Small comma: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 145974871 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 145978647 - Original comment: maybe the fractions go better to the right?** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-05-31 03:57:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>145978647</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>maybe the fractions go better to the right?</tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
| Line 10: | Line 10: | ||
==3-limit commas== | ==3-limit commas== | ||
256/243 = |8 -5>: limma or Pythagorean minor second | 256 / 243 = |8 -5>: limma or Pythagorean minor second (90.225 cents) | ||
2187/2048 = |-11 7>: apotome | 2187 / 2048 = |-11 7>: apotome (113.685 cents) | ||
531441/524288 = |-19 12>: Pythagorean comma | 531441 / 524288 = |-19 12>: Pythagorean comma (23.460 cents) | ||
134217728/129140163 = |27 -17>: 17-comma | 134217728 / 129140163 = |27 -17>: 17-comma (66.765 cents) | ||
70368744177664/68630377364883 = |46, -29>: 29-comma | 70368744177664 / 68630377364883 = |46, -29>: 29-comma (43,305 cents) | ||
|65 -41>: 41-comma | 36893488147419103232 / 36472996377170786403 = |65 -41>: 41-comma (19.845 cents) | ||
|-84 53>: Mercator's comma, 53-comma | 19342813113834066795298816 / 19383245667680019896796723 = |-84 53>: Mercator's comma, 53-comma (-3.615 cents) | ||
</pre></div> | </pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
| Line 24: | Line 23: | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-3-limit commas"></a><!-- ws:end:WikiTextHeadingRule:0 -->3-limit commas</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-3-limit commas"></a><!-- ws:end:WikiTextHeadingRule:0 -->3-limit commas</h2> | ||
<br /> | <br /> | ||
256/243 = |8 -5&gt;: limma or Pythagorean minor second<br /> | 256 / 243 = |8 -5&gt;: limma or Pythagorean minor second (90.225 cents)<br /> | ||
2187/2048 = |-11 7&gt;: apotome<br /> | 2187 / 2048 = |-11 7&gt;: apotome (113.685 cents)<br /> | ||
531441/524288 = |-19 12&gt;: Pythagorean comma<br /> | 531441 / 524288 = |-19 12&gt;: Pythagorean comma (23.460 cents)<br /> | ||
134217728/129140163 = |27 -17&gt;: 17-comma<br /> | 134217728 / 129140163 = |27 -17&gt;: 17-comma (66.765 cents)<br /> | ||
70368744177664/68630377364883 = |46, -29&gt;: 29-comma<br /> | 70368744177664 / 68630377364883 = |46, -29&gt;: 29-comma (43,305 cents)<br /> | ||
|65 -41&gt;: 41-comma<br /> | 36893488147419103232 / 36472996377170786403 = |65 -41&gt;: 41-comma (19.845 cents)<br /> | ||
|-84 53&gt;: Mercator's comma, 53-comma</body></html></pre></div> | 19342813113834066795298816 / 19383245667680019896796723 = |-84 53&gt;: Mercator's comma, 53-comma (-3.615 cents)</body></html></pre></div> | ||
Revision as of 03:57, 31 May 2010
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenwolf and made on 2010-05-31 03:57:09 UTC.
- The original revision id was 145978647.
- The revision comment was: maybe the fractions go better to the right?
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 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) 19342813113834066795298816 / 19383245667680019896796723 = |-84 53>: Mercator's comma, 53-comma (-3.615 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 /> 19342813113834066795298816 / 19383245667680019896796723 = |-84 53>: Mercator's comma, 53-comma (-3.615 cents)</body></html>