Small comma: Difference between revisions
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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. In [[Sagittal notation]], intervals in the smaller part of this category are [[kleisma (interval region)|kleismas]], and intervals in the larger part of this category are [[comma (interval region)|commas]]<ref>[https://sagittal.org/sagittal.pdf ''Sagittal – A Microtonal Notation System''] by [[George Secor|George D. Secor]] and [[Dave Keenan|David C. Keenan]]</ref>. | |||
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 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" | [[Kite's color notation/Temperament names|Color name]] | |||
! [[Ratio]] | |||
! [[Monzo]] | |||
! [[Cents]] | |||
! Named by | |||
|- | |||
| 241-comma | |||
| 241wama | |||
| 241wM | |||
| | |||
| {{Monzo| 382 -241 }} | |||
| 28.845 | |||
| | |||
|- | |||
| 65-comma, <br>Pythagorean septimal comma | |||
| 65wama, Thequiwama | |||
| 65wM | |||
| | |||
| {{Monzo| -103 65 }} | |||
| 27.075 | |||
| | |||
|- | |||
| [[Pythagorean comma]] | |||
| Lalawama, Poma | |||
| LLwM | |||
| 531441 / 524288 | |||
| {{Monzo| -19 12 }} | |||
| 23.460 | |||
| | |||
|- | |||
| [[41-comma]], Pythagorean countercomma, <br>countercomp comma | |||
| 41wama, Fowewama | |||
| 41wM | |||
| <abbr title="36893488147419103232 / 36472996377170786403">(40 digits)</abbr> | |||
| {{Monzo| 65 -41 }} | |||
| 19.845 | |||
| [[Flora Canou]] (2022) | |||
|- | |||
| [[94-comma]], garistearn comma | |||
| 94wama, Fosebiwama | |||
| 94wM | |||
| | |||
| {{Monzo| 149 -94 }} | |||
| 16.230 | |||
| [[User:Xenllium|Xenllium]] (2021) | |||
|- | |||
| 147-comma | |||
| 147wama | |||
| 147wM | |||
| | |||
| {{Monzo| 233 -147 }} | |||
| 12.615 | |||
| | |||
|- | |||
| 200-comma, <br>Pythagorean integer-cent ET comma | |||
| 200wama | |||
| 200wM | |||
| | |||
| {{Monzo| 317 -200 }} | |||
| 8.9998 | |||
| | |||
|- | |||
| 253-comma | |||
| 253wama | |||
| 253wM | |||
| | |||
| {{Monzo| 401 -253 }} | |||
| 5.3848 | |||
| | |||
|- | |||
| [[Mercator's comma]], 53-comma | |||
| 53wama, Fithewama | |||
| 53wM | |||
| <abbr title="19383245667680019896796723 / 19342813113834066795298816">(52 digits)</abbr> | |||
| {{Monzo| -84 53 }} | |||
| 3.6150 | |||
| | |||
|} | |||
=== 5-limit commas === | |||
{| class="wikitable" | |||
! Name(s) | |||
! colspan="2" | [[Kite's color notation/Temperament names|Color name]] | |||
! [[Ratio]] | |||
! [[Monzo]] | |||
! [[Cents]] | |||
! Named by | |||
|- | |||
| [[Magic comma]], small diesis | |||
| Laquinyoma | |||
| L5yM | |||
| 3125 / 3072 | |||
| {{Monzo| -10 -1 5 }} | |||
| 29.614 | |||
| | |||
|- | |||
| [[Triscordial comma]] | |||
| Tribila-triyoma | |||
| 6L3yM | |||
| <abbr title="18761829412124890125 / 18446744073709551616">(40 digits)</abbr> | |||
| {{Monzo| -64 36 3 }} | |||
| 29.321 | |||
| [[User:Xenllium|Xenllium]] (2026) | |||
|- | |||
| [[Hendecatonic comma]] | |||
| Trisa-leguma | |||
| 3s11gM | |||
| 8796093022208 / 8649755859375 | |||
| {{Monzo| 43 -11 -11 }} | |||
| 29.044 | |||
| | |||
|- | |||
| [[Devil's tridecalimma]] | |||
| Lala-theguma | |||
| LL13gM | |||
| 2541865828329 / 2500000000000 | |||
| {{Monzo| -11 26 -13 }} | |||
| 28.752 | |||
| | |||
|- | |||
| [[Anthoine comma]] | |||
| Trila-quinquadyoma | |||
| 3L20yM | |||
| 286102294921875 / 281474976710656 | |||
| {{Monzo| -48 1 20 }} | |||
| 28.229 | |||
| | |||
|- | |||
| [[Tetracot comma]], minimal diesis | |||
| Saquadyoma | |||
| s4yM | |||
| 20000 / 19683 | |||
| {{Monzo| 5 -9 4 }} | |||
| 27.660 | |||
| | |||
|- | |||
| [[Biscordial comma]] | |||
| Quadla-yoyoma | |||
| 4LyyM | |||
| 571919811374025 / 562949953421312 | |||
| {{Monzo| -49 28 2 }} | |||
| 27.367 | |||
| [[User:Xenllium|Xenllium]] (2026) | |||
|- | |||
| [[Semaja comma]] | |||
| Lala-neyoma | |||
| LL19yM | |||
| 19073486328125 / 18786186952704 | |||
| {{Monzo| -33 -7 19 }} | |||
| 26.276 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Quanic comma]] | |||
| Sepsa-quinyoma | |||
| 7s5yM | |||
| | |||
| {{Monzo| 74 -54 5 }} | |||
| 25.999 | |||
| | |||
|- | |||
| [[Roda]], rodan comma | |||
| Sasa-triyoma | |||
| ss3yM | |||
| 131072000 / 129140163 | |||
| {{Monzo| 20 -17 3 }} | |||
| 25.706 | |||
| | |||
|- | |||
| [[Gracecordial comma]] | |||
| Trilayoma | |||
| 3LyM | |||
| 17433922005 / 17179869184 | |||
| {{Monzo| -34 20 1 }} | |||
| 25.414 | |||
| | |||
|- | |||
| [[Trisedodge comma]] | |||
| Saquintriguma | |||
| s15gM | |||
| 30958682112 / 30517578125 | |||
| {{Monzo| 19 10 -15 }} | |||
| 24.844 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Birds comma]] | |||
| Quadsa-thiweguma | |||
| 4s31gM | |||
| | |||
| {{Monzo| 72 0 -31 }} | |||
| 24.275 | |||
| | |||
|- | |||
| [[Neuk comma]] | |||
| Trisa-yoyoma | |||
| 3syyM | |||
| 858993459200 / 847288609443 | |||
| {{Monzo| 35 -25 2 }} | |||
| 23.752 | |||
| [[User:CompactStar|CompactStar]] (2023) | |||
|- | |||
| [[Maja comma]] | |||
| Saseyoma | |||
| s17yM | |||
| 762939453125 / 753145430616 | |||
| {{Monzo| -3 -23 17 }} | |||
| 22.368 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Satin comma]] | |||
| Quinbisa-triyoma | |||
| 10s3yM | |||
| | |||
| {{Monzo| 104 -70 3 }} | |||
| 22.091 | |||
| | |||
|- | |||
| [[Misneb comma]] | |||
| Quadla-quintriyoma | |||
| 4L15yM | |||
| <abbr title="145964630126953125 / 144115188075855872">(36 digits)</abbr> | |||
| {{Monzo| -57 14 15 }} | |||
| 22.076 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Syntonic comma]], Didymus comma, meantone comma | |||
| Guma | |||
| gM | |||
| 81 / 80 | |||
| {{Monzo| -4 4 -1 }} | |||
| 21.506 | |||
| | |||
|- | |||
| [[Maquila comma]] | |||
| Trisa-seguma | |||
| 3s17gM | |||
| 562949953421312 / 556182861328125 | |||
| {{Monzo| 49 -6 -17 }} | |||
| 20.937 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Sfourth comma]] | |||
| Lala-neguma | |||
| LL19gM | |||
| 617673396283947 / 610351562500000 | |||
| {{Monzo| -5 31 -19 }} | |||
| 20.644 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Diaschisma]] | |||
| Saguguma | |||
| sggM | |||
| 2048 / 2025 | |||
| {{Monzo| 11 -4 -2 }} | |||
| 19.553 | |||
| Hermann von Helmholtz, Alexander Ellis (1875) | |||
|- | |||
| [[Countermeantone comma]] | |||
| Quinquadguma | |||
| 20gM | |||
| 96402615118848 / 95367431640625 | |||
| {{Monzo| 10 23 -20 }} | |||
| 18.691 | |||
| [[Petr Pařízek]] (2012) | |||
|- | |||
| [[Ditonma]] | |||
| Lala-theyoma | |||
| LL13yM | |||
| 1220703125 / 1207959552 | |||
| {{Monzo| -27 -2 13 }} | |||
| 18.168 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Misty comma]] | |||
| Sasa-triguma | |||
| ss3gM | |||
| 67108864 / 66430125 | |||
| {{Monzo| 26 -12 -3 }} | |||
| 17.599 | |||
| [[Paul Erlich]] (2002) | |||
|- | |||
| [[Quintile comma]] | |||
| Trila-quinguma | |||
| 3L5gM | |||
| 847288609443 / 838860800000 | |||
| {{Monzo| -28 25 -5 }} | |||
| 17.306 | |||
| See the dedicated page. | |||
|- | |||
| [[Enneadecacot comma]] | |||
| Tribisa-neguma | |||
| 6s19gM | |||
| <abbr title="604462909807314587353088 / 598546211414337158203125">(48 digits)</abbr> | |||
| {{monzo| 79 -22 -19 }} | |||
| 17.029 | |||
| [[User:CompactStar|CompactStar]] (2024) | |||
|- | |||
| [[Oquatonic comma]] | |||
| Quadla-sepquadyoma | |||
| 4L28yM | |||
| <abbr title="37252902984619140625 / 36893488147419103232">(40 digits)</abbr> | |||
| {{Monzo| -65 0 28 }} | |||
| 16.784 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Undim comma]] | |||
| Trisa-quadguma | |||
| 3s4gM | |||
| 2199023255552 / 2179240250625 | |||
| {{Monzo| 41 -20 -4 }} | |||
| 15.645 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Graviton]], gravity comma | |||
| Lala-tribiguma | |||
| LL6gM | |||
| 129140163 / 128000000 | |||
| {{Monzo| -13 17 -6 }} | |||
| 15.353 | |||
| [[Mike Battaglia]] (2011) | |||
|- | |||
| [[Majvam comma]] | |||
| Sasa-lebiguma | |||
| ss22gM | |||
| <abbr title="2404631929946112 / 2384185791015625">(32 digits)</abbr> | |||
| {{Monzo| 40 7 -22 }} | |||
| 14.783 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Quartonic comma]] | |||
| Saleyoma | |||
| s11yM | |||
| 390625000 / 387420489 | |||
| {{Monzo| 3 -18 11 }} | |||
| 14.261 | |||
| | |||
|- | |||
| [[Untritonic comma]] | |||
| Quadla-tritriyoma | |||
| 4L9yM | |||
| <abbr title="2270041927734375 / 2251799813685248">(32 digits)</abbr> | |||
| {{Monzo| -51 19 9 }} | |||
| 13.968 | |||
| [[Petr Pařízek]] (2011) | |||
|- | |||
| [[Quindromeda comma]] | |||
| Quinsa-quinguma | |||
| 5s5gM | |||
| <abbr title="72057594037927936 / 71489976421753125">(34 digits)</abbr> | |||
| {{Monzo| 56 -28 -5 }} | |||
| 13.691 | |||
| [[User:Xenllium|Xenllium]] (2021) | |||
|- | |||
| [[Sensipent comma]], medium semicomma | |||
| Sepguma | |||
| 7gM | |||
| 78732 / 78125 | |||
| {{Monzo| 2 9 -7 }} | |||
| 13.399 | |||
| | |||
|- | |||
| [[Copper comma]] | |||
| Theneyoma | |||
| 41L29yM | |||
| | |||
| {{Monzo| -481 261 29 }} | |||
| 13.353 | |||
| [[Eliora]] (2023) | |||
|- | |||
| [[Counterwürschmidt comma]] | |||
| Trisa-twetheguma | |||
| 3s23gM | |||
| <abbr title="36028797018963968 / 35762786865234375">(34 digits)</abbr> | |||
| {{Monzo| 55 -1 -23 }} | |||
| 12.830 | |||
| [[Flora Canou]] (2023) | |||
|- | |||
| [[Tertiosec comma]] | |||
| Laquadtribiyoma | |||
| 6L24yM | |||
| | |||
| {{Monzo| -89 21 24 }} | |||
| 12.584 | |||
| [[Petr Pařízek]] (2012) | |||
|- | |||
| [[Submajor comma]] | |||
| Trila-quadbiyoma | |||
| 3L8yM | |||
| 69198046875 / 68719476736 | |||
| {{Monzo| -36 11 8 }} | |||
| 12.015 | |||
| | |||
|- | |||
| [[Würschmidt comma]] | |||
| Saquadbiguma | |||
| s8gM | |||
| 393216 / 390625 | |||
| {{Monzo| 17 1 -8 }} | |||
| 11.445 | |||
| | |||
|- | |||
| [[Bicommatic comma]] | |||
| Quadla-quinbiguma | |||
| 4L10gM | |||
| <abbr title="1350851717672992089 / 1342177280000000000">(38 digits)</abbr> | |||
| {{Monzo| -37 38 -10 }} | |||
| 11.153 | |||
| | |||
|- | |||
| [[Counterhanson comma]] | |||
| Quinquinyoma | |||
| 25yM | |||
| <abbr title="298023223876953125 / 296148833645101056">(36 digits)</abbr> | |||
| {{Monzo| -20 -24 25 }} | |||
| 10.923 | |||
| [[Petr Pařízek]] (2012) | |||
|- | |||
| [[Countritonic comma]] | |||
| Quadsa-tritriyoma | |||
| 4s9yM | |||
| <abbr title="16777216000000000 / 16677181699666569">(34 digits)</abbr> | |||
| {{Monzo| 33 -34 9 }} | |||
| 10.353 | |||
| [[User:Xenllium|Xenllium]] (2022) | |||
|- | |||
| [[Semicomma]], Fokker's comma | |||
| Lasepyoma | |||
| L7yM | |||
| 2109375 / 2097152 | |||
| {{Monzo| -21 3 7 }} | |||
| 10.061 | |||
| | |||
|- | |||
| [[Heptacot comma]] | |||
| Sepsa-sepguma | |||
| 7s7gM | |||
| | |||
| {{Monzo| 86 -44 -7 }} | |||
| 9.7840 | |||
| [[Tristan Bay]] (2024) | |||
|- | |||
| [[Escapade comma]] | |||
| Sasa-tritriguma | |||
| ss9gM | |||
| 4294967296 / 4271484375 | |||
| {{Monzo| 32 -7 -9 }} | |||
| 9.4916 | |||
| [[Paul Erlich]] (2002) | |||
|- | |||
| [[Undetritisma]], twentcufo comma | |||
| Trila-leguma | |||
| 3L11gM | |||
| 205891132094649 / 204800000000000 | |||
| {{Monzo| -22 30 -11 }} | |||
| 9.1992 | |||
| | |||
|- | |||
| [[15625/15552|Kleisma]], semicomma majeur | |||
| Tribiyoma | |||
| 6yM | |||
| 15625 / 15552 | |||
| {{Monzo| -6 -5 6 }} | |||
| 8.1073 | |||
| {{W|Shohé Tanaka}} (1890) | |||
|- | |||
| [[Quintosec comma]] | |||
| Quadsa-quinbiguma | |||
| 4s10gM | |||
| 140737488355328 / 140126044921875 | |||
| {{Monzo| 47 -15 -10 }} | |||
| 7.5378 | |||
| [[Petr Pařízek]] (2012) | |||
|- | |||
| 59-5-comma | |||
| Quadbisa-fineguma | |||
| 8s59gM | |||
| | |||
| {{Monzo| 137 0 -59 }} | |||
| 7.4909 | |||
| | |||
|- | |||
| [[Unidecma]] | |||
| Laquadtriguma | |||
| L12gM | |||
| 31381059609 / 31250000000 | |||
| {{Monzo| -7 22 -12 }} | |||
| 7.2455 | |||
| | |||
|- | |||
| [[Mutt comma]] | |||
| Trila-septriyoma | |||
| 3L21yM | |||
| 476837158203125 / 474989023199232 | |||
| {{Monzo| -44 -3 21 }} | |||
| 6.7230 | |||
| [[Gene Ward Smith]] (2004) | |||
|- | |||
| [[Sulfur comma]] | |||
| Lela-quadquadguma | |||
| 11L16gM | |||
| | |||
| {{Monzo| -115 96 -16 }} | |||
| 6.6607 | |||
| | |||
|- | |||
| [[Amity comma]] | |||
| Saquinyoma | |||
| s5yM | |||
| 1600000 / 1594323 | |||
| {{Monzo| 9 -13 5 }} | |||
| 6.1536 | |||
| [[Gene Ward Smith]] (2001) | |||
|- | |||
| [[Parakleisma]] | |||
| Theguma | |||
| 13gM | |||
| 1224440064 / 1220703125 | |||
| {{Monzo| 8 14 -13 }} | |||
| 5.2917 | |||
| [[Gene Ward Smith]] (2001 | |||