Xenharmonic Wiki

Large comma: Difference between revisions

← Older edit
VisualWikitext
Wording and formatting
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,232 edits
 
(5 intermediate revisions by 3 users not shown)
Line 3: Line 3:
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 some, 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 17: Line 22:
! Cents
! Cents
|-
|-
| 26-comma
| [[26-comma]]
| Wa-26
| Wa-26
| L<sup>4</sup>w-2
| w-26
| [[26-comma|2541865828329 / 2199023255552]]
| 2541865828329 / 2199023255552
| {{monzo| -41 26 }}
| {{monzo| -41 26 }}
| 250.83
| 250.83
|-
|-
| Pythagorean whole tone
| 27-comma
| Wa-27
| w-27
| 8796093022208 / 7625597484987
| {{monzo| 43 -27 }}
| 247.21
|-
| [[9/8|Pythagorean whole tone]]
| Wa 2nd
| Wa 2nd
| w2
| w2
| [[9/8|9 / 8]]
| 9 / 8
| {{monzo| -3 2 }}
| {{monzo| -3 2 }}
| 203.91
| 203.91
Line 43: Line 55:
|  
|  
| {{monzo| 100 -63 }}
| {{monzo| 100 -63 }}
| 176.835
| 176.835
|-
|-
| [[31st-octave temperaments|31-comma]]
| [[31st-octave temperaments|31-comma]]
Line 66: Line 78:
| 137.145
| 137.145
|-
|-
| Apotome
| [[2187/2048|Apotome]]
| Lawa
| Lawa
| Lw1
| Lw1
| [[2187/2048|2187 / 2048]]
| 2187 / 2048
| {{monzo| -11 7 }}
| {{monzo| -11 7 }}
| 113.685
| 113.685
Line 90: Line 102:
! Cents
! Cents
|-
|-
| Shallowtone comma
| [[Shallowtone comma]]
| Lalayobi
| Lalayobi
| LLy1
| LLy1
| [[Shallowtone comma|295245 / 262144]]
| 295245 / 262144
| {{monzo| -18 10 1 }}
| {{monzo| -18 10 1 }}
| 205.864
| 205.864
Line 99: 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
|-
|-
| Minor whole tone, yo 2nd
| [[10/9|Minor whole tone]], yo 2nd
| Yo
| Yo
| y2
| y2
| [[10/9|10 / 9]]
| 10 / 9
| {{monzo| 1 -2 1 }}
| {{monzo| 1 -2 1 }}
| 182.404
| 182.404
Line 127: 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 }}
| 181.019
| 181.019
|-
|-
| Nadir comma
| [[Nadir comma]]
| Lalatrigu
| Lalatrigu
| LLg<sup>3</sup>1
| LL3g1
| [[Nadir comma|1162261467 / 1048576000]]
| 1162261467 / 1048576000
| {{monzo| -23 19 -3 }}
| {{monzo| -23 19 -3 }}
| 178.204
| 178.204
Line 141: Line 146:
|  
|  
| Legu
| Legu
| g<sup>11</sup>4
| 11g4
| [[53747712 / 48828125]]
| [[53747712 / 48828125]]
| {{monzo| 13 8 -11 }}
| {{monzo| 13 8 -11 }}
Line 148: Line 153:
| Enipucrop
| Enipucrop
| Latriyobi
| Latriyobi
| Ly<sup>3</sup>1
| L3y1
| 1125 / 1024
| 1125 / 1024
| {{monzo| -10 2 3 }}
| {{monzo| -10 2 3 }}
| 162.851
| 162.851
|-
|-
| Supersharp
| [[800/729|Supersharp]]
| Sayoyo
| Sayoyo
| syy2
| syy2
| [[800/729|800 / 729]]
| 800 / 729
| {{monzo| 5 -6 2 }}
| {{monzo| 5 -6 2 }}
| 160.897
| 160.897
|-
|-
| Nether comma
| [[Nether comma]]
| Lala-gugu
| Lala-gugu
| LLgg1
| LLgg1
| [[Nether comma|14348907 / 13107200]]
| 14348907 / 13107200
| {{monzo| -19 15 -2 }}
| {{monzo| -19 15 -2 }}
| 156.698
| 156.698
Line 169: 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 176: 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 }}
| 154.744
| 154.744
|-
|-
| Smate, symbolic
| [[2048/1875|Smate]], symbolic comma
| Saquadgu
| Saquadgu
| sg<sup>4</sup>3
| s4g3
| [[2048/1875|2048 / 1875]]
| 2048 / 1875
| {{monzo| 11 -1 -4 }}
| {{monzo| 11 -1 -4 }}
| 152.790
| 152.790
Line 190: 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 197: 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 }}
| 136.33
| 136.33
|-
|-
| Deeptone comma, Tragicomma  
| [[177147/163840|Deeptone comma]], Tragicomma  
| Lagu
| Lagu
| Lg1
| Lg1
| [[177147/163840|177147 / 163849]]
| 177147 / 163840
| {{monzo| -15 11 -1 }}
| {{monzo| -15 11 -1 }}
| 135.191
| 135.191
|-
|-
| Large limma
| [[27/25|Large limma]]
| Gugu
| Gugu
| gg2
| gg2
| [[27/25|27 / 25]]
| 27 / 25
| {{monzo| 0 3 -2 }}
| {{monzo| 0 3 -2 }}
| 133.238
| 133.238
Line 218: 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 225: 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 232: 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 244: Line 249:
| 120.622
| 120.622
|-
|-
| Sixix comma
| [[3125/2916|Sixix comma]]
| Quinyo
| Quinyo
| y<sup>5</sup>1
| 5y1
| [[3125/2916|3125 / 2916]]
| 3125 / 2916
| {{monzo| -2 -6 5 }}
| {{monzo| -2 -6 5 }}
| 119.839
| 119.839
Line 253: 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 260: 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 }}
| 117.885
| 117.885
|-
|-
| Just diatonic semitone
| [[16/15|Just diatonic semitone]]
| Gubi
| Gubi
| g2
| g2
| [[16/15|16 / 15]]
| 16 / 15
| {{monzo| 4 -1 -1 }}
| {{monzo| 4 -1 -1 }}
| 111.731
| 111.731
Line 288: Line 293:
| Wronecki
| Wronecki
| Latribigu
| Latribigu
| Lg<sup>6</sup>2
| L6g2
| 531441 / 500000
| 531441 / 500000
| {{monzo| -5 12 -6 }}
| {{monzo| -5 12 -6 }}
| 105.578
| 105.578
|-
|-
| Wesley
| [[Wesley comma]]
| Lasepyobi
| Lasepyobi
| Ly<sup>7</sup>-2
| L7y-2
| [[Wesley comma|78125 / 73728]]
| 78125 / 73728
| {{monzo| -13 -2 7 }}
| {{monzo| -13 -2 7 }}
| 100.286
| 100.286
Line 310: Line 315:
! Cents
! Cents
|-
|-
| Antidilemma
| [[Antidilemma]]
| Sasa-theruquad
| Sasa-theruquad
| ssr<sup>13</sup>-2
| ss13r-2
| [[antidilemma|137438953472 / 96889010407]]
| 137438953472 / 96889010407
| {{monzo| 37 0 0 -13 }}
| {{monzo| 37 0 0 -13 }}
| 605.263
| 605.263
|-
|-
| Dilemma
| [[Dilemma]]
| Lala-thezoquad
| Lala-thezoquad
| LLz<sup>13</sup>9
| LL13z9
| [[dilemma|96889010407 / 68719476736]]
| 96889010407 / 68719476736
| {{monzo| -36 0 0 13 }}
| {{monzo| -36 0 0 13 }}
| 594.737
| 594.737
|-
|-
| Septimal major second, supermajor second,  
| [[8/7|Septimal major second]], supermajor second,  
augmented whole-tone, ru 2nd
augmented whole-tone, ru 2nd
| Rubi
| Rubi
| r2
| r2
| [[8/7|8 / 7]]
| 8 / 7
| {{monzo| 3 0 0 -1 }}
| {{monzo| 3 0 0 -1 }}
| 231.174
| 231.174
Line 334: 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 341: 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 348: 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 355: 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 362: 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 369: 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 376: 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 }}
| 156.421
| 156.421
|-
|-
| Septimal neutral second, 35th harmonic
| [[35/32|Septimal neutral second]], 35th harmonic
| Zoyo
| Zoyo
| zy2
| zy2
| [[35/32|35 / 32]]
| 35 / 32
| {{monzo| -5 0 1 1 }}
| {{monzo| -5 0 1 1 }}
| 155.140
| 155.140
Line 390: 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 }}
| 151.976
| 151.976
|-
|-
| Swetismic neutral second
| [[49/45|Swetismic neutral second]]
| Zozogu
| Zozogu
| zzg3
| zzg3
| [[49/45|49 / 45]]
| 49 / 45
| {{monzo| 0 -2 -1 2 }}
| {{monzo| 0 -2 -1 2 }}
| 147.428
| 147.428
|-
|-
| 160/147
| [[160/147]]
| Ruruyobi
| Ruruyobi
|rry1
| rry1
| [[160/147|160 / 147]]
| 160 / 147
| {{monzo| 5 -1 1 -2 }}
| {{monzo| 5 -1 1 -2 }}
| 146.707
| 146.707
Line 411: 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 }}
| 142.915
| 142.915
|-
|-
| Septimal subtone
| [[243/224|Septimal subtone]]
| Larubi
| Larubi
| Lr1
| Lr1
| [[243/224|243 / 224]]
| 243 / 224
| {{monzo| -5 5 0 -1 }}
| {{monzo| -5 5 0 -1 }}
| 140.949
| 140.949
Line 425: 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 432: 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 439: 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 446: 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 }}
| 120.152
| 120.152
|-
|-
| Major diatonic semitone
| [[15/14|Major diatonic semitone]]
| Ruyo
| Ruyo
| ry1
| ry1
| [[15/14|15 / 14]]
| 15 / 14
| {{monzo| -1 1 1 -1 }}
| {{monzo| -1 1 1 -1 }}
| 119.443
| 119.443
Line 467: 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 474: 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 481: 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 }}
| 110.326
| 110.326
|-
|-
| Triru comma
| [[729/686|Triru comma]]
| Triru
| Triru
| r<sup>3</sup>-2
| 3r-2
| [[729/686|729 / 686]]
| 729 / 686
| {{monzo| -1 6 0 -3 }}
| {{monzo| -1 6 0 -3 }}
| 105.252
| 105.252
Line 505: 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 519: 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 550: 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 571: 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 578: 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 619: 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 633: 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 640: 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 654: 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 }}
| 168.190
| 168.190
|-
|-
| Dog comma
| [[81/76|Dog comma]]
| Inu
| Inu
| 19u1
| 19u1
| [[81/76|81 / 76]]
| 81 / 76
| {{monzo| -2 4 0 0 0 0 0 -1 }}
| {{monzo| -2 4 0 0 0 0 0 -1 }}
| 110.307
| 110.307
Line 714: Line 719:
| 170.423
| 170.423
|-
|-
| 47/44
| [[47/44]]
|  
| Fosolu
|  
| 47o1u2
| [[47/44|47 / 44]]
| 47 / 44
| 2.11.47 {{monzo| -2 -1 1 }}
| 2.11.47 {{monzo| -2 -1 1 }}
| 114.189
| 114.189
Retrieved from "https://en.xen.wiki/w/Large_comma"