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 2010-05-31 21:56:26 UTC.
- The original revision id was 146122899.
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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 //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 cents) 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 cents) 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) 15625 / 15552 = |-6 -5 6>: kleisma, semicomma majeur (8.107 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 cents)<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 cents)<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 /> 15625 / 15552 = |-6 -5 6>: kleisma, semicomma majeur (8.107 cents)</body></html>