Small comma
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2010-06-01 18:42:16 UTC.
- The original revision id was 146346539.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
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 //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) ==5-limit commas== 135 / 128 = |-7 3 1>: major chroma, major limma, pelogic comma (92.179 [[cent]]s) 648 / 625 = |3 4 -4>: major diesis, diminished comma (62.565 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) 128 / 125 = |7 0 -3>: diesis, augmented comma (41.059 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) 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) 15625 / 15552 = |-6 -5 6>: kleisma, semicomma majeur (8.107 cents) 1600000 / 1594323 = |9 -13 5>: amity comma (6.154 cents) |8 14 -13>: parakleisma (5.292 cents) |24 -21 4>: vulture (4.200 cents) 6115295232 / 6103515625 = |23 6 -14>: semisuper comma (3.338 cents) |-14 -19 19>: enneadeca, 19-tone-comma (2.816 cents) |39 -29 3>: tricot comma (2.246 cents) 32805 / 32768 = |-15 8 1>: schisma (1.954 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) |-53 10 16>: kwazy comma (0.569 cents) |54 -37 2>: monzisma (0.292 cents) ==7-limit commas== 1029 / 1000 = |-3 1 -3 3>: keega (49.492 [[cent]]s) 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) 875 / 864 = |-5 -3 3 1>: keemic (21.902 cents) 3125 / 3087 = |0 -2 5 -3>: gariboh (21.181 cents) 2430 / 2401 = |1 5 1 -4>: nuwell (20.785 cents) 245 / 243 = |0 -5 1 2>: sensamagic (14.191 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) 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) 6144 / 6125 = |11 1 -3 -2>: porwell (5.362 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) 250047 / 250000 = |-4 6 -6 3>: landscape comma (0.325 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>tempered out</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 /> <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 /> 135 / 128 = |-7 3 1>: major chroma, major limma, pelogic comma (92.179 <a class="wiki_link" href="/cent">cent</a>s)<br /> 648 / 625 = |3 4 -4>: major diesis, diminished comma (62.565 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 /> 128 / 125 = |7 0 -3>: diesis, augmented comma (41.059 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 /> 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 /> 15625 / 15552 = |-6 -5 6>: kleisma, semicomma majeur (8.107 cents)<br /> 1600000 / 1594323 = |9 -13 5>: amity comma (6.154 cents)<br /> |8 14 -13>: parakleisma (5.292 cents)<br /> |24 -21 4>: vulture (4.200 cents)<br /> 6115295232 / 6103515625 = |23 6 -14>: semisuper comma (3.338 cents)<br /> |-14 -19 19>: enneadeca, 19-tone-comma (2.816 cents)<br /> |39 -29 3>: tricot comma (2.246 cents)<br /> 32805 / 32768 = |-15 8 1>: schisma (1.954 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 /> |-53 10 16>: kwazy comma (0.569 cents)<br /> |54 -37 2>: monzisma (0.292 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 /> 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 /> 875 / 864 = |-5 -3 3 1>: keemic (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 /> 245 / 243 = |0 -5 1 2>: sensamagic (14.191 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 /> 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 /> 6144 / 6125 = |11 1 -3 -2>: porwell (5.362 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 /> 250047 / 250000 = |-4 6 -6 3>: landscape comma (0.325 cents)</body></html>