Large comma: Difference between revisions

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Line 17: Line 17:
! Cents
! Cents
|-
|-
| 26-comma
| [[26-comma]]
| Wa-26
| Wa-26
| L<sup>4</sup>w-2
| L<sup>4</sup>w-2
| [[26-comma|2541865828329 / 2199023255552]]
| 2541865828329 / 2199023255552
| {{monzo| -41 26 }}
| {{monzo| -41 26 }}
| 250.83
| 250.83
|-
|-
| Pythagorean whole tone
| 27-comma
| Wa-27
| s<sup>4</sup>w5
| 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 33: Line 40:
| 43-comma
| 43-comma
| Wa-43
| Wa-43
| w-43
| L<sup>6</sup>w-4
|  
|  
| {{monzo| -68 43 }}
| {{monzo| -68 43 }}
Line 40: Line 47:
| 63-comma
| 63-comma
| Wa-63
| Wa-63
| w-63
| s<sup>9</sup>w8
|  
|  
| {{monzo| 100 -63 }}
| {{monzo| 100 -63 }}
| 176.835
| 176.835
|-
|-
| [[31st-octave temperaments|31-comma]]
| [[31st-octave temperaments|31-comma]]
| Wa-31
| Wa-31
| w-31
| L<sup>4</sup>w-3
| 617673396283947 / <br>562949953421312
| 617673396283947 / <br>562949953421312
| {{monzo| -49 31 }}
| {{monzo| -49 31 }}
Line 54: Line 61:
| 22-comma
| 22-comma
| Wa-22
| Wa-22
| w-22
| s<sup>3</sup>w4
| 34359738368 / <br>31381059609
| 34359738368 / <br>31381059609
| {{monzo| 35 -22 }}
| {{monzo| 35 -22 }}
Line 61: Line 68:
| 19-comma
| 19-comma
| Wa-19
| Wa-19
| w-19
| L<sup>3</sup>w-2
| 1162261467 / 1073741824
| 1162261467 / 1073741824
| {{monzo| -30 19 }}
| {{monzo| -30 19 }}
| 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 75: Line 82:
| 46-comma
| 46-comma
| Wa-46
| Wa-46
| w-46
| s<sup>7</sup>w6
|  
|  
| {{monzo| 73 -46 }}
| {{monzo| 73 -46 }}
Line 90: Line 97:
! 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 118: Line 125:
| 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 132: Line 139:
| 181.019
| 181.019
|-
|-
| Nadir comma
| [[Nadir comma]]
| Lalatrigu
| Lalatrigu
| LLg<sup>3</sup>1
| LLg<sup>3</sup>1
| [[Nadir comma|1162261467 / 1048576000]]
| 1162261467 / 1048576000
| {{monzo| -23 19 -3 }}
| {{monzo| -23 19 -3 }}
| 178.204
| 178.204
Line 153: Line 160:
| 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 181: Line 188:
| 154.744
| 154.744
|-
|-
| Smate, symbolic
| [[2048/1875|Smate]], symbolic comma
| Saquadgu
| Saquadgu
| sg<sup>4</sup>3
| sg<sup>4</sup>3
| [[2048/1875|2048 / 1875]]
| 2048 / 1875
| {{monzo| 11 -1 -4 }}
| {{monzo| 11 -1 -4 }}
| 152.790
| 152.790
Line 202: Line 209:
| 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 244: Line 251:
| 120.622
| 120.622
|-
|-
| Sixix comma
| [[3125/2916|Sixix comma]]
| Quinyo
| Quinyo
| y<sup>5</sup>1
| y<sup>5</sup>1
| [[3125/2916|3125 / 2916]]
| 3125 / 2916
| {{monzo| -2 -6 5 }}
| {{monzo| -2 -6 5 }}
| 119.839
| 119.839
Line 265: Line 272:
| 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 293: Line 300:
| 105.578
| 105.578
|-
|-
| Wesley
| [[Wesley comma]]
| Lasepyobi
| Lasepyobi
| Ly<sup>7</sup>-2
| Ly<sup>7</sup>-2
| [[Wesley comma|78125 / 73728]]
| 78125 / 73728
| {{monzo| -13 -2 7 }}
| {{monzo| -13 -2 7 }}
| 100.286
| 100.286
Line 310: Line 317:
! Cents
! Cents
|-
|-
| Antidilemma
| [[Antidilemma]]
| Sasa-theruquad
| Sasa-theruquad
| ssr<sup>13</sup>-2
| ssr<sup>13</sup>-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
| LLz<sup>13</sup>9
| [[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 381: Line 388:
| 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 395: Line 402:
| 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 416: Line 423:
| 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 451: Line 458:
| 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 486: Line 493:
| 110.326
| 110.326
|-
|-
| Triru comma
| [[729/686|Triru comma]]
| Triru
| Triru
| r<sup>3</sup>-2
| r<sup>3</sup>-2
| [[729/686|729 / 686]]
| 729 / 686
| {{monzo| -1 6 0 -3 }}
| {{monzo| -1 6 0 -3 }}
| 105.252
| 105.252
Line 659: Line 666:
| 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 721:
| 170.423
| 170.423
|-
|-
| 47/44
| [[47/44]]
|  
|  
|  
|  
| [[47/44|47 / 44]]
| 47 / 44
| 2.11.47 {{monzo| -2 -1 1 }}
| 2.11.47 {{monzo| -2 -1 1 }}
| 114.189
| 114.189

Revision as of 13:06, 15 April 2025

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.

Except for the 3-limit commas, the 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.

List of commas, by prime limit

3-limit commas

Name(s) Color Name Ratio Monzo Cents
26-comma Wa-26 L4w-2 2541865828329 / 2199023255552 [-41 26⟩ 250.83
27-comma Wa-27 s4w5 8796093022208 / 7625597484987 [43 -27⟩ 247.21
Pythagorean whole tone Wa 2nd w2 9 / 8 [-3 2⟩ 203.91
43-comma Wa-43 L6w-4 [-68 43⟩ 184.065
63-comma Wa-63 s9w8 [100 -63⟩ 176.835
31-comma Wa-31 L4w-3 617673396283947 /
562949953421312 		[-49 31⟩ 160.605
22-comma Wa-22 s3w4 34359738368 /
31381059609 		[35 -22⟩ 156.99
19-comma Wa-19 L3w-2 1162261467 / 1073741824 [-30 19⟩ 137.145
Apotome Lawa Lw1 2187 / 2048 [-11 7⟩ 113.685
46-comma Wa-46 s7w6 [73 -46⟩ 110.07

5-limit commas

Name(s) Color Name Ratio Monzo Cents
Shallowtone comma Lalayobi LLy1 295245 / 262144 [-18 10 1⟩ 205.864
Delorean Tribigu g63 17496 / 15625 [3 7 -6⟩ 195.803
meantone Integer cents comma[clarification needed] [-1393 0 600⟩ 188.228
31-3/5-comma Thiwegu g317 [23 31 -31⟩ 184.88
Minor whole tone, yo 2nd Yo y2 10 / 9 [1 -2 1⟩ 182.404
5-cycle major second, hexadecathird comma Lala-quadquadyo LLy16-4 152587890625 /
137438953472 		[-37 0 16⟩ 181.019
Nadir comma Lalatrigu LLg31 1162261467 / 1048576000 [-23 19 -3⟩ 178.204
Legu g114 53747712 / 48828125 [13 8 -11⟩ 166.189
Enipucrop Latriyobi Ly31 1125 / 1024 [-10 2 3⟩ 162.851
Supersharp Sayoyo syy2 800 / 729 [5 -6 2⟩ 160.897
Nether comma Lala-gugu LLgg1 14348907 / 13107200 [-19 15 -2⟩ 156.698
Rarity comma Quadla-theyo L4y13-5 [-57 17 13⟩ 155.313
Gorgo, laconic Latrigubi Lg32 2187 / 2000 [-4 7 -3⟩ 154.744
Smate, symbolic comma Saquadgu sg43 2048 / 1875 [11 -1 -4⟩ 152.790
Acute limma Trila-neyobi L3y19-5 19073486328125 /
17592186044416 		[-44 0 19⟩ 139.961
31-15-comma Tritrila-thiweyo L9y31-11 [-121 31 31⟩ 136.33
Deeptone comma, Tragicomma Lagu Lg1 177147 / 163840 [-15 11 -1⟩ 135.191
Large limma Gugu gg2 27 / 25 [0 3 -2⟩ 133.238
11-3/5-comma Leyo y11-2 48828125 / 45349632 [-8 -11 11⟩ 127.946
27-3/5-comma Tritritrigu g276 [20 27 -27⟩ 122.315
Lemba Latribiyo Ly6-2 140625 / 131072 [-17 2 6⟩ 121.792
87-15-comma [340 -87 -87⟩ 120.622
Sixix comma Quinyo y51 3125 / 2916 [-2 -6 5⟩ 119.839
Diesma Lathegu Lg133 10460353203 /
9765625000 		[-3 21 -13⟩ 118.977
Comic comma Saquadyobi sy42 5120000 / 4782969 [13 -14 4⟩ 117.885
Just diatonic semitone Gubi g2 16 / 15 [4 -1 -1⟩ 111.731
Beatles Sasa-gugu ssgg3 524288 / 492075 [19 -9 -2⟩ 109.778
300-3/5-comma [-221 -300 300⟩ 107.614
Wronecki Latribigu Lg62 531441 / 500000 [-5 12 -6⟩ 105.578
Wesley comma Lasepyobi Ly7-2 78125 / 73728 [-13 -2 7⟩ 100.286

7-limit commas

Name(s) Color Name Ratio Monzo Cents
Antidilemma Sasa-theruquad ssr13-2 137438953472 / 96889010407 [37 0 0 -13⟩ 605.263
Dilemma Lala-thezoquad LLz139 96889010407 / 68719476736 [-36 0 0 13⟩ 594.737
Septimal major second, supermajor second,

augmented whole-tone, ru 2nd

Rubi r2 8 / 7 [3 0 0 -1⟩ 231.174
Hexatone comma, 6-7-comma Satribiru sr6-2 131072 / 117649 [17 0 0 -6⟩ 187.045
45-7/5-comma Quintritriruyo r45y45-27 [22 0 45 -45⟩ 186.951
63-35-comma Tritribila-septritrizoyo L18z63y638 [-323 0 63 63⟩ 173.796
8-21-comma Lala-quadbizo LLz84 37822859361 /
34359738368 		[-35 8 0 8⟩ 166.247
46-7-comma Sepla-twethebizobi L7z4618 [-129 0 0 46⟩ 165.992
25-7/5-comma Quinquinzogu z25g2517 [-12 0 -25 25⟩ 162.805
43-21-comma Quadtrisa-fotherubi s12r43-11 [189 -43 0 -43⟩ 156.421
Septimal neutral second, 35th harmonic Zoyo zy2 35 / 32 [-5 0 1 1⟩ 155.140
43-7/5-comma Fotheruyo r43y43-26 [21 0 43 -43⟩ 151.976
Swetismic neutral second Zozogu zzg3 49 / 45 [0 -2 -1 2⟩ 147.428
160/147 Ruruyobi rry1 160 / 147 [5 -1 1 -2⟩ 146.707
Hendecatone comma, 11-7-comma Sasa-leru ssr11-4 2147483648 / 1977326743 [31 0 0 -11⟩ 142.915
Septimal subtone Larubi Lr1 243 / 224 [-5 5 0 -1⟩ 140.949
55-35-comma Quadquadla-lequinzoyobi L16z55y557 [-282 0 55 55⟩ 132.679
27-7/5-comma Tritritrizogu z27g2718 [-13 0 -27 27⟩ 127.829
41-7-comma Tribila-fowezo L6z4116 [-115 0 0 41⟩ 121.862
13-21-comma Quadla-thezobi L4z135 [-57 13 0 13⟩ 120.152
Major diatonic semitone Ruyo ry1 15 / 14 [-1 1 1 -1⟩ 119.443
Primate comma Saru sr2 16384 / 15309 [14 -7 0 -1⟩ 117.489
41-7/5-comma Foweruyo r41y41-25 [20 0 41 -41⟩ 117
7-35-comma Sasa-seprugu ssr7g71 68719476736 /
64339296875 		[36 0 -7 -7⟩ 114.023
38-21-comma Lesa-nebiru s11r38-10 [167 -38 0 -38⟩ 110.326
Triru comma Triru r3-2 729 / 686 [-1 6 0 -3⟩ 105.252

11-limit commas

Name(s) Color Name Ratio Monzo Cents
11-cycle major second prote, 33-11-comma Quinla-letrilobi L51o33-7 [-114 0 0 0 33⟩ 193.492
4/5-tone, Ptolemy's second Logu 1og2 11 / 10 [-1 0 -1 0 1⟩ 165.004
11-enipucrop, 9-11-comma Latritrilo L1o9-2 2357947691 / 2147483648 [-31 0 0 0 9⟩ 161.862
3/4-tone, undecimal neutral second Lu 1u2 12 / 11 [2 1 0 0 -1⟩ 150.637
Undecimal secor Lozo 1oz2 77 / 72 [-3 -2 0 1 1⟩ 116.234

13-limit commas

Name(s) Color Name Ratio Monzo Cents
13-cycle neutral second Quadbila-fithethobi L83o537 [-196 0 0 0 0 53⟩ 147.966
Large tridecimal 2/3-tone, tridecimal neutral second Tho 3o2 13 / 12 [-2 -1 0 0 0 1⟩ 138.573
Small tridecimal 2/3-tone, tridecimal limma, trienthird Thuzo 3uz2 14 / 13 [1 0 0 1 0 -1⟩ 128.298
Heptasixth comma, 13-cycle secor Sasepthu s3u71 67108864 / 62748517 [26 0 0 0 0 -7⟩ 116.306
Heptadecasixth comma, neutral thirteenth comma Sasa-sethubi ss3u7-2 [63 0 0 0 0 -17⟩ 111.030

17-limit commas

Name(s) Color Name Ratio Monzo Cents
17-limit rational eventone Sogubi 17og3 17 / 15 [0 -1 -1 0 0 0 1⟩ 216.687
17th harmonic Iso 17o2 17 / 16 [-4 0 0 0 0 0 1⟩ 104.955

19-limit commas

Name(s) Color Name Ratio Monzo Cents
19-cycle meantone prima Tribila-foweno L619o4113 [-174 0 0 0 0 0 0 41⟩ 198.034
Undevicesimal rational meantone Nosu 19o17u2 19 / 17 [0 0 0 0 0 0 -1 1⟩ 192.558
19-cycle meantone secunda Tribila-quintritrino L619o4514 [-191 0 0 0 0 0 0 45⟩ 188.086
19-cycle minor tone Sepla-sepsepno L719o4915 [-208 0 0 0 0 0 0 49⟩ 178.138
Undevicesimal rational submajor second Nuzo 19uz2 21 / 19 [0 1 0 1 0 0 0 -1⟩ 173.268
19-cycle submajor second Quadbila-fithenobi L819o5316 [-225 0 0 0 0 0 0 53⟩ 168.190
Dog comma Inu 19u1 81 / 76 [-2 4 0 0 0 0 0 -1⟩ 110.307

23-limit commas

Name(s) Color Name Ratio Monzo Cents
Large vicesimotertial neutral second Twethoru 23or2 23 / 21 3.7.23 [-1 -1 1⟩ 157.493
Small vicesimotertial neutral second Twethuyoyo 23uyy1 25 / 23 5.23 [2 -1⟩ 144.353
69th harmonic Twetho 23o2 69 / 64 2.3.23 [-6 1 1⟩ 130.229

Higher-limit commas

Name(s) Color Name Ratio Monzo Cents
29th subharmonic Twenu 29u2 32 / 29 2.29 [5 -1⟩ 170.423
47/44 47 / 44 2.11.47 [-2 -1 1⟩ 114.189
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