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 -->