Large comma: Difference between revisions

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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.  


==[[3-limit commas]]==
== List of commas, by prime limit ==
===[[3-limit commas]]===
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 38: Line 39:
| Wa-31
| Wa-31
| L<sup>4</sup>w-3
| L<sup>4</sup>w-3
| 617673396283947 / 562949953421312
| 617673396283947 / <br>562949953421312
| {{monzo| -49 31 }}
| {{monzo| -49 31 }}
| 160.605
| 160.605
Line 45: Line 46:
| Wa-22
| Wa-22
| s<sup>3</sup>w4
| s<sup>3</sup>w4
| 34359738368 / 31381059609
| 34359738368 / <br>31381059609
| {{monzo| 35 -22 }}
| {{monzo| 35 -22 }}
| 156.99
| 156.99
Line 71: Line 72:
|}
|}


==[[5-limit commas]]==
===[[5-limit commas]]===
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 111: Line 112:
| Lala-quadquadyo
| Lala-quadquadyo
| LLy<sup>16</sup>-4
| LLy<sup>16</sup>-4
| 152587890625 / 137438953472
| 152587890625 / <br>137438953472
| {{monzo| -37 0 16 }}
| {{monzo| -37 0 16 }}
| 181.019
| 181.019
Line 146: Line 147:
| Trila-neyobi
| Trila-neyobi
| L<sup>3</sup>y<sup>19</sup>-5
| L<sup>3</sup>y<sup>19</sup>-5
| 19073486328125 / 17592186044416
| 19073486328125 / <br>17592186044416
| {{monzo| -44 0 19 }}
| {{monzo| -44 0 19 }}
| 139.961
| 139.961
Line 202: Line 203:
| Lathegu
| Lathegu
| Lg<sup>13</sup>3
| Lg<sup>13</sup>3
| 10460353203 / 9765625000
| 10460353203 / <br>9765625000
| {{monzo| -3 21 -13 }}
| {{monzo| -3 21 -13 }}
| 118.977
| 118.977
Line 249: Line 250:
|}
|}


== 7-limit commas ==
=== 7-limit commas ===
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 268: Line 269:
| Satribiru
| Satribiru
| sr<sup>6</sup>-2
| sr<sup>6</sup>-2
|
| 131072 / 117649
| {{monzo| 17 0 0 -6 }}
| {{monzo| 17 0 0 -6 }}
| 187.045
| 187.045
Line 289: Line 290:
| Lala-quadbizo
| Lala-quadbizo
| LLz<sup>8</sup>4
| LLz<sup>8</sup>4
|  
| 37822859361 / <br>34359738368
| {{monzo| -35 8 0 8 }}
| {{monzo| -35 8 0 8 }}
| 166.247
| 166.247
Line 338: Line 339:
| Sasa-leru
| Sasa-leru
| ssr<sup>11</sup>-4
| ssr<sup>11</sup>-4
|
| 2147483648 / 1977326743
| {{monzo| 31 0 0 -11 }}
| {{monzo| 31 0 0 -11 }}
| 142.915
| 142.915
Line 377: Line 378:
| 119.443
| 119.443
|-
|-
| Primate comma
| [[Primate comma]]
| Saru
| Saru
| sr2
| sr2
Line 394: Line 395:
| Sasa-seprugu
| Sasa-seprugu
| ssr<sup>7</sup>g<sup>7</sup>1
| ssr<sup>7</sup>g<sup>7</sup>1
|
| 68719476736 / <br>64339296875
| {{monzo| 36 0 -7 -7 }}
| {{monzo| 36 0 -7 -7 }}
| 114.023
| 114.023
Line 406: Line 407:
|}
|}


== 11-limit commas ==
=== 11-limit commas ===
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 451: Line 452:
|}
|}


== 13-limit commas ==
=== 13-limit commas ===
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 496: Line 497:
|}
|}


== 17-limit commas ==
=== 17-limit commas ===
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 520: Line 521:
|}
|}


== 19-limit commas ==
=== 19-limit commas ===
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 579: Line 580:
|}
|}


== 23-limit commas ==
=== 23-limit commas ===
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 608: Line 609:
| 2.3.23 {{monzo| -6 1 1 }}
| 2.3.23 {{monzo| -6 1 1 }}
| 130.229
| 130.229
|}
=== Higher-limit commas ===
{| class="wikitable"
|-
! Name(s)
! colspan="2" |[[Color notation|Color Name]]
! Ratio
! Monzo
! Cents
|-
|-
| 29th subharmonic
| Twenu
| 29u2
| [[32/29|32 / 29]]
| 2.29 {{monzo| 5 -1 }}
| 170.423
|}
|}


[[Category:Large commas| ]] <!-- main article -->
[[Category:Large commas| ]] <!-- main article -->
[[Category:Lists of commas]]
[[Category:Lists of commas]]

Revision as of 10:02, 10 December 2023

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.

List of commas, by prime limit

3-limit commas

Name(s) Color Name Ratio Monzo Cents
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
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
Enipucrop Latriyobi Ly31 1125 / 1024 [-10 2 3⟩ 162.851
Supersharp Sayoyo syy2 800 / 729 [5 -6 2⟩ 160.897
Gorgo, laconic Latrigubi Lg32 2187 / 2000 [-4 7 -3⟩ 154.744
Smate, symbolic 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
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 Lasepyobi Ly7-2 78125 / 73728 [-13 -2 7⟩ 100.286

7-limit commas

Name(s) Color Name Ratio Monzo Cents
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
Hendecatone comma, 11-7-comma Sasa-leru ssr11-4 2147483648 / 1977326743 [31 0 0 -11⟩ 142.915
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

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
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