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== Definition == | |||
A '''comma''' is a small interval that occurs in [[just intonation]], between two intervals which are close in pitch. Commas are always greater than 1 and not a power such as a square or cube of any other interval, and generally in a [[Harmonic Limit|low prime limit]]. The word is often used in reference to [[Regular Temperaments|regular tempering]] when the comma is ''[[tempering_out|tempered out]]'', which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between 10/9 and 9/8, as well as 81/64 and 5/4, is tempered out by [[Meantone|meantone temperament]]. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in [[cent]]s. | |||
For commas over 100 cents in size, see [[Large commas]]; and for commas under 3.5 cents in size, see [[Unnoticeable commas]] | |||
== List of commas, by prime limit == | |||
= | === 3-limit commas === | ||
==3-limit commas== | |||
{| class="wikitable" | {| class="wikitable" | ||
! Name(s) | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |- | ||
| limma, Pythagorean minor second | |||
| [[256/243|256 / 243]] | |||
| {{Monzo| 8 -5 }} | |||
| 90.225 | |||
|- | |- | ||
| [[Pythagorean comma]] | |||
| 531441/524288 | |||
| | | | | {{Monzo| -19 12 }} | ||
| | | 23.460 | ||
|- | |- | ||
| [[17-comma]] | |||
| | |||
| | | | {{Monzo| 27 -17 }} | ||
| | | 66.765 | ||
|- | |- | ||
| [[29-comma]] | |||
| | |||
| | | | {{Monzo| 46 -29 }} | ||
| | | 43.305 | ||
|- | |- | ||
| [[41-comma]] | |||
| | |||
| | | | {{Monzo| 65 -41 }} | ||
| | | 19.845 | ||
|- | |- | ||
| | | Pythagorean Integer cents comma | ||
| | |||
| | | | {{Monzo| 317 -200 }} | ||
| | | 9.000 | ||
|- | |- | ||
| | | [[Mercator's comma]], 53-comma | ||
| | | 19383245667680019896796723/19342813113834066795298816 | ||
| | | | {{Monzo| -84 53 }} | ||
| | | 3.615 | ||
|- | |- | ||
| 70-comma | |||
| | |||
| {{Monzo| 111 -70 }} | |||
| 63.150 | |||
| | |||
|} | |} | ||
==5-limit commas== | === 5-limit commas === | ||
{| class="wikitable" | {| class="wikitable" | ||
! Name(s) | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |- | ||
| Twenty-two thirds limma | |||
| | |||
| {{Monzo| -51 0 22 }} | |||
| 98.902 | |||
|- | |- | ||
| | | sibbolet | ||
| | |||
| | | {{Monzo| -58 0 25 }} | ||
| | | 57.843 | ||
|- | |- | ||
| | | Hunt 5-cycle comma | ||
| | |||
| | | {{Monzo| -65 0 28 }} | ||
| | | 16.784 | ||
|- | |- | ||
| | | acute thirds comma | ||
| | |||
| | | | {{Monzo| 72 0 -31 }} | ||
| | | 24.275 | ||
|- | |- | ||
| | | 34-5-comma | ||
| | |||
| | | | {{Monzo| 79 0 -34 }} | ||
| | | 65.334 | ||
|- | |- | ||
| | | Schismic thirds chromatic semitone | ||
| | |||
| | | | {{Monzo| -123 0 53 }} | ||
| | | 74.627 | ||
|- | |- | ||
| | | 10-15-comma | ||
| | |||
| | | {{Monzo| -39 10 10 }} | ||
| | | 82.687 | ||
|- | |- | ||
| | | 11-15-comma | ||
| | |||
| | | | {{Monzo| 43 -11 -11 }} | ||
| | | 29.044 | ||
|- | |- | ||
| | | 21-15-comma | ||
| | |||
| | | | {{Monzo| 82 -21 -21 }} | ||
| | | 53.643 | ||
|- | |- | ||
| | | 32-15-comma | ||
| | |||
| | | | {{Monzo| 125 -32 -32 }} | ||
| | | 24.599 | ||
|- | |- | ||
| | | Huntian 15-cycle comma | ||
| | |||
| | | | {{Monzo| -168 43 43 }} | ||
| | | 4.445 | ||
|- | |- | ||
| | | 53-15-comma | ||
| | |||
| | | {{Monzo| -207 53 53 }} | ||
| | | 78.242 | ||
|- | |- | ||
| | | 54-15-comma | ||
| | |||
| | | | {{Monzo| 211 -54 -54 }} | ||
| | | 33.489 | ||
|- | |- | ||
| | | 76-15-comma | ||
| | |||
| | | | {{Monzo| 297 -76 -76 }} | ||
| | | 91.578 | ||
|- | |- | ||
| | | major chroma, major limma, pelogic comma | ||
| | | | [[135/128|135 / 128]] | ||
| | | | {{Monzo| -7 3 1 }} | ||
| | | 92.179 | ||
|- | |- | ||
| | | ripple | ||
| | | 6561 / 6250 | ||
| | | {{Monzo| -1 8 -5 }} | ||
| | | 84.071 | ||
|- | |- | ||
| | | doublewide | ||
| | | | ||
| | | | {{Monzo| -9 -6 8 }} | ||
| | | 78.780 | ||
|- | |- | ||
| | | sevond | ||
| | |||
| | | | {{Monzo| 6 -14 7 }} | ||
| | | 76.826 | ||
|- | |- | ||
| | | nusecond | ||
| | |||
| | | | {{Monzo| 5 13 -11 }} | ||
| | | 75.964 | ||
|- | |- | ||
| | | sentinel | ||
| | |||
| | | | {{Monzo| -33 15 4 }} | ||
| | | 74.580 | ||
|- | |- | ||
| | | chromatic semitone | ||
| | | | [[25/24|25 / 24]] | ||
| | | | {{Monzo| -3 -1 2 }} | ||
| | | 70.672 | ||
|- | |- | ||
| | | superpyth, grave minor second | ||
| | | 20480 / 19683 | ||
| | | | {{Monzo| 12 -9 1 }} | ||
| | | 68.719 | ||
|- | |- | ||
| | | major diesis, diminished comma | ||
| | | | [[648/625|648 / 625]] | ||
| | | | {{Monzo| 3 4 -4 }} | ||
| | | 62.565 | ||
|- | |- | ||
| | | passion | ||
| | | | ||
| | | | {{Monzo| 18 -4 -5 }} | ||
| | | 60.611 | ||
|- | |- | ||
| | | shibboleth | ||
| | |||
| | | | {{Monzo| -5 -10 9 }} | ||
| | | 57.273 | ||
|- | |- | ||
| | | mynic | ||
| | |||
| | | | {{Monzo| 9 9 -10 }} | ||
| | | 54.458 | ||
|- | |- | ||
| | | tritonic | ||
| | |||
| | | | {{Monzo| -29 11 5 }} | ||
| | | 53.074 | ||
|- | |- | ||
| | | [[negri comma]], double augmentation diesis | ||
| | | 16875 / 16384 | ||
| | | {{Monzo| -14 3 4 }} | ||
| | | 51.120 | ||
|- | |- | ||
| | [[ | | maximal diesis, porcupine comma | ||
| | | | [[250/243|250 / 243]] | ||
| {{Monzo| 1 -5 3 }} | |||
| | | 49.166 | ||
|- | |- | ||
| | | immunity | ||
| | | | ||
| | | | {{Monzo| 16 -13 2 }} | ||
| | | 47.212 | ||
|- | |- | ||
| | | diesis, augmented comma | ||
| | | | [[128/125|128 / 125]] | ||
| | | | {{Monzo| 7 0 -3 }} | ||
| | | 41.059 | ||
|- | |- | ||
| | | wizard | ||
| | | | ||
| | | | {{Monzo| -31 2 12 }} | ||
| | | 39.675 | ||
|- | |- | ||
| | | sycamore | ||
| | |||
| | | | {{Monzo| -16 -6 11 }} | ||
| | | 37.721 | ||
|- | |- | ||
| | | fifive | ||
| | |||
| | | {{Monzo| -1 -14 10 }} | ||
| | | 35.767 | ||
|- | |- | ||
| | | unicorn | ||
| | |||
| | | {{Monzo| -2 13 -8 }} | ||
| | | 34.905 | ||
|- | |- | ||
| | | valensixthtone | ||
| | |||
| | | | {{Monzo| 13 5 -9 }} | ||
| | | 32.952 | ||
|- | |- | ||
| | | [[ampersand]], Ampersand's comma | ||
| | |||
| | | | {{Monzo| -25 7 6 }} | ||
| | | 31.567 | ||
|- | |- | ||
| | | small diesis, [[magic comma]] | ||
| | | 3125 / 3072 | ||
| | | | {{Monzo| -10 -1 5 }} | ||
| | | 29.614 | ||
|- | |- | ||
| | | minimal diesis, [[tetracot comma]] | ||
| | | 20000 / 19683 | ||
| | | | {{Monzo| 5 -9 4 }} | ||
| | | 27.660 | ||
|- | |- | ||
| | | roda | ||
| | | | ||
| | | | {{Monzo| 20 -17 3 }} | ||
| | | 25.706 | ||
|- | |- | ||
| | | maja | ||
| | |||
| | | | {{Monzo| -3 -23 17 }} | ||
| | | 22.368 | ||
|- | |- | ||
| | | syntonic comma, Didymos comma, meantone comma | ||
| | | | [[81/80|81 / 80]] | ||
| | | {{Monzo| -4 4 -1 }} | ||
| | | 21.506 | ||
|- | |- | ||
| [[Maquila family|maquila comma]] | |||
| | |||
| | | - | | {{Monzo| 49 -6 -17 }} | ||
| | | 20.937 | ||
|- | |- | ||
| [[diaschisma]] | |||
| | | 2048 / 2025 | ||
| | | | {{Monzo| 11 -4 -2 }} | ||
| | | 19.553 | ||
|- | |- | ||
| | | ditonma | ||
| | | | ||
| | | | {{Monzo| -27 -2 13 }} | ||
| | | 18.168 | ||
|- | |- | ||
| | | [[misty comma]] | ||
| | |||
| | | | {{Monzo| 26 -12 -3 }} | ||
| | | 17.599 | ||
|- | |- | ||
| [[pental comma]] | |||
| | |||
| | | | {{Monzo| -28 25 -5 }} | ||
| 17.306 | |||
|- | |- | ||
| | | [[graviton]], [[Gravity family|gravity]] comma | ||
| | |||
| | | {{Monzo| -13 17 -6 }} | ||
| | | 15.353 | ||
|- | |- | ||
| | | quartonic | ||
| | |||
| | | | {{Monzo| 3 -18 11 }} | ||
| | | 14.261 | ||
|- | |- | ||
| | | medium semicomma, [[sensipent comma]] | ||
| | | 78732 / 78125 | ||
| | | | {{Monzo| 2 9 -7 }} | ||
| | | 13.399 | ||
|- | |- | ||
| | | [[Würschmidt comma]] | ||
| | | | ||
| | | | {{Monzo| 17 1 -8 }} | ||
| | | 11.445 | ||
|- | |- | ||
| [[semicomma]], Fokker comma | |||
| | |||
| | | | {{Monzo| -21 3 7 }} | ||
| | | 10.061 | ||
|- | |- | ||
| [[escapade comma]] | |||
| | |||
| | | | {{Monzo| 32 -7 -9 }} | ||
| | | 9.492 | ||
|- | |- | ||
| [[kleisma]], semicomma majeur | |||
| | | 15625 / 15552 | ||
| | | | {{Monzo| -6 -5 6 }} | ||
| | | 8.107 | ||
|- | |- | ||
| | | unidecma | ||
| | | | ||
| | | {{Monzo| -7 22 -12 }} | ||
| | | 7.245 | ||
|- | |- | ||
| | | [[mutt comma]] | ||
| | |||
| | | {{Monzo| -44 -3 21 }} | ||
| | | 6.723 | ||
|- | |- | ||
| [[amity comma]] | |||
| | |||
| | | | {{Monzo| 9 -13 5 }} | ||
| 6.154 | |||
|- | |- | ||
| [[parakleisma]] | |||
| | |||
| | | | {{Monzo| 8 14 -13 }} | ||
| | | 5.292 | ||
|- | |- | ||
| | | gammic comma | ||
| | |||
| | | | {{Monzo| -29 -11 20 }} | ||
| | | 4.769 | ||
|- | |- | ||
| | | [[vulture comma]] | ||
| | |||
| | | | {{Monzo| 24 -21 4 }} | ||
| 4.200 | |||
|- | |- | ||
| | | 23-3/5-comma | ||
| | |||
| | | | {{Monzo| 17 23 -23 }} | ||
| | | 59.750 | ||
|- | |- | ||
| | | 34-3/5-comma | ||
| | |||
| | | | {{Monzo| -25 -34 34 }} | ||
| | | 68.196 | ||
|- | |- | ||
| 53-3/5-comma | |||
| | |||
| {{Monzo| 39 53 -53 }} | |||
| 71.012 | |||
| | |||
|} | |} | ||
==7-limit commas== | === 7-limit commas === | ||
{| class="wikitable" | {| class="wikitable" | ||
! Name(s) | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |- | ||
| hexadecatone comma, 16-7-comma | |||
| | |||
| {{Monzo| 45 0 0 -16 }} | |||
| 98.7855 | |||
|- | |- | ||
| | | 21-7-comma | ||
| | |||
| | | | {{Monzo| 59 0 0 -21 }} | ||
| | | 54.656 | ||
|- | |- | ||
| | | Hunt 7-cycle comma | ||
| | |||
| | | | {{Monzo| 73 0 0 -26 }} | ||
| | | 10.526 | ||
|- | |- | ||
| | | German sixth comma | ||
| | |||
| | | | {{Monzo| -87 0 0 31 }} | ||
| | | 33.603 | ||
|- | |- | ||
| | | large deep red comma | ||
| | | 6561 / 6272 | ||
| | | {{Monzo| -7, 8, 0 -2 }} | ||
| | | 77.988 | ||
|- | |- | ||
| | | 36-7-comma | ||
| | | | ||
| | | {{Monzo| -101 0 0 36 }} | ||
| 77.737 | |||
|- | |- | ||
| | | 47-7-comma | ||
| | |||
| | | | {{Monzo| 132 0 0 0 -47 }} | ||
| | | 65.182 | ||
|- | |- | ||
| | | slendro integer cents comma | ||
| | |||
| | | | {{Monzo| 1127 0 0 -400 }} | ||
| | | 69.637 | ||
|- | |- | ||
| | | 29-7/5-comma | ||
| | |||
| | | | {{Monzo| -14 0 -29 29 }} | ||
| | | 92.854 | ||
|- | |- | ||
| | | 31-7/5-comma | ||
| | |||
| | | {{Monzo| -15 0 -31 31 }} | ||
| | | 57.878 | ||
|- | |- | ||
| | | 33-7/5-comma | ||
| | |||
| | | {{Monzo| -16 0 -33 33 }} | ||
| | | 22.902 | ||
|- | |- | ||
| | | 35-7/5-comma | ||
| | |||
| | | | {{Monzo| 18 0 35 -35 }} | ||
| | | 12.073 | ||
|- | |- | ||
| | | 37-7/5-comma | ||
| | |||
| | | | {{Monzo| 19 0 37 -37 }} | ||
| | | 47.049 | ||
|- | |- | ||
| | | 39-7/5-comma | ||
| | |||
| | | | {{Monzo| 20 0 39 -39 }} | ||
| | | 82.0245 | ||
|- | |- | ||
| | | 5-21-comma | ||
| | |||
| | | | {{Monzo| 22 -5 0 -5 }} | ||
| | | 46.0955 | ||
|- | |- | ||
| | | 18-21-comma | ||
| | |||
| | | | {{Monzo| -79 18 0 18 }} | ||
| | | 74.056 | ||
|- | |- | ||
| | | 23-21-comma | ||
| | |||
| | | {{Monzo| -101 23 0 23 }} | ||
| | | 27.961 | ||
|- | |- | ||
| | | Huntian 21-cycle comma | ||
| | |||
| | | | {{Monzo| 123 -28 0 -28 }} | ||
| | | 18.135 | ||
|- | |- | ||
| | | 33-21-comma | ||
| | |||
| | | | {{Monzo| 145 -33 0 -33 }} | ||
| | | 64.230 | ||
|- | |- | ||
| | | 8-35-comma | ||
| | |||
| | | | {{Monzo| -41 0 8 8 }} | ||
| | | 41.117 | ||
|- | |- | ||
| | | 15-35-comma | ||
| | |||
| | | | {{Monzo| 77 0 -15 -15 }} | ||
| | | 72.906 | ||
|- | |- | ||
| | | 23-35-comma | ||
| | |||
| | | | {{Monzo| 118 0 -23 -23 }} | ||
| | | 31.789 | ||
|- | |- | ||
| | | 31-35-comma | ||
| | |||
| | | | {{Monzo| -159 0 31 31 }} | ||
| | | 9.328 | ||
|- | |- | ||
| | | 39-35-comma | ||
| | |||
| | | {{Monzo| -200 0 39 39 }} | ||
| | | 50.445 | ||
|- | |- | ||
| | | 47-35-comma | ||
| | |||
| | | {{Monzo| -241 0 47 47 }} | ||
| | | 91.562 | ||
|- | |- | ||
| | | Huntian 35-cycle comma | ||
| | |||
| | | | {{Monzo| 277 0 -54 -54 }} | ||
| | | 22.4605 | ||
|- | |- | ||
| | | greenwoodma | ||
| | | 405 / 392 | ||
| | | | {{Monzo| -3 4 1 -2 }} | ||
| | | 56.482 | ||
|- | |- | ||
| | | Harrison's comma | ||
| | | | [[59049/57344|59049 / 57344]] | ||
| | | | {{Monzo| -13 10 0 -1 }} | ||
| | | 50.724 | ||
|- | |- | ||
| | | keega | ||
| | | 1029 / 1000 | ||
| | | {{Monzo| -3 1 -3 3 }} | ||
| | | 49.492 | ||
|- | |- | ||
| | | septimal quarter tone | ||
| | | | [[36/35|36 / 35]] | ||
| | | | {{Monzo| 2 2 -1 -1 }} | ||
| | | 48.770 | ||
|- | |- | ||
| | | quarter tone comma | ||
| | | | ||
| | | | {{Monzo| 49 50 -25 -25 }} | ||
| | | 19.2595 | ||
|- | |- | ||
| | | cloudy | ||
| | | 16807 / 16384 | ||
| | | | {{Monzo| -14 0 0 5 }} | ||
| | | 44.130 | ||
|- | |- | ||
| | | Avicenna, Avicenna's enharmonic diesis | ||
| | | 525 / 512 | ||
| | | {{Monzo| -9 1 2 1 }} | ||
| | | 43.408 | ||
|- | |- | ||
| | | slendro diesis | ||
| | | | [[49/48|49 / 48]] | ||
| | | | {{Monzo| -4 -1 0 2 }} | ||
| | | 35.597 | ||
|- | |- | ||
| slendro 34-comma | |||
| | | | ||
| | | {{Monzo| -137 -34 0 68 }} | ||
| | | 13.692 | ||
|- | |- | ||
| | | 34-jubilismic comma | ||
| | |||
| | | {{Monzo| -33 0 -68 68 }} | ||
| | | 10.829 | ||
|- | |- | ||
| | | tritonic diesis, jubilisma | ||
| | | | [[50/49|50 / 49]] | ||
| | | | {{Monzo| 1 0 2 -2 }} | ||
| | | 34.976 | ||
|- | |- | ||
| | | eric | ||
| | | | ||
| | | | {{Monzo| 7 8 0 -7 }} | ||
| | | 33.859 | ||
|- | |- | ||
| | | senga | ||
| | | 686 / 675 | ||
| | | | {{Monzo| 1 -3 -2 3 }} | ||
| | | 27.985 | ||
|- | |- | ||
| | | septimal comma, Archytas' comma, Leipziger Komma | ||
| | | | [[64/63|64 / 63]] | ||
| | | | {{Monzo| 6 -2 0 -1 }} | ||
| 27.264 | |||
|- | |- | ||
| | | blackjackisma | ||
| | | | ||
| | | | {{Monzo| -10 7 8 -7 }} | ||
| | | 22.413 | ||
|- | |- | ||
| | | squalentine | ||
| | | 64827 / 64000 | ||
| | | {{Monzo| -9 3 -3 4 }} | ||
| 22.227 | |||
|- | |- | ||
| | | keema | ||
| | | 875 / 864 | ||
| | | | {{Monzo| -5 -3 3 1 }} | ||
| | | 21.902 | ||
|- | |- | ||
| | | gariboh | ||
| | | 3125 / 3087 | ||
| | | | {{Monzo| 0 -2 5 -3 }} | ||
| 21.181 | |||
|- | |- | ||
| | | nuwell | ||
| | | 2430 / 2401 | ||
| | | | {{Monzo| 1 5 1 -4 }} | ||
| | | 20.785 | ||
|- | |- | ||
| | | tolerma | ||
| | | | ||
| | | | {{Monzo| 10 -11 2 1 }} | ||
| | | 19.948 | ||
|- | |- | ||
| | | mirwomo | ||
| | | 33075 / 32768 | ||
| | | | {{Monzo| -15 3 2 2 }} | ||
| | | 16.144 | ||
|- | |- | ||
| | | trimyna | ||
| | | 50421 / 50000 | ||
| | | | {{Monzo| -4 1 -5 5 }} | ||
| | | 14.516 | ||
|- | |- | ||
| | | sensamagic | ||
| | | 245 / 243 | ||
| | | | {{Monzo| 0 -5 1 2 }} | ||
| 14.191 | |||
|- | |- | ||
| | | septimal semicomma, starling comma | ||
| | | | [[126/125|126 / 125]] | ||
| | | | {{Monzo| 1 2 -3 1 }} | ||
| | | 13.795 | ||
|- | |- | ||
| | | octagar | ||
| | | 4000 / 3969 | ||
| | | | {{Monzo| 5 -4 3 -2 }} | ||
| 13.469 | |||
|- | |- | ||
| | | orwellisma, orwell comma | ||
| | | 1728 / 1715 | ||
| | | | {{Monzo| 6 3 -1 -3 }} | ||
| 13.074 | |||
|- | |- | ||
| | | quince | ||
| | | | ||
| | | | {{Monzo| -15 0 -2 7 }} | ||
| | | 9.154 | ||
|- | |- | ||
| | | gamelisma | ||
| | | 1029 / 1024 | ||
| | | {{Monzo| -10 1 0 3 }} | ||
| | | 8.433 | ||
|- | |- | ||
| | | varunisma | ||
| | | | ||
| | | | {{Monzo| -9 8 -4 2 }} | ||
| 8.037 | |||
|- | |- | ||
| | | septimal kleisma, marvel comma | ||
| | | | [[225/224|225 / 224]] | ||
| | | {{Monzo| -5 2 2 -1 }} | ||
| | | 7.712 | ||
|- | |- | ||
| | | dimcomp | ||
| | | | ||
| | | | {{Monzo| -1 -4 8 -4 }} | ||
| 7.386 | |||
|- | |- | ||
| | | cataharry | ||
| | | 19683 / 19600 | ||
| | | {{Monzo| -4 9 -2 -2 }} | ||
| 7.316 | |||
|- | |- | ||
| | | mirkwai | ||
| | | 16875 / 16807 | ||
| | | | {{Monzo| 0 3 4 -5 }} | ||
| | | 6.990 | ||
|- | |- | ||
| | | stearnsma | ||
| | | | ||
| | | | {{Monzo| 1 10 0 -6 }} | ||
| 6.595 | |||
|- | |- | ||
| | | hemimage | ||
| | | 10976 / 10935 | ||
| | | | {{Monzo| 5 -7 -1 3 }} | ||
| 6.479 | |||
|- | |- | ||
| | | hemimean | ||
| | | 3136 / 3125 | ||
| | | | {{Monzo| 6 0 -5 2 }} | ||
| 6.083 | |||
|- | |- | ||
| | | hemifamity | ||
| | | 5120 / 5103 | ||
| | | | {{Monzo| 10 -6 1 -1 }} | ||
| | | 5.758 | ||
|- | |- | ||
| | | linus | ||
| | | | ||
| | | | {{Monzo| 11 -10 -10 10 }} | ||
| 5.572 | |||
|- | |- | ||
| | | porwell | ||
| | | 6144 / 6125 | ||
| | | {{Monzo| 11 1 -3 -2 }} | ||
| 5.362 | |||
|- | |- | ||
| | | garischisma | ||
| | | | ||
| | | | {{Monzo| 25 -14 0 -1 }} | ||
| | | 3.804 | ||
|- | |- | ||
| | | wadisma | ||
| | |||
| | | | {{Monzo| -26 -1 1 9 }} | ||
| 3.792 | |||
|- | |- | ||
| | | quasiorwellisma | ||
| | |||
| | | | {{Monzo| 22 -1 -10 1 }} | ||
| 3.734 | |||
|- | |- | ||
| | | | [[218edo|218edo]] (stacked [[7/4]] and [[10/9]]) comma | ||
| | |||
| | | {{Monzo| 22 -32 16 -3 }} | ||
| | | 11.982 | ||
|- | |- | ||
| bapbo | |||
| 256 / 245 | |||
| {{Monzo| 8 0 -1 -2 }} | |||
| 76.034 | |||
| | |||
|} | |} | ||
==11-limit commas== | === 11-limit commas === | ||
{| class="wikitable" | {| class="wikitable" | ||
! Name(s) | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |- | ||
| 11-cycle chroma, 11-11-comma | |||
| | |||
| {{Monzo| -38 0 0 0 11 }} | |||
| 64.497 | |||
| | |||
|- | |- | ||
| 11-cycle major seventh prote, 35-11-comma | |||
| | |||
| | | {{Monzo| -121 0 0 0 35 }} | ||
| 96.128 | |||
|- | |- | ||
| Hunt 11-cycle comma | |||
| | |||
| | | {{Monzo| -83 0 0 0 24 }} | ||
| 31.631 | |||
|- | |- | ||
| Hunt flat 5 comma | |||
| 8192 / 8019 | |||
| | | {{Monzo| 13 -6 0 0 -1 }} | ||
| 36.952 | |||
|- | |- | ||
| sterno | |||
| 352 / 343 | |||
| | | {{Monzo| 5 0 0 -3 1 }} | ||
| 44.840 | |||
|- | |- | ||
| the Igs boson, 13-11-comma | |||
| | |||
| | | {{Monzo| 45 0 0 0 -13 }} | ||
| 32.867 | |||
|- | |- | ||
| telepathma | |||
| 55 / 54 | |||
| | | {{Monzo| -1 -3 1 0 1 }} | ||
| 31.767 | |||
|- | |- | ||
| thuja comma | |||
| | |||
| | | {{Monzo| 15 0 1 0 -5 }} | ||
| 29.724 | |||
|- | |- | ||
| sensmus | |||
| 1232 / 1215 | |||
| | | {{Monzo| 4 -5 -1 1 1 }} | ||
| 24.055 | |||
|- | |- | ||
| sevnothrush | |||
| 3168 / 3125 | |||
| | | {{Monzo| 5 2 -5 0 1 }} | ||
| 23.659 | |||
|- | |- | ||
| cassacot | |||
| 245 / 242 | |||
| | | {{Monzo| -1 0 1 2 -2 }} | ||
| 21.330 | |||
|- | |- | ||
| [[mothwellsmic triad|mothwellsma]] | |||
| 99 / 98 | |||
| | | {{Monzo| -1 2 0 -2 1 }} | ||
| 17.576 | |||
|- | |- | ||
| [[ptolemismic triad|ptolemisma]] | |||
| [[100/99|100 / 99]] | |||
| | | {{Monzo| 2 -2 2 0 -1 }} | ||
| 17.399 | |||
|- | |- | ||
| hemimin | |||
| 1344 / 1331 | |||
| | | {{Monzo| 6 1 0 1 -3 }} | ||
| 16.827 | |||
|- | |- | ||
| biyatisma | |||
| 121 / 120 | |||
| | | {{Monzo| -3 -1 -1 0 2 }} | ||
| 14.367 | |||
|- | |- | ||
| aphrowe | |||
| 1331 / 1323 | |||
| | | {{Monzo| 0 -3 0 -2 3 }} | ||
| 10.437 | |||
|- | |- | ||
| [[valinorsmic chords|valinorsma]] | |||
| 176 / 175 | |||
| | | {{Monzo| 4 0 -2 -1 1 }} | ||
| 9.865 | |||
|- | |- | ||
| [[pentacircle comma|pentacircle]] | |||
| 896 / 891 | |||
| | | {{Monzo| 7 -4 0 1 -1 }} | ||
| 9.688 | |||
|- | |- | ||
| orgonisma | |||
| 65536 / 65219 | |||
| | | {{Monzo| 16 0 0 -2 -3 }} | ||
| 8.394 | |||
|- | |- | ||
| [[rastmic chords|rastma]] | |||
| 243 / 242 | |||
| | | {{Monzo| -1 5 0 0 -2 }} | ||
| 7.139 | |||
|- | |- | ||
| myhemiwell | |||
| 3388 / 3375 | |||
| | | {{Monzo| 2 -3 -3 1 2 }} | ||
| 6.656 | |||
|- | |- | ||
| [[keenanismic chords|keenanisma]] | |||
| [[385/384|385 / 384]] | |||
| | | {{Monzo| -7 -1 1 1 1 }} | ||
| 4.503 | |||
|- | |- | ||
| [[werckismic chords|werckisma]] | |||
| 441 / 440 | |||
| | | {{Monzo| -3 2 -1 2 -1 }} | ||
| 3.930 | |||
|- | |- | ||
| moctdel | |||
| 1375 / 1372 | |||
| | | {{Monzo| -2 0 3 -3 1 }} | ||
| 3.781 | |||
|} | |} | ||
==13-limit commas== | === 13-limit commas === | ||
{| class="wikitable" | {| class="wikitable" | ||
! Name(s) | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |- | ||
| Hunt 13-cycle comma | |||
| | |||
| {{Monzo| -37 0 0 0 0 0 10 }} | |||
| 5.277 | |||
| | |||
|- | |- | ||
| | | silver half cents comma | ||
| | |||
| | | {{Monzo| -8881 0 0 0 2400 }} | ||
| | | 66.389 | ||
|- | |- | ||
| Hunt minor submediant comma | |||
| 1053 / 1024 | |||
| | | {{Monzo| -10 4 0 0 0 0 1 }} | ||
| 48.348 | |||
|- | |- | ||
| astburyp | |||
| | |||
| | | {{Monzo| -19 -2 0 0 0 6 }} | ||
| 39.255 | |||
|- | |- | ||
| wilsorma | |||
| 65 / 64 | |||
| | | {{Monzo| -6 0 1 0 0 1 }} | ||
| 26.841 | |||
|- | |- | ||
| winmeanma | |||
| 66 / 65 | |||
| | | {{Monzo| 1 1 -1 0 1 -1 }} | ||
| 26.432 | |||
|- | |- | ||
| negustma | |||
| 78 / 77 | |||
| | | {{Monzo| 1 1 0 -1 -1 1 }} | ||
| 22.229 | |||
|- | |- | ||
| superleap | |||
| 91 / 90 | |||
| | | {{Monzo| -1 -2 -1 1 0 1 }} | ||
| 19.130 | |||
|- | |- | ||
| animist | |||
| 105 / 104 | |||
| | | {{Monzo| -3 1 1 1 0 -1 }} | ||
| 16.567 | |||
|- | |- | ||
| secorian | |||
| 28672 / 28431 | |||
| | | {{Monzo| 12 -7 0 1 0 -1 }} | ||
| 14.613 | |||
|- | |- | ||
| mosaic | |||
| 3159 / 3136 | |||
| | | {{Monzo| -6 5 0 -2 0 1}} | ||
| 12.651 | |||
|- | |- | ||
| gassorma | |||
| 275 / 273 | |||
| | | {{Monzo| 0 -1 2 -1 1 -1 }} | ||
| 12.637 | |||
|- | |- | ||
| [[grossma]] | |||
| 144 / 143 | |||
| | | {{Monzo| 4 2 0 0 -1 -1 }} | ||
| 12.064 | |||
|- | |- | ||
| buzurgisma, dhanvantarisma | |||
| 169 / 168 | |||
| | | {{Monzo| -3 -1 0 -1 0 2 }} | ||
| 10.274 | |||
|- | |- | ||
| catadictma | |||
| 1287 / 1280 | |||
| | | {{Monzo| -8 2 -1 0 1 1 }} | ||
| 9.442 | |||
|- | |- | ||
| [[mynucumic chords|mynucuma]] | |||
| 196 / 195 | |||
| | | {{Monzo| 2 -1 -1 2 0 -1 }} | ||
| 8.855 | |||
|- | |- | ||
| [[huntmic chords|huntma]] | |||
| 640 / 637 | |||
| | | {{Monzo| 7 0 1 -2 0 -1 }} | ||
| 8.134 | |||
|- | |- | ||
| [[threedie]] | |||
| 2197 / 2187 | |||
| | | {{Monzo| 0 -7 0 0 0 3 }} | ||
| 7.897 | |||
|- | |- | ||
| [[kestrel chords|kestrel comma]] | |||
| 1188 / 1183 | |||
| | | {{Monzo| 2 3 0 -1 1 -2 }} | ||
| 7.302 | |||
|- | |- | ||
| [[marveltwin]] | |||
| 325 / 324 | |||
| | | {{Monzo| -2 -4 2 0 0 1 }} | ||
| 5.335 | |||
|- | |- | ||
| [[ratwolf triad|ratwolfsma]] | |||
| 351 / 350 | |||
| | | {{Monzo| -1 3 -2 -1 0 1 }} | ||
| 4.939 | |||
|- | |- | ||
| [[minthmic chords|minthma]] | |||
| 352 / 351 | |||
| | | {{Monzo| 5 -3 0 0 1 -1 }} | ||
| 4.925 | |||
|- | |- | ||
| [[gentle chords|gentle comma]] | |||
| 364 / 363 | |||
| | | {{Monzo| 2 -1 0 1 -2 1 }} | ||
| 4.763 | |||
|- | |- | ||
| [[cuthbert triad|cuthbert]] | |||
| 847 / 845 | |||
| | | {{Monzo| 0 0 -1 1 2 -2 }} | ||
| 4.093 | |||
|} | |} | ||
==17-limit commas== | === 17-limit commas === | ||
{| class="wikitable" | {| class="wikitable" | ||
! Name(s) | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |- | ||
| 11 semitone comma | |||
| | |||
| {{Monzo| 45 0 0 0 0 0 -11 }} | |||
| 45.4905 | |||
|- | |- | ||
| | | 12 semitone comma | ||
| | |||
| | | | {{Monzo| -49 0 0 0 0 0 12 }} | ||
| | | 59.465 | ||
|- | |- | ||
| | | 23 semitone comma | ||
| | |||
| | | {{Monzo| -93 0 0 0 0 0 23 }} | ||
| | | 13.974 | ||
|- | |- | ||
| | | Hunt 17-cycle comma | ||
| | |||
| | | {{Monzo| -138 0 0 0 0 0 34 }} | ||
| | | 31.516 | ||
|- | |- | ||
| | | 17-ripple integer cents comma | ||
| | |||
| | | | {{Monzo| 327 0 0 0 0 0 -80 }} | ||
| | | 3.568 | ||
|- | |- | ||
| | | Hunt flat 2 comma | ||
| | | 4131 / 4096 | ||
| | | | {{Monzo| -12 5 0 0 0 0 1 }} | ||
| | | 14.730 | ||
|- | |- | ||
| | | Blume comma | ||
| | | 2057 / 2048 | ||
| | | {{Monzo| -11 0 0 0 2 0 1 }} | ||
| | | 7.591 | ||
|- | |- | ||
| | | Septendecimal Integer Cents comma | ||
| | | 289 / 288 | ||
| | | | {{Monzo| -5 -2 0 0 0 0 2 }} | ||
| | | 6.001 | ||
|- | |- | ||
| Tannisma | |||
| 273/272 | |||
| {{Monzo| -4 1 0 1 0 1 -2}} | |||
| 6.353 | |||
| | |||
|} | |} | ||
==19-limit commas== | === 19-limit commas === | ||
{| class="wikitable" | {| class="wikitable" | ||
! Name(s) | |||
! Ratio | |||
! Monzo | |||
! Cents | |||
|- | |- | ||
| Hunt 19-cycle comma | |||
| | |||
| {{Monzo| 17 0 0 0 0 0 0 -4 }} | |||
| 9.950 | |||
|- | |- | ||
| | | spleen comma | ||
| | | 210 / 209 | ||
| | | | {{Monzo| 1 1 1 1 -1 0 0 -1 }} | ||
| | | 8.264 | ||
|- | |- | ||
| go comma | |||
| 361 / 360 | |||
| {{Monzo| -3 -2 -1 0 0 0 0 2 }} | |||
| 4.802 | |||
| | |||
|} | |} | ||
[[Category:comma]] | [[Category:comma]] | ||
[[Category:interval]] | [[Category:interval]] | ||
[[Category:list]] | [[Category:list]] | ||
[[Category:theory]] | [[Category:theory]] | ||
<!-- interwiki --> | |||
[[de:Komma]] | |||