Small comma: Difference between revisions
Wikispaces>genewardsmith **Imported revision 243122691 - Original comment: ** |
→7-limit commas: 1500625/1492992 is simply the 7-limit comma of uniwiz |
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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 comma]]; for commas in between 30 and 100 cents in size, see [[Medium comma]]; and for commas under 3.5 cents in size, see [[Unnoticeable comma]]. | |||
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. | |||
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. | |||
== | == List of commas, by prime limit == | ||
=== 3-limit commas === | |||
{{See also| Table of 3-limit commas }} | |||
== | {| class="wikitable" | ||
! Name(s) | |||
! colspan="2" |[[Color notation/Temperament names|Color name]] | |||
! [[Ratio]] | |||
! [[Monzo]] | |||
! [[Cents]] | |||
! Named by | |||
|- | |||
| 241-comma | |||
| Wa-241 | |||
| w-241 | |||
| | |||
| {{Monzo| 382 -241 }} | |||
| 28.845 | |||
| | |||
|- | |||
| 65-comma, <br>Pythagorean septimal comma | |||
| Wa-65 | |||
| w-65 | |||
| | |||
| {{Monzo| -103 65 }} | |||
| 27.075 | |||
| | |||
|- | |||
| [[Pythagorean comma]] | |||
| Lalawa | |||
| LLw-2 | |||
| 531441 / 524288 | |||
| {{Monzo| -19 12 }} | |||
| 23.460 | |||
| | |||
|- | |||
| [[41-comma]], Pythagorean countercomma, <br>countercomp comma | |||
| Wa-41 | |||
| w-41 | |||
| <abbr title="36893488147419103232 / 36472996377170786403">(40 digits)</abbr> | |||
| {{Monzo| 65 -41 }} | |||
| 19.845 | |||
| [[Flora Canou]] (2022) | |||
|- | |||
| [[94-comma]], garistearn comma | |||
| Wa-94 | |||
| w-94 | |||
| | |||
| {{Monzo| 149 -94 }} | |||
| 16.230 | |||
| [[User:Xenllium|Xenllium]] (2021) | |||
|- | |||
| 147-comma | |||
| Wa-147 | |||
| w-147 | |||
| | |||
| {{Monzo| 233 -147 }} | |||
| 12.615 | |||
| | |||
|- | |||
| 200-comma, <br>Pythagorean integer-cent ET comma | |||
| Wa-200 | |||
| w-200 | |||
| | |||
| {{Monzo| 317 -200 }} | |||
| 8.9998 | |||
| | |||
|- | |||
| 253-comma | |||
| Wa-253 | |||
| w-253 | |||
| | |||
| {{Monzo| 401 -253 }} | |||
| 5.3848 | |||
| | |||
|- | |||
| [[Mercator's comma]], 53-comma | |||
| Wa-53 | |||
| w-53 | |||
| <abbr title="19383245667680019896796723 / 19342813113834066795298816">(52 digits)</abbr> | |||
| {{Monzo| -84 53 }} | |||
| 3.6150 | |||
| | |||
|} | |||
=== 5-limit commas === | |||
{{See also| Table of 5-limit commas }} | |||
{| class="wikitable" | |||
! Name(s) | |||
! colspan="2" |[[Color notation/Temperament names|Color name]] | |||
! [[Ratio]] | |||
! [[Monzo]] | |||
! [[Cents]] | |||
! Named by | |||
|- | |||
| [[Magic comma]], small diesis | |||
| Laquinyo | |||
| L5y-2 | |||
| 3125 / 3072 | |||
| {{Monzo| -10 -1 5 }} | |||
| 29.614 | |||
| | |||
|- | |||
| [[Hendecatonic comma]] | |||
| Trisa-legu | |||
| 3s11g5 | |||
| 8796093022208 / 8649755859375 | |||
| {{Monzo| 43 -11 -11 }} | |||
| 29.044 | |||
| | |||
|- | |||
| [[Tetracot comma]], minimal diesis | |||
| Saquadyo | |||
| s4y1 | |||
| 20000 / 19683 | |||
| {{Monzo| 5 -9 4 }} | |||
| 27.660 | |||
| | |||
|- | |||
| [[Semaja comma]] | |||
| Lalaneyo | |||
| LL19y-5 | |||
| 19073486328125 / 18786186952704 | |||
| {{Monzo| -33 -7 19 }} | |||
| 26.276 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Quanic comma]] | |||
| Sepsa-quinyo | |||
| 7s5y5 | |||
| | |||
| {{Monzo| 74 -54 5 }} | |||
| 25.999 | |||
| | |||
|- | |||
| [[Roda]], rodan comma | |||
| Sasa-triyo | |||
| ss3y2 | |||
| 131072000 / 129140163 | |||
| {{Monzo| 20 -17 3 }} | |||
| 25.706 | |||
| | |||
|- | |||
| Gracecordial comma | |||
| Trilayo | |||
| 3Ly-3 | |||
| 17433922005 / 17179869184 | |||
| {{Monzo| -34 20 1 }} | |||
| 25.414 | |||
| | |||
|- | |||
| [[Trisedodge comma]] | |||
| Saquintrigu | |||
| s15g4 | |||
| 30958682112 / 30517578125 | |||
| {{Monzo| 19 10 -15 }} | |||
| 24.844 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Birds comma]] | |||
| Quadsa-thiwegu | |||
| 4s31g9 | |||
| | |||
| {{Monzo| 72 0 -31 }} | |||
| 24.275 | |||
| | |||
|- | |||
| [[Neuk comma]] | |||
| Trisa-yoyo | |||
| 3syy3 | |||
| 858993459200 / 847288609443 | |||
| {{Monzo| 35 -25 2 }} | |||
| 23.752 | |||
| [[User:CompactStar|CompactStar]] (2023) | |||
|- | |||
| [[Maja comma]] | |||
| Saseyo | |||
| s17y-3 | |||
| 762939453125 / 753145430616 | |||
| {{Monzo| -3 -23 17 }} | |||
| 22.368 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Satin comma]] | |||
| Quinbisa-triyo | |||
| 10s3y7 | |||
| | |||
| {{Monzo| 104 -70 3 }} | |||
| 22.091 | |||
| | |||
|- | |||
| [[Misneb comma]] | |||
| Quadla-quintriyo | |||
| 4L15y-6 | |||
| <abbr title="145964630126953125 / 144115188075855872">(36 digits)</abbr> | |||
| {{Monzo| -57 14 15 }} | |||
| 22.076 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Syntonic comma]], Didymus comma, meantone comma | |||
| Gu | |||
| g1 | |||
| 81 / 80 | |||
| {{Monzo| -4 4 -1 }} | |||
| 21.506 | |||
| | |||
|- | |||
| [[Maquila comma]] | |||
| Trisa-segu | |||
| 3s17g6 | |||
| 562949953421312 / 556182861328125 | |||
| {{Monzo| 49 -6 -17 }} | |||
| 20.937 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Sfourth comma]] | |||
| Lala-negu | |||
| LL19g3 | |||
| 617673396283947 / 610351562500000 | |||
| {{Monzo| -5 31 -19 }} | |||
| 20.644 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Diaschisma]] | |||
| Sagugu | |||
| sgg2 | |||
| 2048 / 2025 | |||
| {{Monzo| 11 -4 -2 }} | |||
| 19.553 | |||
| Hermann von Helmholtz, Alexander Ellis (1875) | |||
|- | |||
| [[Countermeantone comma]] | |||
| Quinquadgu | |||
| 20g4 | |||
| 96402615118848 / 95367431640625 | |||
| {{Monzo| 10 23 -20 }} | |||
| 18.691 | |||
| [[Petr Pařízek]] (2012) | |||
|- | |||
| [[Ditonma]] | |||
| Lala-theyo | |||
| LL13y-4 | |||
| 1220703125 / 1207959552 | |||
| {{Monzo| -27 -2 13 }} | |||
| 18.168 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Misty comma]] | |||
| Sasa-trigu | |||
| ss3g3 | |||
| 67108864 / 66430125 | |||
| {{Monzo| 26 -12 -3 }} | |||
| 17.599 | |||
| [[Paul Erlich]] (2002) | |||
|- | |||
| [[Quintile comma]] | |||
| Trila-quingu | |||
| 3L5g-2 | |||
| 847288609443 / 838860800000 | |||
| {{Monzo| -28 25 -5 }} | |||
| 17.306 | |||
| See the dedicated page. | |||
|- | |||
| [[Enneadecacot comma]] | |||
| Tribisa-negu | |||
| 6s19g8 | |||
| 562949953421312 / 557439598640741 | |||
| {{monzo| 79 -22 -19 }} | |||
| 17.029 | |||
| [[User:CompactStar|CompactStar]] (2024) | |||
|- | |||
| [[Oquatonic comma]] | |||
| Quadla-sepquadyo | |||
| 4L28y-8 | |||
| <abbr title="37252902984619140625 / 36893488147419103232">(40 digits)</abbr> | |||
| {{Monzo| -65 0 28 }} | |||
| 16.784 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Undim comma]] | |||
| Trisa-quadgu | |||
| 3s4g4 | |||
| 2199023255552 / 2179240250625 | |||
| {{Monzo| 41 -20 -4 }} | |||
| 15.645 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Graviton]], gravity comma | |||
| Lala-tribigu | |||
| LL6g1 | |||
| 129140163 / 128000000 | |||
| {{Monzo| -13 17 -6 }} | |||
| 15.353 | |||
| [[Mike Battaglia]] (2011) | |||
|- | |||
| [[Majvam comma]] | |||
| Sasa-lebigu | |||
| ss22g6 | |||
| <abbr title="2404631929946112 / 2384185791015625">(32 digits)</abbr> | |||
| {{Monzo| 40 7 -22 }} | |||
| 14.783 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Quartonic comma]] | |||
| Saleyo | |||
| s11y-2 | |||
| 390625000 / 387420489 | |||
| {{Monzo| 3 -18 11 }} | |||
| 14.261 | |||
| | |||
|- | |||
| [[Untritonic comma]] | |||
| Quadla-tritriyo | |||
| 4L9y-5 | |||
| <abbr title="2270041927734375 / 2251799813685248">(32 digits)</abbr> | |||
| {{Monzo| -51 19 9 }} | |||
| 13.968 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Quindromeda comma]] | |||
| Quinsa-quingu | |||
| 5s5g5 | |||
| <abbr title="72057594037927936 / 71489976421753125">(34 digits)</abbr> | |||
| {{Monzo| 56 -28 -5 }} | |||
| 13.691 | |||
| [[User:Xenllium|Xenllium]] (2021) | |||
|- | |||
| [[Sensipent comma]], medium semicomma | |||
| Sepgu | |||
| 7g2 | |||
| 78732 / 78125 | |||
| {{Monzo| 2 9 -7 }} | |||
| 13.399 | |||
| | |||
|- | |||
| [[Copper comma]] | |||
| Theneyo | |||
| 41L29y-33 | |||
| | |||
| {{Monzo| -481 261 29 }} | |||
| 13.353 | |||
| [[Eliora]] (2023) | |||
|- | |||
| [[Counterwürschmidt comma]] | |||
| Trisa-twethegu | |||
| 3s23g7 | |||
| <abbr title="36028797018963968 / 35762786865234375">(34 digits)</abbr> | |||
| {{Monzo| 55 -1 -23 }} | |||
| 12.830 | |||
| [[Flora Canou]] (2023) | |||
|- | |||
| [[Tertiosec comma]] | |||
| Laquadtribiyo | |||
| 6L24y-9 | |||
| | |||
| {{Monzo| -89 21 24 }} | |||
| 12.584 | |||
| [[Petr Pařízek]] (2012) | |||
|- | |||
| [[Würschmidt comma]] | |||
| Saquadbigu | |||
| s8g3 | |||
| 393216 / 390625 | |||
| {{Monzo| 17 1 -8 }} | |||
| 11.445 | |||
| | |||
|- | |||
| [[Bicommatic comma]] | |||
| Quadla-quinbigu | |||
| 4L10g-2 | |||
| <abbr title="1350851717672992089 / 1342177280000000000">(38 digits)</abbr> | |||
| {{Monzo| -37 38 -10 }} | |||
| 11.153 | |||
| | |||
|- | |||
| [[Counterhanson comma]] | |||
| Quinquinyo | |||
| 25y-5 | |||
| <abbr title="298023223876953125 / 296148833645101056">(36 digits)</abbr> | |||
| {{Monzo| -20 -24 25 }} | |||
| 10.923 | |||
| [[Petr Pařízek]] (2012) | |||
|- | |||
| [[Countritonic comma]] | |||
| Quadsa-tritriyo | |||
| 4s9y2 | |||
| <abbr title="16777216000000000 / 16677181699666569">(34 digits)</abbr> | |||
| {{Monzo| 33 -34 9 }} | |||
| 10.353 | |||
| [[User:Xenllium|Xenllium]] (2022) | |||
|- | |||
| [[Semicomma]], Fokker's comma | |||
| Lasepyo | |||
| L7y-3 | |||
| 2109375 / 2097152 | |||
| {{Monzo| -21 3 7 }} | |||
| 10.061 | |||
| | |||
|- | |||
| [[Heptacot comma]] | |||
| Sepsa-sepgu | |||
| 7s7g7 | |||
| | |||
| {{Monzo| 86 -44 -7 }} | |||
| 9.7840 | |||
| [[Tristan Bay]] (2024) | |||
|- | |||
| [[Escapade comma]] | |||
| Sasa-tritrigu | |||
| ss9g4 | |||
| 4294967296 / 4271484375 | |||
| {{Monzo| 32 -7 -9 }} | |||
| 9.4916 | |||
| [[Paul Erlich]] (2002) | |||
|- | |||
| [[15625/15552|Kleisma]], semicomma majeur | |||
| Tribiyo | |||
| 6y-2 | |||
| 15625 / 15552 | |||
| {{Monzo| -6 -5 6 }} | |||
| 8.1073 | |||
| {{W|Shohé Tanaka}} (1890) | |||
|- | |||
| [[Quintosec comma]] | |||
| Quadsa-quinbigu | |||
| 4s10g5 | |||
| 140737488355328 / 140126044921875 | |||
| {{Monzo| 47 -15 -10 }} | |||
| 7.5378 | |||
| [[Petr Pařízek]] (2012) | |||
|- | |||
| 59-5-comma | |||
| Quadbisa-finegu | |||
| 8s59g16 | |||
| | |||
| {{Monzo| 137 0 -59 }} | |||
| 7.4909 | |||
| | |||
|- | |||
| [[Unidecma]] | |||
| Laquadtrigu | |||
| L12g2 | |||
| 31381059609 / 31250000000 | |||
| {{Monzo| -7 22 -12 }} | |||
| 7.2455 | |||
| | |||
|- | |||
| [[Mutt comma]] | |||
| Trila-septriyo | |||
| 3L21y-6 | |||
| 476837158203125 / 474989023199232 | |||
| {{Monzo| -44 -3 21 }} | |||
| 6.7230 | |||
| [[Gene Ward Smith]] (2004) | |||
|- | |||
| [[Sulfur comma]] | |||
| Lela-quadquadgu | |||
| 11L16g-6 | |||
| | |||
| {{Monzo| -115 96 -16 }} | |||
| 6.6607 | |||
| | |||
|- | |||
| [[Amity comma]] | |||
| Saquinyo | |||
| s5y1 | |||
| 1600000 / 1594323 | |||
| {{Monzo| 9 -13 5 }} | |||
| 6.1536 | |||
| [[Gene Ward Smith]] (2001) | |||
|- | |||
| [[Parakleisma]] | |||
| Thegu | |||
| 13g3 | |||
| 1224440064 / 1220703125 | |||
| {{Monzo| 8 14 -13 }} | |||
| 5.2917 | |||
| [[Gene Ward Smith]] (2001) | |||
|- | |||
| [[Gammic comma]] | |||
| Laquinquadyo | |||
| L20y-5 | |||
| 95367431640625 / 95105071448064 | |||
| {{Monzo| -29 -11 20 }} | |||
| 4.7693 | |||
| | |||
|- | |||
| [[Squarschmidt comma]] | |||
| Quadsa-twenegu | |||
| 4s29g8 | |||
| <abbr title="186773283746309210112 / 186264514923095703125">(42 digits)</abbr> | |||
| {{Monzo| 61 4 -29 }} | |||
| 4.7223 | |||
| [[Petr Pařízek]] (2012) | |||
|- | |||
| Huntian 15-cycle comma | |||
| Quadtrisa-fothegu | |||
| 12s43g16 | |||
| | |||
| {{Monzo| 168 -43 |