189.543&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;243/242&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/9 15/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121/108&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;196.771&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;242/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[12/11 11/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;55/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;199.980&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;440/441&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/11 10/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;91/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;201.534&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;728/729&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/7 13/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;169/150&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;206.473&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;676/675&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/13 13/10]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;44/39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;208.835&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;352/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/12 11/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;154/135&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;227.965&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;539/540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 11/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;63/55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;235.104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;441/440&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 14/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;55/48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;235.677&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 11/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121/104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;262.108&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;363/364&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/11 11/8]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;64/55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;262.368&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384/385&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[5/4 16/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;90/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;270.080&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540/539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/10 9/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;117/100&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;271.810&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/350&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 13/10]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;198/169&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;274.173&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1188/1183&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/11 18/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;140/117&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310.702&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;350/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/7 20/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;77/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;320.144&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[8/7 11/8]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;65/54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;320.976&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;325/324&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[6/5 13/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;135/112&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;323.353&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 9/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;342.483&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 13/10]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;56/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;378.602&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 4/3]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81/65&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.979&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;324/325&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 18/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;96/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.811&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384/385&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7/6 16/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;169/135&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;388.877&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;676/675&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/13 13/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33/26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;412.745&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;363/364&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/12 11/8]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;143/112&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;423.020&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1573/1568&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/13 11/8]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;216/169&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;424.810&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1188/1183&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/12 18/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;169/132&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;427.782&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1183/1188&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[22/13 13/6]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;50/39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;430.145&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;350/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[6/5 20/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;104/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;432.708&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;728/729&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 13/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;165/128&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;439.587&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 11/8]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;156/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;439.847&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364/363&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[22/13 24/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;117/88&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;493.120&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/9 13/8]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;493.282&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;363/364&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/11 11/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;225/169&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;495.482&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;675/676&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[26/15 30/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;162/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;505.184&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;243/242&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/9 18/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;75/56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;505.757&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 10/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;196/143&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;545.806&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1568/1573&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/7 28/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;169/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;578.419&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;845/847&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[22/13 26/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;88/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;578.582&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;440/441&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 11/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;200/143&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;580.782&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1000/1001&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/10 20/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;108/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;585.721&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540/539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7/6 18/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;77/54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;614.279&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;539/540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[12/11 14/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;143/100&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;619.218&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1001/1000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[20/13 11/5]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;63/44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;621.418&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;441/440&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[8/7 18/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;242/169&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;621.581&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;847/845&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/11 22/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;72/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;666.258&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540/539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7/6 12/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;112/75&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;694.243&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 8/5]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;694.816&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;242/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[18/11 22/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;338/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;704.518&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;676/675&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/13 26/15]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;182/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;706.718&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364/363&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/7 26/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;176/117&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;706.880&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;352/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/8 22/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121/78&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;760.153&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;363/364&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[12/11 22/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;256/165&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;760.413&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384/385&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/8 32/15]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81/52&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;767.292&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;729/728&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/9 9/4]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;769.855&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/350&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/9 26/15]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;264/169&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;772.218&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1188/1183&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/12 22/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;169/108&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;775.190&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1183/1188&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[18/13 13/6]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;224/143&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;776.980&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1568/1573&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/8 28/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;52/33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;787.255&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364/363&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/10 26/15]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;270/169&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;811.123&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;675/676&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/9 30/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;77/48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;818.189&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[12/11 7/4]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;130/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;819.021&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;325/324&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[18/13 20/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;45/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;821.398&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 12/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;64/39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;857.517&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;352/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/12 16/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;224/135&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;876.647&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 16/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;108/65&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;879.024&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;324/325&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/12 9/5]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;128/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;879.856&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384/385&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/8 16/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;117/70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;889.298&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/350&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/13 9/5]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;169/99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;925.827&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1183/1188&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[18/13 26/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;200/117&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;928.190&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;350/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/10 20/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;77/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;929.920&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;539/540&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/14 11/6]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;55/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;937.632&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/15 11/6]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;208/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;937.892&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364/363&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/8 26/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;96/55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;964.323&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384/385&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/9 32/15]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;110/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;964.896&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;440/441&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/11 20/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;135/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;972.035&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540/539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/9 15/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39/22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;991.165&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/9 13/6]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;300/169&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;993.527&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;675/676&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/10 30/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;162/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;998.466&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;729/728&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/9 18/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;98/55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1000.02&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;441/440&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/7 28/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;216/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1003.229&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;243/242&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[11/9 24/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;242/135&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1010.457&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;242/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[15/11 22/9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;70/39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1012.657&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;350/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[6/5 28/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;88/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1013.666&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;440/441&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[14/11 16/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;352/195&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1022.522&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;352/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/11 32/15]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;65/36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1022.931&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;325/324&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[6/5 13/6]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;165/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1030.233&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;363/364&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/11 15/7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;91/50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1036.726&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1001/1000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10/7 13/5]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;308/169&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1039.089&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;847/845&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[13/11 28/13]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;117/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1044.438&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351/352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[16/13 9/4]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;182/99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1054.126&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/6, 24/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364/363, 1183/1188&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9/7 26/11]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
{| class="wikitable"
|-
| | fudger
| | cents
| | approximately
| | commas
| | (example) intervals
|-
| | 128/117
| | 155.562
| | 12/11
| | 352/351
| | [9/8 16/13]
|-
| | 169/154
| | 160.911
| | 11/10
| | 845/847
| | [14/13 13/11]
|-
| | 100/91
| | 163.274
| | 11/10
| | 1000/1001
| | [13/10 10/7]
|-
| | 182/165
| | 169.767
| | 11/10
| | 364/363
| | [15/14 13/11]
|-
| | 72/65
| | 177.069
| | 10/9
| | 324/325
| | [13/12 6/5]
|-
| | 195/176
| | 177.478
| | 10/9
| | 351/352
| | [16/15 13/11]
|-
| | 49/44
| | 186.334
| | 10/9
| | 441/440
| | [8/7 14/11]
|-
| | 39/35
| | 187.343
| | 10/9
| | 351/350
| | [14/13 6/5]
|-
| | 135/121
| | 189.543
| | 10/9
| | 243/242
| | [11/9 15/11]
|-
| | 121/108
| | 196.771
| | 9/8
| | 242/243
| | [12/11 11/9]
|-
| | 55/49
| | 199.980
| | 9/8
| | 440/441
| | [14/11 10/7]
|-
| | 91/81
| | 201.534
| | 9/8
| | 728/729
| | [9/7 13/9]
|-
| | 169/150
| | 206.473
| | 9/8
| | 676/675
| | [15/13 13/10]
|-
| | 44/39
| | 208.835
| | 9/8
| | 352/351
| | [13/12 11/9]
|-
| | 154/135
| | 227.965
| | 8/7
| | 539/540
| | [15/14 11/9]
|-
| | 63/55
| | 235.104
| | 8/7
| | 441/440
| | [10/9 14/11]
|-
| | 55/48
| | 235.677
| | 8/7
| | 385/384
| | [16/15 11/9]
|-
| | 121/104
| | 262.108
| | 7/6
| | 363/364
| | [13/11 11/8]
|-
| | 64/55
| | 262.368
| | 7/6
| | 384/385
| | [5/4 16/11]
|-
| | 90/77
| | 270.080
| | 7/6
| | 540/539
| | [11/10 9/7]
|-
| | 117/100
| | 271.810
| | 7/6
| | 351/350
| | [10/9 13/10]
|-
| | 198/169
| | 274.173
| | 7/6
| | 1188/1183
| | [13/11 18/13]
|-
| | 140/117
| | 310.702
| | 6/5
| | 350/351
| | [9/7 20/13]
|-
| | 77/64
| | 320.144
| | 6/5
| | 385/384
| | [8/7 11/8]
|-
| | 65/54
| | 320.976
| | 6/5
| | 325/324
| | [6/5 13/9]
|-
| | 135/112
| | 323.353
| | 6/5
| | 225/224
| | [16/15 9/7]
|-
| | 39/32
| | 342.483
| | 11/9
| | 351/352
| | [16/15 13/10]
|-
| | 56/45
| | 378.602
| | 5/4
| | 224/225
| | [15/14 4/3]
|-
| | 81/65
| | 380.979
| | 5/4
| | 324/325
| | [10/9 18/13]
|-
| | 96/77
| | 381.811
| | 5/4
| | 384/385
| | [7/6 16/11]
|-
| | 169/135
| | 388.877
| | 5/4
| | 676/675
| | [15/13 13/9]
|-
| | 33/26
| | 412.745
| | 14/11
| | 363/364
| | [13/12 11/8]
|-
| | 143/112
| | 423.020
| | 14/11
| | 1573/1568
| | [14/13 11/8]
|-
| | 216/169
| | 424.810
| | 14/11
| | 1188/1183
| | [13/12 18/13]
|-
| | 169/132
| | 427.782
| | 9/7
| | 1183/1188
| | [22/13 13/6]
|-
| | 50/39
| | 430.145
| | 9/7
| | 350/351
| | [6/5 20/13]
|-
| | 104/81
| | 432.708
| | 9/7
| | 728/729
| | [9/8 13/9]
|-
| | 165/128
| | 439.587
| | 9/7
| | 385/384
| | [16/15 11/8]
|-
| | 156/121
| | 439.847
| | 9/7
| | 364/363
| | [22/13 24/11]
|-
| | 117/88
| | 493.120
| | 4/3
| | 351/352
| | [11/9 13/8]
|-
| | 121/91
| | 493.282
| | 4/3
| | 363/364
| | [13/11 11/7]
|-
| | 225/169
| | 495.482
| | 4/3
| | 675/676
| | [26/15 30/13]
|-
| | 162/121
| | 505.184
| | 4/3
| | 243/242
| | [11/9 18/11]
|-
| | 75/56
| | 505.757
| | 4/3
| | 225/224
| | [16/15 10/7]
|-
| | 196/143
| | 545.806
| | 11/8
| | 1568/1573
| | [11/7 28/13]
|-
| | 169/121
| | 578.419
| | 7/5
| | 845/847
| | [22/13 26/11]
|-
| | 88/63
| | 578.582
| | 7/5
| | 440/441
| | [9/8 11/7]
|-
| | 200/143
| | 580.782
| | 7/5
| | 1000/1001
| | [11/10 20/13]
|-
| | 108/77
| | 585.721
| | 7/5
| | 540/539
| | [7/6 18/11]
|-
| | 77/54
| | 614.279
| | 10/7
| | 539/540
| | [12/11 14/9]
|-
| | 143/100
| | 619.218
| | 10/7
| | 1001/1000
| | [20/13 11/5]
|-
| | 63/44
| | 621.418
| | 10/7
| | 441/440
| | [8/7 18/11]
|-
| | 242/169
| | 621.581
| | 10/7
| | 847/845
| | [13/11 22/13]
|-
| | 72/49
| | 666.258
| | 22/15
| | 540/539
| | [7/6 12/7]
|-
| | 112/75
| | 694.243
| | 3/2
| | 224/225
| | [15/14 8/5]
|-
| | 121/81
| | 694.816
| | 3/2
| | 242/243
| | [18/11 22/9]
|-
| | 338/225
| | 704.518
| | 3/2
| | 676/675
| | [15/13 26/15]
|-
| | 182/121
| | 706.718
| | 3/2
| | 364/363
| | [11/7 26/11]
|-
| | 176/117
| | 706.880
| | 3/2
| | 352/351
| | [9/8 22/13]
|-
| | 121/78
| | 760.153
| | 14/9
| | 363/364
| | [12/11 22/13]
|-
| | 256/165
| | 760.413
| | 14/9
| | 384/385
| | [11/8 32/15]
|-
| | 81/52
| | 767.292
| | 14/9
| | 729/728
| | [13/9 9/4]
|-
| | 39/25
| | 769.855
| | 14/9
| | 351/350
| | [10/9 26/15]
|-
| | 264/169
| | 772.218
| | 14/9
| | 1188/1183
| | [13/12 22/13]
|-
| | 169/108
| | 775.190
| | 11/7
| | 1183/1188
| | [18/13 13/6]
|-
| | 224/143
| | 776.980
| | 11/7
| | 1568/1573
| | [11/8 28/13]
|-
| | 52/33
| | 787.255
| | 11/7
| | 364/363
| | [11/10 26/15]
|-
| | 270/169
| | 811.123
| | 8/5
| | 675/676
| | [13/9 30/13]
|-
| | 77/48
| | 818.189
| | 8/5
| | 385/384
| | [12/11 7/4]
|-
| | 130/81
| | 819.021
| | 8/5
| | 325/324
| | [18/13 20/9]
|-
| | 45/28
| | 821.398
| | 8/5
| | 225/224
| | [16/15 12/7]
|-
| | 64/39
| | 857.517
| | 18/11
| | 352/351
| | [13/12 16/9]
|-
| | 224/135
| | 876.647
| | 5/3
| | 224/225
| | [15/14 16/9]
|-
| | 108/65
| | 879.024
| | 5/3
| | 324/325
| | [13/12 9/5]
|-
| | 128/77
| | 879.856
| | 5/3
| | 384/385
| | [11/8 16/7]
|-
| | 117/70
| | 889.298
| | 5/3
| | 351/350
| | [14/13 9/5]
|-
| | 169/99
| | 925.827
| | 12/7
| | 1183/1188
| | [18/13 26/11]
|-
| | 200/117
| | 928.190
| | 12/7
| | 350/351
| | [13/10 20/9]
|-
| | 77/45
| | 929.920
| | 12/7
| | 539/540
| | [15/14 11/6]
|-
| | 55/32
| | 937.632
| | 12/7
| | 385/384
| | [16/15 11/6]
|-
| | 208/121
| | 937.892
| | 12/7
| | 364/363
| | [11/8 26/11]
|-
| | 96/55
| | 964.323
| | 7/4
| | 384/385
| | [11/9 32/15]
|-
| | 110/63
| | 964.896
| | 7/4
| | 440/441
| | [14/11 20/9]
|-
| | 135/77
| | 972.035
| | 7/4
| | 540/539
| | [11/9 15/7]
|-
| | 39/22
| | 991.165
| | 16/9
| | 351/352
| | [11/9 13/6]
|-
| | 300/169
| | 993.527
| | 16/9
| | 675/676
| | [13/10 30/13]
|-
| | 162/91
| | 998.466
| | 16/9
| | 729/728
| | [13/9 18/7]
|-
| | 98/55
| | 1000.02
| | 16/9
| | 441/440
| | [10/7 28/11]
|-
| | 216/121
| | 1003.229
| | 16/9
| | 243/242
| | [11/9 24/11]
|-
| | 242/135
| | 1010.457
| | 9/5
| | 242/243
| | [15/11 22/9]
|-
| | 70/39
| | 1012.657
| | 9/5
| | 350/351
| | [6/5 28/13]
|-
| | 88/49
| | 1013.666
| | 9/5
| | 440/441
| | [14/11 16/7]
|-
| | 352/195
| | 1022.522
| | 9/5
| | 352/351
| | [13/11 32/15]
|-
| | 65/36
| | 1022.931
| | 9/5
| | 325/324
| | [6/5 13/6]
|-
| | 165/91
| | 1030.233
| | 20/11
| | 363/364
| | [13/11 15/7]
|-
| | 91/50
| | 1036.726
| | 20/11
| | 1001/1000
| | [10/7 13/5]
|-
| | 308/169
| | 1039.089
| | 20/11
| | 847/845
| | [13/11 28/13]
|-
| | 117/64
| | 1044.438
| | 11/6
| | 351/352
| | [16/13 9/4]
|-
| | 182/99
| | 1054.126
| | 11/6, 24/13
| | 364/363, 1183/1188
| | [9/7 26/11]
|}
[[Category:15-limit]]
[[Category:fuging]]
[[Category:interval_list]]
[[Category:just_intonation]]
[[Category:list]]

Revision as of 00:00, 17 July 2018

Fudging, or virtual tempering, is the use of one just intonation interval to approximate another. Below are listed fudging intervals ("fudgers") which are all ratios between two 15-limit tonality diamond intervals (listed in the fifth column) which come within a comma of less than eight cents (listed in the fourth column) of a 15-limit tonality diamond interval (listed in the third column). If the comma is less than 1, the fudger is flat of the interval it approximates; if greater than 1, sharp of it.

A limit-raising fudger is a p prime limit interval which approximates to a q prime limit consonance, with p<q. An example is 100/77, which is 1001/1000 (1.7 cents) flat of 13/10, and which arises in 11-limit scales as the interval between 11/10 and 10/7, giving 13-limit harmony "for free", so to speak. A limit-lowering fudger is an interval such as the marvelous fourth, 75/56, which is 225/224 (7.7 cents) sharp of 4/3, and which arises very often in 7-limit JI scales as the interval between 16/15 and 10/7, 7/5 and 15/8, 8/5 and 15/7, and 28/15 and 5/2, giving a 3-limit interval approximated in the 7-limit.

By tempering out the fudging commas, the error in the fudging may be distributed evenly. Since 225/224, 385/384 and 540/539 occur so commonly as fudging commas, marvel tempering in particular is often an excellent means to introduce smooth 7- and 11-limit harmonies into 5- or 7- limit scales. Adding 441/440 to that list results in miracle tempering, another excellent smoothing option. However, indiscriminate tempering can lead to problems. For example, 112/75, 121/81, 338/225, 182/121 and 176/117 are all fudged fifths, with commas 676/675, 364/363, 352/351, 243/242 and 225/224. Tempering them all out leads to 34d tempering, a rather crude system by comparison.

Fudging Intervals

Up-fudge

fudger cents approximately comma(s) (example) intervals name
242/225 126.098 15/14, 14/13 3388/3375, 1573/1575 [15/11 22/15]
27/25 133.238 14/13, 13/12 351/350, 324/325 [10/9 6/5] large limma
121/112 133.810 14/13, 13/12 1573/1568, 363/364 [14/11 11/8]
225/208 136.010 14/13, 13/12 225/224, 675/676 [16/15 15/13]
49/45 147.428 12/11 539/540 [15/14 7/6] swetismic neutral second
35/32 155.140 12/11 385/384 [16/15 7/6] septimal neutral second
54/49 168.213 11/10 540/539 [7/6 9/7] Zalzal's mujannab
121/105 245.541 15/13 1573/1575 [14/11 22/15]
140/121 252.504 15/13 364/363 [11/10 14/11]
81/70 252.680 15/13 351/350 [10/9 9/7]
75/64 274.582 7/6 225/224 [16/15 5/4]
33/28 284.447 13/11 363/364 [12/11 9/7]
32/27 294.135 13/11 352/351 [9/8 4/3]
128/105 342.905 11/9 384/385 [7/4 32/15]
60/49 350.617 11/9 540/539 [7/6 10/7]
49/40 351.338 11/9 441/440 [8/7 7/5]
100/81 364.807 16/13 325/324 [9/5 20/9]
121/98 364.984 16/13 1573/1568 [14/11 11/7]
80/63 413.578 14/11 440/441 [9/8 10/7]
32/25 427.373 9/7 224/225 [5/4 8/5]
35/27 449.275 13/10 350/351 [6/5 14/9]
100/77 452.484 13/10 1000/1001 [11/10 10/7]
49/36 533.742 15/11 539/540 [8/7 14/9]
308/225 543.606 15/11, 11/8 3388/3375, 224/225 [15/14 22/15]
48/35 546.815 11/8 384/385 [7/6 8/5]
112/81 561.006 18/13 728/729 [9/8 14/9]
168/121 568.145 18/13 364/363 [11/7 24/11]
25/18 568.717 18/13 325/324 [6/5 5/3]
36/25 631.283 13/9 324/325 [10/9 8/5]
121/84 631.855 13/9 363/364 [12/11 11/7]
81/56 638.994 13/9 729/728 [14/9 9/4]
35/24 653.185 16/11 385/384 [16/15 14/9]
143/98 654.194 16/11 1573/1568 [14/13 11/7]
225/154 656.394 16/11, 22/15 225/224, 3375/3388 [22/15 15/7]
77/50 747.516 20/13 1001/1000 [10/7 11/5]
54/35 750.725 20/13 351/350 [10/9 12/7]
25/16 772.627 14/9 225/224 [16/15 5/3]
63/40 786.422 11/7 441/440 [10/9 7/4]
196/121 835.016 13/8 1568/1573 [11/7 28/11]
81/50 835.193 13/8 324/325 [10/9 9/5]
80/49 848.662 18/11 440/441 [7/5 16/7]
49/30 849.383 18/11 539/540 [15/14 7/4]
105/64 857.095 18/11 385/384 [16/15 7/4] ]
27/16 905.865 22/13 351/352 [16/15 9/5]
56/33 915.553 22/13 364/363 [15/14 20/11]
128/75 925.418 12/7 224/225 [5/4 32/15]
140/81 947.320 26/15 350/351 [9/7 20/9]
121/70 947.496 26/15 363/364 [14/11 11/5]
210/121 954.459 26/15 1575/1573 [22/15 28/11]
49/27 1031.787 20/11 539/540 [9/7 7/3]
64/35 1044.86 11/6 384/385 [7/6 32/15]
90/49 1052.572 11/6 540/539 [7/6 15/7]
416/225 1063.99 24/13, 13/7 676/675, 224/225 [15/13 32/15]
224/121 1066.19 24/13, 13/7 364/363, 1568/1573 [11/8 28/11]
50/27 1066.762 24/13, 13/7 325/324, 350/351 [6/5 20/9]
117/110 106.806 16/15 351/352 [10/9 13/11]
180/169 109.168 16/15 675/676 [13/12 15/13]
77/72 116.234 16/15, 15/14 385/384, 539/540 [12/11 7/6] undecimal secor
28/25 196.198 9/8 224/225 [15/14 6/5]
224/195 240.030 15/13 224/225 [15/14 16/13]
52/45 250.304 15/13 676/675 [9/8 13/10]
77/60 431.875 9/7 539/540 [15/14 11/8]
110/81 529.812 15/11 242/243 [18/11 20/9]
160/117 541.876 15/11 352/351 [9/8 20/13]
117/80 658.124 22/15 351/352 [10/9 13/8]
81/55 670.188 22/15 243/242 [10/9 18/11]
120/77 768.125 14/9 540/539 [11/10 12/7]
45/26 949.696 26/15 675/676 [16/15 24/13]
195/112 959.970 26/15 225/224 [16/15 13/7]
25/14 1003.802 16/9 225/224 [6/5 15/7]
144/77 1083.766 28/15, 15/8 540/539, 384/385 [7/6 24/11]
169/90 1090.832 15/8 676/675 [15/13 13/6]
220/117 1093.194 15/8 352/351 [13/11 20/9]

Neutral/ambiguous

fudger cents approximately comma(s) (example) intervals names
130/121 124.205 15/14, 14/13 364/363, 845/847 [11/10 13/11]
88/81 143.498 13/12, 12/11 352/351, 242/243 [9/8 11/9] undecimal subtone
99/91 145.874 13/12, 12/11 1188/1183, 363/364 [13/11 9/7]
256/225 223.463 8/7 224/225 [15/8 32/15]
225/196 238.886 8/7 225/224 [28/15 15/7]
200/169 291.572 13/11 2200/2197 [13/10 20/13]
77/65 293.302 13/11 847/845 [13/11 7/5]
108/91 296.511 13/11 1188/1183 [13/12 9/7]
27/22 354.547 11/9, 16/13 243/242, 351/352 [10/9 15/11]
225/182 367.184 16/13 225/224 [26/15 15/7]
286/225 415.308 14/11 1573/1575 [15/13 22/15]
225/176 425.219 14/11 225/224 [16/15 15/11]
135/104 451.651 13/10 675/676 [16/15 18/13]
220/169 456.576 13/10 2200/2197 [13/11 20/13]
176/135 459.139 13/10 352/351 [9/8 22/15]
224/165 529.239 15/11 224/225 [15/14 16/11]
143/105 534.751 15/11 1573/1575 [14/13 22/15]
91/66 556.081 11/8, 18/13 364/363, 1183/1188 [11/7 13/6]
135/98 554.527 11/8 540/539 [14/9 15/7]
104/75 565.945 18/13 676/675 [15/13 8/5]
45/32 590.224 7/5 225/224 [16/15 3/2]
64/45 609.776 10/7 224/225 [9/8 8/5]
75/52 634.055 675/676 13/9 [16/15 20/13]
132/91 643.919 13/9, 16/11 1188/1183, 363/364 [13/12 11/7]
196/135 645.473 16/11 539/540 [15/14 14/9]
210/143 665.249 22/15 1575/1573 [22/15 28/13]
165/112 670.761 22/15 225/224 [16/15 11/7]
135/88 740.861 20/13 351/352 [16/15 18/11]
169/110 743.424 20/13 2197/2200 [20/13 26/11]
208/135 748.349 20/13 676/675 [9/8 26/15]
352/225 774.781 11/7 224/225 [15/11 32/15]
225/143 784.692 11/7 1575/1573 [22/15 30/13]
364/225 832.816 13/8 224/225 [15/14 26/15]
44/27 845.453 13/8, 18/11 352/351, 242/243 [12/11 16/9]
91/54 903.489 22/13 1183/1188 [9/7 13/6]
130/77 906.698 22/13 845/847 [14/13 20/11]
169/100 908.428 22/13 2197/2200 [20/13 13/5]
392/225 961.114 7/4 224/225 [15/14 28/15]
225/128 976.537 7/4 225/224 [16/15 15/8]
81/44 1056.502 11/6, 24/13 243/242, 351/352 [11/9 9/4]
225/121 1073.902 13/7, 28/15 1575/1573, 3375/3388 [22/15 30/11]
121/65 1075.795 13/7, 28/15 847/845, 363/364 [13/11 11/5]

Down-fudge

fudger cents approximately commas (example) intervals
128/117 155.562 12/11 352/351 [9/8 16/13]
169/154 160.911 11/10 845/847 [14/13 13/11]
100/91 163.274 11/10 1000/1001 [13/10 10/7]
182/165 169.767 11/10 364/363 [15/14 13/11]
72/65 177.069 10/9 324/325 [13/12 6/5]
195/176 177.478 10/9 351/352 [16/15 13/11]
49/44 186.334 10/9 441/440 [8/7 14/11]
39/35 187.343 10/9 351/350 [14/13 6/5]
135/121 189.543 10/9 243/242 [11/9 15/11]
121/108 196.771 9/8 242/243 [12/11 11/9]
55/49 199.980 9/8 440/441 [14/11 10/7]
91/81 201.534 9/8 728/729 [9/7 13/9]
169/150 206.473 9/8 676/675 [15/13 13/10]
44/39 208.835 9/8 352/351 [13/12 11/9]
154/135 227.965 8/7 539/540 [15/14 11/9]
63/55 235.104 8/7 441/440 [10/9 14/11]
55/48 235.677 8/7 385/384 [16/15 11/9]
121/104 262.108 7/6 363/364 [13/11 11/8]
64/55 262.368 7/6 384/385 [5/4 16/11]
90/77 270.080 7/6 540/539 [11/10 9/7]
117/100 271.810 7/6 351/350 [10/9 13/10]
198/169 274.173 7/6 1188/1183 [13/11 18/13]
140/117 310.702 6/5 350/351 [9/7 20/13]
77/64 320.144 6/5 385/384 [8/7 11/8]
65/54 320.976 6/5 325/324 [6/5 13/9]
135/112 323.353 6/5 225/224 [16/15 9/7]
39/32 342.483 11/9 351/352 [16/15 13/10]
56/45 378.602 5/4 224/225 [15/14 4/3]
81/65 380.979 5/4 324/325 [10/9 18/13]
96/77 381.811 5/4 384/385 [7/6 16/11]
169/135 388.877 5/4 676/675 [15/13 13/9]
33/26 412.745 14/11 363/364 [13/12 11/8]
143/112 423.020 14/11 1573/1568 [14/13 11/8]
216/169 424.810 14/11 1188/1183 [13/12 18/13]
169/132 427.782 9/7 1183/1188 [22/13 13/6]
50/39 430.145 9/7 350/351 [6/5 20/13]
104/81 432.708 9/7 728/729 [9/8 13/9]
165/128 439.587 9/7 385/384 [16/15 11/8]
156/121 439.847 9/7 364/363 [22/13 24/11]
117/88 493.120 4/3 351/352 [11/9 13/8]
121/91 493.282 4/3 363/364 [13/11 11/7]
225/169 495.482 4/3 675/676 [26/15 30/13]
162/121 505.184 4/3 243/242 [11/9 18/11]
75/56 505.757 4/3 225/224 [16/15 10/7]
196/143 545.806 11/8 1568/1573 [11/7 28/13]
169/121 578.419 7/5 845/847 [22/13 26/11]
88/63 578.582 7/5 440/441 [9/8 11/7]
200/143 580.782 7/5 1000/1001 [11/10 20/13]
108/77 585.721 7/5 540/539 [7/6 18/11]
77/54 614.279 10/7 539/540 [12/11 14/9]
143/100 619.218 10/7 1001/1000 [20/13 11/5]
63/44 621.418 10/7 441/440 [8/7 18/11]
242/169 621.581 10/7 847/845 [13/11 22/13]
72/49 666.258 22/15 540/539 [7/6 12/7]
112/75 694.243 3/2 224/225 [15/14 8/5]
121/81 694.816 3/2 242/243 [18/11 22/9]
338/225 704.518 3/2 676/675 [15/13 26/15]
182/121 706.718 3/2 364/363 [11/7 26/11]
176/117 706.880 3/2 352/351 [9/8 22/13]
121/78 760.153 14/9 363/364 [12/11 22/13]
256/165 760.413 14/9 384/385 [11/8 32/15]
81/52 767.292 14/9 729/728 [13/9 9/4]
39/25 769.855 14/9 351/350 [10/9 26/15]
264/169 772.218 14/9 1188/1183 [13/12 22/13]
169/108 775.190 11/7 1183/1188 [18/13 13/6]
224/143 776.980 11/7 1568/1573 [11/8 28/13]
52/33 787.255 11/7 364/363 [11/10 26/15]
270/169 811.123 8/5 675/676 [13/9 30/13]
77/48 818.189 8/5 385/384 [12/11 7/4]
130/81 819.021 8/5 325/324 [18/13 20/9]
45/28 821.398 8/5 225/224 [16/15 12/7]
64/39 857.517 18/11 352/351 [13/12 16/9]
224/135 876.647 5/3 224/225 [15/14 16/9]
108/65 879.024 5/3 324/325 [13/12 9/5]
128/77 879.856 5/3 384/385 [11/8 16/7]
117/70 889.298 5/3 351/350 [14/13 9/5]
169/99 925.827 12/7 1183/1188 [18/13 26/11]
200/117 928.190 12/7 350/351 [13/10 20/9]
77/45 929.920 12/7 539/540 [15/14 11/6]
55/32 937.632 12/7 385/384 [16/15 11/6]
208/121 937.892 12/7 364/363 [11/8 26/11]
96/55 964.323 7/4 384/385 [11/9 32/15]
110/63 964.896 7/4 440/441 [14/11 20/9]
135/77 972.035 7/4 540/539 [11/9 15/7]
39/22 991.165 16/9 351/352 [11/9 13/6]
300/169 993.527 16/9 675/676 [13/10 30/13]
162/91 998.466 16/9 729/728 [13/9 18/7]
98/55 1000.02 16/9 441/440 [10/7 28/11]
216/121 1003.229 16/9 243/242 [11/9 24/11]
242/135 1010.457 9/5 242/243 [15/11 22/9]
70/39 1012.657 9/5 350/351 [6/5 28/13]
88/49 1013.666 9/5 440/441 [14/11 16/7]
352/195 1022.522 9/5 352/351 [13/11 32/15]
65/36 1022.931 9/5 325/324 [6/5 13/6]
165/91 1030.233 20/11 363/364 [13/11 15/7]
91/50 1036.726 20/11 1001/1000 [10/7 13/5]
308/169 1039.089 20/11 847/845 [13/11 28/13]
117/64 1044.438 11/6 351/352 [16/13 9/4]
182/99 1054.126 11/6, 24/13 364/363, 1183/1188 [9/7 26/11]
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