Small comma: Difference between revisions

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Line 3: Line 3:
For commas over 100 cents in size, see [[Large comma]]s; for commas in between 30 and 100 cents in size, see [[Medium comma]]s; and for commas under 3.5 cents in size, see [[Unnoticeable comma]]s
For commas over 100 cents in size, see [[Large comma]]s; for commas in between 30 and 100 cents in size, see [[Medium comma]]s; and for commas under 3.5 cents in size, see [[Unnoticeable comma]]s


Due to the wide range of sizes, cents values here and on the other commas pages are listed to 5 significant digits, instead of to a fixed number of decimal places as is the [[conventions|convention]] elsewhere on the wiki.
Due to the wide range of sizes, cents values here and on the other commas pages are listed to 5 significant digits, instead of to a fixed number of decimal places as is the [[Xenharmonic Wiki:Conventions|convention]] elsewhere on the wiki.


== List of commas, by prime limit ==
== List of commas, by prime limit ==
Line 12: Line 12:
! Name(s)
! Name(s)
! colspan="2" |[[Color notation/Temperament Names|Color Name]]
! colspan="2" |[[Color notation/Temperament Names|Color Name]]
! [[Ratio]]
! [[Monzo]]
! [[Monzo]]
! [[Cents]]
! [[Cents]]
Line 18: Line 19:
| Wa-241
| Wa-241
| w-241
| w-241
|
| {{monzo| 382 -241 }}
| {{monzo| 382 -241 }}
| 28.845
| 28.845
Line 24: Line 26:
| Wa-65
| Wa-65
| w-65
| w-65
|
| {{monzo| -103 65 }}
| {{monzo| -103 65 }}
| 27.075
| 27.075
Line 30: Line 33:
| Lalawa
| Lalawa
| LLw-2
| LLw-2
| 531441 / 524288
| {{monzo| -19 12 }}
| {{monzo| -19 12 }}
| 23.460
| 23.460
Line 36: Line 40:
| Wa-41
| Wa-41
| w-41
| w-41
| 36893488147419103232 /<br>36472996377170786403
| {{monzo| 65 -41 }}
| {{monzo| 65 -41 }}
| 19.845
| 19.845
Line 42: Line 47:
| Wa-94
| Wa-94
| w-94
| w-94
|
| {{monzo| 149 -94 }}
| {{monzo| 149 -94 }}
| 16.230
| 16.230
Line 48: Line 54:
| Wa-147
| Wa-147
| w-147
| w-147
|
| {{monzo| 233 -147 }}
| {{monzo| 233 -147 }}
| 12.615
| 12.615
Line 54: Line 61:
| Wa-200
| Wa-200
| w-200
| w-200
|
| {{monzo| 317 -200 }}
| {{monzo| 317 -200 }}
| 8.9998
| 8.9998
Line 60: Line 68:
| Wa-253
| Wa-253
| w-253
| w-253
|
| {{monzo| 401 -253 }}
| {{monzo| 401 -253 }}
| 5.3848
| 5.3848
Line 66: Line 75:
| Wa-53
| Wa-53
| w-53
| w-53
| 19383245667680019896796723 /<br>19342813113834066795298816
| {{monzo| -84 53 }}
| {{monzo| -84 53 }}
| 3.6150
| 3.6150
Line 89: Line 99:
| Trisa-legu
| Trisa-legu
| s<sup>3</sup>g<sup>11</sup>5
| s<sup>3</sup>g<sup>11</sup>5
|  
| 8796093022208 / 8649755859375
| {{monzo| 43 -11 -11 }}
| {{monzo| 43 -11 -11 }}
| 29.044
| 29.044
Line 103: Line 113:
| Lalaneyo
| Lalaneyo
| LLy<sup>19</sup>-5
| LLy<sup>19</sup>-5
|  
| 19073486328125 / 18786186952704
| {{monzo| -33 -7 19 }}
| {{monzo| -33 -7 19 }}
| 26.276
| 26.276
Line 124: Line 134:
| Saquintrigu
| Saquintrigu
| sg<sup>15</sup>4
| sg<sup>15</sup>4
|  
| 30958682112 / 30517578125
| {{monzo| 19 10 -15 }}
| {{monzo| 19 10 -15 }}
| 24.844
| 24.844
Line 131: Line 141:
| Saseyo
| Saseyo
| sy<sup>17</sup>-3
| sy<sup>17</sup>-3
|  
| 762939453125 / 753145430616
| {{monzo| -3 -23 17 }}
| {{monzo| -3 -23 17 }}
| 22.368
| 22.368
Line 149: Line 159:
| 22.076
| 22.076
|-
|-
| syntonic / Didymos / meantone comma
| syntonic / Didymus / meantone comma
| Gu
| Gu
| g1
| g1
Line 159: Line 169:
| Trisa-segu
| Trisa-segu
| s<sup>3</sup>g<sup>17</sup>6
| s<sup>3</sup>g<sup>17</sup>6
|  
| 562949953421312 / 556182861328125
| {{monzo| 49 -6 -17 }}
| {{monzo| 49 -6 -17 }}
| 20.937
| 20.937
Line 173: Line 183:
| Quinquadgu
| Quinquadgu
| g<sup>20</sup>4
| g<sup>20</sup>4
|  
| 96402615118848 / 95367431640625
| {{monzo| 10 23 -20 }}
| {{monzo| 10 23 -20 }}
| 18.691
| 18.691
Line 180: Line 190:
| Lala-theyo
| Lala-theyo
| LLy<sup>13</sup>-4
| LLy<sup>13</sup>-4
|  
| 1220703125 / 1207959552
| {{monzo| -27 -2 13 }}
| {{monzo| -27 -2 13 }}
| 18.168
| 18.168
Line 187: Line 197:
| Sasa-trigu
| Sasa-trigu
| ssg<sup>3</sup>3
| ssg<sup>3</sup>3
|  
| 67108864 / 66430125
| {{monzo| 26 -12 -3 }}
| {{monzo| 26 -12 -3 }}
| 17.599
| 17.599
Line 194: Line 204:
| Trila-quingu
| Trila-quingu
| L<sup>3</sup>g<sup>5</sup>-2
| L<sup>3</sup>g<sup>5</sup>-2
|  
| 847288609443 / 838860800000
| {{monzo| -28 25 -5 }}
| {{monzo| -28 25 -5 }}
| 17.306
| 17.306
Line 201: Line 211:
| Trisa-quadgu
| Trisa-quadgu
| s<sup>3</sup>g<sup>4</sup>4
| s<sup>3</sup>g<sup>4</sup>4
|  
| 2199023255552 / 2179240250625
| {{monzo| 41 -20 -4 }}
| {{monzo| 41 -20 -4 }}
| 15.645
| 15.645
Line 208: Line 218:
| Lala-tribigu
| Lala-tribigu
| LLg<sup>6</sup>1
| LLg<sup>6</sup>1
|  
| 129140163 / 128000000
| {{monzo| -13 17 -6 }}
| {{monzo| -13 17 -6 }}
| 15.353
| 15.353
Line 250: Line 260:
| Saquadbigu
| Saquadbigu
| sg<sup>8</sup>3
| sg<sup>8</sup>3
|  
| 393216 / 390625
| {{monzo| 17 1 -8 }}
| {{monzo| 17 1 -8 }}
| 11.445
| 11.445
Line 264: Line 274:
| Lasepyo
| Lasepyo
| Ly<sup>7</sup>-3
| Ly<sup>7</sup>-3
|  
| 2109375 / 2097152
| {{monzo| -21 3 7 }}
| {{monzo| -21 3 7 }}
| 10.061
| 10.061
Line 271: Line 281:
| Sasa-tritrigu
| Sasa-tritrigu
| ssg<sup>9</sup>4
| ssg<sup>9</sup>4
|  
| 4294967296 / 4271484375
| {{monzo| 32 -7 -9 }}
| {{monzo| 32 -7 -9 }}
| 9.4916
| 9.4916
Line 285: Line 295:
| Quadsa-quinbigu
| Quadsa-quinbigu
| s<sup>4</sup>g<sup>10</sup>5
| s<sup>4</sup>g<sup>10</sup>5
|  
| 140737488355328 / 140126044921875
| {{monzo| 47 -15 -10 }}
| {{monzo| 47 -15 -10 }}
| 7.5378
| 7.5378
Line 299: Line 309:
| Laquadtrigu
| Laquadtrigu
| Lg<sup>12</sup>2
| Lg<sup>12</sup>2
|  
| 31381059609 / 31250000000
| {{monzo| -7 22 -12 }}
| {{monzo| -7 22 -12 }}
| 7.2455
| 7.2455
Line 306: Line 316:
| Trila-septriyo
| Trila-septriyo
| L<sup>3</sup>y<sup>21</sup>-6
| L<sup>3</sup>y<sup>21</sup>-6
|  
| 476837158203125 / 474989023199232
| {{monzo| -44 -3 21 }}
| {{monzo| -44 -3 21 }}
| 6.7230
| 6.7230
Line 313: Line 323:
| Saquinyo
| Saquinyo
| sy<sup>5</sup>1
| sy<sup>5</sup>1
|  
| 1600000 / 1594323
| {{monzo| 9 -13 5 }}
| {{monzo| 9 -13 5 }}
| 6.1536
| 6.1536
Line 320: Line 330:
| Thegu
| Thegu
| g<sup>13</sup>3
| g<sup>13</sup>3
|  
| 1224440064 / 1220703125
| {{monzo| 8 14 -13 }}
| {{monzo| 8 14 -13 }}
| 5.2917
| 5.2917
Line 327: Line 337:
| Laquinquadyo
| Laquinquadyo
| Ly<sup>20</sup>-5
| Ly<sup>20</sup>-5
|  
| 95367431640625 / 95105071448064
| {{monzo| -29 -11 20 }}
| {{monzo| -29 -11 20 }}
| 4.7693
| 4.7693
Line 355: Line 365:
| Sasa-quadyo
| Sasa-quadyo
| ssy<sup>4</sup>2
| ssy<sup>4</sup>2
|  
| 10485760000 / 10460353203
| {{monzo| 24 -21 4 }}
| {{monzo| 24 -21 4 }}
| 4.1998
| 4.1998
Line 407: Line 417:
| Satritriru-aquadyo
| Satritriru-aquadyo
| sr<sup>9</sup>y<sup>4</sup>-5
| sr<sup>9</sup>y<sup>4</sup>-5
|  
| 40960000 / 40353607
| {{monzo| 16 0 4 -9 }}
| {{monzo| 16 0 4 -9 }}
| 25.822
| 25.822
Line 428: Line 438:
| Lasepru-aquadbiyo
| Lasepru-aquadbiyo
| Lr<sup>7</sup>y<sup>8</sup>-6
| Lr<sup>7</sup>y<sup>8</sup>-6
|  
| 854296875 / 843308032
| {{monzo| -10 7 8 -7 }}
| {{monzo| -10 7 8 -7 }}
| 22.413
| 22.413
Line 449: Line 459:
| Satritrizo-agugu
| Satritrizo-agugu
| sz<sup>9</sup>gg6
| sz<sup>9</sup>gg6
|  
| 40353607/39858075
| {{monzo| 0 -13 -2 9 }}
| {{monzo| 0 -13 -2 9 }}
| 21.391
| 21.391
Line 463: Line 473:
| Laruquingu
| Laruquingu
| Lrg<sup>5</sup>1
| Lrg<sup>5</sup>1
|  
| 177147/175000
| {{monzo| -3 11 -5 -1 }}
| {{monzo| -3 11 -5 -1 }}
| 21.111
| 21.111
Line 477: Line 487:
| Sepruyo
| Sepruyo
| r<sup>7</sup>y<sup>7</sup>-5
| r<sup>7</sup>y<sup>7</sup>-5
|  
| 2500000 / 2470629
| {{monzo| 5 -1 7 -7 }}
| {{monzo| 5 -1 7 -7 }}
| 20.460
| 20.460
Line 484: Line 494:
| Saquadzogu
| Saquadzogu
| sz<sup>4</sup>g<sup>4</sup>4
| sz<sup>4</sup>g<sup>4</sup>4
|  
| 153664 / 151875
| {{monzo| 6 -5 -4 4 }}
| {{monzo| 6 -5 -4 4 }}
| 20.274
| 20.274
Line 491: Line 501:
| Sazoyoyo
| Sazoyoyo
| szyy2
| szyy2
|  
| 179200 / 177147
| {{monzo| 10 -11 2 1 }}
| {{monzo| 10 -11 2 1 }}
| 19.948
| 19.948
Line 505: Line 515:
| Sarutribigu
| Sarutribigu
| srg<sup>6</sup>1
| srg<sup>6</sup>1
|  
| 110592/109375
| {{monzo| 12 3 -6 -1 }}
| {{monzo| 12 3 -6 -1 }}
| 19.157
| 19.157
Line 533: Line 543:
| Laruquadbiyo
| Laruquadbiyo
| Lry<sup>8</sup>-3
| Lry<sup>8</sup>-3
|  
| 390625 / 387072
| {{monzo| -11 -3 8 -1 }}
| {{monzo| -11 -3 8 -1 }}
| 15.819
| 15.819
Line 540: Line 550:
| Quinruyoyo
| Quinruyoyo
| r<sup>5</sup>y<sup>10</sup>-5
| r<sup>5</sup>y<sup>10</sup>-5
|  
| 9765625 / 9680832
| {{monzo| -6 -2 10 -5 }}
| {{monzo| -6 -2 10 -5 }}
| 15.098
| 15.098
Line 589: Line 599:
| Sepru-ayo
| Sepru-ayo
| r<sup>7</sup>y-4
| r<sup>7</sup>y-4
|  
| 829440 / 823543
| {{monzo| 11 4 1 -7 }}
| {{monzo| 11 4 1 -7 }}
| 12.352
| 12.352
Line 603: Line 613:
| Trisa-triru-aquadquadyo
| Trisa-triru-aquadquadyo
| s<sup>3</sup>r<sup>3</sup>y<sup>16</sup>-3
| s<sup>3</sup>r<sup>3</sup>y<sup>16</sup>-3
|  
| 640000000000000000 / 635585924776181463
| {{monzo| 22 -32 16 -3 }}
| {{monzo| 22 -32 16 -3 }}
| 11.982
| 11.982
Line 610: Line 620:
| Sazoquadgu
| Sazoquadgu
| szg<sup>4</sup>3
| szg<sup>4</sup>3
|  
| 458752 / 455625
| {{monzo| 16 -6 -4 1 }}
| {{monzo| 16 -6 -4 1 }}
| 11.841
| 11.841
Line 631: Line 641:
| Sasasepru
| Sasasepru
| ssr<sup>7</sup>-3
| ssr<sup>7</sup>-3
|  
| 67108864 / 66706983
| {{monzo| 26 -4 0 -7 }}
| {{monzo| 26 -4 0 -7 }}
| 10.399
| 10.399
Line 645: Line 655:
| Lasepzo-agugu
| Lasepzo-agugu
| Lz<sup>7</sup>gg4
| Lz<sup>7</sup>gg4
|  
| 823543 / 819200
| {{monzo| -15 0 -2 7 }}
| {{monzo| -15 0 -2 7 }}
| 9.1539
| 9.1539
Line 659: Line 669:
| Labizogugu
| Labizogugu
| Lzzg<sup>4</sup>2
| Lzzg<sup>4</sup>2
|  
| 321489 / 320000
| {{monzo| -9 8 -4 2 }}
| {{monzo| -9 8 -4 2 }}
| 8.0370
| 8.0370
Line 673: Line 683:
| Quadruyoyo
| Quadruyoyo
| r<sup>4</sup>y<sup>8</sup>-4
| r<sup>4</sup>y<sup>8</sup>-4
|  
| 390625 / 388962
| {{monzo| -1 -4 8 -4 }}
| {{monzo| -1 -4 8 -4 }}
| 7.3861
| 7.3861
Line 687: Line 697:
| Sasepzo-atrigu
| Sasepzo-atrigu
| sz<sup>7</sup>g<sup>3</sup>5
| sz<sup>7</sup>g<sup>3</sup>5
|  
| 823543 / 820125
| {{monzo| 0 -8 -3 7 }}
| {{monzo| 0 -8 -3 7 }}
| 7.2002
| 7.2002
Line 701: Line 711:
| Saquadzo-atriyo
| Saquadzo-atriyo
| Sz<sup>4</sup>y<sup>3</sup>3
| Sz<sup>4</sup>y<sup>3</sup>3
|  
| 4802000 / 4782969
| {{monzo|4 -14 3 4}}
| {{monzo|4 -14 3 4}}
| 6.8748
| 6.8748
Line 708: Line 718:
| Tribizo-asepgu
| Tribizo-asepgu
| z<sup>6</sup>g<sup>7</sup>5
| z<sup>6</sup>g<sup>7</sup>5
|  
| 235298 / 234375
| {{monzo|1 -1 -7 6}}
| {{monzo|1 -1 -7 6}}
| 6.8044
| 6.8044
Line 715: Line 725:
| Latribiru
| Latribiru
| Lr<sup>6</sup>-4
| Lr<sup>6</sup>-4
|  
| 118098 / 117649
| {{monzo| 1 10 0 -6 }}
| {{monzo| 1 10 0 -6 }}
| 6.5946
| 6.5946
Line 743: Line 753:
| Zotritrigu
| Zotritrigu
| zg<sup>9</sup>3
| zg<sup>9</sup>3
|  
| 1959552 / 1953125
| {{monzo| 7 7 -9 1 }}
| {{monzo| 7 7 -9 1 }}
| 5.6875
| 5.6875
Line 750: Line 760:
| Saquinbizogu
| Saquinbizogu
| sz<sup>10</sup>g<sup>10</sup>8
| sz<sup>10</sup>g<sup>10</sup>8
|  
| 578509309952 / 576650390625
| {{monzo| 11 -10 -10 10 }}
| {{monzo| 11 -10 -10 10 }}
| 5.5719
| 5.5719
Line 764: Line 774:
| Saquadru-atriyo
| Saquadru-atriyo
| sr<sup>4</sup>y<sup>3</sup>-3
| sr<sup>4</sup>y<sup>3</sup>-3
|  
| 4096000 / 4084101
| {{monzo| 15 -5 3 -5 }}
| {{monzo| 15 -5 3 -5 }}
| 5.0366
| 5.0366
Line 771: Line 781:
| Satribiru-agu
| Satribiru-agu
| sr<sup>6</sup>g-3
| sr<sup>6</sup>g-3
|  
| 589824 / 588245
| {{monzo| 16 2 -1 -6 }}
| {{monzo| 16 2 -1 -6 }}
| 4.6408
| 4.6408
Line 778: Line 788:
| Sasaru
| Sasaru
| ssr2
| ssr2
|  
| 33554432 / 33480783
| {{monzo| 25 -14 0 -1 }}
| {{monzo| 25 -14 0 -1 }}
| 3.8041
| 3.8041
Line 785: Line 795:
| Latritrizo-ayo
| Latritrizo-ayo
| Lz<sup>9</sup>y4
| Lz<sup>9</sup>y4
|  
| 201768035 / 201326592
| {{monzo| -26 -1 1 9 }}
| {{monzo| -26 -1 1 9 }}
| 3.7919
| 3.7919
Line 792: Line 802:
| Sazoquinbigu
| Sazoquinbigu
| szg<sup>10</sup>4
| szg<sup>10</sup>4
|  
| 29360128 / 29296875
| {{monzo| 22 -1 -10 1 }}
| {{monzo| 22 -1 -10 1 }}
| 3.7338
| 3.7338
Line 809: Line 819:
| Saquinlu-ayo
| Saquinlu-ayo
| s1u<sup>5</sup>y2
| s1u<sup>5</sup>y2
|  
| 163840 / 161051
| {{monzo| 15 0 1 0 -5 }}
| {{monzo| 15 0 1 0 -5 }}
| 29.724
| 29.724
Line 865: Line 875:
| Lalolo
| Lalolo
| L1oo-2
| L1oo-2
|  
| 264627 / 262144
| {{monzo| -18 7 0 0 2 }}
| {{monzo| -18 7 0 0 2 }}
| 16.321
| 16.321
Line 900: Line 910:
| Laquadlo
| Laquadlo
| L1o<sup>4</sup>-2
| L1o<sup>4</sup>-2
|  
| 131769 / 131072
| {{monzo| -17 2 0 0 4 }}
| {{monzo| -17 2 0 0 4 }}
| 9.1818
| 9.1818
Line 956: Line 966:
| Quadbilu
| Quadbilu
| 1u<sup>8</sup>2
| 1u<sup>8</sup>2
|  
| 214990848 / 214358881
| {{monzo| 15 8 0 0 -8 }}
| {{monzo| 15 8 0 0 -8 }}
| 5.0965
| 5.0965
Line 1,141: Line 1,151:
| Laquinbitho
| Laquinbitho
| L3o<sup>10</sup>2
| L3o<sup>10</sup>2
|  
| 137858491849 / 137438953472
| {{monzo| -37 0 0 0 0 10 }}
| {{monzo| -37 0 0 0 0 10 }}
| 5.2766
| 5.2766
Line 1,350: Line 1,360:
| Saquadnu
| Saquadnu
| s19u<sup>4</sup>-2
| s19u<sup>4</sup>-2
|  
| 131072 / 130321
| {{monzo| 17 0 0 0 0 0 0 -4 }}
| {{monzo| 17 0 0 0 0 0 0 -4 }}
| 9.9479
| 9.9479
Line 1,397: Line 1,407:
|}
|}


=== 23-limit commas ===
== Higher-limit commas ==
 
=== 29-limit commas ===
{| class="wikitable"
{| class="wikitable"
|+
! Name(s)
!Name(s)
! colspan="2" |[[Color name]]
! colspan="2" |[[Color name]]
!Ratio
! Ratio
!Monzo
! Monzo
!Cents
! Cents
|-
|Classical mediant of Didymos’ and Archytas’ commas
|
|
|145/143
|{{Monzo|0 0 1 0 -1 -1 0 0 0 1}}
|24.045
|-
|
|
|
|
|
|
|-
|-
| Classical mediant of Didymus' and Archytas' commas
|
|
|
|
|
| 145/143
|
| {{Monzo| 0 0 1 0 -1 -1 0 0 0 1 }}
|
| 24.045
|
|}
|}
<references />
<references />


[[Category:Comma]]
[[Category:Comma]]
[[Category:Small comma| ]] <!-- main article -->
[[Category:Small comma| ]] <!-- main article -->

Revision as of 00:58, 6 November 2021

A small comma is a comma whose size is approximately between 3.5 and 30 cents. These intervals are in the range from just noticeable up to usable as melodic steps. The actual perception of course varies.

For commas over 100 cents in size, see Large commas; for commas in between 30 and 100 cents in size, see Medium commas; and for commas under 3.5 cents in size, see Unnoticeable commas

Due to the wide range of sizes, cents values here and on the other commas pages are listed to 5 significant digits, instead of to a fixed number of decimal places as is the convention elsewhere on the wiki.

List of commas, by prime limit

3-limit commas

Name(s) Color Name Ratio Monzo Cents
241-comma Wa-241 w-241 [382 -241⟩ 28.845
65-comma,
Pythagorean septimal comma 		Wa-65 w-65 [-103 65⟩ 27.075
Pythagorean comma Lalawa LLw-2 531441 / 524288 [-19 12⟩ 23.460
41-comma, counterpyth comma Wa-41 w-41 36893488147419103232 /
36472996377170786403 		[65 -41⟩ 19.845
94-comma, garistearn comma Wa-94 w-94 [149 -94⟩ 16.230
147-comma Wa-147 w-147 [233 -147⟩ 12.615
200-comma,
Pythagorean integer-cent ET comma 		Wa-200 w-200 [317 -200⟩ 8.9998
253-comma Wa-253 w-253 [401 -253⟩ 5.3848
Mercator's comma, 53-comma Wa-53 w-53 19383245667680019896796723 /
19342813113834066795298816 		[-84 53⟩ 3.6150

5-limit commas

Name(s) Color Name Ratio Monzo Cents
small diesis, magic comma Laquinyo Ly5-2 3125/3072 [-10 -1 5⟩ 29.614
11-15-comma, hendecatonic comma Trisa-legu s3g115 8796093022208 / 8649755859375 [43 -11 -11⟩ 29.044
minimal diesis, tetracot comma Saquadyo sy41 20000 / 19683 [5 -9 4⟩ 27.660
semaja Lalaneyo LLy19-5 19073486328125 / 18786186952704 [-33 -7 19⟩ 26.276
quanic comma Sepsa-quinyo s7y55 [74 -54 5⟩ 25.999
roda Sasa-triyo ssy32 131072000 / 129140163 [20 -17 3⟩ 25.706
trisedodge comma Saquintrigu sg154 30958682112 / 30517578125 [19 10 -15⟩ 24.844
maja Saseyo sy17-3 762939453125 / 753145430616 [-3 -23 17⟩ 22.368
satin comma Quinbisa-triyo s10y37 [104 -70 3⟩ 22.091
misneb Quadla-quintriyo L4y15-6 [-57 14 15⟩ 22.076
syntonic / Didymus / meantone comma Gu g1 81/80 [-4 4 -1⟩ 21.506
maquila comma Trisa-segu s3g176 562949953421312 / 556182861328125 [49 -6 -17⟩ 20.937
diaschisma Sagugu sgg2 2048/2025 [11 -4 -2⟩ 19.553
countermeantone comma Quinquadgu g204 96402615118848 / 95367431640625 [10 23 -20⟩ 18.691
ditonma Lala-theyo LLy13-4 1220703125 / 1207959552 [-27 -2 13⟩ 18.168
misty comma Sasa-trigu ssg33 67108864 / 66430125 [26 -12 -3⟩ 17.599
pental comma Trila-quingu L3g5-2 847288609443 / 838860800000 [-28 25 -5⟩ 17.306
undim comma Trisa-quadgu s3g44 2199023255552 / 2179240250625 [41 -20 -4⟩ 15.645
graviton, gravity comma Lala-tribigu LLg61 129140163 / 128000000 [-13 17 -6⟩ 15.353
majvam Sasa-lebigu ssg226 [40 7 -22⟩ 14.783
quartonic Saleyo sy11-2 390625000 / 387420489 [3 -18 11⟩ 14.261
untritonic comma Quadla-tritriyo L4y9-5 [-51 19 9⟩ 13.968
medium semicomma, sensipent comma Sepgu g72 78732 / 78125 [2 9 -7⟩ 13.399
tertiosec comma Laquadtribiyo L6y24-9 [-89 21 24⟩ 12.584
Würschmidt comma Saquadbigu sg83 393216 / 390625 [17 1 -8⟩ 11.445
counterhanson comma Quinquinyo y25-5 [-20 -24 25⟩ 10.923
semicomma, Fokker comma Lasepyo Ly7-3 2109375 / 2097152 [-21 3 7⟩ 10.061
escapade comma Sasa-tritrigu ssg94 4294967296 / 4271484375 [32 -7 -9⟩ 9.4916
kleisma, semicomma majeur Tribiyo y6-2 15625 / 15552 [-6 -5 6⟩ 8.1073
qintosec comma Quadsa-quinbigu s4g105 140737488355328 / 140126044921875 [47 -15 -10⟩ 7.5378
59-5-comma [137 0 -59⟩ 7.4909
unidecma Laquadtrigu Lg122 31381059609 / 31250000000 [-7 22 -12⟩ 7.2455
mutt comma Trila-septriyo L3y21-6 476837158203125 / 474989023199232 [-44 -3 21⟩ 6.7230
amity comma Saquinyo sy51 1600000 / 1594323 [9 -13 5⟩ 6.1536
parakleisma Thegu g133 1224440064 / 1220703125 [8 14 -13⟩ 5.2917
gammic comma Laquinquadyo Ly20-5 95367431640625 / 95105071448064 [-29 -11 20⟩ 4.7693
squarschmidt comma Quadsa-twenegu s4g298 [61 4 -29⟩ 4.7223
Huntian 15-cycle comma Quadtrisa-fothegu s12g4316 [168 -43 -43⟩ 4.4453
56-syntonic comma Quadtribila-sepquadbigu L24g56-8 [-225 224 -56⟩ 4.3522
vulture comma Sasa-quadyo ssy42 10485760000 / 10460353203 [24 -21 4⟩ 4.1998
lafa comma Tribisa-quadtrigu s6g127 [77 -31 -12⟩ 3.6304

7-limit commas

Name(s) Color Name Ratio Monzo Cents
senga Trizo-agugu z3gg3 686 / 675 [1 -3 -2 3⟩ 27.985
23-21-comma Sepla-twethezo L7z237 [-101 23 0 23⟩ 27.961
septimal comma, Archytas' comma, Leipziger Komma Ru r1 64 / 63 [6 -2 0 -1⟩ 27.264
mandos Birugugu rrg41 31104 / 30625 [7 5 -4 -2⟩ 26.868
slither Satritriru-aquadyo sr9y4-5 40960000 / 40353607 [16 0 4 -9⟩ 25.822
33-7/5-comma Letrizogu z33g3321 [-16 0 -33 33⟩ 22.902
Huntian 35-cycle comma Quintrisa-tritritribirugu s15r54g54-6 [277 0 -54 -54⟩ 22.461
blackjackisma Lasepru-aquadbiyo Lr7y8-6 854296875 / 843308032 [-10 7 8 -7⟩ 22.413
squalentine Laquadzo-atrigu Lz4g33 64827 / 64000 [-9 3 -3 4⟩ 22.227
keema Zotriyo zy31 875 / 864 [-5 -3 3 1⟩ 21.902
betelgeuse Satritrizo-agugu sz9gg6 40353607/39858075 [0 -13 -2 9⟩ 21.391
gariboh Triru-aquinyo r3y5-3 3125 / 3087 [0 -2 5 -3⟩ 21.181
secanticornisma Laruquingu Lrg51 177147/175000 [-3 11 -5 -1⟩ 21.111
nuwell Quadru-ayo r4y-3 2430 / 2401 [1 5 1 -4⟩ 20.785
mermisma Sepruyo r7y7-5 2500000 / 2470629 [5 -1 7 -7⟩ 20.460
negricorn, small quadruple bluish Saquadzogu sz4g44 153664 / 151875 [6 -5 -4 4⟩ 20.274
tolerma Sazoyoyo szyy2 179200 / 177147 [10 -11 2 1⟩ 19.948
25-36/35-comma, icosipentatonic comma Quinquinrugu r25g25-8 [49 50 -25 -25⟩ 19.260
valenwuer Sarutribigu srg61 110592/109375 [12 3 -6 -1⟩ 19.157
buzzardisma Saquadru sr4-2 65536 / 64827 [16 -3 0 -4⟩ 18.831
Huntian 21-cycle comma Quadbisa-sepquadru s8r28-8 [123 -28 0 -28⟩ 18.135
mirwomo Labizoyo Lzzyy1 33075 / 32768 [-15 3 2 2⟩ 16.144
catasyc Laruquadbiyo Lry8-3 390625 / 387072 [-11 -3 8 -1⟩ 15.819
compass comma Quinruyoyo r5y10-5 9765625 / 9680832 [-6 -2 10 -5⟩ 15.098
trimyna Quinzogu z5g54 50421 / 50000 [-4 1 -5 5⟩ 14.516
sensamagic Zozoyo zzy2 245 / 243 [0 -5 1 2⟩ 14.191
septimal semicomma, starling comma Zotrigu zg32 126 / 125 [1 2 -3 1⟩ 13.795
slendro 34-comma Quinla-sequadzo L5z6828 [-137 -34 0 68⟩ 13.692
octagar Rurutriyo rry3-2 4000 / 3969 [5 -4 3 -2⟩ 13.469
orwellisma, orwell comma Triru-agu r3g-2 1728 / 1715 [6 3 -1 -3⟩ 13.074
mynaslender comma Sepru-ayo r7y-4 829440 / 823543 [11 4 1 -7⟩ 12.352
35-7/5-comma Sepquinruyo r35y35-22 [17 0 35 -35⟩ 12.073
chromatisma Trisa-triru-aquadquadyo s3r3y16-3 640000000000000000 / 635585924776181463 [22 -32 16 -3⟩ 11.982
mistisma Sazoquadgu szg43 458752 / 455625 [16 -6 -4 1⟩ 11.841
34-jubilismic comma Sequadzogu z68g6842 [-33 0 -68 68⟩ 10.829
Hunt 7-cycle comma Quadsa-thebiru s4r26-10 [73 0 0 -26⟩ 10.526
septiness comma Sasasepru ssr7-3 67108864 / 66706983 [26 -4 0 -7⟩ 10.399
31-35-comma Tritrila-thiwezoyo L9z31y314 [-159 0 31 31⟩ 9.3282
quince Lasepzo-agugu Lz7gg4 823543 / 819200 [-15 0 -2 7⟩ 9.1539
gamelisma Latrizo Lz32 1029 / 1024 [-10 1 0 3⟩ 8.4327
varunisma Labizogugu Lzzg42 321489 / 320000 [-9 8 -4 2⟩ 8.0370
septimal kleisma, marvel comma Ruyoyo ryy-2 225 / 224 [-5 2 2 -1⟩ 7.7115
dimcomp Quadruyoyo r4y8-4 390625 / 388962 [-1 -4 8 -4⟩ 7.3861
cataharry Labirugu Lrrgg-2 19683 / 19600 [-4 9 -2 -2⟩ 7.3158
procyon comma Sasepzo-atrigu sz7g35 823543 / 820125 [0 -8 -3 7⟩ 7.2002
mirkwai Quinru-aquadyo r5y4-4 16875 / 16807 [0 3 4 -5⟩ 6.9903
canousma Saquadzo-atriyo Sz4y33 4802000 / 4782969 [4 -14 3 4⟩ 6.8748
triwellisma Tribizo-asepgu z6g75 235298 / 234375 [1 -1 -7 6⟩ 6.8044
stearnsma Latribiru Lr6-4 118098 / 117649 [1 10 0 -6⟩ 6.5946
hemimage Satrizo-agu sz3g3 10976 / 10935 [5 -7 -1 3⟩ 6.4790
hemimean Zozoquingu zzg53 3136 / 3125 [6 0 -5 2⟩ 6.0832
hemifamity, 5/7-kleisma Saruyo sry1 5120 / 5103 [10 -6 1 -1⟩ 5.7578
parkleiness Zotritrigu zg93 1959552 / 1953125 [7 7 -9 1⟩ 5.6875
linus comma Saquinbizogu sz10g108 578509309952 / 576650390625 [11 -10 -10 10⟩ 5.5719
porwell Sarurutrigu srrg31 6144 / 6125 [11 1 -3 -2⟩ 5.3620
hemfiness comma Saquadru-atriyo sr4y3-3 4096000 / 4084101 [15 -5 3 -5⟩ 5.0366
hewuermera Satribiru-agu sr6g-3 589824 / 588245 [16 2 -1 -6⟩ 4.6408
garischisma, septimal schisma Sasaru ssr2 33554432 / 33480783 [25 -14 0 -1⟩ 3.8041
wadisma Latritrizo-ayo Lz9y4 201768035 / 201326592 [-26 -1 1 9⟩ 3.7919
quasiorwellisma Sazoquinbigu szg104 29360128 / 29296875 [22 -1 -10 1⟩ 3.7338

11-limit commas

Name(s) Color Name Ratio Monzo Cents
thuja comma Saquinlu-ayo s1u5y2 163840 / 161051 [15 0 1 0 -5⟩ 29.724
sensmus Salozogu s1ozg2 1232/1215 [4 -5 -1 1 1⟩ 24.055
sevnothrush Loquingu 1og52 3168/3125 [5 2 -5 0 1⟩ 23.659
cassacot Biluzo-ayo 1uuzzy2 245/242 [-1 0 1 2 -2⟩ 21.330
antimisma Lobizogu 1ozzgg2 1617/1600 [-6 1 -2 2 1⟩ 18.297
mothwellsma Loruru 1orr-2 99/98 [-1 2 0 -2 1⟩ 17.576
ptolemisma Luyoyo 1uyy1 100/99 [2 -2 2 0 -1⟩ 17.399
hemimin Trilu-azo 1u3z2 1344/1331 [6 1 0 1 -3⟩ 16.827
Betarabian comma Lalolo L1oo-2 264627 / 262144 [-18 7 0 0 2⟩ 16.321
biyatisma Lologu 1oog1 121/120 [-3 -1 -1 0 2⟩ 14.367
aphrowe Trilo-aruru 1o3rr-2 1331/1323 [0 -3 0 -2 3⟩ 10.437
valinorsma Lorugugu 1orgg1 176/175 [4 0 -2 -1 1⟩ 9.8646
pentacircle Saluzo s1uz2 896/891 [7 -4 0 1 -1⟩ 9.6880
Alpharabian comma Laquadlo L1o4-2 131769 / 131072 [-17 2 0 0 4⟩ 9.1818
orgonisma Satrilu-aruru s1u3rr1 65536 / 65219 [16 0 0 -2 -3⟩ 8.3944
quindecic comma Sasa-quintriloru ss1o15r15-8 [14 -15 0 -15 15⟩ 8.0555
fantares comma Luluzoquadyo 1uuzy41 4375 / 4356 [-2 -2 4 1 -2⟩ 7.5349
semicanousma Quadlo-agu 1o4g1 14641 / 14580 [-2 -6 -1 0 4⟩ 7.2281
rastma Lulu 1uu1 243/242 [-1 5 0 0 -2⟩ 7.1391
myhemiwell Lolozotrigu 1oozg32 3388/3375 [2 -3 -3 1 2⟩ 6.6556
semiporwellisma Salulugu s1uug2 16384 / 16335 [14 -3 -1 0 -2⟩ 5.1854
octatonic comma Quadbilu 1u82 214990848 / 214358881 [15 8 0 0 -8⟩ 5.0965
keenanisma Lozoyo 1ozy1 385/384 [-7 -1 1 1 1⟩ 4.5026
trimitone comma Lalotrigu L1og31 8019/8000 [-6 6 -3 0 1⟩ 4.1068
werckisma Luzozogu 1uzzg2 441/440 [-3 2 -1 2 -1⟩ 3.9302
moctdel Lotriruyo 1or3y3-3 1375/1372 [-2 0 3 -3 1⟩ 3.7814
liganellus comma, liganellisma Luruquinyo 1ury5-2 6250/6237 [1 -4 5 -1 -1⟩ 3.60473

13-limit commas

Name(s) Color Name Ratio Monzo Cents
wilsorma Thoyo 3oy1 65/64 [-6 0 1 0 0 1⟩ 26.841
hyperpyth comma Quadtho-aquingu 3o4g53 28561/28125 [0 -2 -5 0 0 4⟩ 26.632
winmeanma Thulogu 3u1og1 66/65 [1 1 -1 0 1 -1⟩ 26.432
negustma Tholuru 3o1ur1 78/77 [1 1 0 -1 -1 1⟩ 22.339
superleap Thozogu 3ozg2 91/90 [-1 -2 -1 1 0 1⟩ 19.130
tridecimal neutral 3rd comma Thuthu 3uu1 512/507 [9 -1 0 0 0 -2⟩ 16.990
animist Thuzoyo 3uzy1 105/104 [-3 1 1 1 0 -1⟩ 16.567
secorian Sathuzo s3uz2 28672 / 28431 [12 -7 0 1 0 -1⟩ 14.613
mosaic Lathoruru L3orr-2 3159/3136 [-6 5 0 -2 0 1⟩ 12.651
gassorma Thuloruyoyo 3u1oryy-2 275/273 [0 -1 2 -1 1 -1⟩ 12.637
grossma Thulu 3u1u1 144/143 [4 2 0 0 -1 -1⟩ 12.064
buzurgisma, dhanvantarisma Thothoru 3oor1 169/168 [-3 -1 0 -1 0 2⟩ 10.274
greater nelindic comma Thothoquinru-ayoyo 3oor5yy-3 16900/16807 [2 0 2 -5 0 2⟩ 9.5532
catadictma Thologu 3o1og1 1287/1280 [-8 2 -1 0 1 1⟩ 9.4419
mynucuma Thuzozogu 3uzzg2 196/195 [2 -1 -1 2 0 -1⟩ 8.8554
huntma, lesser nelindic comma Thururuyo 3urry-2 640/637 [7 0 1 -2 0 -1⟩ 8.1342
threedie Satritho s3o32 2197/2187 [0 -7 0 0 0 3⟩ 7.8980
kestrel comma Thuthuloru 3uu1or-2 1188/1183 [2 3 0 -1 1 -2⟩ 7.3017
marveltwin Thoyoyo 3oyy1 325/324 [-2 -4 2 0 0 1⟩ 5.3351
Hunt 13-cycle comma Laquinbitho L3o102 137858491849 / 137438953472 [-37 0 0 0 0 10⟩ 5.2766
ratwolfsma Thorugugu 3orgg1 351/350 [-1 3 -2 -1 0 1⟩ 4.9393
minthma, 11/13-kleisma Thulo 3u1o1 352/351 [5 -3 0 0 1 -1⟩ 4.9253
gentle comma Tholuluzo 3o1uuz2 364/363 [2 -1 0 1 -2 1⟩ 4.7627
cuthbert Bithulo-azogu 3uu1oozg1 847/845 [0 0 -1 1 2 -2⟩ 4.0928

17-limit commas

Name(s) Color Name Ratio Monzo Cents
soruyo unison Soruyo 17ory1 85/84 [-2 -1 1 -1 0 0 1⟩ 20.488
lum comma Sosothulu 17oo3u1u2 289/286 [-1 0 0 0 -1 -1 2⟩ 18.065
mey comma Sutritho 17u3u31 2197/2176 [-7 0 0 0 0 3 -1⟩ 16.628
septendecimal comma, Hunt flat 2 comma Laso L17o1 4131/4096 [-12 5 0 0 0 0 1⟩ 14.730
suruyo comma Suruyo 17ury-2 120/119 [3 1 1 -1 0 0 -1⟩ 14.487
23 semitone comma Trila-twetheso L317o2310 [-94 0 0 0 0 0 23⟩ 13.974
sothuthuyo unison Sothuthuyo 17o3uuy1 170/169 [1 0 1 0 0 -2 1⟩ 10.214
septendecimal schisma[1] Lasu L17u-2 2187/2176 [-7 7 0 0 0 0 -1⟩ 8.7296
Blume comma Sololo 17o1oo1 2057/2048 [-11 0 0 0 2 0 1⟩ 7.5913
septendecimal kleisma Sugu 17ug1 256/255 [8 -1 -1 0 0 0 -1⟩ 6.7759
tannisma Suthozo 17u3oz1 273/272 [-4 1 0 1 0 1 -1⟩ 6.3532
septendecimal integer cents comma Soso 17oo2 289/288 [-5 -2 0 0 0 0 2⟩ 6.0008
17-ripple integer cents comma [327 0 0 0 0 0 -80⟩ 3.5672

19-limit commas

Name(s) Color name Ratio Monzo Cents
nuruyo comma Nuruyo 19ury-2 135/133 [0 3 1 -1 0 0 0 -1⟩ 25.84
nogugu 2nd Nogugu 19ogg2 76/75 [2 -1 -2 0 0 0 0 1⟩ 22.931
nulozo unison (approximation to the adjacent step of 53edo) Nulozo 19u1oz1 77/76 [-2 0 0 1 1 0 0 -1⟩ 22.631
19th-partial chroma Nugu 19ug1 96/95 [5 1 -1 0 0 0 0 -1⟩ 18.128
ume comma Nutriso 19u17o32 4913/4864 [-8 0 0 0 0 0 3 -1⟩ 17.353
noluzo 2nd Noluzo 19o1uz2 133/132 [-2 -1 0 1 -1 0 0 1⟩ 13.066
ganassisma, Ganassi's comma Nuso 19u17o1 153/152 [-3 2 0 0 0 0 1 -1⟩ 11.352
nosugu unison Nosugu 19o17ug1 171/170 [-1 2 -1 0 0 0 -1 1⟩ 10.154
eye comma Nusosolulu 19u17oo1uu2 2312/2299 [3 0 0 0 -2 0 2 -1⟩ 9.7619
Hunt 19-cycle comma Saquadnu s19u4-2 131072 / 130321 [17 0 0 0 0 0 0 -4⟩ 9.9479
binulo comma Binulo 19uu1oo-2 363/361 [0 1 0 0 2 0 0 -2⟩ 9.5649
yama comma Nothulo 19o3u1o1 209/208 [-4 0 0 0 1 -1 0 1⟩ 8.3033
spleen comma Nuluzoyo 19u1uzy1 210/209 [1 1 1 1 -1 0 0 -1⟩ 8.2637
nuthologu comma Nuthologu 19u3o1og1 286/285 [1 -1 -1 0 1 1 0 -1⟩ 6.0639
nusu comma Nusu 19u17u-2 324/323 [2 4 0 0 0 0 -1 -1⟩ 5.3516
go comma Nonogu 19oog2 361/360 [-3 -2 -1 0 0 0 0 2⟩ 4.8023

Higher-limit commas

Name(s) Color name Ratio Monzo Cents
Classical mediant of Didymus' and Archytas' commas 145/143 [0 0 1 0 -1 -1 0 0 0 1⟩ 24.045
  1. ↑ The Helmholtz-Ellis JI Pitch Notation (HEJI)
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