List of superparticular intervals: 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:

: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2017-08-13 13:30:36 UTC</tt>.

: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2017-08-13 13:43:18 UTC</tt>.

: The original revision id was <tt>~~616359519~~</tt>.

: The original revision id was <tt>616359767</tt>.

: The revision comment was: <tt>added ~~monzos (through 19-limit)~~</tt>

: The revision comment was: <tt>added OEIS link</tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<h4>Original Wikitext content:</h4>

Line 10:

The list below is ordered by [[harmonic limit]], or the largest prime involved in the prime factorization. [[36_35|36/35]], for instance, is an interval of the [[7-limit]], as it factors to (22*32)/(5*7), while 37/36 would belong to the 37-limit.

[[http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem|Størmer's theorem]] guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8.

[[http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem|Størmer's theorem]] guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. [[https://oeis.org/A145604|OEIS A145604]] gives the number of superparticular ratios in each prime limit.

See also: [[Gallery of Just Intervals]]. Many of the names below come from [[http://www.huygens-fokker.org/docs/intervals.html|here]].

Line 28:

|| [[25_24|25/24]] || 70.672 || 52/(23*3) || | -3 -1 2 > || chroma, (classic) chromatic semitone, Zarlinian semitone ||

|| [[81_80|81/80]] || 21.506 || (3/2)4/5 || | -4 4 -1 > || syntonic comma, Didymus comma ||

||||||||||~ 7-limit (complete?) ||

||||||||||~ 7-limit (complete) ||

|| [[7_6|7/6]] || 266.871 || 7/(2*3) || | -1 -1 0 1 > || (septimal) subminor third, septimal minor third, augmented second ||

|| [[8_7|8/7]] || 231.174 || 23/7 || | 3 0 0 -1 > || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic ||

Line 42:

|| [[2401_2400|2401/2400]] || 0.72120 || 74/(25*3*52) || | -5 -1 -2 4 > || breedsma ||

|| [[4375_4374|4375/4374]] || 0.39576 || (54*7)/(2*37) || | -1 -7 4 1 > || ragisma ||

||||||||||~ 11-limit (complete?) ||

||||||||||~ 11-limit (complete) ||

|| [[11_10|11/10]] || 165.004 || 11/(2*5) || | -1 0 -1 0 1 > || (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second ||

|| [[12_11|12/11]] || 150.637 || (22*3)/11 || | 2 1 0 0 -1 > || (small) (undecimal) neutral second, 3/4-tone ||

Line 60:

|| [[3025_3024|3025/3024]] || 0.57240 || (5*11)2/(24*32*7) || | -4 -3 2 -1 2 > || Lehmerisma ||

|| [[9801_9800|9801/9800]] || 0.17665 || [11/(5*7)]2*34/23 || | -3 4 -2 -2 2 > || Gauss comma, kalisma ||

||||||||||~ 13-limit (complete?) ||

||||||||||~ 13-limit (complete) ||

|| [[13_12|13/12]] || 138.573 || 13/(22*3) || | -2 -1 0 0 0 1 > || tridecimal 2/3-tone ||

|| [[14_13|14/13]] || 128.298 || (2*7)/13 || | 1 0 0 1 0 -1 > || 2/3-tone, trienthird ||

Line 89:

|| [[10648_10647|10648/10647]] || 0.16260 || || | 3 -2 0 -1 3 -2 > || harmonisma ||

|| [[123201_123200|123201/123200]] || 0.014052 || || | -6 6 -2 -1 -1 2 > || chalmersia ||

||||||||||~ 17-limit (complete!) ||

||||||||||~ 17-limit (complete) ||

|| [[17_16|17/16]] || 104.955 || 17/24 || | -4 0 0 0 0 0 1 > || 17th harmonic (octave reduced) ||

|| [[18_17|18/17]] || 98.955 || (2*32)/17 || | 1 2 0 0 0 0 -1 > || Arabic lute index finger ||

Line 231:

The list below is ordered by <a class="wiki_link" href="/harmonic%20limit">harmonic limit</a>, or the largest prime involved in the prime factorization. <a class="wiki_link" href="/36_35">36/35</a>, for instance, is an interval of the <a class="wiki_link" href="/7-limit">7-limit</a>, as it factors to (22*32)/(5*7), while 37/36 would belong to the 37-limit.

<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem" rel="nofollow">Størmer's theorem</a> guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8.

<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem" rel="nofollow">Størmer's theorem</a> guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. <a class="wiki_link_ext" href="https://oeis.org/A145604" rel="nofollow">OEIS A145604</a> gives the number of superparticular ratios in each prime limit.

See also: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a>. Many of the names below come from <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/intervals.html" rel="nofollow">here</a>.

Line 383:

</tr>

<tr>

<th colspan="5">7-limit (complete?)

<th colspan="5">7-limit (complete)

</th>

</tr>

Line 543:

</tr>

<tr>

<th colspan="5">11-limit (complete?)

<th colspan="5">11-limit (complete)

</th>

</tr>

Line 751:

</tr>

<tr>

<th colspan="5">13-limit (complete?)

<th colspan="5">13-limit (complete)

</th>

</tr>

Line 1,091:

</tr>

<tr>

<th colspan="5">17-limit (complete!)

<th colspan="5">17-limit (complete)

</th>

</tr>

@@ 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:spt3125|spt3125]] and made on <tt>2017-08-13 13:30:36 UTC</tt>.<br>
+: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2017-08-13 13:43:18 UTC</tt>.<br>
-: The original revision id was <tt>616359519</tt>.<br>
+: The original revision id was <tt>616359767</tt>.<br>
-: The revision comment was: <tt>added monzos (through 19-limit)</tt><br>
+: The revision comment was: <tt>added OEIS link</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>
@@ Line 10: / Line 10: @@
 The list below is ordered by [[harmonic limit]], or the largest prime involved in the prime factorization. [[36_35|36/35]], for instance, is an interval of the [[7-limit]], as it factors to (2&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;)/(5*7), while 37/36 would belong to the 37-limit.
-[[http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem|Størmer's theorem]] guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8.
+[[http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem|Størmer's theorem]] guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. [[https://oeis.org/A145604|OEIS A145604]] gives the number of superparticular ratios in each prime limit.
 See also: [[Gallery of Just Intervals]]. Many of the names below come from [[http://www.huygens-fokker.org/docs/intervals.html|here]].
@@ Line 28: / Line 28: @@
 || [[25_24|25/24]] || 70.672 || 5&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="font-size: 70%; vertical-align: super;"&gt;3&lt;/span&gt;*3) || | -3 -1 2 &gt; || chroma, (classic) chromatic semitone, Zarlinian semitone ||
 || [[81_80|81/80]] || 21.506 || (3/2)&lt;span style="font-size: 70%; vertical-align: super;"&gt;4&lt;/span&gt;/5 || | -4 4 -1 &gt; || syntonic comma, Didymus comma ||
-||||||||||~ 7-limit (complete?) ||
+||||||||||~ 7-limit (complete) ||
 || [[7_6|7/6]] || 266.871 || 7/(2*3) || | -1 -1 0 1 &gt; || (septimal) subminor third, septimal minor third, augmented second ||
 || [[8_7|8/7]] || 231.174 || 2&lt;span style="font-size: 70%; vertical-align: super;"&gt;3&lt;/span&gt;/7 || | 3 0 0 -1 &gt; || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
@@ Line 42: / Line 42: @@
 || [[2401_2400|2401/2400]] || 0.72120 || 7&lt;span style="font-size: 70%; vertical-align: super;"&gt;4&lt;/span&gt;/(2&lt;span style="font-size: 70%; vertical-align: super;"&gt;5&lt;/span&gt;*3*5&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;) || | -5 -1 -2 4 &gt; || breedsma ||
 || [[4375_4374|4375/4374]] || 0.39576 || (5&lt;span style="font-size: 70%; vertical-align: super;"&gt;4&lt;/span&gt;*7)/(2*3&lt;span style="font-size: 70%; vertical-align: super;"&gt;7&lt;/span&gt;) || | -1 -7 4 1 &gt; || ragisma ||
-||||||||||~ 11-limit (complete?) ||
+||||||||||~ 11-limit (complete) ||
 || [[11_10|11/10]] || 165.004 || 11/(2*5) || | -1 0 -1 0 1 &gt; || (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second ||
 || [[12_11|12/11]] || 150.637 || (2&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;*3)/11 || | 2 1 0 0 -1 &gt; || (small) (undecimal) neutral second, 3/4-tone ||
@@ Line 60: / Line 60: @@
 || [[3025_3024|3025/3024]] || 0.57240 || (5*11)&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="font-size: 70%; vertical-align: super;"&gt;4&lt;/span&gt;*3&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;*7) || | -4 -3 2 -1 2 &gt; || Lehmerisma ||
 || [[9801_9800|9801/9800]] || 0.17665 || [11/(5*7)]&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="font-size: 70%; vertical-align: super;"&gt;4&lt;/span&gt;/2&lt;span style="font-size: 70%; vertical-align: super;"&gt;3&lt;/span&gt; || | -3 4 -2 -2 2 &gt; || Gauss comma, kalisma ||
-||||||||||~ 13-limit (complete?) ||
+||||||||||~ 13-limit (complete) ||
 || [[13_12|13/12]] || 138.573 || 13/(2&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;*3) || | -2 -1 0 0 0 1 &gt; || tridecimal 2/3-tone ||
 || [[14_13|14/13]] || 128.298 || (2*7)/13 || | 1 0 0 1 0 -1 &gt; || 2/3-tone, trienthird ||
@@ Line 89: / Line 89: @@
 || [[10648_10647|10648/10647]] || 0.16260 ||   || | 3 -2 0 -1 3 -2 &gt; || harmonisma ||
 || [[123201_123200|123201/123200]] || 0.014052 ||   || | -6 6 -2 -1 -1 2 &gt; || chalmersia ||
-||||||||||~ 17-limit (complete!) ||
+||||||||||~ 17-limit (complete) ||
 || [[17_16|17/16]] || 104.955 || 17/2&lt;span style="font-size: 70%; vertical-align: super;"&gt;4&lt;/span&gt; || | -4 0 0 0 0 0 1 &gt; || 17th harmonic (octave reduced) ||
 || [[18_17|18/17]] || 98.955 || (2*3&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;)/17 || | 1 2 0 0 0 0 -1 &gt; || Arabic lute index finger ||
@@ Line 231: / Line 231: @@
 The list below is ordered by &lt;a class="wiki_link" href="/harmonic%20limit"&gt;harmonic limit&lt;/a&gt;, or the largest prime involved in the prime factorization. &lt;a class="wiki_link" href="/36_35"&gt;36/35&lt;/a&gt;, for instance, is an interval of the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, as it factors to (2&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;)/(5*7), while 37/36 would belong to the 37-limit.&lt;br /&gt;
 &lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem" rel="nofollow"&gt;Størmer's theorem&lt;/a&gt; guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8.&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem" rel="nofollow"&gt;Størmer's theorem&lt;/a&gt; guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. &lt;a class="wiki_link_ext" href="https://oeis.org/A145604" rel="nofollow"&gt;OEIS A145604&lt;/a&gt; gives the number of superparticular ratios in each prime limit.&lt;br /&gt;
 &lt;br /&gt;
 See also: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;. Many of the names below come from &lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/intervals.html" rel="nofollow"&gt;here&lt;/a&gt;.&lt;br /&gt;
@@ Line 383: / Line 383: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;th colspan="5"&gt;7-limit (complete?)&lt;br /&gt;
+         &lt;th colspan="5"&gt;7-limit (complete)&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 543: / Line 543: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;th colspan="5"&gt;11-limit (complete?)&lt;br /&gt;
+         &lt;th colspan="5"&gt;11-limit (complete)&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 751: / Line 751: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;th colspan="5"&gt;13-limit (complete?)&lt;br /&gt;
+         &lt;th colspan="5"&gt;13-limit (complete)&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 1,091: / Line 1,091: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;th colspan="5"&gt;17-limit (complete!)&lt;br /&gt;
+         &lt;th colspan="5"&gt;17-limit (complete)&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;