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| <h2>IMPORTED REVISION FROM WIKISPACES</h2> | | <span style="display: block; text-align: right;">[[:de:Komma Deutsch]]</span> |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2017-12-26 17:18:22 UTC</tt>.<br>
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| : The original revision id was <tt>624242145</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"><span style="display: block; text-align: right;">[[xenharmonie/Komma|Deutsch]]
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| </span>
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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.
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| For commas over 100 cents in size, see [[Large commas]]; and for commas under 3.5 cents in size, see [[Unnoticeable commas]]
| | =Definition= |
| | A '''comma''' is a small interval that occurs in [[Just_intonation|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|cent]]s. |
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| =List of commas, by prime limit=
| | For commas over 100 cents in size, see [[Large_commas|Large commas]]; and for commas under 3.5 cents in size, see [[Unnoticeable_commas|Unnoticeable commas]] |
| ==3-limit commas==
| |
| ||~ name(s) ||~ ratio ||~ monzo ||~ cents ||
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| || limma, Pythagorean minor second || [[256_243|256 / 243]] || | 8 -5 > || 90.225 ||
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| || [[Pythagorean comma]] || || | -19 12 > || 23.460 ||
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| || [[17-comma]] || || | 27 -17 > || 66.765 ||
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| || [[29-comma]] || || | 46 -29 > || 43.305 ||
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| || [[41-comma]] || || | 65 -41 > || 19.845 ||
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| || Pythagorean Integer cents comma || || | 317 -200 > || 9.000 ||
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| || [[Mercator's comma]], 53-comma || || | -84 53 > || 3.615 ||
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| || 70-comma || || | 111 -70 > || 63.150 ||
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| ==5-limit commas==
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| ||~ name(s) ||~ ratio ||~ monzo ||~ cents ||
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| || Twenty-two thirds limma || || | -51 0 22 > || 98.902 ||
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| || sibbolet || || | -58 0 25 > || 57.843 ||
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| || Hunt 5-cycle comma || || | -65 0 28 > || 16.784 ||
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| || acute thirds comma || || | 72 0 -31 > || 24.275 ||
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| || 34-5-comma || || | 79 0 -34 > || 65.334 ||
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| || Schismic thirds chromatic semitone || || | -123 0 53 > || 74.627 ||
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| || 10-15-comma || || | -39 10 10 > || 82.687 ||
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| || 11-15-comma || || | 43 -11 -11 > || 29.044 ||
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| || 21-15-comma || || | 82 -21 -21 > || 53.643 ||
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| || 32-15-comma || || | 125 -32 -32 > || 24.599 ||
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| || Huntian 15-cycle comma || || | -168 43 43 > || 4.445 ||
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| || 53-15-comma || || | -207 53 53 > || 78.242 ||
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| || 54-15-comma || || | 211 -54 -54 > || 33.489 ||
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| || 76-15-comma || || | 297 -76 -76 > || 91.578 ||
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| || major chroma, major limma, pelogic comma || [[135_128|135 / 128]] || | -7 3 1 > || 92.179 ||
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| || ripple || 6561 / 6250 || | -1 8 -5 > || 84.071 ||
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| || doublewide || || | -9 -6 8 > || 78.780 ||
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| || sevond || || | 6 -14 7 > || 76.826 ||
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| || nusecond || || | 5 13 -11 > || 75.964 ||
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| || sentinel || || | -33 15 4 > || 74.580 ||
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| || chromatic semitone || [[25_24|25 / 24]] || | -3 -1 2 > || 70.672 ||
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| || superpyth, grave minor second || 20480 / 19683 || | 12 -9 1 > || 68.719 ||
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| || major diesis, diminished comma || [[648_625|648 / 625]] || | 3 4 -4 > || 62.565 ||
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| || passion || || | 18 -4 -5 > || 60.611 ||
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| || shibboleth || || | -5 -10 9 > || 57.273 ||
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| || mynic || || | 9 9 -10 > || 54.458 ||
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| || tritonic || || | -29 11 5 > || 53.074 ||
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| || [[negri comma]], double augmentation diesis || 16875 / 16384 || | -14 3 4 > || 51.120 ||
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| || maximal diesis, porcupine comma || [[250_243|250 / 243]] || | 1 -5 3 > || 49.166 ||
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| || immunity || || | 16 -13 2 > || 47.212 ||
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| || diesis, augmented comma || [[128_125|128 / 125]] || | 7 0 -3 > || 41.059 ||
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| || wizard || || | -31 2 12 > || 39.675 ||
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| || sycamore || || | -16 -6 11 > || 37.721 ||
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| || fifive || || | -1 -14 10 > || 35.767 ||
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| || unicorn || || | -2 13 -8 > || 34.905 ||
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| || valensixthtone || || | 13 5 -9 > || 32.952 ||
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| || [[ampersand]], Ampersand's comma || || | -25 7 6 > || 31.567 ||
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| || small diesis, [[magic comma]] || 3125 / 3072 || | -10 -1 5 > || 29.614 ||
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| || minimal diesis, [[tetracot comma]] || 20000 / 19683 || | 5 -9 4 > || 27.660 ||
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| || roda || || | 20 -17 3 > || 25.706 ||
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| || maja || || | -3 -23 17 > || 22.368 ||
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| || syntonic comma, Didymos comma, meantone comma || [[81_80|81 / 80]] || | -4 4 -1 > || 21.506 ||
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| || [[Maquila family|maquila comma]] || || | 49 -6 -17 > || 20.937 ||
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| || [[diaschisma]] || 2048 / 2025 || | 11 -4 -2 > || 19.553 ||
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| || ditonma || || | -27 -2 13 > || 18.168 ||
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| || [[misty comma]] || || | 26 -12 -3 > || 17.599 ||
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| || [[Pental family|pental comma]] || || | -28 25 -5 > || 17.306 ||
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| || [[graviton]], [[Gravity family|gravity]] comma || || | -13 17 -6 > || 15.353 ||
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| || quartonic || || | 3 -18 11 > || 14.261 ||
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| || medium semicomma, [[sensipent comma]] || 78732 / 78125 || | 2 9 -7 > || 13.399 ||
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| || [[Würschmidt comma]] || || | 17 1 -8 > || 11.445 ||
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| || [[semicomma]], Fokker comma || || | -21 3 7 > || 10.061 ||
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| || [[escapade comma]] || || | 32 -7 -9 > || 9.492 ||
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| || [[kleisma]], semicomma majeur || 15625 / 15552 || | -6 -5 6 > || 8.107 ||
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| || unidecma || || | -7 22 -12 > || 7.245 ||
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| || [[mutt comma]] || || | -44 -3 21 > || 6.723 ||
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| || [[amity comma]] || || | 9 -13 5 > || 6.154 ||
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| || [[parakleisma]] || || | 8 14 -13 > || 5.292 ||
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| || gammic comma || || | -29 -11 20 > || 4.769 ||
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| || [[vulture comma]] || || | 24 -21 4 > || 4.200 ||
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| || 23-3/5-comma || || | 17 23 -23 > || 59.750 ||
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| || 34-3/5-comma || || | -25 -34 34 > || 68.196 ||
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| || 53-3/5-comma || || | 39 53 -53 > || 71.012 ||
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| ==7-limit commas== | | =List of commas, by prime limit= |
| ||~ name(s) ||~ ratio ||~ monzo ||~ cents ||
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| || hexadecatone comma, 16-7-comma || || | 45 0 0 -16 > || 98.7855 ||
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| || 21-7-comma || || | 59 0 0 -21 > || 54.656 ||
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| || Hunt 7-cycle comma || || | 73 0 0 -26 > || 10.526 ||
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| || German sixth comma || || | -87 0 0 31 > || 33.603 ||
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| || large deep red comma || 6561 / 6272 || | -7, 8, 0 -2 > || 77.988 ||
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| || 36-7-comma || || | -101 0 0 36 > || 77.737 ||
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| || 47-7-comma || || | 132 0 0 0 -47 > || 65.182 ||
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| || slendro integer cents comma || || | 1127 0 0 -400 > || 69.637 ||
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| || 29-7/5-comma || || | -14 0 -29 29 > || 92.854 ||
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| || 31-7/5-comma || || | -15 0 -31 31 > || 57.878 ||
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| || 33-7/5-comma || || | -16 0 -33 33 > || 22.902 ||
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| || 35-7/5-comma || || | 18 0 35 -35 > || 12.073 ||
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| || 37-7/5-comma || || | 19 0 37 -37 > || 47.049 ||
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| || 39-7/5-comma || || | 20 0 39 -39 > || 82.0245 ||
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| || 5-21-comma || || | 22 -5 0 -5 > || 46.0955 ||
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| || 18-21-comma || || | -79 18 0 18 > || 74.056 ||
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| || 23-21-comma || || | -101 23 0 23 > || 27.961 ||
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| || Huntian 21-cycle comma || || | 123 -28 0 -28 > || 18.135 ||
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| || 33-21-comma || || | 145 -33 0 -33 > || 64.230 ||
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| || 8-35-comma || || | -41 0 8 8 > || 41.117 ||
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| || 15-35-comma || || | 77 0 -15 -15 > || 72.906 ||
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| || 23-35-comma || || | 118 0 -23 -23 > || 31.789 ||
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| || 31-35-comma || || | -159 0 31 31 > || 9.328 ||
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| || 39-35-comma || || | -200 0 39 39 > || 50.445 ||
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| || 47-35-comma || || | -241 0 47 47 > || 91.562 ||
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| || Huntian 35-cycle comma || || | 277 0 -54 -54 > || 22.4605 ||
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| || greenwoodma || 405 / 392 || | -3 4 1 -2 > || 56.482 ||
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| || Harrison's comma || [[59049_57344|59049 / 57344]] || | -13 10 0 -1 > || 50.724 ||
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| || keega || 1029 / 1000 || | -3 1 -3 3 > || 49.492 ||
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| || septimal quarter tone || [[36_35|36 / 35]] || | 2 2 -1 -1 > || 48.770 ||
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| || quarter tone comma || || | 49 50 -25 -25 > || 19.2595 ||
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| || cloudy || 16807 / 16384 || | -14 0 0 5 > || 44.130 ||
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| || Avicenna, Avicenna's enharmonic diesis || 525 / 512 || | -9 1 2 1 > || 43.408 ||
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| || slendro diesis || [[49_48|49 / 48]] || | -4 -1 0 2 > || 35.597 ||
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| || slendro 34-comma || || | -137 -34 0 68 > || 13.692 ||
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| || 34-jubilismic comma || || | -33 0 -68 68 > || 10.829 ||
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| || tritonic diesis, jubilisma || [[50_49|50 / 49]] || | 1 0 2 -2 > || 34.976 ||
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| || eric || || | 7 8 0 -7 > || 33.859 ||
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| || senga || 686 / 675 || | 1 -3 -2 3 > || 27.985 ||
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| || septimal comma, Archytas' comma, Leipziger Komma || [[64_63|64 / 63]] || | 6 -2 0 -1 > || 27.264 ||
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| || blackjackisma || || | -10 7 8 -7 > || 22.413 ||
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| || squalentine || 64827 / 64000 || | -9 3 -3 4 > || 22.227 ||
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| || keema || 875 / 864 || | -5 -3 3 1 > || 21.902 ||
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| || gariboh || 3125 / 3087 || | 0 -2 5 -3 > || 21.181 ||
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| || nuwell || 2430 / 2401 || | 1 5 1 -4 > || 20.785 ||
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| || tolerma || || | 10 -11 2 1 > || 19.948 ||
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| || mirwomo || 33075 / 32768 || | -15 3 2 2 > || 16.144 ||
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| || trimyna || 50421 / 50000 || | -4 1 -5 5 > || 14.516 ||
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| || sensamagic || 245 / 243 || | 0 -5 1 2 > || 14.191 ||
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| || septimal semicomma, starling comma || [[126_125|126 / 125]] || | 1 2 -3 1 > || 13.795 ||
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| || octagar || 4000 / 3969 || | 5 -4 3 -2 > || 13.469 ||
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| || orwellisma, orwell comma || 1728 / 1715 || | 6 3 -1 -3 > || 13.074 ||
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| || quince || || | -15 0 -2 7 > || 9.154 ||
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| || gamelisma || 1029 / 1024 || | -10 1 0 3 > || 8.433 ||
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| || varunisma || || | -9 8 -4 2 > || 8.037 ||
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| || septimal kleisma, marvel comma || [[225_224|225 / 224]] || | -5 2 2 -1 > || 7.712 ||
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| || dimcomp || || | -1 -4 8 -4 > || 7.386 ||
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| || cataharry || 19683 / 19600 || | -4 9 -2 -2 > || 7.316 ||
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| || mirkwai || 16875 / 16807 || | 0 3 4 -5 > || 6.990 ||
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| || stearnsma || || | 1 10 0 -6 > || 6.595 ||
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| || hemimage || 10976 / 10935 || | 5 -7 -1 3 > || 6.479 ||
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| || hemimean || 3136 / 3125 || | 6 0 -5 2 > || 6.083 ||
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| || hemifamity || 5120 / 5103 || | 10 -6 1 -1 > || 5.758 ||
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| || linus || || | 11 -10 -10 10 > || 5.572 ||
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| || porwell || 6144 / 6125 || | 11 1 -3 -2 > || 5.362 ||
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| || garischisma || || | 25 -14 0 -1 > || 3.804 ||
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| || wadisma || || | -26 -1 1 9 > || 3.792 ||
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| || quasiorwellisma || || | 22 -1 -10 1 > || 3.734 ||
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| || [[218edo]] (stacked 7/4 and 10/9) comma || || | 22 -32 16 -3 > || 11.982 ||
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| || bapbo || 256 / 245 || | 8 0 -1 -2 > || 76.034 ||
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| ==11-limit commas== | | ==3-limit commas== |
| ||~ name(s) ||~ ratio ||~ monzo ||~ cents ||
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| || 11-cycle chroma, 11-11-comma || || | -38 0 0 0 11 > || 64.497 ||
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| || 11-cycle major seventh prote, 35-11-comma || || | -121 0 0 0 35 > || 96.128 ||
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| || Hunt 11-cycle comma || || | -83 0 0 0 24 > || 31.631 ||
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| || Hunt flat 5 comma || 8192 / 8019 || | 13 -6 0 0 -1 > || 36.952 ||
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| || sterno || 352 / 343 || | 5 0 0 -3 1 > || 44.840 ||
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| || the Igs boson<span style="line-height: 1.5;">, 13-11-comma</span> || || | 45 0 0 0 -13 > || 32.867 ||
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| || telepathma || 55 / 54 || | -1 -3 1 0 1 > || 31.767 ||
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| || thuja comma || || | 15 0 1 0 -5 > || 29.724 ||
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| || sensmus || 1232 / 1215 || | 4 -5 -1 1 1 > || 24.055 ||
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| || sevnothrush || 3168 / 3125 || | 5 2 -5 0 1 > || 23.659 ||
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| || cassacot || 245 / 242 || | -1 0 1 2 -2 > || 21.330 ||
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| || [[mothwellsmic triad|mothwellsma]] || 99 / 98 || | -1 2 0 -2 1 > || 17.576 ||
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| || [[ptolemismic triad|ptolemisma]] || [[100_99|100 / 99]] || | 2 -2 2 0 -1 > || 17.399 ||
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| || hemimin || 1344 / 1331 || | 6 1 0 1 -3 > || 16.827 ||
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| || biyatisma || 121 / 120 || | -3 -1 -1 0 2 > || 14.367 ||
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| || aphrowe || 1331 / 1323 || | 0 -3 0 -2 3 > || 10.437 ||
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| || [[valinorsmic chords|valinorsma]] || 176 / 175 || | 4 0 -2 -1 1 > || 9.865 ||
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| || [[pentacircle comma|pentacircle]] || 896 / 891 || | 7 -4 0 1 -1 > || 9.688 ||
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| || orgonisma || 65536 / 65219 || | 16 0 0 -2 -3 > || 8.394 ||
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| || [[rastmic chords|rastma]] || 243 / 242 || | -1 5 0 0 -2 > || 7.139 ||
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| || myhemiwell || 3388 / 3375 || | 2 -3 -3 1 2 > || 6.656 ||
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| || [[keenanismic chords|keenanisma]] || [[385_384|385 / 384]] || | -7 -1 1 1 1 > || 4.503 ||
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| || [[werckismic chords|werckisma]] || 441 / 440 || | -3 2 -1 2 -1 > || 3.930 ||
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| || moctdel || 1375 / 1372 || | -2 0 3 -3 1 > || 3.781 ||
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| ==13-limit commas== | | {| class="wikitable" |
| ||~ name(s) ||~ ratio ||~ monzo ||~ cents || | | |- |
| || Hunt 13-cycle comma || || | -37 0 0 0 0 0 10 > || 5.277 || | | ! | name(s) |
| || <span style="font-size: 12.8000001907349px;">silver half cents comma</span> || || <span style="font-size: 12.8000001907349px;">| -8881 0 0 0 2400 ></span> || <span style="font-size: 12.8000001907349px;">66.389</span> || | | ! | ratio |
| || Hunt minor submediant comma || 1053 / 1024 || | -10 4 0 0 0 0 1 > || 48.348 ||
| | ! | monzo |
| || astburyp || || | -19 -2 0 0 0 6 > || 39.255 || | | ! | cents |
| || wilsorma || 65 / 64 || | -6 0 1 0 0 1 > || 26.841 ||
| | |- |
| || winmeanma || 66 / 65 || | 1 1 -1 0 1 -1 > || 26.432 || | | | | limma, Pythagorean minor second |
| || negustma || 78 / 77 || | 1 1 0 -1 -1 1 > || 22.229 ||
| | | | [[256/243|256 / 243]] |
| || superleap || 91 / 90 || | -1 -2 -1 1 0 1 > || 19.130 ||
| | | | | 8 -5 > |
| || animist || 105 / 104 || | -3 1 1 1 0 -1 > || 16.567 ||
| | | | 90.225 |
| || secorian || 28672 / 28431 || | 12 -7 0 1 0 -1 > || 14.613 ||
| | |- |
| || mosaic || 3159 / 3136 || |-6 5 0 -2 0 1> || 12.651 || | | | | [[Pythagorean_comma|Pythagorean comma]] |
| || gassorma || 275 / 273 || | 0 -1 2 -1 1 -1 > || 12.637 || | | | | |
| || [[grossma]] || 144 / 143 || | 4 2 0 0 -1 -1 > || 12.064 || | | | | | -19 12 > |
| || buzurgisma, dhanvantarisma || 169 / 168 || | -3 -1 0 -1 0 2 > || 10.274 || | | | | 23.460 |
| || catadictma || 1287 / 1280 || | -8 2 -1 0 1 1 > || 9.442 || | | |- |
| || [[mynucumic chords|mynucuma]] || 196 / 195 || | 2 -1 -1 2 0 -1 > || 8.855 || | | | | [[17-comma|17-comma]] |
| || [[huntmic chords|huntma]] || 640 / 637 || | 7 0 1 -2 0 -1 > || 8.134 || | | | | |
| || [[threedie]] || 2197 / 2187 || | 0 -7 0 0 0 3 > || 7.897 || | | | | | 27 -17 > |
| || [[kestrel chords|kestrel comma]] || 1188 / 1183 || | 2 3 0 -1 1 -2 > || 7.302 || | | | | 66.765 |
| || [[marveltwin]] || 325 / 324 || | -2 -4 2 0 0 1 > || 5.335 || | | |- |
| || [[ratwolf triad|ratwolfsma]] || 351 / 350 || | -1 3 -2 -1 0 1 > || 4.939 || | | | | [[29-comma|29-comma]] |
| || [[minthmic chords|minthma]] || 352 / 351 || | 5 -3 0 0 1 -1 > || 4.925 || | | | | |
| || [[gentle chords|gentle comma]] || 364 / 363 || | 2 -1 0 1 -2 1 > || 4.763 || | | | | | 46 -29 > |
| || [[cuthbert triad|cuthbert]] || 847 / 845 || | 0 0 -1 1 2 -2 > || 4.093 || | | | | 43.305 |
| | |- |
| | | | [[41-comma|41-comma]] |
| | | | |
| | | | | 65 -41 > |
| | | | 19.845 |
| | |- |
| | | | Pythagorean Integer cents comma |
| | | | |
| | | | | 317 -200 > |
| | | | 9.000 |
| | |- |
| | | | [[Mercator's_comma|Mercator's comma]], 53-comma |
| | | | |
| | | | | -84 53 > |
| | | | 3.615 |
| | |- |
| | | | 70-comma |
| | | | |
| | | | | 111 -70 > |
| | | | 63.150 |
| | |} |
|
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| ==17-limit commas== | | ==5-limit commas== |
| ||~ name(s) ||~ ratio ||~ monzo ||~ cents ||
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| || 11 semitone comma || || | 45 0 0 0 0 0 -11 > || 45.4905 ||
| |
| || 12 semitone comma || || | -49 0 0 0 0 0 12 > || 59.465 ||
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| || 23 semitone comma || || | -93 0 0 0 0 0 23 > || 13.974 ||
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| || Hunt 17-cycle comma || || | -138 0 0 0 0 0 34 > || 31.516 ||
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| || 17-ripple integer cents comma || || | 327 0 0 0 0 0 -80 > || 3.568 ||
| |
| || Hunt flat 2 comma || 4131 / 4096 || | -12 5 0 0 0 0 1 > || 14.730 ||
| |
| || Blume comma || 2057 / 2048 || | -11 0 0 0 2 0 1 > || 7.591 ||
| |
| || Septendecimal Integer Cents comma || 289 / 288 || | -5 -2 0 0 0 0 2 > || 6.001 ||
| |
| || Tannisma || 273/272 || |-4 1 0 1 0 1 -2> || 6.353 ||
| |
|
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|
| ==19-limit commas== | | {| class="wikitable" |
| ||~ name(s) ||~ ratio ||~ monzo ||~ cents || | | |- |
| || Hunt 19-cycle comma || || | 17 0 0 0 0 0 0 -4 > || 9.950 || | | ! | name(s) |
| || spleen comma || 210 / 209 || | 1 1 1 1 -1 0 0 -1 > || 8.264 || | | ! | ratio |
| || go comma || 361 / 360 || | -3 -2 -1 0 0 0 0 2 > || 4.802 || | | ! | monzo |
| [[media type="custom" key="25699772"]]</pre></div>
| | ! | cents |
| <h4>Original HTML content:</h4>
| | |- |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Comma</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/Komma">Deutsch</a><br />
| | | | Twenty-two thirds limma |
| </span><br />
| | | | |
| <!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Definition"></a><!-- ws:end:WikiTextHeadingRule:1 -->Definition</h1>
| | | | | -51 0 22 > |
| A <strong>comma</strong> is a small interval that occurs in <a class="wiki_link" href="/just%20intonation">just intonation</a>, 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 <a class="wiki_link" href="/Harmonic%20Limit">low prime limit</a>. The word is often used in reference to <a class="wiki_link" href="/Regular%20Temperaments">regular tempering</a> when the comma is <em><a class="wiki_link" href="/tempering%20out">tempered out</a></em>, 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 <a class="wiki_link" href="/Meantone">meantone temperament</a>. 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 <a class="wiki_link" href="/cent">cent</a>s.<br />
| | | | 98.902 |
| <br />
| | |- |
| For commas over 100 cents in size, see <a class="wiki_link" href="/Large%20commas">Large commas</a>; and for commas under 3.5 cents in size, see <a class="wiki_link" href="/Unnoticeable%20commas">Unnoticeable commas</a><br />
| | | | sibbolet |
| <br />
| | | | |
| <!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="List of commas, by prime limit"></a><!-- ws:end:WikiTextHeadingRule:3 -->List of commas, by prime limit</h1>
| | | | | -58 0 25 > |
| <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="List of commas, by prime limit-3-limit commas"></a><!-- ws:end:WikiTextHeadingRule:5 -->3-limit commas</h2>
| | | | 57.843 |
|
| | |- |
| | | | Hunt 5-cycle comma |
| | | | |
| | | | | -65 0 28 > |
| | | | 16.784 |
| | |- |
| | | | acute thirds comma |
| | | | |
| | | | | 72 0 -31 > |
| | | | 24.275 |
| | |- |
| | | | 34-5-comma |
| | | | |
| | | | | 79 0 -34 > |
| | | | 65.334 |
| | |- |
| | | | Schismic thirds chromatic semitone |
| | | | |
| | | | | -123 0 53 > |
| | | | 74.627 |
| | |- |
| | | | 10-15-comma |
| | | | |
| | | | | -39 10 10 > |
| | | | 82.687 |
| | |- |
| | | | 11-15-comma |
| | | | |
| | | | | 43 -11 -11 > |
| | | | 29.044 |
| | |- |
| | | | 21-15-comma |
| | | | |
| | | | | 82 -21 -21 > |
| | | | 53.643 |
| | |- |
| | | | 32-15-comma |
| | | | |
| | | | | 125 -32 -32 > |
| | | | 24.599 |
| | |- |
| | | | Huntian 15-cycle comma |
| | | | |
| | | | | -168 43 43 > |
| | | | 4.445 |
| | |- |
| | | | 53-15-comma |
| | | | |
| | | | | -207 53 53 > |
| | | | 78.242 |
| | |- |
| | | | 54-15-comma |
| | | | |
| | | | | 211 -54 -54 > |
| | | | 33.489 |
| | |- |
| | | | 76-15-comma |
| | | | |
| | | | | 297 -76 -76 > |
| | | | 91.578 |
| | |- |
| | | | major chroma, major limma, pelogic comma |
| | | | [[135/128|135 / 128]] |
| | | | | -7 3 1 > |
| | | | 92.179 |
| | |- |
| | | | ripple |
| | | | 6561 / 6250 |
| | | | | -1 8 -5 > |
| | | | 84.071 |
| | |- |
| | | | doublewide |
| | | | |
| | | | | -9 -6 8 > |
| | | | 78.780 |
| | |- |
| | | | sevond |
| | | | |
| | | | | 6 -14 7 > |
| | | | 76.826 |
| | |- |
| | | | nusecond |
| | | | |
| | | | | 5 13 -11 > |
| | | | 75.964 |
| | |- |
| | | | sentinel |
| | | | |
| | | | | -33 15 4 > |
| | | | 74.580 |
| | |- |
| | | | chromatic semitone |
| | | | [[25/24|25 / 24]] |
| | | | | -3 -1 2 > |
| | | | 70.672 |
| | |- |
| | | | superpyth, grave minor second |
| | | | 20480 / 19683 |
| | | | | 12 -9 1 > |
| | | | 68.719 |
| | |- |
| | | | major diesis, diminished comma |
| | | | [[648/625|648 / 625]] |
| | | | | 3 4 -4 > |
| | | | 62.565 |
| | |- |
| | | | passion |
| | | | |
| | | | | 18 -4 -5 > |
| | | | 60.611 |
| | |- |
| | | | shibboleth |
| | | | |
| | | | | -5 -10 9 > |
| | | | 57.273 |
| | |- |
| | | | mynic |
| | | | |
| | | | | 9 9 -10 > |
| | | | 54.458 |
| | |- |
| | | | tritonic |
| | | | |
| | | | | -29 11 5 > |
| | | | 53.074 |
| | |- |
| | | | [[negri_comma|negri comma]], double augmentation diesis |
| | | | 16875 / 16384 |
| | | | | -14 3 4 > |
| | | | 51.120 |
| | |- |
| | | | maximal diesis, porcupine comma |
| | | | [[250/243|250 / 243]] |
| | | | | 1 -5 3 > |
| | | | 49.166 |
| | |- |
| | | | immunity |
| | | | |
| | | | | 16 -13 2 > |
| | | | 47.212 |
| | |- |
| | | | diesis, augmented comma |
| | | | [[128/125|128 / 125]] |
| | | | | 7 0 -3 > |
| | | | 41.059 |
| | |- |
| | | | wizard |
| | | | |
| | | | | -31 2 12 > |
| | | | 39.675 |
| | |- |
| | | | sycamore |
| | | | |
| | | | | -16 -6 11 > |
| | | | 37.721 |
| | |- |
| | | | fifive |
| | | | |
| | | | | -1 -14 10 > |
| | | | 35.767 |
| | |- |
| | | | unicorn |
| | | | |
| | | | | -2 13 -8 > |
| | | | 34.905 |
| | |- |
| | | | valensixthtone |
| | | | |
| | | | | 13 5 -9 > |
| | | | 32.952 |
| | |- |
| | | | [[ampersand|ampersand]], Ampersand's comma |
| | | | |
| | | | | -25 7 6 > |
| | | | 31.567 |
| | |- |
| | | | small diesis, [[magic_comma|magic comma]] |
| | | | 3125 / 3072 |
| | | | | -10 -1 5 > |
| | | | 29.614 |
| | |- |
| | | | minimal diesis, [[tetracot_comma|tetracot comma]] |
| | | | 20000 / 19683 |
| | | | | 5 -9 4 > |
| | | | 27.660 |
| | |- |
| | | | roda |
| | | | |
| | | | | 20 -17 3 > |
| | | | 25.706 |
| | |- |
| | | | maja |
| | | | |
| | | | | -3 -23 17 > |
| | | | 22.368 |
| | |- |
| | | | syntonic comma, Didymos comma, meantone comma |
| | | | [[81/80|81 / 80]] |
| | | | | -4 4 -1 > |
| | | | 21.506 |
| | |- |
| | | | [[Maquila_family|maquila comma]] |
| | | | |
| | | | | 49 -6 -17 > |
| | | | 20.937 |
| | |- |
| | | | [[diaschisma|diaschisma]] |
| | | | 2048 / 2025 |
| | | | | 11 -4 -2 > |
| | | | 19.553 |
| | |- |
| | | | ditonma |
| | | | |
| | | | | -27 -2 13 > |
| | | | 18.168 |
| | |- |
| | | | [[misty_comma|misty comma]] |
| | | | |
| | | | | 26 -12 -3 > |
| | | | 17.599 |
| | |- |
| | | | [[Pental_family|pental comma]] |
| | | | |
| | | | | -28 25 -5 > |
| | | | 17.306 |
| | |- |
| | | | [[graviton|graviton]], [[Gravity_family|gravity]] comma |
| | | | |
| | | | | -13 17 -6 > |
| | | | 15.353 |
| | |- |
| | | | quartonic |
| | | | |
| | | | | 3 -18 11 > |
| | | | 14.261 |
| | |- |
| | | | medium semicomma, [[sensipent_comma|sensipent comma]] |
| | | | 78732 / 78125 |
| | | | | 2 9 -7 > |
| | | | 13.399 |
| | |- |
| | | | [[Würschmidt_comma|Würschmidt comma]] |
| | | | |
| | | | | 17 1 -8 > |
| | | | 11.445 |
| | |- |
| | | | [[semicomma|semicomma]], Fokker comma |
| | | | |
| | | | | -21 3 7 > |
| | | | 10.061 |
| | |- |
| | | | [[escapade_comma|escapade comma]] |
| | | | |
| | | | | 32 -7 -9 > |
| | | | 9.492 |
| | |- |
| | | | [[kleisma|kleisma]], semicomma majeur |
| | | | 15625 / 15552 |
| | | | | -6 -5 6 > |
| | | | 8.107 |
| | |- |
| | | | unidecma |
| | | | |
| | | | | -7 22 -12 > |
| | | | 7.245 |
| | |- |
| | | | [[mutt_comma|mutt comma]] |
| | | | |
| | | | | -44 -3 21 > |
| | | | 6.723 |
| | |- |
| | | | [[amity_comma|amity comma]] |
| | | | |
| | | | | 9 -13 5 > |
| | | | 6.154 |
| | |- |
| | | | [[parakleisma|parakleisma]] |
| | | | |
| | | | | 8 14 -13 > |
| | | | 5.292 |
| | |- |
| | | | gammic comma |
| | | | |
| | | | | -29 -11 20 > |
| | | | 4.769 |
| | |- |
| | | | [[vulture_comma|vulture comma]] |
| | | | |
| | | | | 24 -21 4 > |
| | | | 4.200 |
| | |- |
| | | | 23-3/5-comma |
| | | | |
| | | | | 17 23 -23 > |
| | | | 59.750 |
| | |- |
| | | | 34-3/5-comma |
| | | | |
| | | | | -25 -34 34 > |
| | | | 68.196 |
| | |- |
| | | | 53-3/5-comma |
| | | | |
| | | | | 39 53 -53 > |
| | | | 71.012 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==7-limit commas== |
| <tr>
| |
| <th>name(s)<br />
| |
| </th>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>monzo<br />
| |
| </th>
| |
| <th>cents<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>limma, Pythagorean minor second<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/256_243">256 / 243</a><br />
| |
| </td>
| |
| <td>| 8 -5 &gt;<br />
| |
| </td>
| |
| <td>90.225<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/Pythagorean%20comma">Pythagorean comma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -19 12 &gt;<br />
| |
| </td>
| |
| <td>23.460<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/17-comma">17-comma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 27 -17 &gt;<br />
| |
| </td>
| |
| <td>66.765<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/29-comma">29-comma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 46 -29 &gt;<br />
| |
| </td>
| |
| <td>43.305<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/41-comma">41-comma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 65 -41 &gt;<br />
| |
| </td>
| |
| <td>19.845<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Pythagorean Integer cents comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 317 -200 &gt;<br />
| |
| </td>
| |
| <td>9.000<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/Mercator%27s%20comma">Mercator's comma</a>, 53-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -84 53 &gt;<br />
| |
| </td>
| |
| <td>3.615<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>70-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 111 -70 &gt;<br />
| |
| </td>
| |
| <td>63.150<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="List of commas, by prime limit-5-limit commas"></a><!-- ws:end:WikiTextHeadingRule:7 -->5-limit commas</h2> | | {| class="wikitable" |
|
| | |- |
| | ! | name(s) |
| | ! | ratio |
| | ! | monzo |
| | ! | cents |
| | |- |
| | | | hexadecatone comma, 16-7-comma |
| | | | |
| | | | | 45 0 0 -16 > |
| | | | 98.7855 |
| | |- |
| | | | 21-7-comma |
| | | | |
| | | | | 59 0 0 -21 > |
| | | | 54.656 |
| | |- |
| | | | Hunt 7-cycle comma |
| | | | |
| | | | | 73 0 0 -26 > |
| | | | 10.526 |
| | |- |
| | | | German sixth comma |
| | | | |
| | | | | -87 0 0 31 > |
| | | | 33.603 |
| | |- |
| | | | large deep red comma |
| | | | 6561 / 6272 |
| | | | | -7, 8, 0 -2 > |
| | | | 77.988 |
| | |- |
| | | | 36-7-comma |
| | | | |
| | | | | -101 0 0 36 > |
| | | | 77.737 |
| | |- |
| | | | 47-7-comma |
| | | | |
| | | | | 132 0 0 0 -47 > |
| | | | 65.182 |
| | |- |
| | | | slendro integer cents comma |
| | | | |
| | | | | 1127 0 0 -400 > |
| | | | 69.637 |
| | |- |
| | | | 29-7/5-comma |
| | | | |
| | | | | -14 0 -29 29 > |
| | | | 92.854 |
| | |- |
| | | | 31-7/5-comma |
| | | | |
| | | | | -15 0 -31 31 > |
| | | | 57.878 |
| | |- |
| | | | 33-7/5-comma |
| | | | |
| | | | | -16 0 -33 33 > |
| | | | 22.902 |
| | |- |
| | | | 35-7/5-comma |
| | | | |
| | | | | 18 0 35 -35 > |
| | | | 12.073 |
| | |- |
| | | | 37-7/5-comma |
| | | | |
| | | | | 19 0 37 -37 > |
| | | | 47.049 |
| | |- |
| | | | 39-7/5-comma |
| | | | |
| | | | | 20 0 39 -39 > |
| | | | 82.0245 |
| | |- |
| | | | 5-21-comma |
| | | | |
| | | | | 22 -5 0 -5 > |
| | | | 46.0955 |
| | |- |
| | | | 18-21-comma |
| | | | |
| | | | | -79 18 0 18 > |
| | | | 74.056 |
| | |- |
| | | | 23-21-comma |
| | | | |
| | | | | -101 23 0 23 > |
| | | | 27.961 |
| | |- |
| | | | Huntian 21-cycle comma |
| | | | |
| | | | | 123 -28 0 -28 > |
| | | | 18.135 |
| | |- |
| | | | 33-21-comma |
| | | | |
| | | | | 145 -33 0 -33 > |
| | | | 64.230 |
| | |- |
| | | | 8-35-comma |
| | | | |
| | | | | -41 0 8 8 > |
| | | | 41.117 |
| | |- |
| | | | 15-35-comma |
| | | | |
| | | | | 77 0 -15 -15 > |
| | | | 72.906 |
| | |- |
| | | | 23-35-comma |
| | | | |
| | | | | 118 0 -23 -23 > |
| | | | 31.789 |
| | |- |
| | | | 31-35-comma |
| | | | |
| | | | | -159 0 31 31 > |
| | | | 9.328 |
| | |- |
| | | | 39-35-comma |
| | | | |
| | | | | -200 0 39 39 > |
| | | | 50.445 |
| | |- |
| | | | 47-35-comma |
| | | | |
| | | | | -241 0 47 47 > |
| | | | 91.562 |
| | |- |
| | | | Huntian 35-cycle comma |
| | | | |
| | | | | 277 0 -54 -54 > |
| | | | 22.4605 |
| | |- |
| | | | greenwoodma |
| | | | 405 / 392 |
| | | | | -3 4 1 -2 > |
| | | | 56.482 |
| | |- |
| | | | Harrison's comma |
| | | | [[59049/57344|59049 / 57344]] |
| | | | | -13 10 0 -1 > |
| | | | 50.724 |
| | |- |
| | | | keega |
| | | | 1029 / 1000 |
| | | | | -3 1 -3 3 > |
| | | | 49.492 |
| | |- |
| | | | septimal quarter tone |
| | | | [[36/35|36 / 35]] |
| | | | | 2 2 -1 -1 > |
| | | | 48.770 |
| | |- |
| | | | quarter tone comma |
| | | | |
| | | | | 49 50 -25 -25 > |
| | | | 19.2595 |
| | |- |
| | | | cloudy |
| | | | 16807 / 16384 |
| | | | | -14 0 0 5 > |
| | | | 44.130 |
| | |- |
| | | | Avicenna, Avicenna's enharmonic diesis |
| | | | 525 / 512 |
| | | | | -9 1 2 1 > |
| | | | 43.408 |
| | |- |
| | | | slendro diesis |
| | | | [[49/48|49 / 48]] |
| | | | | -4 -1 0 2 > |
| | | | 35.597 |
| | |- |
| | | | slendro 34-comma |
| | | | |
| | | | | -137 -34 0 68 > |
| | | | 13.692 |
| | |- |
| | | | 34-jubilismic comma |
| | | | |
| | | | | -33 0 -68 68 > |
| | | | 10.829 |
| | |- |
| | | | tritonic diesis, jubilisma |
| | | | [[50/49|50 / 49]] |
| | | | | 1 0 2 -2 > |
| | | | 34.976 |
| | |- |
| | | | eric |
| | | | |
| | | | | 7 8 0 -7 > |
| | | | 33.859 |
| | |- |
| | | | senga |
| | | | 686 / 675 |
| | | | | 1 -3 -2 3 > |
| | | | 27.985 |
| | |- |
| | | | septimal comma, Archytas' comma, Leipziger Komma |
| | | | [[64/63|64 / 63]] |
| | | | | 6 -2 0 -1 > |
| | | | 27.264 |
| | |- |
| | | | blackjackisma |
| | | | |
| | | | | -10 7 8 -7 > |
| | | | 22.413 |
| | |- |
| | | | squalentine |
| | | | 64827 / 64000 |
| | | | | -9 3 -3 4 > |
| | | | 22.227 |
| | |- |
| | | | keema |
| | | | 875 / 864 |
| | | | | -5 -3 3 1 > |
| | | | 21.902 |
| | |- |
| | | | gariboh |
| | | | 3125 / 3087 |
| | | | | 0 -2 5 -3 > |
| | | | 21.181 |
| | |- |
| | | | nuwell |
| | | | 2430 / 2401 |
| | | | | 1 5 1 -4 > |
| | | | 20.785 |
| | |- |
| | | | tolerma |
| | | | |
| | | | | 10 -11 2 1 > |
| | | | 19.948 |
| | |- |
| | | | mirwomo |
| | | | 33075 / 32768 |
| | | | | -15 3 2 2 > |
| | | | 16.144 |
| | |- |
| | | | trimyna |
| | | | 50421 / 50000 |
| | | | | -4 1 -5 5 > |
| | | | 14.516 |
| | |- |
| | | | sensamagic |
| | | | 245 / 243 |
| | | | | 0 -5 1 2 > |
| | | | 14.191 |
| | |- |
| | | | septimal semicomma, starling comma |
| | | | [[126/125|126 / 125]] |
| | | | | 1 2 -3 1 > |
| | | | 13.795 |
| | |- |
| | | | octagar |
| | | | 4000 / 3969 |
| | | | | 5 -4 3 -2 > |
| | | | 13.469 |
| | |- |
| | | | orwellisma, orwell comma |
| | | | 1728 / 1715 |
| | | | | 6 3 -1 -3 > |
| | | | 13.074 |
| | |- |
| | | | quince |
| | | | |
| | | | | -15 0 -2 7 > |
| | | | 9.154 |
| | |- |
| | | | gamelisma |
| | | | 1029 / 1024 |
| | | | | -10 1 0 3 > |
| | | | 8.433 |
| | |- |
| | | | varunisma |
| | | | |
| | | | | -9 8 -4 2 > |
| | | | 8.037 |
| | |- |
| | | | septimal kleisma, marvel comma |
| | | | [[225/224|225 / 224]] |
| | | | | -5 2 2 -1 > |
| | | | 7.712 |
| | |- |
| | | | dimcomp |
| | | | |
| | | | | -1 -4 8 -4 > |
| | | | 7.386 |
| | |- |
| | | | cataharry |
| | | | 19683 / 19600 |
| | | | | -4 9 -2 -2 > |
| | | | 7.316 |
| | |- |
| | | | mirkwai |
| | | | 16875 / 16807 |
| | | | | 0 3 4 -5 > |
| | | | 6.990 |
| | |- |
| | | | stearnsma |
| | | | |
| | | | | 1 10 0 -6 > |
| | | | 6.595 |
| | |- |
| | | | hemimage |
| | | | 10976 / 10935 |
| | | | | 5 -7 -1 3 > |
| | | | 6.479 |
| | |- |
| | | | hemimean |
| | | | 3136 / 3125 |
| | | | | 6 0 -5 2 > |
| | | | 6.083 |
| | |- |
| | | | hemifamity |
| | | | 5120 / 5103 |
| | | | | 10 -6 1 -1 > |
| | | | 5.758 |
| | |- |
| | | | linus |
| | | | |
| | | | | 11 -10 -10 10 > |
| | | | 5.572 |
| | |- |
| | | | porwell |
| | | | 6144 / 6125 |
| | | | | 11 1 -3 -2 > |
| | | | 5.362 |
| | |- |
| | | | garischisma |
| | | | |
| | | | | 25 -14 0 -1 > |
| | | | 3.804 |
| | |- |
| | | | wadisma |
| | | | |
| | | | | -26 -1 1 9 > |
| | | | 3.792 |
| | |- |
| | | | quasiorwellisma |
| | | | |
| | | | | 22 -1 -10 1 > |
| | | | 3.734 |
| | |- |
| | | | [[218edo|218edo]] (stacked 7/4 and 10/9) comma |
| | | | |
| | | | | 22 -32 16 -3 > |
| | | | 11.982 |
| | |- |
| | | | bapbo |
| | | | 256 / 245 |
| | | | | 8 0 -1 -2 > |
| | | | 76.034 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==11-limit commas== |
| <tr>
| |
| <th>name(s)<br />
| |
| </th>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>monzo<br />
| |
| </th>
| |
| <th>cents<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>Twenty-two thirds limma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -51 0 22 &gt;<br />
| |
| </td>
| |
| <td>98.902<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>sibbolet<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -58 0 25 &gt;<br />
| |
| </td>
| |
| <td>57.843<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Hunt 5-cycle comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -65 0 28 &gt;<br />
| |
| </td>
| |
| <td>16.784<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>acute thirds comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 72 0 -31 &gt;<br />
| |
| </td>
| |
| <td>24.275<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34-5-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 79 0 -34 &gt;<br />
| |
| </td>
| |
| <td>65.334<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Schismic thirds chromatic semitone<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -123 0 53 &gt;<br />
| |
| </td>
| |
| <td>74.627<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10-15-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -39 10 10 &gt;<br />
| |
| </td>
| |
| <td>82.687<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11-15-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 43 -11 -11 &gt;<br />
| |
| </td>
| |
| <td>29.044<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21-15-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 82 -21 -21 &gt;<br />
| |
| </td>
| |
| <td>53.643<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32-15-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 125 -32 -32 &gt;<br />
| |
| </td>
| |
| <td>24.599<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Huntian 15-cycle comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -168 43 43 &gt;<br />
| |
| </td>
| |
| <td>4.445<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>53-15-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -207 53 53 &gt;<br />
| |
| </td>
| |
| <td>78.242<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>54-15-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 211 -54 -54 &gt;<br />
| |
| </td>
| |
| <td>33.489<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>76-15-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 297 -76 -76 &gt;<br />
| |
| </td>
| |
| <td>91.578<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>major chroma, major limma, pelogic comma<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/135_128">135 / 128</a><br />
| |
| </td>
| |
| <td>| -7 3 1 &gt;<br />
| |
| </td>
| |
| <td>92.179<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>ripple<br />
| |
| </td>
| |
| <td>6561 / 6250<br />
| |
| </td>
| |
| <td>| -1 8 -5 &gt;<br />
| |
| </td>
| |
| <td>84.071<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>doublewide<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -9 -6 8 &gt;<br />
| |
| </td>
| |
| <td>78.780<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>sevond<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 6 -14 7 &gt;<br />
| |
| </td>
| |
| <td>76.826<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>nusecond<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 5 13 -11 &gt;<br />
| |
| </td>
| |
| <td>75.964<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>sentinel<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -33 15 4 &gt;<br />
| |
| </td>
| |
| <td>74.580<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>chromatic semitone<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/25_24">25 / 24</a><br />
| |
| </td>
| |
| <td>| -3 -1 2 &gt;<br />
| |
| </td>
| |
| <td>70.672<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>superpyth, grave minor second<br />
| |
| </td>
| |
| <td>20480 / 19683<br />
| |
| </td>
| |
| <td>| 12 -9 1 &gt;<br />
| |
| </td>
| |
| <td>68.719<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>major diesis, diminished comma<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/648_625">648 / 625</a><br />
| |
| </td>
| |
| <td>| 3 4 -4 &gt;<br />
| |
| </td>
| |
| <td>62.565<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>passion<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 18 -4 -5 &gt;<br />
| |
| </td>
| |
| <td>60.611<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>shibboleth<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -5 -10 9 &gt;<br />
| |
| </td>
| |
| <td>57.273<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>mynic<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 9 9 -10 &gt;<br />
| |
| </td>
| |
| <td>54.458<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>tritonic<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -29 11 5 &gt;<br />
| |
| </td>
| |
| <td>53.074<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/negri%20comma">negri comma</a>, double augmentation diesis<br />
| |
| </td>
| |
| <td>16875 / 16384<br />
| |
| </td>
| |
| <td>| -14 3 4 &gt;<br />
| |
| </td>
| |
| <td>51.120<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>maximal diesis, porcupine comma<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/250_243">250 / 243</a><br />
| |
| </td>
| |
| <td>| 1 -5 3 &gt;<br />
| |
| </td>
| |
| <td>49.166<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>immunity<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 16 -13 2 &gt;<br />
| |
| </td>
| |
| <td>47.212<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>diesis, augmented comma<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/128_125">128 / 125</a><br />
| |
| </td>
| |
| <td>| 7 0 -3 &gt;<br />
| |
| </td>
| |
| <td>41.059<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>wizard<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -31 2 12 &gt;<br />
| |
| </td>
| |
| <td>39.675<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>sycamore<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -16 -6 11 &gt;<br />
| |
| </td>
| |
| <td>37.721<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>fifive<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -1 -14 10 &gt;<br />
| |
| </td>
| |
| <td>35.767<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>unicorn<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -2 13 -8 &gt;<br />
| |
| </td>
| |
| <td>34.905<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>valensixthtone<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 13 5 -9 &gt;<br />
| |
| </td>
| |
| <td>32.952<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/ampersand">ampersand</a>, Ampersand's comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -25 7 6 &gt;<br />
| |
| </td>
| |
| <td>31.567<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>small diesis, <a class="wiki_link" href="/magic%20comma">magic comma</a><br />
| |
| </td>
| |
| <td>3125 / 3072<br />
| |
| </td>
| |
| <td>| -10 -1 5 &gt;<br />
| |
| </td>
| |
| <td>29.614<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>minimal diesis, <a class="wiki_link" href="/tetracot%20comma">tetracot comma</a><br />
| |
| </td>
| |
| <td>20000 / 19683<br />
| |
| </td>
| |
| <td>| 5 -9 4 &gt;<br />
| |
| </td>
| |
| <td>27.660<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>roda<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 20 -17 3 &gt;<br />
| |
| </td>
| |
| <td>25.706<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>maja<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -3 -23 17 &gt;<br />
| |
| </td>
| |
| <td>22.368<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>syntonic comma, Didymos comma, meantone comma<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/81_80">81 / 80</a><br />
| |
| </td>
| |
| <td>| -4 4 -1 &gt;<br />
| |
| </td>
| |
| <td>21.506<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/Maquila%20family">maquila comma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 49 -6 -17 &gt;<br />
| |
| </td>
| |
| <td>20.937<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/diaschisma">diaschisma</a><br />
| |
| </td>
| |
| <td>2048 / 2025<br />
| |
| </td>
| |
| <td>| 11 -4 -2 &gt;<br />
| |
| </td>
| |
| <td>19.553<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>ditonma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -27 -2 13 &gt;<br />
| |
| </td>
| |
| <td>18.168<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/misty%20comma">misty comma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 26 -12 -3 &gt;<br />
| |
| </td>
| |
| <td>17.599<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/Pental%20family">pental comma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -28 25 -5 &gt;<br />
| |
| </td>
| |
| <td>17.306<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/graviton">graviton</a>, <a class="wiki_link" href="/Gravity%20family">gravity</a> comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -13 17 -6 &gt;<br />
| |
| </td>
| |
| <td>15.353<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>quartonic<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 3 -18 11 &gt;<br />
| |
| </td>
| |
| <td>14.261<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>medium semicomma, <a class="wiki_link" href="/sensipent%20comma">sensipent comma</a><br />
| |
| </td>
| |
| <td>78732 / 78125<br />
| |
| </td>
| |
| <td>| 2 9 -7 &gt;<br />
| |
| </td>
| |
| <td>13.399<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/W%C3%BCrschmidt%20comma">Würschmidt comma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 17 1 -8 &gt;<br />
| |
| </td>
| |
| <td>11.445<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/semicomma">semicomma</a>, Fokker comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -21 3 7 &gt;<br />
| |
| </td>
| |
| <td>10.061<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/escapade%20comma">escapade comma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 32 -7 -9 &gt;<br />
| |
| </td>
| |
| <td>9.492<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/kleisma">kleisma</a>, semicomma majeur<br />
| |
| </td>
| |
| <td>15625 / 15552<br />
| |
| </td>
| |
| <td>| -6 -5 6 &gt;<br />
| |
| </td>
| |
| <td>8.107<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>unidecma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -7 22 -12 &gt;<br />
| |
| </td>
| |
| <td>7.245<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/mutt%20comma">mutt comma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -44 -3 21 &gt;<br />
| |
| </td>
| |
| <td>6.723<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/amity%20comma">amity comma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 9 -13 5 &gt;<br />
| |
| </td>
| |
| <td>6.154<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/parakleisma">parakleisma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 8 14 -13 &gt;<br />
| |
| </td>
| |
| <td>5.292<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>gammic comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -29 -11 20 &gt;<br />
| |
| </td>
| |
| <td>4.769<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/vulture%20comma">vulture comma</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 24 -21 4 &gt;<br />
| |
| </td>
| |
| <td>4.200<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23-3/5-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 17 23 -23 &gt;<br />
| |
| </td>
| |
| <td>59.750<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34-3/5-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -25 -34 34 &gt;<br />
| |
| </td>
| |
| <td>68.196<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>53-3/5-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 39 53 -53 &gt;<br />
| |
| </td>
| |
| <td>71.012<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br /> | | {| class="wikitable" |
| <!-- ws:start:WikiTextHeadingRule:9:&lt;h2&gt; --><h2 id="toc4"><a name="List of commas, by prime limit-7-limit commas"></a><!-- ws:end:WikiTextHeadingRule:9 -->7-limit commas</h2> | | |- |
|
| | ! | name(s) |
| | ! | ratio |
| | ! | monzo |
| | ! | cents |
| | |- |
| | | | 11-cycle chroma, 11-11-comma |
| | | | |
| | | | | -38 0 0 0 11 > |
| | | | 64.497 |
| | |- |
| | | | 11-cycle major seventh prote, 35-11-comma |
| | | | |
| | | | | -121 0 0 0 35 > |
| | | | 96.128 |
| | |- |
| | | | Hunt 11-cycle comma |
| | | | |
| | | | | -83 0 0 0 24 > |
| | | | 31.631 |
| | |- |
| | | | Hunt flat 5 comma |
| | | | 8192 / 8019 |
| | | | | 13 -6 0 0 -1 > |
| | | | 36.952 |
| | |- |
| | | | sterno |
| | | | 352 / 343 |
| | | | | 5 0 0 -3 1 > |
| | | | 44.840 |
| | |- |
| | | | the Igs boson<span style="line-height: 1.5;">, 13-11-comma</span> |
| | | | |
| | | | | 45 0 0 0 -13 > |
| | | | 32.867 |
| | |- |
| | | | telepathma |
| | | | 55 / 54 |
| | | | | -1 -3 1 0 1 > |
| | | | 31.767 |
| | |- |
| | | | thuja comma |
| | | | |
| | | | | 15 0 1 0 -5 > |
| | | | 29.724 |
| | |- |
| | | | sensmus |
| | | | 1232 / 1215 |
| | | | | 4 -5 -1 1 1 > |
| | | | 24.055 |
| | |- |
| | | | sevnothrush |
| | | | 3168 / 3125 |
| | | | | 5 2 -5 0 1 > |
| | | | 23.659 |
| | |- |
| | | | cassacot |
| | | | 245 / 242 |
| | | | | -1 0 1 2 -2 > |
| | | | 21.330 |
| | |- |
| | | | [[mothwellsmic_triad|mothwellsma]] |
| | | | 99 / 98 |
| | | | | -1 2 0 -2 1 > |
| | | | 17.576 |
| | |- |
| | | | [[ptolemismic_triad|ptolemisma]] |
| | | | [[100/99|100 / 99]] |
| | | | | 2 -2 2 0 -1 > |
| | | | 17.399 |
| | |- |
| | | | hemimin |
| | | | 1344 / 1331 |
| | | | | 6 1 0 1 -3 > |
| | | | 16.827 |
| | |- |
| | | | biyatisma |
| | | | 121 / 120 |
| | | | | -3 -1 -1 0 2 > |
| | | | 14.367 |
| | |- |
| | | | aphrowe |
| | | | 1331 / 1323 |
| | | | | 0 -3 0 -2 3 > |
| | | | 10.437 |
| | |- |
| | | | [[valinorsmic_chords|valinorsma]] |
| | | | 176 / 175 |
| | | | | 4 0 -2 -1 1 > |
| | | | 9.865 |
| | |- |
| | | | [[pentacircle_comma|pentacircle]] |
| | | | 896 / 891 |
| | | | | 7 -4 0 1 -1 > |
| | | | 9.688 |
| | |- |
| | | | orgonisma |
| | | | 65536 / 65219 |
| | | | | 16 0 0 -2 -3 > |
| | | | 8.394 |
| | |- |
| | | | [[rastmic_chords|rastma]] |
| | | | 243 / 242 |
| | | | | -1 5 0 0 -2 > |
| | | | 7.139 |
| | |- |
| | | | myhemiwell |
| | | | 3388 / 3375 |
| | | | | 2 -3 -3 1 2 > |
| | | | 6.656 |
| | |- |
| | | | [[keenanismic_chords|keenanisma]] |
| | | | [[385/384|385 / 384]] |
| | | | | -7 -1 1 1 1 > |
| | | | 4.503 |
| | |- |
| | | | [[werckismic_chords|werckisma]] |
| | | | 441 / 440 |
| | | | | -3 2 -1 2 -1 > |
| | | | 3.930 |
| | |- |
| | | | moctdel |
| | | | 1375 / 1372 |
| | | | | -2 0 3 -3 1 > |
| | | | 3.781 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==13-limit commas== |
| <tr>
| |
| <th>name(s)<br />
| |
| </th>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>monzo<br />
| |
| </th>
| |
| <th>cents<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>hexadecatone comma, 16-7-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 45 0 0 -16 &gt;<br />
| |
| </td>
| |
| <td>98.7855<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21-7-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 59 0 0 -21 &gt;<br />
| |
| </td>
| |
| <td>54.656<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Hunt 7-cycle comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 73 0 0 -26 &gt;<br />
| |
| </td>
| |
| <td>10.526<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>German sixth comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -87 0 0 31 &gt;<br />
| |
| </td>
| |
| <td>33.603<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>large deep red comma<br />
| |
| </td>
| |
| <td>6561 / 6272<br />
| |
| </td>
| |
| <td>| -7, 8, 0 -2 &gt;<br />
| |
| </td>
| |
| <td>77.988<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36-7-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -101 0 0 36 &gt;<br />
| |
| </td>
| |
| <td>77.737<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47-7-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 132 0 0 0 -47 &gt;<br />
| |
| </td>
| |
| <td>65.182<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>slendro integer cents comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 1127 0 0 -400 &gt;<br />
| |
| </td>
| |
| <td>69.637<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29-7/5-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -14 0 -29 29 &gt;<br />
| |
| </td>
| |
| <td>92.854<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31-7/5-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -15 0 -31 31 &gt;<br />
| |
| </td>
| |
| <td>57.878<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33-7/5-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -16 0 -33 33 &gt;<br />
| |
| </td>
| |
| <td>22.902<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35-7/5-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 18 0 35 -35 &gt;<br />
| |
| </td>
| |
| <td>12.073<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37-7/5-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 19 0 37 -37 &gt;<br />
| |
| </td>
| |
| <td>47.049<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39-7/5-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 20 0 39 -39 &gt;<br />
| |
| </td>
| |
| <td>82.0245<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5-21-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 22 -5 0 -5 &gt;<br />
| |
| </td>
| |
| <td>46.0955<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18-21-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -79 18 0 18 &gt;<br />
| |
| </td>
| |
| <td>74.056<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23-21-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -101 23 0 23 &gt;<br />
| |
| </td>
| |
| <td>27.961<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Huntian 21-cycle comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 123 -28 0 -28 &gt;<br />
| |
| </td>
| |
| <td>18.135<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33-21-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 145 -33 0 -33 &gt;<br />
| |
| </td>
| |
| <td>64.230<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8-35-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -41 0 8 8 &gt;<br />
| |
| </td>
| |
| <td>41.117<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15-35-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 77 0 -15 -15 &gt;<br />
| |
| </td>
| |
| <td>72.906<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23-35-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 118 0 -23 -23 &gt;<br />
| |
| </td>
| |
| <td>31.789<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31-35-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -159 0 31 31 &gt;<br />
| |
| </td>
| |
| <td>9.328<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39-35-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -200 0 39 39 &gt;<br />
| |
| </td>
| |
| <td>50.445<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47-35-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -241 0 47 47 &gt;<br />
| |
| </td>
| |
| <td>91.562<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Huntian 35-cycle comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 277 0 -54 -54 &gt;<br />
| |
| </td>
| |
| <td>22.4605<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>greenwoodma<br />
| |
| </td>
| |
| <td>405 / 392<br />
| |
| </td>
| |
| <td>| -3 4 1 -2 &gt;<br />
| |
| </td>
| |
| <td>56.482<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Harrison's comma<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/59049_57344">59049 / 57344</a><br />
| |
| </td>
| |
| <td>| -13 10 0 -1 &gt;<br />
| |
| </td>
| |
| <td>50.724<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>keega<br />
| |
| </td>
| |
| <td>1029 / 1000<br />
| |
| </td>
| |
| <td>| -3 1 -3 3 &gt;<br />
| |
| </td>
| |
| <td>49.492<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>septimal quarter tone<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/36_35">36 / 35</a><br />
| |
| </td>
| |
| <td>| 2 2 -1 -1 &gt;<br />
| |
| </td>
| |
| <td>48.770<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>quarter tone comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 49 50 -25 -25 &gt;<br />
| |
| </td>
| |
| <td>19.2595<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>cloudy<br />
| |
| </td>
| |
| <td>16807 / 16384<br />
| |
| </td>
| |
| <td>| -14 0 0 5 &gt;<br />
| |
| </td>
| |
| <td>44.130<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Avicenna, Avicenna's enharmonic diesis<br />
| |
| </td>
| |
| <td>525 / 512<br />
| |
| </td>
| |
| <td>| -9 1 2 1 &gt;<br />
| |
| </td>
| |
| <td>43.408<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>slendro diesis<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/49_48">49 / 48</a><br />
| |
| </td>
| |
| <td>| -4 -1 0 2 &gt;<br />
| |
| </td>
| |
| <td>35.597<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>slendro 34-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -137 -34 0 68 &gt;<br />
| |
| </td>
| |
| <td>13.692<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34-jubilismic comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -33 0 -68 68 &gt;<br />
| |
| </td>
| |
| <td>10.829<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>tritonic diesis, jubilisma<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/50_49">50 / 49</a><br />
| |
| </td>
| |
| <td>| 1 0 2 -2 &gt;<br />
| |
| </td>
| |
| <td>34.976<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>eric<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 7 8 0 -7 &gt;<br />
| |
| </td>
| |
| <td>33.859<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>senga<br />
| |
| </td>
| |
| <td>686 / 675<br />
| |
| </td>
| |
| <td>| 1 -3 -2 3 &gt;<br />
| |
| </td>
| |
| <td>27.985<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>septimal comma, Archytas' comma, Leipziger Komma<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/64_63">64 / 63</a><br />
| |
| </td>
| |
| <td>| 6 -2 0 -1 &gt;<br />
| |
| </td>
| |
| <td>27.264<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>blackjackisma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -10 7 8 -7 &gt;<br />
| |
| </td>
| |
| <td>22.413<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>squalentine<br />
| |
| </td>
| |
| <td>64827 / 64000<br />
| |
| </td>
| |
| <td>| -9 3 -3 4 &gt;<br />
| |
| </td>
| |
| <td>22.227<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>keema<br />
| |
| </td>
| |
| <td>875 / 864<br />
| |
| </td>
| |
| <td>| -5 -3 3 1 &gt;<br />
| |
| </td>
| |
| <td>21.902<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>gariboh<br />
| |
| </td>
| |
| <td>3125 / 3087<br />
| |
| </td>
| |
| <td>| 0 -2 5 -3 &gt;<br />
| |
| </td>
| |
| <td>21.181<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>nuwell<br />
| |
| </td>
| |
| <td>2430 / 2401<br />
| |
| </td>
| |
| <td>| 1 5 1 -4 &gt;<br />
| |
| </td>
| |
| <td>20.785<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>tolerma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 10 -11 2 1 &gt;<br />
| |
| </td>
| |
| <td>19.948<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>mirwomo<br />
| |
| </td>
| |
| <td>33075 / 32768<br />
| |
| </td>
| |
| <td>| -15 3 2 2 &gt;<br />
| |
| </td>
| |
| <td>16.144<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>trimyna<br />
| |
| </td>
| |
| <td>50421 / 50000<br />
| |
| </td>
| |
| <td>| -4 1 -5 5 &gt;<br />
| |
| </td>
| |
| <td>14.516<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>sensamagic<br />
| |
| </td>
| |
| <td>245 / 243<br />
| |
| </td>
| |
| <td>| 0 -5 1 2 &gt;<br />
| |
| </td>
| |
| <td>14.191<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>septimal semicomma, starling comma<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/126_125">126 / 125</a><br />
| |
| </td>
| |
| <td>| 1 2 -3 1 &gt;<br />
| |
| </td>
| |
| <td>13.795<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>octagar<br />
| |
| </td>
| |
| <td>4000 / 3969<br />
| |
| </td>
| |
| <td>| 5 -4 3 -2 &gt;<br />
| |
| </td>
| |
| <td>13.469<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>orwellisma, orwell comma<br />
| |
| </td>
| |
| <td>1728 / 1715<br />
| |
| </td>
| |
| <td>| 6 3 -1 -3 &gt;<br />
| |
| </td>
| |
| <td>13.074<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>quince<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -15 0 -2 7 &gt;<br />
| |
| </td>
| |
| <td>9.154<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>gamelisma<br />
| |
| </td>
| |
| <td>1029 / 1024<br />
| |
| </td>
| |
| <td>| -10 1 0 3 &gt;<br />
| |
| </td>
| |
| <td>8.433<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>varunisma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -9 8 -4 2 &gt;<br />
| |
| </td>
| |
| <td>8.037<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>septimal kleisma, marvel comma<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/225_224">225 / 224</a><br />
| |
| </td>
| |
| <td>| -5 2 2 -1 &gt;<br />
| |
| </td>
| |
| <td>7.712<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>dimcomp<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -1 -4 8 -4 &gt;<br />
| |
| </td>
| |
| <td>7.386<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>cataharry<br />
| |
| </td>
| |
| <td>19683 / 19600<br />
| |
| </td>
| |
| <td>| -4 9 -2 -2 &gt;<br />
| |
| </td>
| |
| <td>7.316<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>mirkwai<br />
| |
| </td>
| |
| <td>16875 / 16807<br />
| |
| </td>
| |
| <td>| 0 3 4 -5 &gt;<br />
| |
| </td>
| |
| <td>6.990<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>stearnsma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 1 10 0 -6 &gt;<br />
| |
| </td>
| |
| <td>6.595<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>hemimage<br />
| |
| </td>
| |
| <td>10976 / 10935<br />
| |
| </td>
| |
| <td>| 5 -7 -1 3 &gt;<br />
| |
| </td>
| |
| <td>6.479<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>hemimean<br />
| |
| </td>
| |
| <td>3136 / 3125<br />
| |
| </td>
| |
| <td>| 6 0 -5 2 &gt;<br />
| |
| </td>
| |
| <td>6.083<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>hemifamity<br />
| |
| </td>
| |
| <td>5120 / 5103<br />
| |
| </td>
| |
| <td>| 10 -6 1 -1 &gt;<br />
| |
| </td>
| |
| <td>5.758<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>linus<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 11 -10 -10 10 &gt;<br />
| |
| </td>
| |
| <td>5.572<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>porwell<br />
| |
| </td>
| |
| <td>6144 / 6125<br />
| |
| </td>
| |
| <td>| 11 1 -3 -2 &gt;<br />
| |
| </td>
| |
| <td>5.362<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>garischisma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 25 -14 0 -1 &gt;<br />
| |
| </td>
| |
| <td>3.804<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>wadisma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -26 -1 1 9 &gt;<br />
| |
| </td>
| |
| <td>3.792<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>quasiorwellisma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 22 -1 -10 1 &gt;<br />
| |
| </td>
| |
| <td>3.734<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/218edo">218edo</a> (stacked 7/4 and 10/9) comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 22 -32 16 -3 &gt;<br />
| |
| </td>
| |
| <td>11.982<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>bapbo<br />
| |
| </td>
| |
| <td>256 / 245<br />
| |
| </td>
| |
| <td>| 8 0 -1 -2 &gt;<br />
| |
| </td>
| |
| <td>76.034<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br /> | | {| class="wikitable" |
| <!-- ws:start:WikiTextHeadingRule:11:&lt;h2&gt; --><h2 id="toc5"><a name="List of commas, by prime limit-11-limit commas"></a><!-- ws:end:WikiTextHeadingRule:11 -->11-limit commas</h2> | | |- |
|
| | ! | name(s) |
| | ! | ratio |
| | ! | monzo |
| | ! | cents |
| | |- |
| | | | Hunt 13-cycle comma |
| | | | |
| | | | | -37 0 0 0 0 0 10 > |
| | | | 5.277 |
| | |- |
| | | | <span style="font-size: 12.8000001907349px;">silver half cents comma</span> |
| | | | |
| | | | <span style="font-size: 12.8000001907349px;">| -8881 0 0 0 2400 ></span> |
| | | | <span style="font-size: 12.8000001907349px;">66.389</span> |
| | |- |
| | | | Hunt minor submediant comma |
| | | | 1053 / 1024 |
| | | | | -10 4 0 0 0 0 1 > |
| | | | 48.348 |
| | |- |
| | | | astburyp |
| | | | |
| | | | | -19 -2 0 0 0 6 > |
| | | | 39.255 |
| | |- |
| | | | wilsorma |
| | | | 65 / 64 |
| | | | | -6 0 1 0 0 1 > |
| | | | 26.841 |
| | |- |
| | | | winmeanma |
| | | | 66 / 65 |
| | | | | 1 1 -1 0 1 -1 > |
| | | | 26.432 |
| | |- |
| | | | negustma |
| | | | 78 / 77 |
| | | | | 1 1 0 -1 -1 1 > |
| | | | 22.229 |
| | |- |
| | | | superleap |
| | | | 91 / 90 |
| | | | | -1 -2 -1 1 0 1 > |
| | | | 19.130 |
| | |- |
| | | | animist |
| | | | 105 / 104 |
| | | | | -3 1 1 1 0 -1 > |
| | | | 16.567 |
| | |- |
| | | | secorian |
| | | | 28672 / 28431 |
| | | | | 12 -7 0 1 0 -1 > |
| | | | 14.613 |
| | |- |
| | | | mosaic |
| | | | 3159 / 3136 |
| | | | |-6 5 0 -2 0 1> |
| | | | 12.651 |
| | |- |
| | | | gassorma |
| | | | 275 / 273 |
| | | | | 0 -1 2 -1 1 -1 > |
| | | | 12.637 |
| | |- |
| | | | [[grossma|grossma]] |
| | | | 144 / 143 |
| | | | | 4 2 0 0 -1 -1 > |
| | | | 12.064 |
| | |- |
| | | | buzurgisma, dhanvantarisma |
| | | | 169 / 168 |
| | | | | -3 -1 0 -1 0 2 > |
| | | | 10.274 |
| | |- |
| | | | catadictma |
| | | | 1287 / 1280 |
| | | | | -8 2 -1 0 1 1 > |
| | | | 9.442 |
| | |- |
| | | | [[mynucumic_chords|mynucuma]] |
| | | | 196 / 195 |
| | | | | 2 -1 -1 2 0 -1 > |
| | | | 8.855 |
| | |- |
| | | | [[huntmic_chords|huntma]] |
| | | | 640 / 637 |
| | | | | 7 0 1 -2 0 -1 > |
| | | | 8.134 |
| | |- |
| | | | [[threedie|threedie]] |
| | | | 2197 / 2187 |
| | | | | 0 -7 0 0 0 3 > |
| | | | 7.897 |
| | |- |
| | | | [[kestrel_chords|kestrel comma]] |
| | | | 1188 / 1183 |
| | | | | 2 3 0 -1 1 -2 > |
| | | | 7.302 |
| | |- |
| | | | [[Marveltwin|marveltwin]] |
| | | | 325 / 324 |
| | | | | -2 -4 2 0 0 1 > |
| | | | 5.335 |
| | |- |
| | | | [[ratwolf_triad|ratwolfsma]] |
| | | | 351 / 350 |
| | | | | -1 3 -2 -1 0 1 > |
| | | | 4.939 |
| | |- |
| | | | [[minthmic_chords|minthma]] |
| | | | 352 / 351 |
| | | | | 5 -3 0 0 1 -1 > |
| | | | 4.925 |
| | |- |
| | | | [[gentle_chords|gentle comma]] |
| | | | 364 / 363 |
| | | | | 2 -1 0 1 -2 1 > |
| | | | 4.763 |
| | |- |
| | | | [[cuthbert_triad|cuthbert]] |
| | | | 847 / 845 |
| | | | | 0 0 -1 1 2 -2 > |
| | | | 4.093 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==17-limit commas== |
| <tr>
| |
| <th>name(s)<br />
| |
| </th>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>monzo<br />
| |
| </th>
| |
| <th>cents<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>11-cycle chroma, 11-11-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -38 0 0 0 11 &gt;<br />
| |
| </td>
| |
| <td>64.497<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11-cycle major seventh prote, 35-11-comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -121 0 0 0 35 &gt;<br />
| |
| </td>
| |
| <td>96.128<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Hunt 11-cycle comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -83 0 0 0 24 &gt;<br />
| |
| </td>
| |
| <td>31.631<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Hunt flat 5 comma<br />
| |
| </td>
| |
| <td>8192 / 8019<br />
| |
| </td>
| |
| <td>| 13 -6 0 0 -1 &gt;<br />
| |
| </td>
| |
| <td>36.952<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>sterno<br />
| |
| </td>
| |
| <td>352 / 343<br />
| |
| </td>
| |
| <td>| 5 0 0 -3 1 &gt;<br />
| |
| </td>
| |
| <td>44.840<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>the Igs boson<span style="line-height: 1.5;">, 13-11-comma</span><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 45 0 0 0 -13 &gt;<br />
| |
| </td>
| |
| <td>32.867<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>telepathma<br />
| |
| </td>
| |
| <td>55 / 54<br />
| |
| </td>
| |
| <td>| -1 -3 1 0 1 &gt;<br />
| |
| </td>
| |
| <td>31.767<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>thuja comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 15 0 1 0 -5 &gt;<br />
| |
| </td>
| |
| <td>29.724<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>sensmus<br />
| |
| </td>
| |
| <td>1232 / 1215<br />
| |
| </td>
| |
| <td>| 4 -5 -1 1 1 &gt;<br />
| |
| </td>
| |
| <td>24.055<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>sevnothrush<br />
| |
| </td>
| |
| <td>3168 / 3125<br />
| |
| </td>
| |
| <td>| 5 2 -5 0 1 &gt;<br />
| |
| </td>
| |
| <td>23.659<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>cassacot<br />
| |
| </td>
| |
| <td>245 / 242<br />
| |
| </td>
| |
| <td>| -1 0 1 2 -2 &gt;<br />
| |
| </td>
| |
| <td>21.330<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/mothwellsmic%20triad">mothwellsma</a><br />
| |
| </td>
| |
| <td>99 / 98<br />
| |
| </td>
| |
| <td>| -1 2 0 -2 1 &gt;<br />
| |
| </td>
| |
| <td>17.576<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/ptolemismic%20triad">ptolemisma</a><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/100_99">100 / 99</a><br />
| |
| </td>
| |
| <td>| 2 -2 2 0 -1 &gt;<br />
| |
| </td>
| |
| <td>17.399<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>hemimin<br />
| |
| </td>
| |
| <td>1344 / 1331<br />
| |
| </td>
| |
| <td>| 6 1 0 1 -3 &gt;<br />
| |
| </td>
| |
| <td>16.827<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>biyatisma<br />
| |
| </td>
| |
| <td>121 / 120<br />
| |
| </td>
| |
| <td>| -3 -1 -1 0 2 &gt;<br />
| |
| </td>
| |
| <td>14.367<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>aphrowe<br />
| |
| </td>
| |
| <td>1331 / 1323<br />
| |
| </td>
| |
| <td>| 0 -3 0 -2 3 &gt;<br />
| |
| </td>
| |
| <td>10.437<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/valinorsmic%20chords">valinorsma</a><br />
| |
| </td>
| |
| <td>176 / 175<br />
| |
| </td>
| |
| <td>| 4 0 -2 -1 1 &gt;<br />
| |
| </td>
| |
| <td>9.865<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/pentacircle%20comma">pentacircle</a><br />
| |
| </td>
| |
| <td>896 / 891<br />
| |
| </td>
| |
| <td>| 7 -4 0 1 -1 &gt;<br />
| |
| </td>
| |
| <td>9.688<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>orgonisma<br />
| |
| </td>
| |
| <td>65536 / 65219<br />
| |
| </td>
| |
| <td>| 16 0 0 -2 -3 &gt;<br />
| |
| </td>
| |
| <td>8.394<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/rastmic%20chords">rastma</a><br />
| |
| </td>
| |
| <td>243 / 242<br />
| |
| </td>
| |
| <td>| -1 5 0 0 -2 &gt;<br />
| |
| </td>
| |
| <td>7.139<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>myhemiwell<br />
| |
| </td>
| |
| <td>3388 / 3375<br />
| |
| </td>
| |
| <td>| 2 -3 -3 1 2 &gt;<br />
| |
| </td>
| |
| <td>6.656<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/keenanismic%20chords">keenanisma</a><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/385_384">385 / 384</a><br />
| |
| </td>
| |
| <td>| -7 -1 1 1 1 &gt;<br />
| |
| </td>
| |
| <td>4.503<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/werckismic%20chords">werckisma</a><br />
| |
| </td>
| |
| <td>441 / 440<br />
| |
| </td>
| |
| <td>| -3 2 -1 2 -1 &gt;<br />
| |
| </td>
| |
| <td>3.930<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>moctdel<br />
| |
| </td>
| |
| <td>1375 / 1372<br />
| |
| </td>
| |
| <td>| -2 0 3 -3 1 &gt;<br />
| |
| </td>
| |
| <td>3.781<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br /> | | {| class="wikitable" |
| <!-- ws:start:WikiTextHeadingRule:13:&lt;h2&gt; --><h2 id="toc6"><a name="List of commas, by prime limit-13-limit commas"></a><!-- ws:end:WikiTextHeadingRule:13 -->13-limit commas</h2>
| | |- |
|
| | ! | name(s) |
| | ! | ratio |
| | ! | monzo |
| | ! | cents |
| | |- |
| | | | 11 semitone comma |
| | | | |
| | | | | 45 0 0 0 0 0 -11 > |
| | | | 45.4905 |
| | |- |
| | | | 12 semitone comma |
| | | | |
| | | | | -49 0 0 0 0 0 12 > |
| | | | 59.465 |
| | |- |
| | | | 23 semitone comma |
| | | | |
| | | | | -93 0 0 0 0 0 23 > |
| | | | 13.974 |
| | |- |
| | | | Hunt 17-cycle comma |
| | | | |
| | | | | -138 0 0 0 0 0 34 > |
| | | | 31.516 |
| | |- |
| | | | 17-ripple integer cents comma |
| | | | |
| | | | | 327 0 0 0 0 0 -80 > |
| | | | 3.568 |
| | |- |
| | | | Hunt flat 2 comma |
| | | | 4131 / 4096 |
| | | | | -12 5 0 0 0 0 1 > |
| | | | 14.730 |
| | |- |
| | | | Blume comma |
| | | | 2057 / 2048 |
| | | | | -11 0 0 0 2 0 1 > |
| | | | 7.591 |
| | |- |
| | | | Septendecimal Integer Cents comma |
| | | | 289 / 288 |
| | | | | -5 -2 0 0 0 0 2 > |
| | | | 6.001 |
| | |- |
| | | | Tannisma |
| | | | 273/272 |
| | | | |-4 1 0 1 0 1 -2> |
| | | | 6.353 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==19-limit commas== |
| <tr>
| |
| <th>name(s)<br />
| |
| </th>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>monzo<br />
| |
| </th>
| |
| <th>cents<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>Hunt 13-cycle comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -37 0 0 0 0 0 10 &gt;<br />
| |
| </td>
| |
| <td>5.277<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="font-size: 12.8000001907349px;">silver half cents comma</span><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><span style="font-size: 12.8000001907349px;">| -8881 0 0 0 2400 &gt;</span><br />
| |
| </td>
| |
| <td><span style="font-size: 12.8000001907349px;">66.389</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Hunt minor submediant comma<br />
| |
| </td>
| |
| <td>1053 / 1024<br />
| |
| </td>
| |
| <td>| -10 4 0 0 0 0 1 &gt;<br />
| |
| </td>
| |
| <td>48.348<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>astburyp<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -19 -2 0 0 0 6 &gt;<br />
| |
| </td>
| |
| <td>39.255<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>wilsorma<br />
| |
| </td>
| |
| <td>65 / 64<br />
| |
| </td>
| |
| <td>| -6 0 1 0 0 1 &gt;<br />
| |
| </td>
| |
| <td>26.841<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>winmeanma<br />
| |
| </td>
| |
| <td>66 / 65<br />
| |
| </td>
| |
| <td>| 1 1 -1 0 1 -1 &gt;<br />
| |
| </td>
| |
| <td>26.432<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>negustma<br />
| |
| </td>
| |
| <td>78 / 77<br />
| |
| </td>
| |
| <td>| 1 1 0 -1 -1 1 &gt;<br />
| |
| </td>
| |
| <td>22.229<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>superleap<br />
| |
| </td>
| |
| <td>91 / 90<br />
| |
| </td>
| |
| <td>| -1 -2 -1 1 0 1 &gt;<br />
| |
| </td>
| |
| <td>19.130<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>animist<br />
| |
| </td>
| |
| <td>105 / 104<br />
| |
| </td>
| |
| <td>| -3 1 1 1 0 -1 &gt;<br />
| |
| </td>
| |
| <td>16.567<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>secorian<br />
| |
| </td>
| |
| <td>28672 / 28431<br />
| |
| </td>
| |
| <td>| 12 -7 0 1 0 -1 &gt;<br />
| |
| </td>
| |
| <td>14.613<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>mosaic<br />
| |
| </td>
| |
| <td>3159 / 3136<br />
| |
| </td>
| |
| <td>|-6 5 0 -2 0 1&gt;<br />
| |
| </td>
| |
| <td>12.651<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>gassorma<br />
| |
| </td>
| |
| <td>275 / 273<br />
| |
| </td>
| |
| <td>| 0 -1 2 -1 1 -1 &gt;<br />
| |
| </td>
| |
| <td>12.637<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/grossma">grossma</a><br />
| |
| </td>
| |
| <td>144 / 143<br />
| |
| </td>
| |
| <td>| 4 2 0 0 -1 -1 &gt;<br />
| |
| </td>
| |
| <td>12.064<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>buzurgisma, dhanvantarisma<br />
| |
| </td>
| |
| <td>169 / 168<br />
| |
| </td>
| |
| <td>| -3 -1 0 -1 0 2 &gt;<br />
| |
| </td>
| |
| <td>10.274<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>catadictma<br />
| |
| </td>
| |
| <td>1287 / 1280<br />
| |
| </td>
| |
| <td>| -8 2 -1 0 1 1 &gt;<br />
| |
| </td>
| |
| <td>9.442<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/mynucumic%20chords">mynucuma</a><br />
| |
| </td>
| |
| <td>196 / 195<br />
| |
| </td>
| |
| <td>| 2 -1 -1 2 0 -1 &gt;<br />
| |
| </td>
| |
| <td>8.855<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/huntmic%20chords">huntma</a><br />
| |
| </td>
| |
| <td>640 / 637<br />
| |
| </td>
| |
| <td>| 7 0 1 -2 0 -1 &gt;<br />
| |
| </td>
| |
| <td>8.134<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/threedie">threedie</a><br />
| |
| </td>
| |
| <td>2197 / 2187<br />
| |
| </td>
| |
| <td>| 0 -7 0 0 0 3 &gt;<br />
| |
| </td>
| |
| <td>7.897<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/kestrel%20chords">kestrel comma</a><br />
| |
| </td>
| |
| <td>1188 / 1183<br />
| |
| </td>
| |
| <td>| 2 3 0 -1 1 -2 &gt;<br />
| |
| </td>
| |
| <td>7.302<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/marveltwin">marveltwin</a><br />
| |
| </td>
| |
| <td>325 / 324<br />
| |
| </td>
| |
| <td>| -2 -4 2 0 0 1 &gt;<br />
| |
| </td>
| |
| <td>5.335<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/ratwolf%20triad">ratwolfsma</a><br />
| |
| </td>
| |
| <td>351 / 350<br />
| |
| </td>
| |
| <td>| -1 3 -2 -1 0 1 &gt;<br />
| |
| </td>
| |
| <td>4.939<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/minthmic%20chords">minthma</a><br />
| |
| </td>
| |
| <td>352 / 351<br />
| |
| </td>
| |
| <td>| 5 -3 0 0 1 -1 &gt;<br />
| |
| </td>
| |
| <td>4.925<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/gentle%20chords">gentle comma</a><br />
| |
| </td>
| |
| <td>364 / 363<br />
| |
| </td>
| |
| <td>| 2 -1 0 1 -2 1 &gt;<br />
| |
| </td>
| |
| <td>4.763<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/cuthbert%20triad">cuthbert</a><br />
| |
| </td>
| |
| <td>847 / 845<br />
| |
| </td>
| |
| <td>| 0 0 -1 1 2 -2 &gt;<br />
| |
| </td>
| |
| <td>4.093<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | {| class="wikitable" |
| <!-- ws:start:WikiTextHeadingRule:15:&lt;h2&gt; --><h2 id="toc7"><a name="List of commas, by prime limit-17-limit commas"></a><!-- ws:end:WikiTextHeadingRule:15 -->17-limit commas</h2>
| | |- |
|
| | ! | name(s) |
| | | ! | ratio |
| <table class="wiki_table">
| | ! | monzo |
| <tr>
| | ! | cents |
| <th>name(s)<br />
| | |- |
| </th>
| | | | Hunt 19-cycle comma |
| <th>ratio<br />
| | | | |
| </th>
| | | | | 17 0 0 0 0 0 0 -4 > |
| <th>monzo<br />
| | | | 9.950 |
| </th>
| | |- |
| <th>cents<br />
| | | | spleen comma |
| </th>
| | | | 210 / 209 |
| </tr>
| | | | | 1 1 1 1 -1 0 0 -1 > |
| <tr>
| | | | 8.264 |
| <td>11 semitone comma<br />
| | |- |
| </td>
| | | | go comma |
| <td><br />
| | | | 361 / 360 |
| </td>
| | | | | -3 -2 -1 0 0 0 0 2 > |
| <td>| 45 0 0 0 0 0 -11 &gt;<br />
| | | | 4.802 |
| </td>
| | |} |
| <td>45.4905<br />
| | [[Category:comma]] |
| </td>
| | [[Category:interval]] |
| </tr>
| | [[Category:list]] |
| <tr>
| | [[Category:theory]] |
| <td>12 semitone comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -49 0 0 0 0 0 12 &gt;<br />
| |
| </td>
| |
| <td>59.465<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23 semitone comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -93 0 0 0 0 0 23 &gt;<br />
| |
| </td>
| |
| <td>13.974<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Hunt 17-cycle comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| -138 0 0 0 0 0 34 &gt;<br />
| |
| </td>
| |
| <td>31.516<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17-ripple integer cents comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 327 0 0 0 0 0 -80 &gt;<br />
| |
| </td>
| |
| <td>3.568<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Hunt flat 2 comma<br />
| |
| </td>
| |
| <td>4131 / 4096<br />
| |
| </td>
| |
| <td>| -12 5 0 0 0 0 1 &gt;<br />
| |
| </td>
| |
| <td>14.730<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Blume comma<br />
| |
| </td>
| |
| <td>2057 / 2048<br />
| |
| </td>
| |
| <td>| -11 0 0 0 2 0 1 &gt;<br />
| |
| </td>
| |
| <td>7.591<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Septendecimal Integer Cents comma<br />
| |
| </td>
| |
| <td>289 / 288<br />
| |
| </td>
| |
| <td>| -5 -2 0 0 0 0 2 &gt;<br />
| |
| </td>
| |
| <td>6.001<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>Tannisma<br />
| |
| </td>
| |
| <td>273/272<br />
| |
| </td>
| |
| <td>|-4 1 0 1 0 1 -2&gt;<br />
| |
| </td>
| |
| <td>6.353<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:17:&lt;h2&gt; --><h2 id="toc8"><a name="List of commas, by prime limit-19-limit commas"></a><!-- ws:end:WikiTextHeadingRule:17 -->19-limit commas</h2>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>name(s)<br />
| |
| </th>
| |
| <th>ratio<br />
| |
| </th>
| |
| <th>monzo<br />
| |
| </th>
| |
| <th>cents<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>Hunt 19-cycle comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>| 17 0 0 0 0 0 0 -4 &gt;<br />
| |
| </td>
| |
| <td>9.950<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>spleen comma<br />
| |
| </td>
| |
| <td>210 / 209<br />
| |
| </td>
| |
| <td>| 1 1 1 1 -1 0 0 -1 &gt;<br />
| |
| </td>
| |
| <td>8.264<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>go comma<br />
| |
| </td>
| |
| <td>361 / 360<br />
| |
| </td>
| |
| <td>| -3 -2 -1 0 0 0 0 2 &gt;<br />
| |
| </td>
| |
| <td>4.802<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/25699772?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;25699772&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><!-- makes tables pretty -->
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| |
| /*<![CDATA[*/
| |
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| |
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| |
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| |