5-limit: 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:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-09~~-10 14~~:37:38 UTC</tt>.<br>

: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-10-11 09:49:16 UTC</tt>.<br>

: The original revision id was <tt>~~591574348~~</tt>.<br>

: The original revision id was <tt>594912366</tt>.<br>

: 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>

Line 14:

==Syntonic Comma Pairs==

A significant interval in 5-limit JI is [[81_80|81/80]], the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby [[3-limit]] (Pythagorean) interval. 81/80 is tempered out in [[12edo]], [[meantone]], and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely [[12edo]] musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). **Bold** fractions are simplest for this interval category. ~~(125/72 is simpler for diminished seventh, but it's out of table as you need to flatten 59049/32768 by 3 syntonic commas to reach it)~~

A significant interval in 5-limit JI is [[81_80|81/80]], the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby [[3-limit]] (Pythagorean) interval. 81/80 is tempered out in [[12edo]], [[meantone]], and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely [[12edo]] musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). **Bold** fractions are simplest for this interval category.

||||~ 3-limit interval ||||~ interval category ||||~ |5-limit interval (81/80) ||||~ |Another 5-limit (6561/6400) ||

Line 60:

<h2 id="toc0"><a name="x-Syntonic Comma Pairs"></a>Syntonic Comma Pairs</h2>

<br />

A significant interval in 5-limit JI is <a class="wiki_link" href="/81_80">81/80</a>, the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby <a class="wiki_link" href="/3-limit">3-limit</a> (Pythagorean) interval. 81/80 is tempered out in <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/meantone">meantone</a>, and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely <a class="wiki_link" href="/12edo">12edo</a> musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). <strong>Bold</strong> fractions are simplest for this interval category. ~~(125/72 is simpler for diminished seventh, but it's out of table as you need to flatten 59049/32768 by 3 syntonic commas to reach it)~~<br />

A significant interval in 5-limit JI is <a class="wiki_link" href="/81_80">81/80</a>, the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby <a class="wiki_link" href="/3-limit">3-limit</a> (Pythagorean) interval. 81/80 is tempered out in <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/meantone">meantone</a>, and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely <a class="wiki_link" href="/12edo">12edo</a> musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). <strong>Bold</strong> fractions are simplest for this interval category.<br />

<br />

@@ 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:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-09-10 14:37:38 UTC</tt>.<br>
+: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-10-11 09:49:16 UTC</tt>.<br>
-: The original revision id was <tt>591574348</tt>.<br>
+: The original revision id was <tt>594912366</tt>.<br>
 : 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>
@@ Line 14: / Line 14: @@
 ==Syntonic Comma Pairs==
-A significant interval in 5-limit JI is [[81_80|81/80]], the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby [[3-limit]] (Pythagorean) interval. 81/80 is tempered out in [[12edo]], [[meantone]], and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely [[12edo]] musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). **Bold** fractions are simplest for this interval category. (125/72 is simpler for diminished seventh, but it's out of table as you need to flatten 59049/32768 by 3 syntonic commas to reach it)
+A significant interval in 5-limit JI is [[81_80|81/80]], the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby [[3-limit]] (Pythagorean) interval. 81/80 is tempered out in [[12edo]], [[meantone]], and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely [[12edo]] musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). **Bold** fractions are simplest for this interval category.
 ||||~ 3-limit interval ||||~ interval category ||||~ |5-limit interval (81/80) ||||~ |Another 5-limit (6561/6400) ||
@@ Line 60: / Line 60: @@
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Syntonic Comma Pairs"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Syntonic Comma Pairs&lt;/h2&gt;
   &lt;br /&gt;
-A significant interval in 5-limit JI is &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;, the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby &lt;a class="wiki_link" href="/3-limit"&gt;3-limit&lt;/a&gt; (Pythagorean) interval. 81/80 is tempered out in &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;, and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). &lt;strong&gt;Bold&lt;/strong&gt; fractions are simplest for this interval category. (125/72 is simpler for diminished seventh, but it's out of table as you need to flatten 59049/32768 by 3 syntonic commas to reach it)&lt;br /&gt;
+A significant interval in 5-limit JI is &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;, the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby &lt;a class="wiki_link" href="/3-limit"&gt;3-limit&lt;/a&gt; (Pythagorean) interval. 81/80 is tempered out in &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;, and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). &lt;strong&gt;Bold&lt;/strong&gt; fractions are simplest for this interval category.&lt;br /&gt;
 &lt;br /&gt;