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Large comma: Difference between revisions

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For commas under 100 cents, see [[Medium comma]] for commas in between 30 and 100 cents or [[Small comma]] for commas under 30 cents. For commas under 3.5 cents, see [[Unnoticeable comma]].
For commas under 100 cents, see [[Medium comma]] for commas in between 30 and 100 cents or [[Small comma]] for commas under 30 cents. For commas under 3.5 cents, see [[Unnoticeable comma]].


Except for the 3-limit commas, the [[Color notation|color name]] refers to both the comma and the temperament created when it is tempered out.  
Except for the 3-limit commas, the [[Color notation|color name]] refers to both the comma and the temperament created when it is [[tempered out]].


The commas might be numerous, but there is no need to memorise all the names. For pretty much all use cases, it is perfectly acceptable – preferred by many, even – to just refer to a comma by the monzo or ratio, whichever is simpler.  
The commas might be numerous, but there is no need to memorise all the names. For pretty much all use cases, it is perfectly acceptable – preferred, even – to just refer to a comma by the monzo or ratio, whichever is simpler.
 
== Disputed status ==
To varying degrees, the status of each of the commas on this page as "a comma" is disputed. Due to their large size in [[cents]], many of these commas lead to high-[[damage]] temperaments when tempered out. Which calls into question whether they can actually be used as commas.
 
Those which have a highly complex monzo and ratio tend to distribute their error more thinly across a wide number of [[JI]] intervals, making them more 'comma-like' than the others on this page. Some still dispute this due to their perhaps limited ability to make [[comma pump]]s. However they are more widely accepted than the ones on this page with simpler monzos and ratios.


== List of commas, by prime limit ==
== List of commas, by prime limit ==
Line 19: Line 24:
| [[26-comma]]
| [[26-comma]]
| Wa-26
| Wa-26
| L<sup>4</sup>w-2
| w-26
| 2541865828329 / 2199023255552
| 2541865828329 / 2199023255552
| {{monzo| -41 26 }}
| {{monzo| -41 26 }}
Line 26: Line 31:
| 27-comma
| 27-comma
| Wa-27
| Wa-27
| s<sup>4</sup>w5
| w-27
| 8796093022208 / 7625597484987
| 8796093022208 / 7625597484987
| {{monzo| 43 -27 }}
| {{monzo| 43 -27 }}
Line 40: Line 45:
| 43-comma
| 43-comma
| Wa-43
| Wa-43
| L<sup>6</sup>w-4
| w-43
|  
|  
| {{monzo| -68 43 }}
| {{monzo| -68 43 }}
Line 47: Line 52:
| 63-comma
| 63-comma
| Wa-63
| Wa-63
| s<sup>9</sup>w8
| w-63
|  
|  
| {{monzo| 100 -63 }}
| {{monzo| 100 -63 }}
Line 54: Line 59:
| [[31st-octave temperaments|31-comma]]
| [[31st-octave temperaments|31-comma]]
| Wa-31
| Wa-31
| L<sup>4</sup>w-3
| w-31
| 617673396283947 / <br>562949953421312
| 617673396283947 / <br>562949953421312
| {{monzo| -49 31 }}
| {{monzo| -49 31 }}
Line 61: Line 66:
| 22-comma
| 22-comma
| Wa-22
| Wa-22
| s<sup>3</sup>w4
| w-22
| 34359738368 / <br>31381059609
| 34359738368 / <br>31381059609
| {{monzo| 35 -22 }}
| {{monzo| 35 -22 }}
Line 68: Line 73:
| 19-comma
| 19-comma
| Wa-19
| Wa-19
| L<sup>3</sup>w-2
| w-19
| 1162261467 / 1073741824
| 1162261467 / 1073741824
| {{monzo| -30 19 }}
| {{monzo| -30 19 }}
Line 82: Line 87:
| 46-comma
| 46-comma
| Wa-46
| Wa-46
| s<sup>7</sup>w6
| w-46
|  
|  
| {{monzo| 73 -46 }}
| {{monzo| 73 -46 }}
Line 106: Line 111:
| Delorean
| Delorean
| Tribigu
| Tribigu
| g<sup>6</sup>3
| 6g3
| 17496 / 15625
| 17496 / 15625
| {{monzo| 3 7 -6 }}
| {{monzo| 3 7 -6 }}
| 195.803
| 195.803
|-
| <strike>meantone Integer cents comma</strike>{{clarify}}
|
|
|
| {{monzo| -1393 0 600 }}
| 188.228
|-
|-
| 31-3/5-comma
| 31-3/5-comma
| Thiwegu
| Thiwegu
| g<sup>31</sup>7
| 31g7
|  
|
| {{monzo| 23 31 -31 }}
| {{monzo| 23 31 -31 }}
| 184.88
| 184.88
Line 134: Line 132:
| 5-cycle major second, hexadecathird comma
| 5-cycle major second, hexadecathird comma
| Lala-quadquadyo
| Lala-quadquadyo
| LLy<sup>16</sup>-4
| LL16y-4
| 152587890625 / <br>137438953472
| 152587890625 / <br>137438953472
| {{monzo| -37 0 16 }}
| {{monzo| -37 0 16 }}
Line 141: Line 139:
| [[Nadir comma]]
| [[Nadir comma]]
| Lalatrigu
| Lalatrigu
| LLg<sup>3</sup>1
| LL3g1
| 1162261467 / 1048576000
| 1162261467 / 1048576000
| {{monzo| -23 19 -3 }}
| {{monzo| -23 19 -3 }}
Line 148: Line 146:
|  
|  
| Legu
| Legu
| g<sup>11</sup>4
| 11g4
| [[53747712 / 48828125]]
| [[53747712 / 48828125]]
| {{monzo| 13 8 -11 }}
| {{monzo| 13 8 -11 }}
Line 155: Line 153:
| Enipucrop
| Enipucrop
| Latriyobi
| Latriyobi
| Ly<sup>3</sup>1
| L3y1
| 1125 / 1024
| 1125 / 1024
| {{monzo| -10 2 3 }}
| {{monzo| -10 2 3 }}
Line 176: Line 174:
| [[Rarity comma]]
| [[Rarity comma]]
| Quadla-theyo
| Quadla-theyo
| L<sup>4</sup>y<sup>13</sup>-5
| 4L13y-5
|  
|  
| {{monzo| -57 17 13 }}
| {{monzo| -57 17 13 }}
Line 183: Line 181:
| Gorgo, laconic
| Gorgo, laconic
| Latrigubi
| Latrigubi
| Lg<sup>3</sup>2
| L3g2
| 2187 / 2000
| 2187 / 2000
| {{monzo| -4 7 -3 }}
| {{monzo| -4 7 -3 }}
Line 190: Line 188:
| [[2048/1875|Smate]], symbolic comma
| [[2048/1875|Smate]], symbolic comma
| Saquadgu
| Saquadgu
| sg<sup>4</sup>3
| s4g3
| 2048 / 1875
| 2048 / 1875
| {{monzo| 11 -1 -4 }}
| {{monzo| 11 -1 -4 }}
Line 197: Line 195:
| Acute limma
| Acute limma
| Trila-neyobi
| Trila-neyobi
| L<sup>3</sup>y<sup>19</sup>-5
| 3L19y-5
| 19073486328125 / <br>17592186044416
| 19073486328125 / <br>17592186044416
| {{monzo| -44 0 19 }}
| {{monzo| -44 0 19 }}
Line 204: Line 202:
| 31-15-comma
| 31-15-comma
| Tritrila-thiweyo
| Tritrila-thiweyo
| L<sup>9</sup>y<sup>31</sup>-11
| 9L31y-11
|  
|  
| {{monzo| -121 31 31 }}
| {{monzo| -121 31 31 }}
Line 225: Line 223:
| 11-3/5-comma
| 11-3/5-comma
| Leyo
| Leyo
| y<sup>11</sup>-2
| 11y-2
| 48828125 / 45349632
| 48828125 / 45349632
| {{monzo| -8 -11 11 }}
| {{monzo| -8 -11 11 }}
Line 232: Line 230:
| 27-3/5-comma
| 27-3/5-comma
| Tritritrigu
| Tritritrigu
| g<sup>27</sup>6
| 27g6
|  
|  
| {{monzo| 20 27 -27 }}
| {{monzo| 20 27 -27 }}
Line 239: Line 237:
| Lemba
| Lemba
| Latribiyo
| Latribiyo
| Ly<sup>6</sup>-2
| L6y-2
| 140625 / 131072
| 140625 / 131072
| {{monzo| -17 2 6 }}
| {{monzo| -17 2 6 }}
Line 253: Line 251:
| [[3125/2916|Sixix comma]]
| [[3125/2916|Sixix comma]]
| Quinyo
| Quinyo
| y<sup>5</sup>1
| 5y1
| 3125 / 2916
| 3125 / 2916
| {{monzo| -2 -6 5 }}
| {{monzo| -2 -6 5 }}
Line 260: Line 258:
| Diesma
| Diesma
| Lathegu
| Lathegu
| Lg<sup>13</sup>3
| L13g3
| 10460353203 / <br>9765625000
| 10460353203 / <br>9765625000
| {{monzo| -3 21 -13 }}
| {{monzo| -3 21 -13 }}
Line 267: Line 265:
| Comic comma
| Comic comma
| Saquadyobi
| Saquadyobi
| sy<sup>4</sup>2
| s4y2
| 5120000 / 4782969
| 5120000 / 4782969
| {{monzo| 13 -14 4 }}
| {{monzo| 13 -14 4 }}
Line 295: Line 293:
| Wronecki
| Wronecki
| Latribigu
| Latribigu
| Lg<sup>6</sup>2
| L6g2
| 531441 / 500000
| 531441 / 500000
| {{monzo| -5 12 -6 }}
| {{monzo| -5 12 -6 }}
Line 302: Line 300:
| [[Wesley comma]]
| [[Wesley comma]]
| Lasepyobi
| Lasepyobi
| Ly<sup>7</sup>-2
| L7y-2
| 78125 / 73728
| 78125 / 73728
| {{monzo| -13 -2 7 }}
| {{monzo| -13 -2 7 }}
Line 319: Line 317:
| [[Antidilemma]]
| [[Antidilemma]]
| Sasa-theruquad
| Sasa-theruquad
| ssr<sup>13</sup>-2
| ss13r-2
| 137438953472 / 96889010407
| 137438953472 / 96889010407
| {{monzo| 37 0 0 -13 }}
| {{monzo| 37 0 0 -13 }}
Line 326: Line 324:
| [[Dilemma]]
| [[Dilemma]]
| Lala-thezoquad
| Lala-thezoquad
| LLz<sup>13</sup>9
| LL13z9
| 96889010407 / 68719476736
| 96889010407 / 68719476736
| {{monzo| -36 0 0 13 }}
| {{monzo| -36 0 0 13 }}
Line 341: Line 339:
| Hexatone comma, 6-7-comma
| Hexatone comma, 6-7-comma
| Satribiru
| Satribiru
| sr<sup>6</sup>-2
| s6r-2
| 131072 / 117649
| 131072 / 117649
| {{monzo| 17 0 0 -6 }}
| {{monzo| 17 0 0 -6 }}
Line 348: Line 346:
| 45-7/5-comma
| 45-7/5-comma
| Quintritriruyo
| Quintritriruyo
| r<sup>45</sup>y<sup>45</sup>-27
| 45ry-27
|
|
| {{monzo| 22 0 45 -45 }}
| {{monzo| 22 0 45 -45 }}
Line 355: Line 353:
| 63-35-comma
| 63-35-comma
| Tritribila-septritrizoyo
| Tritribila-septritrizoyo
| L<sup>18</sup>z<sup>63</sup>y<sup>63</sup>8
| 18L63zy8
|
|
| {{monzo| -323 0 63 63 }}
| {{monzo| -323 0 63 63 }}
Line 362: Line 360:
| 8-21-comma
| 8-21-comma
| Lala-quadbizo
| Lala-quadbizo
| LLz<sup>8</sup>4
| LL8z4
| 37822859361 / <br>34359738368
| 37822859361 / <br>34359738368
| {{monzo| -35 8 0 8 }}
| {{monzo| -35 8 0 8 }}
Line 369: Line 367:
| 46-7-comma
| 46-7-comma
| Sepla-twethebizobi
| Sepla-twethebizobi
| L<sup>7</sup>z<sup>46</sup>18
| 7L46z18
|
|
| {{monzo| -129 0 0 46 }}
| {{monzo| -129 0 0 46 }}
Line 376: Line 374:
| 25-7/5-comma
| 25-7/5-comma
| Quinquinzogu
| Quinquinzogu
| z<sup>25</sup>g<sup>25</sup>17
| 25zg17
|
|
| {{monzo| -12 0 -25 25 }}
| {{monzo| -12 0 -25 25 }}
Line 383: Line 381:
| 43-21-comma
| 43-21-comma
| Quadtrisa-fotherubi
| Quadtrisa-fotherubi
| s<sup>12</sup>r<sup>43</sup>-11
| 12s43r-11
|
|
| {{monzo| 189 -43 0 -43 }}
| {{monzo| 189 -43 0 -43 }}
Line 397: Line 395:
| 43-7/5-comma
| 43-7/5-comma
| Fotheruyo
| Fotheruyo
| r<sup>43</sup>y<sup>43</sup>-26
| 43ry-26
|
|
| {{monzo| 21 0 43 -43 }}
| {{monzo| 21 0 43 -43 }}
Line 418: Line 416:
| Hendecatone comma, 11-7-comma
| Hendecatone comma, 11-7-comma
| Sasa-leru
| Sasa-leru
| ssr<sup>11</sup>-4
| ss11r-4
| 2147483648 / 1977326743
| 2147483648 / 1977326743
| {{monzo| 31 0 0 -11 }}
| {{monzo| 31 0 0 -11 }}
Line 432: Line 430:
| 55-35-comma
| 55-35-comma
| Quadquadla-lequinzoyobi
| Quadquadla-lequinzoyobi
| L<sup>16</sup>z<sup>55</sup>y<sup>55</sup>7
| 16L55zy7
|
|
| {{monzo| -282 0 55 55 }}
| {{monzo| -282 0 55 55 }}
Line 439: Line 437:
| 27-7/5-comma
| 27-7/5-comma
| Tritritrizogu
| Tritritrizogu
| z<sup>27</sup>g<sup>27</sup>18
| 27zg18
|
|
| {{monzo| -13 0 -27 27 }}
| {{monzo| -13 0 -27 27 }}
Line 446: Line 444:
| 41-7-comma
| 41-7-comma
| Tribila-fowezo
| Tribila-fowezo
| L<sup>6</sup>z<sup>41</sup>16
| 6L41z16
|
|
| {{monzo| -115 0 0 41 }}
| {{monzo| -115 0 0 41 }}
Line 453: Line 451:
| 13-21-comma
| 13-21-comma
| Quadla-thezobi
| Quadla-thezobi
| L<sup>4</sup>z<sup>13</sup>5
| 4L13z5
|
|
| {{monzo| -57 13 0 13 }}
| {{monzo| -57 13 0 13 }}
Line 474: Line 472:
| 41-7/5-comma
| 41-7/5-comma
| Foweruyo
| Foweruyo
| r<sup>41</sup>y<sup>41</sup>-25
| 41ry-25
|
|
| {{monzo| 20 0 41 -41 }}
| {{monzo| 20 0 41 -41 }}
Line 481: Line 479:
| 7-35-comma
| 7-35-comma
| Sasa-seprugu
| Sasa-seprugu
| ssr<sup>7</sup>g<sup>7</sup>1
| ss7rg1
| 68719476736 / <br>64339296875
| 68719476736 / <br>64339296875
| {{monzo| 36 0 -7 -7 }}
| {{monzo| 36 0 -7 -7 }}
Line 488: Line 486:
| 38-21-comma
| 38-21-comma
| Lesa-nebiru
| Lesa-nebiru
| s<sup>11</sup>r<sup>38</sup>-10
| 11s38r-10
|
|
| {{monzo| 167 -38 0 -38 }}
| {{monzo| 167 -38 0 -38 }}
Line 495: Line 493:
| [[729/686|Triru comma]]
| [[729/686|Triru comma]]
| Triru
| Triru
| r<sup>3</sup>-2
| 3r-2
| 729 / 686
| 729 / 686
| {{monzo| -1 6 0 -3 }}
| {{monzo| -1 6 0 -3 }}
Line 512: Line 510:
| 11-cycle major second prote, 33-11-comma
| 11-cycle major second prote, 33-11-comma
| Quinla-letrilobi
| Quinla-letrilobi
| L<sup>5</sup>1o<sup>33</sup>-7
| 5L33(1o)-7
|
|
| {{monzo| -114 0 0 0 33 }}
| {{monzo| -114 0 0 0 33 }}
Line 526: Line 524:
| 11-enipucrop, 9-11-comma
| 11-enipucrop, 9-11-comma
| Latritrilo
| Latritrilo
| L1o<sup>9</sup>-2
| L9(1o)-2
| 2357947691 / 2147483648
| 2357947691 / 2147483648
| {{monzo| -31 0 0 0 9 }}
| {{monzo| -31 0 0 0 9 }}
Line 557: Line 555:
| 13-cycle neutral second
| 13-cycle neutral second
| Quadbila-fithethobi
| Quadbila-fithethobi
| L<sup>8</sup>3o<sup>53</sup>7
| 8L53(3o)7
|
|
| {{monzo| -196 0 0 0 0 53 }}
| {{monzo| -196 0 0 0 0 53 }}
Line 578: Line 576:
| Heptasixth comma, 13-cycle secor
| Heptasixth comma, 13-cycle secor
| Sasepthu
| Sasepthu
| s3u<sup>7</sup>1
| s7(3u)1
| 67108864 / 62748517
| 67108864 / 62748517
| {{monzo| 26 0 0 0 0 -7 }}
| {{monzo| 26 0 0 0 0 -7 }}
Line 585: Line 583:
| Heptadecasixth comma, neutral thirteenth comma
| Heptadecasixth comma, neutral thirteenth comma
| Sasa-sethubi
| Sasa-sethubi
| ss3u<sup>7</sup>-2
| ss17(3u)-2
|
|
| {{monzo| 63 0 0 0 0 -17 }}
| {{monzo| 63 0 0 0 0 -17 }}
Line 626: Line 624:
| 19-cycle meantone prima
| 19-cycle meantone prima
| Tribila-foweno
| Tribila-foweno
| L<sup>6</sup>19o<sup>41</sup>13
| 6L41(19o)13
|
|
| {{monzo| -174 0 0 0 0 0 0 41 }}
| {{monzo| -174 0 0 0 0 0 0 41 }}
Line 640: Line 638:
| 19-cycle meantone secunda
| 19-cycle meantone secunda
| Tribila-quintritrino
| Tribila-quintritrino
| L<sup>6</sup>19o<sup>45</sup>14
| 6L45(19o)14
|
|
| {{monzo| -191 0 0 0 0 0 0 45 }}
| {{monzo| -191 0 0 0 0 0 0 45 }}
Line 647: Line 645:
| 19-cycle minor tone
| 19-cycle minor tone
| Sepla-sepsepno
| Sepla-sepsepno
| L<sup>7</sup>19o<sup>49</sup>15
| 7L49(19o)15
|
|
| {{monzo| -208 0 0 0 0 0 0 49 }}
| {{monzo| -208 0 0 0 0 0 0 49 }}
Line 661: Line 659:
| 19-cycle submajor second
| 19-cycle submajor second
| Quadbila-fithenobi
| Quadbila-fithenobi
| L<sup>8</sup>19o<sup>53</sup>16
| 8L53(19o)16
|
|
| {{monzo| -225 0 0 0 0 0 0 53 }}
| {{monzo| -225 0 0 0 0 0 0 53 }}
Line 722: Line 720:
|-
|-
| [[47/44]]
| [[47/44]]
|  
| Fosolu
|  
| 47o1u2
| 47 / 44
| 47 / 44
| 2.11.47 {{monzo| -2 -1 1 }}
| 2.11.47 {{monzo| -2 -1 1 }}
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