Small comma: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2011-05-~~23 14~~:40:05 UTC</tt>.<br>

: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 15:21:32 UTC</tt>.<br>

: The original revision id was <tt>~~231057878~~</tt>.<br>

: The original revision id was <tt>233249020</tt>.<br>

: The revision comment was: <tt></tt><br>

: The revision comment was: <tt>Fixed exponents on 50421 / 50000 (trimyna) and 99 / 98 (mothwellsma)</tt><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>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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)

Line 18:

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)

Line 56:

|161 -84 -12>: atom (0.015 cents)

==7-limit commas==

1029 / 1000 = |-3 1 -3 3>: keega (49.492 [[cent]]s)

Line 70:

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)

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)

Line 92:

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)

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)

Line 104:

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)

540 / 539 = |2 3 1 -2 -1>: swetisma (3.209 cents)

Line 111:

9801 / 9800 = |-3 4 -2 -2 2>: kalisma, Gauss' comma (0.177 cents)

==13-limit commas==

91 / 90 = |-1 -2 -1 1 0 1>: superleap (19.130 cents)

676/675 = |2 -3 -2 0 0 2>: parizeksma (2.563 cents)

676/675 = |2 -3 -2 0 0 2>: parizeksma (2.563 cents)</pre></div>

</pre></div>

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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 />

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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 />

<h2 id="toc0"><a name="x-3-limit commas"></a>3-limit commas</h2>

<br />

256 / 243 = |8 -5&gt;: limma or Pythagorean minor second (90.225 <a class="wiki_link" href="/cent">cent</a>s)<br />

2187 / 2048 = |-11 7&gt;: apotome (113.685 cents)<br />

Line 130:

Line 129:

<br />

<h2 id="toc1"><a name="x-5-limit commas"></a>5-limit commas</h2>

<br />

135 / 128 = |-7 3 1&gt;: major chroma, major limma, pelogic comma (92.179 <a class="wiki_link" href="/cent">cent</a>s)<br />

648 / 625 = |3 4 -4&gt;: major diesis, diminished comma (62.565 cents)<br />

Line 168:

Line 167:

<br />

<h2 id="toc2"><a name="x-7-limit commas"></a>7-limit commas</h2>

<br />

1029 / 1000 = |-3 1 -3 3&gt;: keega (49.492 <a class="wiki_link" href="/cent">cent</a>s)<br />

36 / 35 = |2 2 -1 -1&gt;: septimal quarter tone (48.770 cents)<br />

Line 181:

Line 180:

3125 / 3087 = |0 -2 5 -3&gt;: gariboh (21.181 cents)<br />

2430 / 2401 = |1 5 1 -4&gt;: nuwell (20.785 cents)<br />

50421 / 50000 = |-4 1 5 -5&gt;: trimyna (14.516 cents)<br />

50421 / 50000 = |-4 1 -5 5&gt;: trimyna (14.516 cents)<br />

245 / 243 = |0 -5 1 2&gt;: sensamagic (14.191 cents)<br />

126 / 125 = |1 2 -3 1&gt;: septimal semicomma, starling comma (13.795 cents)<br />

Line 203:

Line 202:

2401 / 2400 = |-5 -1 -2 4&gt;: breedsma (0.721 cents)<br />

4375 / 4374 = |-1 -7 4 1&gt;: ragisma (0.396 cents)<br />

140737488355328 / 140710042265625 = |47, -7, -7, -7&gt;: akjaysma, 5\7 octave comma, (0.338 cents)<br />

250047 / 250000 = |-4 6 -6 3&gt;: landscape comma (0.325 cents)<br />

<br />

<h2 id="toc3"><a name="x-11-limit commas"></a>11-limit commas</h2>

<br />

99 / 98 = |-1 2 0 2 1&gt;: mothwellsma (17.576 cents)<br />

99 / 98 = |-1 2 0 -2 1&gt;: mothwellsma (17.576 cents)<br />

100 / 99 = |2 -2 2 0 -1&gt;: ptolemisma (17.399 cents)<br />

121 / 120 = |-3 -1 -1 0 2&gt;: biyatisma (14.367 cents)<br />

Line 215:

Line 214:

65536 / 65219 = |16 0 0 -2 -3&gt;: orgonisma (8.394 cents)<br />

243 / 242 = |-1 5 0 0 -2&gt;: rastma (7.139 cents)<br />

385 / 384 = |-7 -1 1 1 1&gt;: keenanisma (4.503 cents)<br />

441 / 440 = |-3 2 -1 2 -1&gt;: werckisma (3.930 cents)<br />

540 / 539 = |2 3 1 -2 -1&gt;: swetisma (3.209 cents)<br />

Line 223:

Line 222:

<br />

<h2 id="toc4"><a name="x-13-limit commas"></a>13-limit commas</h2>

<br />

91 / 90 = |-1 -2 -1 1 0 1&gt;: superleap (19.130 cents)<br />

676/675 = |2 -3 -2 0 0 2&gt;: parizeksma (2.563 cents)</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-23 14:40:05 UTC</tt>.<br>
+: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 15:21:32 UTC</tt>.<br>
-: The original revision id was <tt>231057878</tt>.<br>
+: The original revision id was <tt>233249020</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>Fixed exponents on 50421 / 50000 (trimyna) and 99 / 98 (mothwellsma)</tt><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>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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==
 / 243 = |8 -5&gt;: limma or Pythagorean minor second (90.225 [[cent]]s)
@@ Line 18: / Line 18: @@
 19383245667680019896796723 / 19342813113834066795298816 = |-84 53&gt;: Mercator's comma, 53-comma (3.615 cents)
 ==5-limit commas==
 / 128 = |-7 3 1&gt;: major chroma, major limma, pelogic comma (92.179 [[cent]]s)
@@ Line 56: / Line 56: @@
 |161 -84 -12&gt;: atom (0.015 cents)
 ==7-limit commas==
 / 1000 = |-3 1 -3 3&gt;: keega (49.492 [[cent]]s)
@@ Line 70: / Line 70: @@
 / 3087 = |0 -2 5 -3&gt;: gariboh (21.181 cents)
 / 2401 = |1 5 1 -4&gt;: nuwell (20.785 cents)
-/ 50000 = |-4 1 5 -5&gt;: trimyna (14.516 cents)
+/ 50000 = |-4 1 -5 5&gt;: trimyna (14.516 cents)
 / 243 = |0 -5 1 2&gt;: sensamagic (14.191 cents)
 / 125 = |1 2 -3 1&gt;: septimal semicomma, starling comma (13.795 cents)
@@ Line 92: / Line 92: @@
 / 2400 = |-5 -1 -2 4&gt;: breedsma (0.721 cents)
 / 4374 = |-1 -7 4 1&gt;: ragisma (0.396 cents)
-140737488355328 / 140710042265625 = |47, -7, -7, -7&gt;: akjaysma, 5\7 octave comma,  (0.338 cents)
+140737488355328 / 140710042265625 = |47, -7, -7, -7&gt;: akjaysma, 5\7 octave comma, (0.338 cents)
 / 250000 = |-4 6 -6 3&gt;: landscape comma (0.325 cents)
 ==11-limit commas==
-/ 98 = |-1 2 0 2 1&gt;: mothwellsma (17.576 cents)
+/ 98 = |-1 2 0 -2 1&gt;: mothwellsma (17.576 cents)
 / 99 = |2 -2 2 0 -1&gt;: ptolemisma (17.399 cents)
 / 120 = |-3 -1 -1 0 2&gt;: biyatisma (14.367 cents)
@@ Line 104: / Line 104: @@
 / 65219 = |16 0 0 -2 -3&gt;: orgonisma (8.394 cents)
 / 242 = |-1 5 0 0 -2&gt;: rastma (7.139 cents)
-/ 384 = |-7 -1 1 1 1&gt;:  keenanisma (4.503 cents)
+/ 384 = |-7 -1 1 1 1&gt;: keenanisma (4.503 cents)
 / 440 = |-3 2 -1 2 -1&gt;: werckisma (3.930 cents)
 / 539 = |2 3 1 -2 -1&gt;: swetisma (3.209 cents)
@@ Line 111: / Line 111: @@
 / 9800 = |-3 4 -2 -2 2&gt;: kalisma, Gauss' comma (0.177 cents)
 ==13-limit commas==
 / 90 = |-1 -2 -1 1 0 1&gt;: superleap (19.130 cents)
-/675 = |2 -3 -2 0 0 2&gt;: parizeksma (2.563 cents)
+/675 = |2 -3 -2 0 0 2&gt;: parizeksma (2.563 cents)</pre></div>
-</pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;strong&gt;comma&lt;/strong&gt; 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 &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;low prime limit&lt;/a&gt;. The word is often used in reference to &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;regular tempering&lt;/a&gt; when the comma is &lt;em&gt;tempered out&lt;/em&gt;, which is to say reduced to a unison, by the temperament. For example the Didymos comma of 81/80 is tempered out by &lt;a class="wiki_link" href="/Meantone"&gt;meantone temperament&lt;/a&gt;. &lt;br /&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;strong&gt;comma&lt;/strong&gt; 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 &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;low prime limit&lt;/a&gt;. The word is often used in reference to &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;regular tempering&lt;/a&gt; when the comma is &lt;em&gt;tempered out&lt;/em&gt;, which is to say reduced to a unison, by the temperament. For example the Didymos comma of 81/80 is tempered out by &lt;a class="wiki_link" href="/Meantone"&gt;meantone temperament&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-3-limit commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;3-limit commas&lt;/h2&gt;
-&lt;br /&gt;
+ &lt;br /&gt;
 / 243 = |8 -5&amp;gt;: limma or Pythagorean minor second (90.225 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s)&lt;br /&gt;
 / 2048 = |-11 7&amp;gt;: apotome (113.685 cents)&lt;br /&gt;
@@ Line 130: / Line 129: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-5-limit commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;5-limit commas&lt;/h2&gt;
-&lt;br /&gt;
+ &lt;br /&gt;
 / 128 = |-7 3 1&amp;gt;: major chroma, major limma, pelogic comma (92.179 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s)&lt;br /&gt;
 / 625 = |3 4 -4&amp;gt;: major diesis, diminished comma (62.565 cents)&lt;br /&gt;
@@ Line 168: / Line 167: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-7-limit commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;7-limit commas&lt;/h2&gt;
-&lt;br /&gt;
+ &lt;br /&gt;
 / 1000 = |-3 1 -3 3&amp;gt;: keega (49.492 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s)&lt;br /&gt;
 / 35 = |2 2 -1 -1&amp;gt;: septimal quarter tone (48.770 cents)&lt;br /&gt;
@@ Line 181: / Line 180: @@
 / 3087 = |0 -2 5 -3&amp;gt;: gariboh (21.181 cents)&lt;br /&gt;
 / 2401 = |1 5 1 -4&amp;gt;: nuwell (20.785 cents)&lt;br /&gt;
-/ 50000 = |-4 1 5 -5&amp;gt;: trimyna (14.516 cents)&lt;br /&gt;
+/ 50000 = |-4 1 -5 5&amp;gt;: trimyna (14.516 cents)&lt;br /&gt;
 / 243 = |0 -5 1 2&amp;gt;: sensamagic (14.191 cents)&lt;br /&gt;
 / 125 = |1 2 -3 1&amp;gt;: septimal semicomma, starling comma (13.795 cents)&lt;br /&gt;
@@ Line 203: / Line 202: @@
 / 2400 = |-5 -1 -2 4&amp;gt;: breedsma (0.721 cents)&lt;br /&gt;
 / 4374 = |-1 -7 4 1&amp;gt;: ragisma (0.396 cents)&lt;br /&gt;
-140737488355328 / 140710042265625 = |47, -7, -7, -7&amp;gt;: akjaysma, 5\7 octave comma,  (0.338 cents)&lt;br /&gt;
+140737488355328 / 140710042265625 = |47, -7, -7, -7&amp;gt;: akjaysma, 5\7 octave comma, (0.338 cents)&lt;br /&gt;
 / 250000 = |-4 6 -6 3&amp;gt;: landscape comma (0.325 cents)&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-11-limit commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;11-limit commas&lt;/h2&gt;
-&lt;br /&gt;
+ &lt;br /&gt;
-/ 98 = |-1 2 0 2 1&amp;gt;: mothwellsma (17.576 cents)&lt;br /&gt;
+/ 98 = |-1 2 0 -2 1&amp;gt;: mothwellsma (17.576 cents)&lt;br /&gt;
 / 99 = |2 -2 2 0 -1&amp;gt;: ptolemisma (17.399 cents)&lt;br /&gt;
 / 120 = |-3 -1 -1 0 2&amp;gt;: biyatisma (14.367 cents)&lt;br /&gt;
@@ Line 215: / Line 214: @@
 / 65219 = |16 0 0 -2 -3&amp;gt;: orgonisma (8.394 cents)&lt;br /&gt;
 / 242 = |-1 5 0 0 -2&amp;gt;: rastma (7.139 cents)&lt;br /&gt;
-/ 384 = |-7 -1 1 1 1&amp;gt;:  keenanisma (4.503 cents)&lt;br /&gt;
+/ 384 = |-7 -1 1 1 1&amp;gt;: keenanisma (4.503 cents)&lt;br /&gt;
 / 440 = |-3 2 -1 2 -1&amp;gt;: werckisma (3.930 cents)&lt;br /&gt;
 / 539 = |2 3 1 -2 -1&amp;gt;: swetisma (3.209 cents)&lt;br /&gt;
@@ Line 223: / Line 222: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-13-limit commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit commas&lt;/h2&gt;
-&lt;br /&gt;
+ &lt;br /&gt;
 / 90 = |-1 -2 -1 1 0 1&amp;gt;: superleap (19.130 cents)&lt;br /&gt;
 /675 = |2 -3 -2 0 0 2&amp;gt;: parizeksma (2.563 cents)&lt;/body&gt;&lt;/html&gt;</pre></div>