Small comma: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>xenwolf **Imported revision 145978647 - Original comment: maybe the fractions go better to the right?** |
Wikispaces>genewardsmith **Imported revision 146040847 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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:genewardsmith|genewardsmith]] and made on <tt>2010-05-31 12:57:25 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>146040847</tt>.<br> | ||
: The revision comment was: <tt> | : The revision comment was: <tt></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 16: | Line 16: | ||
70368744177664 / 68630377364883 = |46, -29>: 29-comma (43,305 cents) | 70368744177664 / 68630377364883 = |46, -29>: 29-comma (43,305 cents) | ||
36893488147419103232 / 36472996377170786403 = |65 -41>: 41-comma (19.845 cents) | 36893488147419103232 / 36472996377170786403 = |65 -41>: 41-comma (19.845 cents) | ||
19342813113834066795298816 | 19383245667680019896796723 / 19342813113834066795298816 = |-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 29: | Line 29: | ||
70368744177664 / 68630377364883 = |46, -29&gt;: 29-comma (43,305 cents)<br /> | 70368744177664 / 68630377364883 = |46, -29&gt;: 29-comma (43,305 cents)<br /> | ||
36893488147419103232 / 36472996377170786403 = |65 -41&gt;: 41-comma (19.845 cents)<br /> | 36893488147419103232 / 36472996377170786403 = |65 -41&gt;: 41-comma (19.845 cents)<br /> | ||
19342813113834066795298816 | 19383245667680019896796723 / 19342813113834066795298816 = |-84 53&gt;: Mercator's comma, 53-comma (3.615 cents)</body></html></pre></div> | ||
Revision as of 12:57, 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 genewardsmith and made on 2010-05-31 12:57:25 UTC.
- The original revision id was 146040847.
- 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 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)
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)</body></html>