Xenharmonic Wiki

Large comma: Difference between revisions

← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,215 edits
m →7-limit commas: add septimal subtone
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,215 edits
 
(35 intermediate revisions by 6 users not shown)
Line 1: Line 1:
A '''Large comma''' is a [[comma]] whose size is approximately 100 cents and larger. As intervals, these commas are steps or even skips.
A '''large comma''' is a [[comma]] whose size is approximately 100 cents and larger. As intervals, these commas are steps or even skips.


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, 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 15: Line 22:
! Cents
! Cents
|-
|-
| Pythagorean whole tone
| [[26-comma]]
| wa 2nd
| Wa-26
| w-26
| 2541865828329 / 2199023255552
| {{monzo| -41 26 }}
| 250.83
|-
| 27-comma
| Wa-27
| w-27
| 8796093022208 / 7625597484987
| {{monzo| 43 -27 }}
| 247.21
|-
| [[9/8|Pythagorean whole tone]]
| Wa 2nd
| w2
| w2
| [[9/8|9 / 8]]
| 9 / 8
| {{monzo| -3 2 }}
| {{monzo| -3 2 }}
| 203.91
| 203.91
Line 34: Line 55:
|  
|  
| {{monzo| 100 -63 }}
| {{monzo| 100 -63 }}
| 176.835
| 176.835
|-
|-
| [[31st-octave temperaments|31-comma]]
| [[31st-octave temperaments|31-comma]]
Line 57: 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 80: Line 101:
! Monzo
! Monzo
! Cents
! Cents
|-
| [[Shallowtone comma]]
| Lalayobi
| LLy1
| 295245 / 262144
| {{monzo| -18 10 1 }}
| 205.864
|-
|-
| 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 111: 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]]
| Lalatrigu
| LL3g1
| 1162261467 / 1048576000
| {{monzo| -23 19 -3 }}
| 178.204
|-
|
| Legu
| 11g4
| [[53747712 / 48828125]]
| {{monzo| 13 8 -11 }}
| 166.189
|-
|-
| 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
Line 129: Line 164:
| {{monzo| 5 -6 2 }}
| {{monzo| 5 -6 2 }}
| 160.897
| 160.897
|-
| [[Nether comma]]
| Lala-gugu
| LLgg1
| 14348907 / 13107200
| {{monzo| -19 15 -2 }}
| 156.698
|-
|-
| [[Rarity comma]]
| [[Rarity comma]]
|  
| Quadla-theyo
|  
| 4L13y-5
|  
|  
| {{monzo| -57 17 13 }}
| {{monzo| -57 17 13 }}
Line 139: 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 153: 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 160: 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
|  
| 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 181: 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 188: 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 195: 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 207: Line 249:
| 120.622
| 120.622
|-
|-
| 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 216: 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 223: 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 251: 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
| 78125 / 73728
| 78125 / 73728
| {{monzo| -13 -2 7 }}
| {{monzo| -13 -2 7 }}
Line 273: Line 315:
! Cents
! Cents
|-
|-
| Septimal major second, supermajor second, augmented whole-tone, ru 2nd
| [[Antidilemma]]
| Sasa-theruquad
| ss13r-2
| 137438953472 / 96889010407
| {{monzo| 37 0 0 -13 }}
| 605.263
|-
| [[Dilemma]]
| Lala-thezoquad
| LL13z9
| 96889010407 / 68719476736
| {{monzo| -36 0 0 13 }}
| 594.737
|-
| [[8/7|Septimal major second]], supermajor second,  
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 282: 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 289: 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 296: 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 303: 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 310: 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 317: 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 324: 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 338: 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
|-
|-
| Neutral sedgecond
| [[160/147]]
|  
| Ruruyobi
|
| rry1
| [[160/147|160 / 147]]
| 160 / 147
| {{monzo| 5 -1 1 -2 }}
| {{monzo| 5 -1 1 -2 }}
| 146.707
| 146.707
Line 359: 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
|  
| Lr1
| [[243/224|243 / 224]]
| 243 / 224
| {{monzo| -5 5 0 -1 }}
| {{monzo| -5 5 0 -1 }}
| 140.949
| 140.949
Line 373: 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 380: 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 387: 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 394: 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 415: 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 422: 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 429: 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
|-
| [[729/686|Triru comma]]
| Triru
| 3r-2
| 729 / 686
| {{monzo| -1 6 0 -3 }}
| 105.252
|}
|}


Line 446: 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 460: 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 491: 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 512: 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 519: 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 560: 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 574: 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 581: 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 595: 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 647: Line 711:
! Monzo
! Monzo
! Cents
! Cents
|-
|-
|-
| 29th subharmonic
| 29th subharmonic
Line 655: Line 718:
| 2.29 {{monzo| 5 -1 }}
| 2.29 {{monzo| 5 -1 }}
| 170.423
| 170.423
|-
| [[47/44]]
| Fosolu
| 47o1u2
| 47 / 44
| 2.11.47 {{monzo| -2 -1 1 }}
| 114.189
|}
|}


Retrieved from "https://en.xen.wiki/w/Large_comma"