Small comma
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- This revision was by author genewardsmith and made on 2011-07-10 14:20:47 UTC.
- The original revision id was 240715621.
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Original Wikitext content:
A **comma** is a small just interval, greater than 1 and not a power such as a square or cube of any other interval, 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. For example the Didymos comma of 81/80 is tempered out by [[Meantone|meantone temperament]]. ==3-limit commas== 256 / 243 = |8 -5>: limma or Pythagorean minor second (90.225 [[cent]]s) 2187 / 2048 = |-11 7>: apotome (113.685 cents) 531441 / 524288 = |-19 12>: Pythagorean comma (23.460 cents) 134217728 / 129140163 = |27 -17>: 17-comma (66.765 cents) 70368744177664 / 68630377364883 = |46 -29>: 29-comma (43.305 cents) 36893488147419103232 / 36472996377170786403 = |65 -41>: 41-comma (19.845 cents) 19383245667680019896796723 / 19342813113834066795298816 = |-84 53>: Mercator's comma, 53-comma (3.615 cents) |485 -306>: Sasktel comma (1.770 cents) |-1054 665>: Satanic comma (0.076 cents) ==5-limit commas== [[135_128|135 / 128]] = |-7 3 1>: [[major chroma]], [[major limma]], [[pelogic comma]] (92.179 [[cent]]s) 5000000 / 4782969 = |6 -14 7>: sevond (76.826 cents) 25 /24 = |-3 -1 2>: chromatic semitone (70.672 cents) 20480 / 19683 = |12 -9 1>: grave minor second (68.719 cents) 648 / 625 = |3 4 -4>: major diesis, diminished comma (62.565 cents) 1953125 / 1889568 |-5 -10 9>: shibboleth (57.273 cents) 16875 / 16384 = |-14 3 4>: negri comma, double augmentation diesis (51.120 cents) 250 / 243 = |1 -5 3>: maximal diesis, porcupine comma (49.166 cents) 1638400 / 1594323 = |16 -13 2>: immunity (47.212 cents) 128 / 125 = |7 0 -3>: diesis, augmented comma (41.059 cents) 9765625 / 9565938 = |-1 -14 10>: fifive (35.767 cents) 1594323 / 1562500 = |-2 13 -8>: unicorn (34.905 cents) 1990656 / 1953125 = |13 5 -9>: valensixthtone (32.952 cents) 34171875 / 33554432 = |-25 7 6>: ampersand, Ampersand's comma (31.567 cents) 3125 / 3072 = |-10 -1 5> small diesis, magic comma (29.614 cents) 20000 / 19683 = |5 -9 4>: minimal diesis, tetracot comma (27.660 cents) 131072000 / 129140163 = |20 -17 3> roda (25.706 cents) 81 / 80 = |-4 4 -1>: syntonic comma, Didymos comma, meantone comma (21.506 cents) 2048 / 2025 = |11 -4 -2>: diaschisma (19.553 cents) 67108864 / 66430125 = |26 -12 -3>: misty comma (17.599 cents) 78732 / 78125 = |2 9 -7>: medium semicomma, sensipent comma (13.399 cents) 393216 / 390625 = |17 1 -8>: Wuerschmidt comma (11.445 cents) 2109375 / 2097152 = |-21 3 7>: semicomma, Fokker comma (10.061 cents) |32 -7 -9>: escapade comma (9.492 cents) 15625 / 15552 = |-6 -5 6>: kleisma, semicomma majeur (8.107 cents) |-44 -3 21>: mutt comma (6.723 cents) 1600000 / 1594323 = |9 -13 5>: amity comma (6.154 cents) |8 14 -13>: parakleisma (5.292 cents) |-29 -11 20>: gammic comma (4.769 cents) |24 -21 4>: vulture (4.200 cents) 6115295232 / 6103515625 = |23 6 -14>: vishnuzma, semisuper (3.338 cents) |-14 -19 19>: enneadeca, 19-tone-comma (2.816 cents) |-68 18 17>: vavoom (2.523 cents) |39 -29 3>: tricot comma (2.246 cents) 32805 / 32768 = |-15 8 1>: schisma (1.954 cents) |-69 45 -1>: countercata (1.661 cents) |-52 -17 34>: septendecima (1.431 cents) 274877906944 / 274658203125 = |38 -2 -15>: hemithirds comma (1.384 cents) |-16 35 -17>: minortone comma (1.092 cents) 7629394531250 / 7625597484987 = |1 -27 18>: ennealimma (0.862 cents) |91 -12 -31>: astro (0.815 cents) |-53 10 16>: kwazy (0.569 cents) |37 25 -33>: whoosh (0.522 cents) |-36 -52 51>: egads (0.339 cents) |54 -37 2>: monzisma (0.292 cents) |-107 47 14>: fortune (0.277 cents) |144 -22 -47>: gross (0.245 cents) |-17 62 -35>: senior (0.230 cents) |71 -99 37>: raider (0.062 cents) |-90 -15 49>: pirate (0.047 cents) |161 -84 -12>: atom (0.015 cents) ==7-limit commas== 1029 / 1000 = |-3 1 -3 3>: keega (49.492 [[cent]]s) 36 / 35 = |2 2 -1 -1>: septimal quarter tone (48.770 cents) 525 / 512 = |-9 1 2 1>: avicennma, Avicenna's enharmonic diesis (43.408 cents) 49 / 48 = |-4 -1 0 2>: slendro diesis (35.597 cents) 50 / 49 = |1 0 2 -2>: tritonic diesis, jubilisma (34.976 cents) 686 / 675 = |1 -3 -2 3>: senga (27.985 cents) 64 / 63 = |6 -2 0 -1>: septimal comma, Archytas' comma ([[http://de.wikipedia.org/wiki/Komma_%28Musik%29#Leipziger_Komma|"Leipziger Komma"]]) (27.264 cents) 854296875 / 843308032 = |-10 7 8 -7>: blackjackisma (22.413 cents) 64827 / 64000 = |-9 3 -3 4>: squalentine (22.227 cents) 875 / 864 = |-5 -3 3 1>: keema (21.902 cents) 3125 / 3087 = |0 -2 5 -3>: gariboh (21.181 cents) 2430 / 2401 = |1 5 1 -4>: nuwell (20.785 cents) 50421 / 50000 = |-4 1 -5 5>: trimyna (14.516 cents) 245 / 243 = |0 -5 1 2>: sensamagic (14.191 cents) 126 / 125 = |1 2 -3 1>: septimal semicomma, starling comma (13.795 cents) 4000 / 3969 = |5 -4 3 -2>: octagar (13.469 cents) 1728 /1715 = |6 3 -1 -3>: orwellisma, orwell comma (13.074 cents) 1029 / 1024 = |-10 1 0 3>: gamelisma (8.433 cents) 321489 / 320000 = |-9 8 -4 2>: varunisma (8.037 cents) 225 / 224 = |-5 2 2 -1>: septimal kleisma, marvel comma (7.712 cents) 19683 / 19600 = |-4 9 -2 -2>: cataharry (7.316 cents) 16875 / 16807 = |0 3 4 -5>: mirkwai (6.990 cents) 10976 / 10935 = |5 -7 -1 3>: hemimage (6.479 cents) 3136 / 3125 = |6 0 -5 2>: hemimean (6.083 cents) 5120 / 5103 = |10 -6 1 -1>: hemifamity (5.758 cents) 578509309952 / 576650390625 = |11 -10 -10 10>: linus (5.572 cents) 6144 / 6125 = |11 1 -3 -2>: porwell (5.362 cents) 33554432 / 33480743 = |25 -14 0 -1>: garischisma (3.804 cents) 201768035 / 201326592 = |-26 -1 1 9>: wadisma (3.792 cents) 65625 / 65536 = |-16 1 5 1>: horwell (2.349 cents) 703125 / 702464 = |-11 2 7 -3>: meter (1.628 cents) 420175 / 419904 = |-6 -8 2 5>: wizma (1.117 cents) 2401 / 2400 = |-5 -1 -2 4>: breedsma (0.721 cents) 4375 / 4374 = |-1 -7 4 1>: ragisma (0.396 cents) 140737488355328 / 140710042265625 = |47, -7, -7, -7>: akjaysma, 5\7 octave comma, (0.338 cents) 250047 / 250000 = |-4 6 -6 3>: landscape comma (0.325 cents) ==11-limit commas== 99 / 98 = |-1 2 0 -2 1>: mothwellsma (17.576 cents) 100 / 99 = |2 -2 2 0 -1>: ptolemisma (17.399 cents) 121 / 120 = |-3 -1 -1 0 2>: biyatisma (14.367 cents) 176 / 175 = |4 0 -2 -1 1>: valinorsma (9.865 cents) 896 / 891 = |7 -4 0 1 -1>: pentacircle (9.688 cents) 65536 / 65219 = |16 0 0 -2 -3>: orgonisma (8.394 cents) 243 / 242 = |-1 5 0 0 -2>: rastma (7.139 cents) 385 / 384 = |-7 -1 1 1 1>: keenanisma (4.503 cents) 441 / 440 = |-3 2 -1 2 -1>: werckisma (3.930 cents) 1375 / 1372 = |-2 0 3 -3 1>: moctdel (3.781 cents) 540 / 539 = |2 3 1 -2 -1>: swetisma (3.209 cents) 4000 / 3993 = |5 -1 3 0 -3>: wizardharry (3.032 cents) 5632 / 5625 = |9 -2 -4 0 1>: vishdel (2.153 cents) 43923 / 43904 = |-7 1 0 -3 4>: hemigail (0.749 cents) 3025 / 3024 = |-4 -3 2 -1 2>: lehmerisma (0.572 cents) 9801 / 9800 = |-3 4 -2 -2 2>: kalisma, Gauss' comma (0.177 cents) 151263 / 151250 = |-1 2 -4 5 -2>: odiheim (0.149 cents) 3294225 / 3294172 = |-2 2 2 -7 4>: ultimo (0.028 cents) ==13-limit commas== 78 / 77 = |1 1 0 -1 -1 1>: negustma (22.229 cents) 91 / 90 = |-1 -2 -1 1 0 1>: superleap (19.130 cents) 105 / 104 = |-3 1 1 1 0 1>: wintone (16.567 cents) 144 / 143 = |4 2 0 0 -1 -1>: grossma (12.064 cents) 196 / 195 = |2 -1 -1 2 0 -1>: mynucuma (8.855 cents) 325 / 324 = |-2 -4 2 0 0 1>: [[Marveltwin|marveltwin]] (5.335 cents) 676 / 675 = |2 -3 -2 0 0 2>: [[The Archipelago|parizeksma]] (2.563 cents)
Original HTML content:
<html><head><title>Comma</title></head><body>A <strong>comma</strong> is a small just interval, greater than 1 and not a power such as a square or cube of any other interval, 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. For example the Didymos comma of 81/80 is tempered out by <a class="wiki_link" href="/Meantone">meantone temperament</a>.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-3-limit commas"></a><!-- ws:end:WikiTextHeadingRule:0 -->3-limit commas</h2> <br /> 256 / 243 = |8 -5>: limma or Pythagorean minor second (90.225 <a class="wiki_link" href="/cent">cent</a>s)<br /> 2187 / 2048 = |-11 7>: apotome (113.685 cents)<br /> 531441 / 524288 = |-19 12>: Pythagorean comma (23.460 cents)<br /> 134217728 / 129140163 = |27 -17>: 17-comma (66.765 cents)<br /> 70368744177664 / 68630377364883 = |46 -29>: 29-comma (43.305 cents)<br /> 36893488147419103232 / 36472996377170786403 = |65 -41>: 41-comma (19.845 cents)<br /> 19383245667680019896796723 / 19342813113834066795298816 = |-84 53>: Mercator's comma, 53-comma (3.615 cents)<br /> |485 -306>: Sasktel comma (1.770 cents)<br /> |-1054 665>: Satanic comma (0.076 cents)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-5-limit commas"></a><!-- ws:end:WikiTextHeadingRule:2 -->5-limit commas</h2> <br /> <a class="wiki_link" href="/135_128">135 / 128</a> = |-7 3 1>: <a class="wiki_link" href="/major%20chroma">major chroma</a>, <a class="wiki_link" href="/major%20limma">major limma</a>, <a class="wiki_link" href="/pelogic%20comma">pelogic comma</a> (92.179 <a class="wiki_link" href="/cent">cent</a>s)<br /> 5000000 / 4782969 = |6 -14 7>: sevond (76.826 cents)<br /> 25 /24 = |-3 -1 2>: chromatic semitone (70.672 cents)<br /> 20480 / 19683 = |12 -9 1>: grave minor second (68.719 cents)<br /> 648 / 625 = |3 4 -4>: major diesis, diminished comma (62.565 cents)<br /> 1953125 / 1889568 |-5 -10 9>: shibboleth (57.273 cents)<br /> 16875 / 16384 = |-14 3 4>: negri comma, double augmentation diesis (51.120 cents)<br /> 250 / 243 = |1 -5 3>: maximal diesis, porcupine comma (49.166 cents)<br /> 1638400 / 1594323 = |16 -13 2>: immunity (47.212 cents)<br /> 128 / 125 = |7 0 -3>: diesis, augmented comma (41.059 cents)<br /> 9765625 / 9565938 = |-1 -14 10>: fifive (35.767 cents)<br /> 1594323 / 1562500 = |-2 13 -8>: unicorn (34.905 cents)<br /> 1990656 / 1953125 = |13 5 -9>: valensixthtone (32.952 cents)<br /> 34171875 / 33554432 = |-25 7 6>: ampersand, Ampersand's comma (31.567 cents)<br /> 3125 / 3072 = |-10 -1 5> small diesis, magic comma (29.614 cents)<br /> 20000 / 19683 = |5 -9 4>: minimal diesis, tetracot comma (27.660 cents)<br /> 131072000 / 129140163 = |20 -17 3> roda (25.706 cents)<br /> 81 / 80 = |-4 4 -1>: syntonic comma, Didymos comma, meantone comma (21.506 cents)<br /> 2048 / 2025 = |11 -4 -2>: diaschisma (19.553 cents)<br /> 67108864 / 66430125 = |26 -12 -3>: misty comma (17.599 cents)<br /> 78732 / 78125 = |2 9 -7>: medium semicomma, sensipent comma (13.399 cents)<br /> 393216 / 390625 = |17 1 -8>: Wuerschmidt comma (11.445 cents)<br /> 2109375 / 2097152 = |-21 3 7>: semicomma, Fokker comma (10.061 cents)<br /> |32 -7 -9>: escapade comma (9.492 cents)<br /> 15625 / 15552 = |-6 -5 6>: kleisma, semicomma majeur (8.107 cents)<br /> |-44 -3 21>: mutt comma (6.723 cents)<br /> 1600000 / 1594323 = |9 -13 5>: amity comma (6.154 cents)<br /> |8 14 -13>: parakleisma (5.292 cents)<br /> |-29 -11 20>: gammic comma (4.769 cents)<br /> |24 -21 4>: vulture (4.200 cents)<br /> 6115295232 / 6103515625 = |23 6 -14>: vishnuzma, semisuper (3.338 cents)<br /> |-14 -19 19>: enneadeca, 19-tone-comma (2.816 cents)<br /> |-68 18 17>: vavoom (2.523 cents)<br /> |39 -29 3>: tricot comma (2.246 cents)<br /> 32805 / 32768 = |-15 8 1>: schisma (1.954 cents)<br /> |-69 45 -1>: countercata (1.661 cents)<br /> |-52 -17 34>: septendecima (1.431 cents)<br /> 274877906944 / 274658203125 = |38 -2 -15>: hemithirds comma (1.384 cents)<br /> |-16 35 -17>: minortone comma (1.092 cents)<br /> 7629394531250 / 7625597484987 = |1 -27 18>: ennealimma (0.862 cents)<br /> |91 -12 -31>: astro (0.815 cents)<br /> |-53 10 16>: kwazy (0.569 cents)<br /> |37 25 -33>: whoosh (0.522 cents)<br /> |-36 -52 51>: egads (0.339 cents)<br /> |54 -37 2>: monzisma (0.292 cents)<br /> |-107 47 14>: fortune (0.277 cents)<br /> |144 -22 -47>: gross (0.245 cents)<br /> |-17 62 -35>: senior (0.230 cents)<br /> |71 -99 37>: raider (0.062 cents)<br /> |-90 -15 49>: pirate (0.047 cents)<br /> |161 -84 -12>: atom (0.015 cents)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x-7-limit commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->7-limit commas</h2> <br /> 1029 / 1000 = |-3 1 -3 3>: keega (49.492 <a class="wiki_link" href="/cent">cent</a>s)<br /> 36 / 35 = |2 2 -1 -1>: septimal quarter tone (48.770 cents)<br /> 525 / 512 = |-9 1 2 1>: avicennma, Avicenna's enharmonic diesis (43.408 cents)<br /> 49 / 48 = |-4 -1 0 2>: slendro diesis (35.597 cents)<br /> 50 / 49 = |1 0 2 -2>: tritonic diesis, jubilisma (34.976 cents)<br /> 686 / 675 = |1 -3 -2 3>: senga (27.985 cents)<br /> 64 / 63 = |6 -2 0 -1>: septimal comma, Archytas' comma (<a class="wiki_link_ext" href="http://de.wikipedia.org/wiki/Komma_%28Musik%29#Leipziger_Komma" rel="nofollow">"Leipziger Komma"</a>) (27.264 cents)<br /> 854296875 / 843308032 = |-10 7 8 -7>: blackjackisma (22.413 cents)<br /> 64827 / 64000 = |-9 3 -3 4>: squalentine (22.227 cents)<br /> 875 / 864 = |-5 -3 3 1>: keema (21.902 cents)<br /> 3125 / 3087 = |0 -2 5 -3>: gariboh (21.181 cents)<br /> 2430 / 2401 = |1 5 1 -4>: nuwell (20.785 cents)<br /> 50421 / 50000 = |-4 1 -5 5>: trimyna (14.516 cents)<br /> 245 / 243 = |0 -5 1 2>: sensamagic (14.191 cents)<br /> 126 / 125 = |1 2 -3 1>: septimal semicomma, starling comma (13.795 cents)<br /> 4000 / 3969 = |5 -4 3 -2>: octagar (13.469 cents)<br /> 1728 /1715 = |6 3 -1 -3>: orwellisma, orwell comma (13.074 cents)<br /> 1029 / 1024 = |-10 1 0 3>: gamelisma (8.433 cents)<br /> 321489 / 320000 = |-9 8 -4 2>: varunisma (8.037 cents)<br /> 225 / 224 = |-5 2 2 -1>: septimal kleisma, marvel comma (7.712 cents)<br /> 19683 / 19600 = |-4 9 -2 -2>: cataharry (7.316 cents)<br /> 16875 / 16807 = |0 3 4 -5>: mirkwai (6.990 cents)<br /> 10976 / 10935 = |5 -7 -1 3>: hemimage (6.479 cents)<br /> 3136 / 3125 = |6 0 -5 2>: hemimean (6.083 cents)<br /> 5120 / 5103 = |10 -6 1 -1>: hemifamity (5.758 cents)<br /> 578509309952 / 576650390625 = |11 -10 -10 10>: linus (5.572 cents)<br /> 6144 / 6125 = |11 1 -3 -2>: porwell (5.362 cents)<br /> 33554432 / 33480743 = |25 -14 0 -1>: garischisma (3.804 cents)<br /> 201768035 / 201326592 = |-26 -1 1 9>: wadisma (3.792 cents)<br /> 65625 / 65536 = |-16 1 5 1>: horwell (2.349 cents)<br /> 703125 / 702464 = |-11 2 7 -3>: meter (1.628 cents)<br /> 420175 / 419904 = |-6 -8 2 5>: wizma (1.117 cents)<br /> 2401 / 2400 = |-5 -1 -2 4>: breedsma (0.721 cents)<br /> 4375 / 4374 = |-1 -7 4 1>: ragisma (0.396 cents)<br /> 140737488355328 / 140710042265625 = |47, -7, -7, -7>: akjaysma, 5\7 octave comma, (0.338 cents)<br /> 250047 / 250000 = |-4 6 -6 3>: landscape comma (0.325 cents)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x-11-limit commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit commas</h2> <br /> 99 / 98 = |-1 2 0 -2 1>: mothwellsma (17.576 cents)<br /> 100 / 99 = |2 -2 2 0 -1>: ptolemisma (17.399 cents)<br /> 121 / 120 = |-3 -1 -1 0 2>: biyatisma (14.367 cents)<br /> 176 / 175 = |4 0 -2 -1 1>: valinorsma (9.865 cents)<br /> 896 / 891 = |7 -4 0 1 -1>: pentacircle (9.688 cents)<br /> 65536 / 65219 = |16 0 0 -2 -3>: orgonisma (8.394 cents)<br /> 243 / 242 = |-1 5 0 0 -2>: rastma (7.139 cents)<br /> 385 / 384 = |-7 -1 1 1 1>: keenanisma (4.503 cents)<br /> 441 / 440 = |-3 2 -1 2 -1>: werckisma (3.930 cents)<br /> 1375 / 1372 = |-2 0 3 -3 1>: moctdel (3.781 cents)<br /> 540 / 539 = |2 3 1 -2 -1>: swetisma (3.209 cents)<br /> 4000 / 3993 = |5 -1 3 0 -3>: wizardharry (3.032 cents)<br /> 5632 / 5625 = |9 -2 -4 0 1>: vishdel (2.153 cents)<br /> 43923 / 43904 = |-7 1 0 -3 4>: hemigail (0.749 cents)<br /> 3025 / 3024 = |-4 -3 2 -1 2>: lehmerisma (0.572 cents)<br /> 9801 / 9800 = |-3 4 -2 -2 2>: kalisma, Gauss' comma (0.177 cents)<br /> 151263 / 151250 = |-1 2 -4 5 -2>: odiheim (0.149 cents)<br /> 3294225 / 3294172 = |-2 2 2 -7 4>: ultimo (0.028 cents)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="x-13-limit commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit commas</h2> <br /> 78 / 77 = |1 1 0 -1 -1 1>: negustma (22.229 cents)<br /> 91 / 90 = |-1 -2 -1 1 0 1>: superleap (19.130 cents)<br /> 105 / 104 = |-3 1 1 1 0 1>: wintone (16.567 cents)<br /> 144 / 143 = |4 2 0 0 -1 -1>: grossma (12.064 cents)<br /> 196 / 195 = |2 -1 -1 2 0 -1>: mynucuma (8.855 cents)<br /> 325 / 324 = |-2 -4 2 0 0 1>: <a class="wiki_link" href="/Marveltwin">marveltwin</a> (5.335 cents)<br /> 676 / 675 = |2 -3 -2 0 0 2>: <a class="wiki_link" href="/The%20Archipelago">parizeksma</a> (2.563 cents)</body></html>