Xenharmonic Wiki

List of superparticular intervals: Difference between revisions

← Older editNewer edit →
VisualWikitext
Wikispaces>kai.lugheidh
**Imported revision 616162505 - Original comment: **
Wikispaces>spt3125
**Imported revision 616349117 - Original comment: added 325/324, cleaned up exponent formatting**
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:kai.lugheidh|kai.lugheidh]] and made on <tt>2017-08-05 02:02:15 UTC</tt>.<br>
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2017-08-12 19:02:58 UTC</tt>.<br>
: The original revision id was <tt>616162505</tt>.<br>
: The original revision id was <tt>616349117</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt>added 325/324, cleaned up exponent formatting</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>
<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">=&lt;span style="color: #800080;"&gt;List of Superparticular Intervals&lt;/span&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;white-space: pre-wrap ! important" class="old-revision-html">[[Superparticular]] numbers are ratios of the form (n+1)/n, or 1+1/n, where n is a whole number other than 1. They appear frequently in [[Just Intonation]] and [[OverToneSeries|Harmonic Series]] music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio [[21_20|21/20]]. As the overtones get closer together, the superparticular intervals get smaller and smaller. Thus, an examination of the superparticular intervals is an examination of some of the simplest small intervals in rational tuning systems. Indeed, many but not all common [[comma]]s are superparticular ratios.


[[Superparticular]] numbers are ratios of the form (n+1)/n, or 1+1/n, where n is a whole number other than 1. They appear frequently in [[Just Intonation]] and [[OverToneSeries|Harmonic Series]] music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio [[21_20|21/20]]. As the overtones get closer together, the superparticular intervals get smaller and smaller. Thus, an examination of the superparticular intervals is an examination of some of the simplest small intervals in rational tuning systems. Indeed, many but not all common [[comma]]s are superparticular ratios.
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="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(5*7), while 37/36 would belong to the 37-limit.
 
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="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="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.
Line 17: Line 15:


||~ Ratio ||~ Cents Value ||~ Factorization ||~ Name(s) ||
||~ Ratio ||~ Cents Value ||~ Factorization ||~ Name(s) ||
||||||||~ 2-limit ||
||||||||~ 2-limit (complete) ||
|| [[2_1|2/1]] || 1200.000 || 2/1 || (perfect) unison, unity, perfect prime, tonic, duple ||
|| [[2_1|2/1]] || 1200.000 || 2/1 || (perfect) unison, unity, perfect prime, tonic, duple ||
||||||||~ 3-limit ||
||||||||~ 3-limit (complete) ||
|| [[3_2|3/2]] || 701.995 || 3/2 || [[perfect fifth]], 3rd harmonic (octave reduced), diapente ||
|| [[3_2|3/2]] || 701.995 || 3/2 || [[perfect fifth]], 3rd harmonic (octave reduced), diapente ||
|| [[4_3|4/3]] || 498.045 || 2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/3 || perfect fourth, 3rd subharmonic (octave reduced), diatessaron ||
|| [[4_3|4/3]] || 498.045 || 2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/3 || perfect fourth, 3rd subharmonic (octave reduced), diatessaron ||
|| [[9_8|9/8]] || 203.910 || 3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt; || (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced) ||
|| [[9_8|9/8]] || 203.910 || 3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt; || (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced) ||
||||||||~ 5-limit ||
||||||||~ 5-limit (complete) ||
|| [[5_4|5/4]] || 386.314 || 5/2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; || (classic) (5-limit) major third, 5th harmonic (octave reduced) ||
|| [[5_4|5/4]] || 386.314 || 5/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt; || (classic) (5-limit) major third, 5th harmonic (octave reduced) ||
|| [[6_5|6/5]] || 315.641 || (2*3)/5 || (classic) (5-limit) minor third ||
|| [[6_5|6/5]] || 315.641 || (2*3)/5 || (classic) (5-limit) minor third ||
|| [[10_9|10/9]] || 182.404 || (2*5)/3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; || classic (whole) tone, classic major second, minor whole tone ||
|| [[10_9|10/9]] || 182.404 || (2*5)/3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt; || classic (whole) tone, classic major second, minor whole tone ||
|| [[16_15|16/15]] || 111.713 || 2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;/(3*5) || minor diatonic semitone, 15th subharmonic ||
|| [[16_15|16/15]] || 111.713 || 2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;/(3*5) || minor diatonic semitone, 15th subharmonic ||
|| [[25_24|25/24]] || 70.672 || 5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3) || chroma, (classic) chromatic semitone, Zarlinian semitone ||
|| [[25_24|25/24]] || 70.672 || 5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3) || chroma, (classic) chromatic semitone, Zarlinian semitone ||
|| [[81_80|81/80]] || 21.506 || &lt;span style="line-height: 15.6000003814697px;"&gt;(&lt;/span&gt;3&lt;span style="line-height: 1.5;"&gt;/&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;2)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;4&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;/&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;5&lt;/span&gt; || syntonic comma, Didymus comma ||
|| [[81_80|81/80]] || 21.506 || (3/2)&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;/5 || syntonic comma, Didymus comma ||
||||||||~ 7-limit ||
||||||||~ 7-limit (complete?) ||
|| [[7_6|7/6]] || 266.871 || 7/(2*3) || (septimal) subminor third, septimal minor third, augmented second ||
|| [[7_6|7/6]] || 266.871 || 7/(2*3) || (septimal) subminor third, septimal minor third, augmented second ||
|| [[8_7|8/7]] || 231.174 || 2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;/7 || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
|| [[8_7|8/7]] || 231.174 || 2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;/7 || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
|| [[15_14|15/14]] || 119.443 || (3*5)/(2*7) || septimal diatonic semitone ||
|| [[15_14|15/14]] || 119.443 || (3*5)/(2*7) || septimal diatonic semitone ||
|| [[21_20|21/20]] || 84.467 || (3*7)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5) || minor semitone, large septimal chromatic semitone ||
|| [[21_20|21/20]] || 84.467 || (3*7)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5) || minor semitone, large septimal chromatic semitone ||
|| [[28_27|28/27]] || 62.961 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)/3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt; || septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone ||
|| [[28_27|28/27]] || 62.961 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7)/3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt; || septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone ||
|| [[36_35|36/35]] || 48.770 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(5*7) || septimal quarter tone, septimal diesis ||
|| [[36_35|36/35]] || 48.770 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;)/(5*7) || septimal quarter tone, septimal diesis ||
|| [[49_48|49/48]] || 35.697 || 7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3) || large septimal diesis, slendro diesis, septimal 1/6-tone ||
|| [[49_48|49/48]] || 35.697 || 7&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*3) || large septimal diesis, slendro diesis, septimal 1/6-tone ||
|| [[50_49|50/49]] || 34.976 || 2*(5&lt;span style="line-height: 1.5;"&gt;/7)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt; || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma ||
|| [[50_49|50/49]] || 34.976 || 2*(5/7)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt; || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma ||
|| [[64_63|64/63]] || 27.264 || 2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7) || septimal comma, Archytas' comma ||
|| [[64_63|64/63]] || 27.264 || 2&lt;span style="vertical-align: super; font-size: 70%;"&gt;6&lt;/span&gt;/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7) || septimal comma, Archytas' comma ||
|| [[126_125|126/125]] || 13.795 || (2*3^2*7)/5^3 || starling comma, septimal semicomma ||
|| [[126_125|126/125]] || 13.795 || (2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7)/5&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt; || starling comma, septimal semicomma ||
|| [[225_224|225/224]] || 7.7115 || (3*5)&lt;span style="line-height: 1.5;"&gt;^2/(2^5*7)&lt;/span&gt; || marvel comma, septimal kleisma ||
|| [[225_224|225/224]] || 7.7115 || (3*5)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*7) || marvel comma, septimal kleisma ||
|| [[2401_2400|2401/2400]] || 0.72120 || 7^4/(2^5*3*5^2) || breedsma ||
|| [[2401_2400|2401/2400]] || 0.72120 || 7&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*3*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;) || breedsma ||
|| [[4375_4374|4375/4374]] || 0.39576 || (5^4*7)/(2*3^7) || ragisma ||
|| [[4375_4374|4375/4374]] || 0.39576 || (5&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*7)/(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;7&lt;/span&gt;) || ragisma ||
||||||||~ 11-limit ||
||||||||~ 11-limit (complete?) ||
|| [[11_10|11/10]] || 165.004 || 11/(2*5) || (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second ||
|| [[11_10|11/10]] || 165.004 || 11/(2*5) || (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second ||
|| [[12_11|12/11]] || 150.637 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3)/11 || (small) (undecimal) neutral second, 3/4-tone ||
|| [[12_11|12/11]] || 150.637 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3)/11 || (small) (undecimal) neutral second, 3/4-tone ||
|| [[22_21|22/21]] || 80.537 || (2*11)/(3*7) || undecimal minor semitone ||
|| [[22_21|22/21]] || 80.537 || (2*11)/(3*7) || undecimal minor semitone ||
|| [[33_32|33/32]] || 53.273 || (3*11)/2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt; || undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced) ||
|| [[33_32|33/32]] || 53.273 || (3*11)/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt; || undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced) ||
|| [[45_44|45/44]] || 38.906 || (3&lt;span style="line-height: 15.6000003814697px;"&gt;/&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;2)^&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;2*&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;(&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;5/&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;11)&lt;/span&gt; || 1/5-tone ||
|| [[45_44|45/44]] || 38.906 || (3/2)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*(5/11) || 1/5-tone ||
|| [[55_54|55/54]] || 31.767 || (5*11)/(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;) || undecimal diasecundal comma, eleventyfive comma ||
|| [[55_54|55/54]] || 31.767 || (5*11)/(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;) || undecimal diasecundal comma, eleventyfive comma ||
|| [[56_55|56/55]] || 31.194 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7)/(5*11) || undecimal tritonic comma, konbini comma ||
|| [[56_55|56/55]] || 31.194 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*7)/(5*11) || undecimal tritonic comma, konbini comma ||
|| [[99_98|99/98]] || 17.576 || (3&lt;span style="line-height: 1.5;"&gt;/7)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*(11/2)&lt;/span&gt; || small undecimal comma, mothwellsma ||
|| [[99_98|99/98]] || 17.576 || (3/7)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*(11/2) || small undecimal comma, mothwellsma ||
|| [[100_99|100/99]] || 17.399 || (2&lt;span style="line-height: 1.5;"&gt;*5/3)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;/11)&lt;/span&gt; || Ptolemy's comma, ptolemisma ||
|| [[100_99|100/99]] || 17.399 || (2*5/3)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/11) || Ptolemy's comma, ptolemisma ||
|| [[121_120|121/120]] || 14.376 || 11^2/(2^3*3*5) || undecimal seconds comma, biyatisma ||
|| [[121_120|121/120]] || 14.376 || 11&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3*5) || undecimal seconds comma, biyatisma ||
|| [[176_175|176/175]] || 9.8646 || (2^4*11)/(5^2*7) || valinorsma ||
|| [[176_175|176/175]] || 9.8646 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*11)/(5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7) || valinorsma ||
|| [[243_242|243/242]] || 7.1391 || 3^5/(2*11^2) || neutral third comma, rastma ||
|| [[243_242|243/242]] || 7.1391 || 3&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;/(2*11&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;) || neutral third comma, rastma ||
|| [[385_384|385/384]] || 4.5026 || (5*7*11)/(2^7*3) || keenanisma ||
|| [[385_384|385/384]] || 4.5026 || (5*7*11)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;7&lt;/span&gt;*3) || keenanisma ||
|| [[441_440|441/440]] || 3.9302 || (3*7)^2/(2^3*5*11) || Werckmeister's undecimal septenarian schisma, werckisma ||
|| [[441_440|441/440]] || 3.9302 || (3*7)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*5*11) || Werckmeister's undecimal septenarian schisma, werckisma ||
|| [[540_539|540/539]] || 3.2090 || (2/7)^2*3^3*5/11 || Swets' comma, swetisma ||
|| [[540_539|540/539]] || 3.2090 || (2/7)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*5/11 || Swets' comma, swetisma ||
|| [[3025_3024|3025/3024]] || 0.57240 || (5*11)^2/(2^4*3^3*7) || Lehmerisma ||
|| [[3025_3024|3025/3024]] || 0.57240 || (5*11)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7) || Lehmerisma ||
|| [[9801_9800|9801/9800]] || 0.17665 || &lt;span style="line-height: 1.5;"&gt;[11/(5*7)]&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;^2*&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;3^4/2^3&lt;/span&gt; || Gauss comma, kalisma ||
|| [[9801_9800|9801/9800]] || 0.17665 || [11/(5*7)]&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt; || Gauss comma, kalisma ||
||||||||~ 13-limit ||
||||||||~ 13-limit ||
|| [[13_12|13/12]] || 138.573 || 13/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3) || tridecimal 2/3-tone ||
|| [[13_12|13/12]] || 138.573 || 13/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3) || tridecimal 2/3-tone ||
|| [[14_13|14/13]] || 128.298 || (2*7)/13 || 2/3-tone, trienthird ||
|| [[14_13|14/13]] || 128.298 || (2*7)/13 || 2/3-tone, trienthird ||
|| [[26_25|26/25]] || 67.900 || (2*13)/5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; || tridecimal 1/3-tone ||
|| [[26_25|26/25]] || 67.900 || (2*13)/5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt; || tridecimal 1/3-tone ||
|| [[27_26|27/26]] || 65.337 || 3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;/(2*13) || tridecimal comma ||
|| [[27_26|27/26]] || 65.337 || 3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;/(2*13) || tridecimal comma ||
|| [[40_39|40/39]] || 43.831 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5)/(3*13) || tridecimal minor diesis ||
|| [[40_39|40/39]] || 43.831 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*5)/(3*13) || tridecimal minor diesis ||
|| [[65_64|65/64]] || 26.841 || (5*13)/2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt; || wilsorma, 13th-partial chroma ||
|| [[65_64|65/64]] || 26.841 || (5*13)/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;6&lt;/span&gt; || wilsorma, 13th-partial chroma ||
|| [[66_65|66/65]] || 26.432 || (2*3*11)/(5*13) || winmeanma ||
|| [[66_65|66/65]] || 26.432 || (2*3*11)/(5*13) || winmeanma ||
|| [[78_77|78/77]] || 22.339 || (2*3*13)/(7*11) || negustma ||
|| [[78_77|78/77]] || 22.339 || (2*3*13)/(7*11) || negustma ||
|| [[91_90|91/90]] || 19.130 || (7*13)/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5) || [[The Biosphere|Biome]] comma, superleap comma ||
|| [[91_90|91/90]] || 19.130 || (7*13)/(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5) || [[The Biosphere|Biome]] comma, superleap comma ||
|| [[105_104|105/104]] || 16.567 || (3*5*7)/(2^3*13) || small tridecimal comma, animist comma ||
|| [[105_104|105/104]] || 16.567 || (3*5*7)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*13) || small tridecimal comma, animist comma ||
|| [[144_143|144/143]] || 12.064 || (&lt;span style="line-height: 1.5;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*3)^2/(11*13)&lt;/span&gt; || grossma ||
|| [[144_143|144/143]] || 12.064 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(11*13) || grossma ||
|| [[169_168|169/168]] || 10.274 || 13&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3*7) || buzurgisma, dhanvantarisma ||
|| [[169_168|169/168]] || 10.274 || 13&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3*7) || buzurgisma, dhanvantarisma ||
|| [[196_195|196/195]] || 8.8554 || (2*7)^2/(3*5*13) || marveltwin comma ||
|| [[196_195|196/195]] || 8.8554 || (2*7)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(3*5*13) || marveltwin comma ||
|| [[351_350|351/350]] || 4.9393 || (3/5)^2*13/(2*7) || ratwolfsma ||
|| 325/324 || 5.3351 || (5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;)|| ||
|| [[352_351|352/351]] || 4.9253 || (&lt;span style="line-height: 1.5;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;5&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*11)/(&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;3^&lt;/span&gt;2&lt;span style="line-height: 15.6000003814697px;"&gt;*13)&lt;/span&gt; || minthma ||
|| [[351_350|351/350]] || 4.9393 || (3/5)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13/(2*7) || ratwolfsma ||
|| [[364_363|364/363]] || 4.7627 || (2/11)^2*7*13/3 || gentle comma ||
|| [[352_351|352/351]] || 4.9253 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*11)/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13) || minthma ||
|| [[364_363|364/363]] || 4.7627 || (2/11)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7*13/3 || gentle comma ||
|| [[625_624|625/624]] || 2.7722 ||  || tunbarsma ||
|| [[625_624|625/624]] || 2.7722 ||  || tunbarsma ||
|| [[676_675|676/675]] || 2.5629 ||  || island comma ||
|| [[676_675|676/675]] || 2.5629 ||  || island comma ||
Line 91: Line 90:
|| [[123201_123200|123201/123200]] || 0.014052 ||  || chalmersia ||
|| [[123201_123200|123201/123200]] || 0.014052 ||  || chalmersia ||
||||||||~ 17-limit (complete!) ||
||||||||~ 17-limit (complete!) ||
|| [[17_16|17/16]] || 104.955 || 17/2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt; || 17th harmonic (octave reduced) ||
|| [[17_16|17/16]] || 104.955 || 17/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt; || 17th harmonic (octave reduced) ||
|| [[18_17|18/17]] || 98.955 || (2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/17 || Arabic lute index finger ||
|| [[18_17|18/17]] || 98.955 || (2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/17 || Arabic lute index finger ||
|| [[34_33|34/33]] || 51.682 || (2*17)/(3*11) ||  ||
|| [[34_33|34/33]] || 51.682 || (2*17)/(3*11) ||  ||
|| [[35_34|35/34]] || 50.184 || (5*7)/(2*17) || septendecimal 1/4-tone ||
|| [[35_34|35/34]] || 50.184 || (5*7)/(2*17) || septendecimal 1/4-tone ||
|| [[51_50|51/50]] || 34.283 || (3*17)/(2*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) || 17th-partial chroma ||
|| [[51_50|51/50]] || 34.283 || (3*17)/(2*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;) || 17th-partial chroma ||
|| [[52_51|52/51]] || 33.617 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)/(3*17) ||  ||
|| [[52_51|52/51]] || 33.617 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13)/(3*17) ||  ||
|| [[85_84|85/84]] || 20.488 || (5*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*7) ||  ||
|| [[85_84|85/84]] || 20.488 || (5*17)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3*7) ||  ||
|| 120/119 || 14.487 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3*5)/(7*17) ||  ||
|| 120/119 || 14.487 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3*5)/(7*17) ||  ||
|| 136/135 || 12.777 || (2/&lt;span style="line-height: 1.5;"&gt;3)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;3&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*17/5&lt;/span&gt; ||  ||
|| 136/135 || 12.777 || (2/3)&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*17/5 ||  ||
|| 154/153 || 11.278 || (2*7*11)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) ||  ||
|| 154/153 || 11.278 || (2*7*11)/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17) ||  ||
|| 170/169 || 10.214 || (2*5*17)/13&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; ||  ||
|| 170/169 || 10.214 || (2*5*17)/13&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt; ||  ||
|| 221/220 || 7.8514 || (13*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5*11) ||  ||
|| 221/220 || 7.8514 || (13*17)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5*11) ||  ||
|| 256/255 || 6.7759 || (2^8)/(3*5*17) || 255th subharmonic ||
|| 256/255 || 6.7759 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;8&lt;/span&gt;)/(3*5*17) || 255th subharmonic ||
|| 273/272 || 6.3532 || (3*7*13)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*17) ||  ||
|| 273/272 || 6.3532 || (3*7*13)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*17) ||  ||
|| 289/288 || 6.0008 || (17&lt;span style="line-height: 1.5;"&gt;/3)^&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;/2&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;5&lt;/span&gt; ||  ||
|| 289/288 || 6.0008 || (17/3)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt; ||  ||
|| 375/374 || 4.6228 || (3*5&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(2*11*17) ||  ||
|| 375/374 || 4.6228 || (3*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;)/(2*11*17) ||  ||
|| 442/441 || 3.9213 || (2*13*17)/(3*7)&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; ||  ||
|| 442/441 || 3.9213 || (2*13*17)/(3*7)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt; ||  ||
|| 561/560 || 3.0887 || (3*11*17)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5*7) ||  ||
|| 561/560 || 3.0887 || (3*11*17)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*5*7) ||  ||
|| 595/594 || 2.9121 || (5*7*17)/(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11) ||  ||
|| 595/594 || 2.9121 || (5*7*17)/(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*11) ||  ||
|| 715/714 || 2.4230 || (5*11*13)/(2*3*7*17) ||  ||
|| 715/714 || 2.4230 || (5*11*13)/(2*3*7*17) ||  ||
|| 833/832 || 2.0796 || (7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;*13) ||  ||
|| 833/832 || 2.0796 || (7&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;6&lt;/span&gt;*13) ||  ||
|| 936/935 || 1.8506 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)/(5*11*17) ||  ||
|| 936/935 || 1.8506 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13)/(5*11*17) ||  ||
|| 1089/1088 || 1.5905 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;*17) ||  ||
|| 1089/1088 || 1.5905 || (3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*11&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;6&lt;/span&gt;*17) ||  ||
|| 1156/1155 || 1.4983 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(3*5*7*11) ||  ||
|| 1156/1155 || 1.4983 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(3*5*7*11) ||  ||
|| 1225/1224 || 1.4138 || (5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) ||  ||
|| 1225/1224 || 1.4138 || (5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17) ||  ||
|| 1275/1274 || 1.3584 || (3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/(2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13) ||  ||
|| 1275/1274 || 1.3584 || (3*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)/(2*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13) ||  ||
|| 1701/1700 || 1.0181 || (3&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*7)/[(2*5)&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17] ||  ||
|| 1701/1700 || 1.0181 || (3&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*7)/[(2*5)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17] ||  ||
|| 2058/2057 || 0.8414 || (2*3*7&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(11&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) || xenisma ||
|| 2058/2057 || 0.8414 || (2*3*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;)/(11&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17) || xenisma ||
|| 2431/2430 || 0.7123 || (11*13*17)/(2*3&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*5) ||  ||
|| 2431/2430 || 0.7123 || (11*13*17)/(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*5) ||  ||
|| 2500/2499 || 0.6926 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;)/(3*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) ||  ||
|| 2500/2499 || 0.6926 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;)/(3*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17) ||  ||
|| 2601/2600 || 0.6657 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13) ||  ||
|| 2601/2600 || 0.6657 || (3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13) ||  ||
|| 4914/4913 || 0.3523 || (2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7*13)/(17&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;) ||  ||
|| 4914/4913 || 0.3523 || (2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*7*13)/(17&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;) ||  ||
|| 5832/5831 || 0.2969 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;)/(7&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*17) ||  ||
|| 5832/5831 || 0.2969 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;6&lt;/span&gt;)/(7&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*17) ||  ||
|| 12376/12375 || 0.1399 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7*13*17)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11) ||  ||
|| 12376/12375 || 0.1399 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*7*13*17)/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*11) ||  ||
|| 14400/14399 || 0.1202 || (2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(7*11&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) ||  ||
|| 14400/14399 || 0.1202 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;6&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(7*11&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17) ||  ||
|| 28561/28560 || 0.0606 || (13&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3*5*7*17) ||  ||
|| 28561/28560 || 0.0606 || (13&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*3*5*7*17) ||  ||
|| 31213/31212 || 0.0555 || (7&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*13)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*17&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) ||  ||
|| 31213/31212 || 0.0555 || (7&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*13)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*17&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;) ||  ||
|| 37180/37179 || 0.0466 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5*11*13&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(3&lt;span style="vertical-align: super;"&gt;7&lt;/span&gt;*17) ||  ||
|| 37180/37179 || 0.0466 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5*11*13&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;7&lt;/span&gt;*17) ||  ||
|| 194481/194480 || 0.0089 || (3&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*7&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5*11*13*17) || scintillisma ||
|| 194481/194480 || 0.0089 || (3&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*5*11*13*17) || scintillisma ||
|| 336141/336140 || 0.0052 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5*7&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;) ||  ||
|| 336141/336140 || 0.0052 || (3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;) ||  ||
||||||||~ 19-limit (incomplete) ||
||||||||~ 19-limit (incomplete) ||
|| [[19_18|19/18]] || 93.603 || 19/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) || undevicesimal semitone ||
|| [[19_18|19/18]] || 93.603 || 19/(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;) || undevicesimal semitone ||
|| [[20_19|20/19]] || 88.801 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/19 || small undevicesimal semitone ||
|| [[20_19|20/19]] || 88.801 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5)/19 || small undevicesimal semitone ||
|| [[39_38|39/38]] || 44.970 || (3*13)/(2*19) ||  ||
|| [[39_38|39/38]] || 44.970 || (3*13)/(2*19) ||  ||
|| [[57_56|57/56]] || 30.642 || (3*19)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7) ||  ||
|| [[57_56|57/56]] || 30.642 || (3*19)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*7) ||  ||
|| [[76_75|76/75]] || 22.931 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)/(3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) ||  ||
|| [[76_75|76/75]] || 22.931 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*19)/(3*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;) ||  ||
|| [[77_76|77/76]] || 22.631 || (7*11)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19) ||  ||
|| [[77_76|77/76]] || 22.631 || (7*11)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*19) ||  ||
|| [[96_95|96/95]] || 18.128 || (2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3)/(5*19) ||  ||
|| [[96_95|96/95]] || 18.128 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*3)/(5*19) ||  ||
|| 133/132 || 13.066 || (19*7)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*11) ||  ||
|| 133/132 || 13.066 || (19*7)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3*11) ||  ||
|| 153/152 || 11.352 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*19) ||  ||
|| 153/152 || 11.352 || (3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*19) ||  ||
|| 171/170 || 10.154 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)/(2*5*17) ||  ||
|| 171/170 || 10.154 || (3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*19)/(2*5*17) ||  ||
|| 190/189 || 9.1358 || (2*5*19)/(3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7) ||  ||
|| 190/189 || 9.1358 || (2*5*19)/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*7) ||  ||
|| 209/208 || 8.3033 || (11*19)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*13) ||  ||
|| 209/208 || 8.3033 || (11*19)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*13) ||  ||
|| 210/209 || 8.2637 || (2*3*5*7)/(11*19) ||  ||
|| 210/209 || 8.2637 || (2*3*5*7)/(11*19) ||  ||
|| 286/285 || 6.0639 || (2*11*13)/(3*5*19) ||  ||
|| 286/285 || 6.0639 || (2*11*13)/(3*5*19) ||  ||
|| 400/399 || 4.3335 || (2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(3*7*19) ||  ||
|| 400/399 || 4.3335 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(3*7*19) ||  ||
|| 456/455 || 3.8007 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3*19)/(5*7*13) ||  ||
|| 456/455 || 3.8007 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3*19)/(5*7*13) ||  ||
|| 476/475 || 3.6409 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7*17)/(5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19) ||  ||
|| 476/475 || 3.6409 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7*17)/(5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*19) ||  ||
|| 495/494 || 3.501 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5*11)/(2*13*19) ||  ||
|| 495/494 || 3.501 || (3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5*11)/(2*13*19) ||  ||
|| 513/512 || 3.378 || &lt;span style="vertical-align: super;"&gt;(3^3*19)/2^9&lt;/span&gt; || 513th harmonic ||
|| 513/512 || 3.378 || (3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*19)/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;9&lt;/span&gt; || 513th harmonic ||
||||||||~ 23-limit (incomplete) ||
||||||||~ 23-limit (incomplete) ||
|| [[23_22|23/22]] || 76.956 || 23/(2*11) ||  ||
|| [[23_22|23/22]] || 76.956 || 23/(2*11) ||  ||
|| [[24_23|24/23]] || 73.681 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3)/23 ||  ||
|| [[24_23|24/23]] || 73.681 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3)/23 ||  ||
|| [[46_45|46/45]] || 38.051 || (2*23)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5) ||  ||
|| [[46_45|46/45]] || 38.051 || (2*23)/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5) ||  ||
|| [[69_68|69/68]] || 25.274 || (3*23)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) ||  ||
|| [[69_68|69/68]] || 25.274 || (3*23)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17) ||  ||
|| [[70_69|70/69]] || 24.910 || (2*5*7)/(3*23) ||  ||
|| [[70_69|70/69]] || 24.910 || (2*5*7)/(3*23) ||  ||
|| [[92_91|92/91]] || 18.921 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23)/(7*13) ||  ||
|| [[92_91|92/91]] || 18.921 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*23)/(7*13) ||  ||
|| 115/114 || 15.120 || (5*23)/(2*3*19) ||  ||
|| 115/114 || 15.120 || (5*23)/(2*3*19) ||  ||
|| 161/160 || 10.7865 || (7*23)/(2^5*5) ||  ||
|| 161/160 || 10.7865 || (7*23)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*5) ||  ||
|| 162/161 || 10.720 || (2*3^4)/(7*23) ||  ||
|| 162/161 || 10.720 || (2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;)/(7*23) ||  ||
|| 208/207 || 8.343 || (16*13)/(23*9) ||  ||
|| 208/207 || 8.343 || (16*13)/(23*9) ||  ||
|| 576/575 || 3.008 || (64*9)/(23*25) ||  ||
|| 576/575 || 3.008 || (64*9)/(23*25) ||  ||
||||||||~ 29-limit (incomplete) ||
||||||||~ 29-limit (incomplete) ||
|| [[29_28|29/28]] || 60.751 || 29/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7) ||  ||
|| [[29_28|29/28]] || 60.751 || 29/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7) ||  ||
|| [[30_29|30/29]] || 58.692 || (2*3*5)/29 ||  ||
|| [[30_29|30/29]] || 58.692 || (2*3*5)/29 ||  ||
|| [[58_57|58/57]] || 30.109 || (2*29)/(3*19) ||  ||
|| [[58_57|58/57]] || 30.109 || (2*29)/(3*19) ||  ||
|| [[88_87|88/87]] || 19.786 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11)/(3*29) ||  ||
|| [[88_87|88/87]] || 19.786 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*11)/(3*29) ||  ||
||||||||~ 31-limit (incomplete) ||
||||||||~ 31-limit (incomplete) ||
|| [[31_30|31/30]] || 56.767 || 31/(2*3*5) ||  ||
|| [[31_30|31/30]] || 56.767 || 31/(2*3*5) ||  ||
|| [[32_31|32/31]] || 54.964 || 2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;/31 || 31st subharmonic ||
|| [[32_31|32/31]] || 54.964 || 2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;/31 || 31st subharmonic ||
|| [[63_62|63/62]] || 27.700 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)/(2*31) ||  ||
|| [[63_62|63/62]] || 27.700 || (3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7)/(2*31) ||  ||
|| [[93_92|93/92]] || 18.716 || (3*31)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23) ||  ||
|| [[93_92|93/92]] || 18.716 || (3*31)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*23) ||  ||
||||||||~ 37-limit (incomplete) ||
||||||||~ 37-limit (incomplete) ||
|| [[37_36|37/36]] || 47.434 || 37/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) ||  ||
|| [[37_36|37/36]] || 47.434 || 37/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;) ||  ||
|| [[38_37|38/37]] || 46.169 || (2*19)/37 ||  ||
|| [[38_37|38/37]] || 46.169 || (2*19)/37 ||  ||
|| [[75_74|75/74]] || 23.238 || (3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(2*37) ||  ||
|| [[75_74|75/74]] || 23.238 || (3*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(2*37) ||  ||
||||||||~ 41-limit (incomplete) ||
||||||||~ 41-limit (incomplete) ||
|| [[41_40|41/40]] || 42.749 || 41/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5) ||  ||
|| [[41_40|41/40]] || 42.749 || 41/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*5) ||  ||
|| [[42_41|42/41]] || 41.719 || (2*3*7)/41 ||  ||
|| [[42_41|42/41]] || 41.719 || (2*3*7)/41 ||  ||
|| [[82_81|82/81]] || 21.242 || (2*41)/3&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt; ||  ||
|| [[82_81|82/81]] || 21.242 || (2*41)/3&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt; ||  ||
||||||||~ 43-limit (incomplete) ||
||||||||~ 43-limit (incomplete) ||
|| [[43_42|43/42]] || 40.737 || 43/(2*3*7) ||  ||
|| [[43_42|43/42]] || 40.737 || 43/(2*3*7) ||  ||
|| [[44_43|44/43]] || 39.800 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)/43 ||  ||
|| [[44_43|44/43]] || 39.800 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*11)/43 ||  ||
|| [[86_85|86/85]] || 20.249 || (2*43)/(5*17) ||  ||
|| [[86_85|86/85]] || 20.249 || (2*43)/(5*17) ||  ||
|| [[87_86|87/86]] || 20.014 || (3*29)/(2*43) ||  ||
|| [[87_86|87/86]] || 20.014 || (3*29)/(2*43) ||  ||
||||||||~ 47-limit (incomplete) ||
||||||||~ 47-limit (incomplete) ||
|| [[47_46|47/46]] || 37.232 || 47/(2*23) ||  ||
|| [[47_46|47/46]] || 37.232 || 47/(2*23) ||  ||
|| [[48_47|48/47]] || 36.448 || (2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3)/47 ||  ||
|| [[48_47|48/47]] || 36.448 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*3)/47 ||  ||
|| [[94_93|94/93]] || 18.516 || (2*47)/(3*31) ||  ||
|| [[94_93|94/93]] || 18.516 || (2*47)/(3*31) ||  ||
|| [[95_94|95/94]] || 18.320 || (5*19)/(2*47) ||  ||
|| [[95_94|95/94]] || 18.320 || (5*19)/(2*47) ||  ||
||||||||~ 53-limit (incomplete) ||
||||||||~ 53-limit (incomplete) ||
|| [[53_52|53/52]] || 32.977 || 53/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13) ||  ||
|| [[53_52|53/52]] || 32.977 || 53/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13) ||  ||
|| [[54_53|54/53]] || 32.360 || (2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/53 ||  ||
|| [[54_53|54/53]] || 32.360 || (2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;)/53 ||  ||
||||||||~ 59-limit (incomplete) ||
||||||||~ 59-limit (incomplete) ||
|| [[59_58|59/58]] || 29.594 || 59/(2*29) ||  ||
|| [[59_58|59/58]] || 29.594 || 59/(2*29) ||  ||
|| [[60_59|60/59]] || 29.097 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*5)/59 ||  ||
|| [[60_59|60/59]] || 29.097 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3*5)/59 ||  ||
||||||||~ 61-limit (incomplete) ||
||||||||~ 61-limit (incomplete) ||
|| [[61_60|61/60]] || 28.616 || 61/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*5) ||  ||
|| [[61_60|61/60]] || 28.616 || 61/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3*5) ||  ||
|| [[62_61|62/61]] || 28.151 || (2*31)/61 ||  ||
|| [[62_61|62/61]] || 28.151 || (2*31)/61 ||  ||
||||||||~ 67-limit (incomplete) ||
||||||||~ 67-limit (incomplete) ||
|| [[67_66|67/66]] || 26.034 || 67/(2*3*11) ||  ||
|| [[67_66|67/66]] || 26.034 || 67/(2*3*11) ||  ||
|| [[68_67|68/67]] || 25.648 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/67 ||  ||
|| [[68_67|68/67]] || 25.648 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)/67 ||  ||
||||||||~ 71-limit (incomplete) ||
||||||||~ 71-limit (incomplete) ||
|| [[71_70|71/70]] || 24.557 || 71/(2*5*7) ||  ||
|| [[71_70|71/70]] || 24.557 || 71/(2*5*7) ||  ||
|| [[72_71|72/71]] || 24.213 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/71 ||  ||
|| [[72_71|72/71]] || 24.213 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/71 ||  ||
||||||||~ 73-limit (incomplete) ||
||||||||~ 73-limit (incomplete) ||
|| [[73_72|73/72]] || 23.879 || 73/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) ||  ||
|| [[73_72|73/72]] || 23.879 || 73/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;) ||  ||
|| [[74_73|74/73]] || 23.555 || (2*37)/73 ||  ||
|| [[74_73|74/73]] || 23.555 || (2*37)/73 ||  ||
||||||||~ 79-limit (incomplete) ||
||||||||~ 79-limit (incomplete) ||
|| [[79_78|79/78]] || 22.054 || 79/(2*3*13) ||  ||
|| [[79_78|79/78]] || 22.054 || 79/(2*3*13) ||  ||
|| [[80_79|80/79]] || 21.777 || (2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5)/79 ||  ||
|| [[80_79|80/79]] || 21.777 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*5)/79 ||  ||
||||||||~ 83-limit (incomplete) ||
||||||||~ 83-limit (incomplete) ||
|| [[83_82|83/82]] || 20.985 || 83/(2*41) ||  ||
|| [[83_82|83/82]] || 20.985 || 83/(2*41) ||  ||
|| [[84_83|84/83]] || 20.734 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*7)/83 ||  ||
|| [[84_83|84/83]] || 20.734 || (2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3*7)/83 ||  ||
||||||||~ 89-limit (incomplete) ||
||||||||~ 89-limit (incomplete) ||
|| [[89_88|89/88]] || 19.562 || 89/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11) ||  ||
|| [[89_88|89/88]] || 19.562 || 89/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*11) ||  ||
|| [[90_89|90/89]] || 19.344 || (2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/89 ||  ||
|| [[90_89|90/89]] || 19.344 || (2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5)/89 ||  ||
||||||||~ 97-limit (incomplete) ||
||||||||~ 97-limit (incomplete) ||
|| [[97_96|97/96]] || 17.940 || 97/(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3) ||  ||
|| [[97_96|97/96]] || 17.940 || 97/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*3) ||  ||
|| [[98_97|98/97]] || 17.756 || (2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/97 ||  ||
|| [[98_97|98/97]] || 17.756 || (2*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/97 ||  ||
||||||||~ 101-limit (incomplete) ||
||||||||~ 101-limit (incomplete) ||
|| [[101_100|101/100]] || 17.226 || 101/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) ||  ||
|| [[101_100|101/100]] || 17.226 || 101/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;) ||  ||
|| 102/101 || 17.057 || (2*3*17)/101 ||  ||</pre></div>
|| 102/101 || 17.057 || (2*3*17)/101 ||  ||</pre></div>
<h4>Original HTML content:</h4>
<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;List of Superparticular Intervals&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="List of Superparticular Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #800080;"&gt;List of Superparticular Intervals&lt;/span&gt;&lt;/h1&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;List of Superparticular Intervals&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/Superparticular"&gt;Superparticular&lt;/a&gt; numbers are ratios of the form (n+1)/n, or 1+1/n, where n is a whole number other than 1. They appear frequently in &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt; and &lt;a class="wiki_link" href="/OverToneSeries"&gt;Harmonic Series&lt;/a&gt; music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio &lt;a class="wiki_link" href="/21_20"&gt;21/20&lt;/a&gt;. As the overtones get closer together, the superparticular intervals get smaller and smaller. Thus, an examination of the superparticular intervals is an examination of some of the simplest small intervals in rational tuning systems. Indeed, many but not all common &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s are superparticular ratios.&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Superparticular"&gt;Superparticular&lt;/a&gt; numbers are ratios of the form (n+1)/n, or 1+1/n, where n is a whole number other than 1. They appear frequently in &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt; and &lt;a class="wiki_link" href="/OverToneSeries"&gt;Harmonic Series&lt;/a&gt; music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio &lt;a class="wiki_link" href="/21_20"&gt;21/20&lt;/a&gt;. As the overtones get closer together, the superparticular intervals get smaller and smaller. Thus, an examination of the superparticular intervals is an examination of some of the simplest small intervals in rational tuning systems. Indeed, many but not all common &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s are superparticular ratios.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(5*7), while 37/36 would belong to the 37-limit.&lt;br /&gt;
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="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(5*7), while 37/36 would belong to the 37-limit.&lt;br /&gt;
&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;br /&gt;
Line 249: Line 246:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;th colspan="4"&gt;2-limit&lt;br /&gt;
         &lt;th colspan="4"&gt;2-limit (complete)&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 263: Line 260:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;th colspan="4"&gt;3-limit&lt;br /&gt;
         &lt;th colspan="4"&gt;3-limit (complete)&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 281: Line 278:
         &lt;td&gt;498.045&lt;br /&gt;
         &lt;td&gt;498.045&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/3&lt;br /&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;perfect fourth, 3rd subharmonic (octave reduced), diatessaron&lt;br /&gt;
         &lt;td&gt;perfect fourth, 3rd subharmonic (octave reduced), diatessaron&lt;br /&gt;
Line 291: Line 288:
         &lt;td&gt;203.910&lt;br /&gt;
         &lt;td&gt;203.910&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)&lt;br /&gt;
         &lt;td&gt;(Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)&lt;br /&gt;
Line 297: Line 294:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;th colspan="4"&gt;5-limit&lt;br /&gt;
         &lt;th colspan="4"&gt;5-limit (complete)&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 305: Line 302:
         &lt;td&gt;386.314&lt;br /&gt;
         &lt;td&gt;386.314&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5/2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;5/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(classic) (5-limit) major third, 5th harmonic (octave reduced)&lt;br /&gt;
         &lt;td&gt;(classic) (5-limit) major third, 5th harmonic (octave reduced)&lt;br /&gt;
Line 325: Line 322:
         &lt;td&gt;182.404&lt;br /&gt;
         &lt;td&gt;182.404&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*5)/3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(2*5)/3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;classic (whole) tone, classic major second, minor whole tone&lt;br /&gt;
         &lt;td&gt;classic (whole) tone, classic major second, minor whole tone&lt;br /&gt;
Line 335: Line 332:
         &lt;td&gt;111.713&lt;br /&gt;
         &lt;td&gt;111.713&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;/(3*5)&lt;br /&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;/(3*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;minor diatonic semitone, 15th subharmonic&lt;br /&gt;
         &lt;td&gt;minor diatonic semitone, 15th subharmonic&lt;br /&gt;
Line 345: Line 342:
         &lt;td&gt;70.672&lt;br /&gt;
         &lt;td&gt;70.672&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3)&lt;br /&gt;
         &lt;td&gt;5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;chroma, (classic) chromatic semitone, Zarlinian semitone&lt;br /&gt;
         &lt;td&gt;chroma, (classic) chromatic semitone, Zarlinian semitone&lt;br /&gt;
Line 355: Line 352:
         &lt;td&gt;21.506&lt;br /&gt;
         &lt;td&gt;21.506&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;(&lt;/span&gt;3&lt;span style="line-height: 1.5;"&gt;/&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;2)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;4&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;/&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;5&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(3/2)&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;/5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;syntonic comma, Didymus comma&lt;br /&gt;
         &lt;td&gt;syntonic comma, Didymus comma&lt;br /&gt;
Line 361: Line 358:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;th colspan="4"&gt;7-limit&lt;br /&gt;
         &lt;th colspan="4"&gt;7-limit (complete?)&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 379: Line 376:
         &lt;td&gt;231.174&lt;br /&gt;
         &lt;td&gt;231.174&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;/7&lt;br /&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;/7&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic&lt;br /&gt;
         &lt;td&gt;(septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic&lt;br /&gt;
Line 399: Line 396:
         &lt;td&gt;84.467&lt;br /&gt;
         &lt;td&gt;84.467&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*7)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)&lt;br /&gt;
         &lt;td&gt;(3*7)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;minor semitone, large septimal chromatic semitone&lt;br /&gt;
         &lt;td&gt;minor semitone, large septimal chromatic semitone&lt;br /&gt;
Line 409: Line 406:
         &lt;td&gt;62.961&lt;br /&gt;
         &lt;td&gt;62.961&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)/3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7)/3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone&lt;br /&gt;
         &lt;td&gt;septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone&lt;br /&gt;
Line 419: Line 416:
         &lt;td&gt;48.770&lt;br /&gt;
         &lt;td&gt;48.770&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(5*7)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;)/(5*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;septimal quarter tone, septimal diesis&lt;br /&gt;
         &lt;td&gt;septimal quarter tone, septimal diesis&lt;br /&gt;
Line 429: Line 426:
         &lt;td&gt;35.697&lt;br /&gt;
         &lt;td&gt;35.697&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3)&lt;br /&gt;
         &lt;td&gt;7&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*3)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;large septimal diesis, slendro diesis, septimal 1/6-tone&lt;br /&gt;
         &lt;td&gt;large septimal diesis, slendro diesis, septimal 1/6-tone&lt;br /&gt;
Line 439: Line 436:
         &lt;td&gt;34.976&lt;br /&gt;
         &lt;td&gt;34.976&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2*(5&lt;span style="line-height: 1.5;"&gt;/7)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;2*(5/7)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma&lt;br /&gt;
         &lt;td&gt;septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma&lt;br /&gt;
Line 449: Line 446:
         &lt;td&gt;27.264&lt;br /&gt;
         &lt;td&gt;27.264&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)&lt;br /&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super; font-size: 70%;"&gt;6&lt;/span&gt;/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;septimal comma, Archytas' comma&lt;br /&gt;
         &lt;td&gt;septimal comma, Archytas' comma&lt;br /&gt;
Line 459: Line 456:
         &lt;td&gt;13.795&lt;br /&gt;
         &lt;td&gt;13.795&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3^2*7)/5^3&lt;br /&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7)/5&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;starling comma, septimal semicomma&lt;br /&gt;
         &lt;td&gt;starling comma, septimal semicomma&lt;br /&gt;
Line 469: Line 466:
         &lt;td&gt;7.7115&lt;br /&gt;
         &lt;td&gt;7.7115&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*5)&lt;span style="line-height: 1.5;"&gt;^2/(2^5*7)&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(3*5)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;marvel comma, septimal kleisma&lt;br /&gt;
         &lt;td&gt;marvel comma, septimal kleisma&lt;br /&gt;
Line 479: Line 476:
         &lt;td&gt;0.72120&lt;br /&gt;
         &lt;td&gt;0.72120&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7^4/(2^5*3*5^2)&lt;br /&gt;
         &lt;td&gt;7&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*3*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;breedsma&lt;br /&gt;
         &lt;td&gt;breedsma&lt;br /&gt;
Line 489: Line 486:
         &lt;td&gt;0.39576&lt;br /&gt;
         &lt;td&gt;0.39576&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5^4*7)/(2*3^7)&lt;br /&gt;
         &lt;td&gt;(5&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*7)/(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;7&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;ragisma&lt;br /&gt;
         &lt;td&gt;ragisma&lt;br /&gt;
Line 495: Line 492:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;th colspan="4"&gt;11-limit&lt;br /&gt;
         &lt;th colspan="4"&gt;11-limit (complete?)&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 513: Line 510:
         &lt;td&gt;150.637&lt;br /&gt;
         &lt;td&gt;150.637&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3)/11&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3)/11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(small) (undecimal) neutral second, 3/4-tone&lt;br /&gt;
         &lt;td&gt;(small) (undecimal) neutral second, 3/4-tone&lt;br /&gt;
Line 533: Line 530:
         &lt;td&gt;53.273&lt;br /&gt;
         &lt;td&gt;53.273&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*11)/2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(3*11)/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)&lt;br /&gt;
         &lt;td&gt;undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)&lt;br /&gt;
Line 543: Line 540:
         &lt;td&gt;38.906&lt;br /&gt;
         &lt;td&gt;38.906&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="line-height: 15.6000003814697px;"&gt;/&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;2)^&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;2*&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;(&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;5/&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;11)&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(3/2)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*(5/11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1/5-tone&lt;br /&gt;
         &lt;td&gt;1/5-tone&lt;br /&gt;
Line 553: Line 550:
         &lt;td&gt;31.767&lt;br /&gt;
         &lt;td&gt;31.767&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5*11)/(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;(5*11)/(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;undecimal diasecundal comma, eleventyfive comma&lt;br /&gt;
         &lt;td&gt;undecimal diasecundal comma, eleventyfive comma&lt;br /&gt;
Line 563: Line 560:
         &lt;td&gt;31.194&lt;br /&gt;
         &lt;td&gt;31.194&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7)/(5*11)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*7)/(5*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;undecimal tritonic comma, konbini comma&lt;br /&gt;
         &lt;td&gt;undecimal tritonic comma, konbini comma&lt;br /&gt;
Line 573: Line 570:
         &lt;td&gt;17.576&lt;br /&gt;
         &lt;td&gt;17.576&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="line-height: 1.5;"&gt;/7)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*(11/2)&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(3/7)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*(11/2)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;small undecimal comma, mothwellsma&lt;br /&gt;
         &lt;td&gt;small undecimal comma, mothwellsma&lt;br /&gt;
Line 583: Line 580:
         &lt;td&gt;17.399&lt;br /&gt;
         &lt;td&gt;17.399&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="line-height: 1.5;"&gt;*5/3)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;/11)&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(2*5/3)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Ptolemy's comma, ptolemisma&lt;br /&gt;
         &lt;td&gt;Ptolemy's comma, ptolemisma&lt;br /&gt;
Line 593: Line 590:
         &lt;td&gt;14.376&lt;br /&gt;
         &lt;td&gt;14.376&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11^2/(2^3*3*5)&lt;br /&gt;
         &lt;td&gt;11&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;undecimal seconds comma, biyatisma&lt;br /&gt;
         &lt;td&gt;undecimal seconds comma, biyatisma&lt;br /&gt;
Line 603: Line 600:
         &lt;td&gt;9.8646&lt;br /&gt;
         &lt;td&gt;9.8646&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2^4*11)/(5^2*7)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*11)/(5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;valinorsma&lt;br /&gt;
         &lt;td&gt;valinorsma&lt;br /&gt;
Line 613: Line 610:
         &lt;td&gt;7.1391&lt;br /&gt;
         &lt;td&gt;7.1391&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3^5/(2*11^2)&lt;br /&gt;
         &lt;td&gt;3&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;/(2*11&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;neutral third comma, rastma&lt;br /&gt;
         &lt;td&gt;neutral third comma, rastma&lt;br /&gt;
Line 623: Line 620:
         &lt;td&gt;4.5026&lt;br /&gt;
         &lt;td&gt;4.5026&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5*7*11)/(2^7*3)&lt;br /&gt;
         &lt;td&gt;(5*7*11)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;7&lt;/span&gt;*3)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;keenanisma&lt;br /&gt;
         &lt;td&gt;keenanisma&lt;br /&gt;
Line 633: Line 630:
         &lt;td&gt;3.9302&lt;br /&gt;
         &lt;td&gt;3.9302&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*7)^2/(2^3*5*11)&lt;br /&gt;
         &lt;td&gt;(3*7)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*5*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Werckmeister's undecimal septenarian schisma, werckisma&lt;br /&gt;
         &lt;td&gt;Werckmeister's undecimal septenarian schisma, werckisma&lt;br /&gt;
Line 643: Line 640:
         &lt;td&gt;3.2090&lt;br /&gt;
         &lt;td&gt;3.2090&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2/7)^2*3^3*5/11&lt;br /&gt;
         &lt;td&gt;(2/7)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*5/11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Swets' comma, swetisma&lt;br /&gt;
         &lt;td&gt;Swets' comma, swetisma&lt;br /&gt;
Line 653: Line 650:
         &lt;td&gt;0.57240&lt;br /&gt;
         &lt;td&gt;0.57240&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5*11)^2/(2^4*3^3*7)&lt;br /&gt;
         &lt;td&gt;(5*11)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Lehmerisma&lt;br /&gt;
         &lt;td&gt;Lehmerisma&lt;br /&gt;
Line 663: Line 660:
         &lt;td&gt;0.17665&lt;br /&gt;
         &lt;td&gt;0.17665&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;span style="line-height: 1.5;"&gt;[11/(5*7)]&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;^2*&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;3^4/2^3&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;[11/(5*7)]&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Gauss comma, kalisma&lt;br /&gt;
         &lt;td&gt;Gauss comma, kalisma&lt;br /&gt;
Line 677: Line 674:
         &lt;td&gt;138.573&lt;br /&gt;
         &lt;td&gt;138.573&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3)&lt;br /&gt;
         &lt;td&gt;13/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;tridecimal 2/3-tone&lt;br /&gt;
         &lt;td&gt;tridecimal 2/3-tone&lt;br /&gt;
Line 697: Line 694:
         &lt;td&gt;67.900&lt;br /&gt;
         &lt;td&gt;67.900&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*13)/5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(2*13)/5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;tridecimal 1/3-tone&lt;br /&gt;
         &lt;td&gt;tridecimal 1/3-tone&lt;br /&gt;
Line 707: Line 704:
         &lt;td&gt;65.337&lt;br /&gt;
         &lt;td&gt;65.337&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;/(2*13)&lt;br /&gt;
         &lt;td&gt;3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;/(2*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;tridecimal comma&lt;br /&gt;
         &lt;td&gt;tridecimal comma&lt;br /&gt;
Line 717: Line 714:
         &lt;td&gt;43.831&lt;br /&gt;
         &lt;td&gt;43.831&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5)/(3*13)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*5)/(3*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;tridecimal minor diesis&lt;br /&gt;
         &lt;td&gt;tridecimal minor diesis&lt;br /&gt;
Line 727: Line 724:
         &lt;td&gt;26.841&lt;br /&gt;
         &lt;td&gt;26.841&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5*13)/2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(5*13)/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;6&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;wilsorma, 13th-partial chroma&lt;br /&gt;
         &lt;td&gt;wilsorma, 13th-partial chroma&lt;br /&gt;
Line 757: Line 754:
         &lt;td&gt;19.130&lt;br /&gt;
         &lt;td&gt;19.130&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(7*13)/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)&lt;br /&gt;
         &lt;td&gt;(7*13)/(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/The%20Biosphere"&gt;Biome&lt;/a&gt; comma, superleap comma&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/The%20Biosphere"&gt;Biome&lt;/a&gt; comma, superleap comma&lt;br /&gt;
Line 767: Line 764:
         &lt;td&gt;16.567&lt;br /&gt;
         &lt;td&gt;16.567&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*5*7)/(2^3*13)&lt;br /&gt;
         &lt;td&gt;(3*5*7)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;small tridecimal comma, animist comma&lt;br /&gt;
         &lt;td&gt;small tridecimal comma, animist comma&lt;br /&gt;
Line 777: Line 774:
         &lt;td&gt;12.064&lt;br /&gt;
         &lt;td&gt;12.064&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(&lt;span style="line-height: 1.5;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*3)^2/(11*13)&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(11*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;grossma&lt;br /&gt;
         &lt;td&gt;grossma&lt;br /&gt;
Line 787: Line 784:
         &lt;td&gt;10.274&lt;br /&gt;
         &lt;td&gt;10.274&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3*7)&lt;br /&gt;
         &lt;td&gt;13&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;buzurgisma, dhanvantarisma&lt;br /&gt;
         &lt;td&gt;buzurgisma, dhanvantarisma&lt;br /&gt;
Line 797: Line 794:
         &lt;td&gt;8.8554&lt;br /&gt;
         &lt;td&gt;8.8554&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*7)^2/(3*5*13)&lt;br /&gt;
         &lt;td&gt;(2*7)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/(3*5*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;marveltwin comma&lt;br /&gt;
         &lt;td&gt;marveltwin comma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;325/324&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5.3351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 807: Line 814:
         &lt;td&gt;4.9393&lt;br /&gt;
         &lt;td&gt;4.9393&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3/5)^2*13/(2*7)&lt;br /&gt;
         &lt;td&gt;(3/5)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13/(2*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;ratwolfsma&lt;br /&gt;
         &lt;td&gt;ratwolfsma&lt;br /&gt;
Line 817: Line 824:
         &lt;td&gt;4.9253&lt;br /&gt;
         &lt;td&gt;4.9253&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(&lt;span style="line-height: 1.5;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;5&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*11)/(&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;3^&lt;/span&gt;2&lt;span style="line-height: 15.6000003814697px;"&gt;*13)&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*11)/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;minthma&lt;br /&gt;
         &lt;td&gt;minthma&lt;br /&gt;
Line 827: Line 834:
         &lt;td&gt;4.7627&lt;br /&gt;
         &lt;td&gt;4.7627&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2/11)^2*7*13/3&lt;br /&gt;
         &lt;td&gt;(2/11)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7*13/3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;gentle comma&lt;br /&gt;
         &lt;td&gt;gentle comma&lt;br /&gt;
Line 951: Line 958:
         &lt;td&gt;104.955&lt;br /&gt;
         &lt;td&gt;104.955&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17/2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;17/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17th harmonic (octave reduced)&lt;br /&gt;
         &lt;td&gt;17th harmonic (octave reduced)&lt;br /&gt;
Line 961: Line 968:
         &lt;td&gt;98.955&lt;br /&gt;
         &lt;td&gt;98.955&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/17&lt;br /&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Arabic lute index finger&lt;br /&gt;
         &lt;td&gt;Arabic lute index finger&lt;br /&gt;
Line 991: Line 998:
         &lt;td&gt;34.283&lt;br /&gt;
         &lt;td&gt;34.283&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*17)/(2*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;(3*17)/(2*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17th-partial chroma&lt;br /&gt;
         &lt;td&gt;17th-partial chroma&lt;br /&gt;
Line 1,001: Line 1,008:
         &lt;td&gt;33.617&lt;br /&gt;
         &lt;td&gt;33.617&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)/(3*17)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13)/(3*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,011: Line 1,018:
         &lt;td&gt;20.488&lt;br /&gt;
         &lt;td&gt;20.488&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*7)&lt;br /&gt;
         &lt;td&gt;(5*17)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,021: Line 1,028:
         &lt;td&gt;14.487&lt;br /&gt;
         &lt;td&gt;14.487&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3*5)/(7*17)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3*5)/(7*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,031: Line 1,038:
         &lt;td&gt;12.777&lt;br /&gt;
         &lt;td&gt;12.777&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2/&lt;span style="line-height: 1.5;"&gt;3)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;3&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*17/5&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(2/3)&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*17/5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,041: Line 1,048:
         &lt;td&gt;11.278&lt;br /&gt;
         &lt;td&gt;11.278&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*7*11)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
         &lt;td&gt;(2*7*11)/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,051: Line 1,058:
         &lt;td&gt;10.214&lt;br /&gt;
         &lt;td&gt;10.214&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*5*17)/13&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(2*5*17)/13&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,061: Line 1,068:
         &lt;td&gt;7.8514&lt;br /&gt;
         &lt;td&gt;7.8514&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(13*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5*11)&lt;br /&gt;
         &lt;td&gt;(13*17)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,071: Line 1,078:
         &lt;td&gt;6.7759&lt;br /&gt;
         &lt;td&gt;6.7759&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2^8)/(3*5*17)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;8&lt;/span&gt;)/(3*5*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;255th subharmonic&lt;br /&gt;
         &lt;td&gt;255th subharmonic&lt;br /&gt;
Line 1,081: Line 1,088:
         &lt;td&gt;6.3532&lt;br /&gt;
         &lt;td&gt;6.3532&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*7*13)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*17)&lt;br /&gt;
         &lt;td&gt;(3*7*13)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,091: Line 1,098:
         &lt;td&gt;6.0008&lt;br /&gt;
         &lt;td&gt;6.0008&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(17&lt;span style="line-height: 1.5;"&gt;/3)^&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;/2&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;5&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(17/3)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,101: Line 1,108:
         &lt;td&gt;4.6228&lt;br /&gt;
         &lt;td&gt;4.6228&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*5&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(2*11*17)&lt;br /&gt;
         &lt;td&gt;(3*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;)/(2*11*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,111: Line 1,118:
         &lt;td&gt;3.9213&lt;br /&gt;
         &lt;td&gt;3.9213&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*13*17)/(3*7)&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(2*13*17)/(3*7)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,121: Line 1,128:
         &lt;td&gt;3.0887&lt;br /&gt;
         &lt;td&gt;3.0887&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*11*17)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5*7)&lt;br /&gt;
         &lt;td&gt;(3*11*17)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*5*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,131: Line 1,138:
         &lt;td&gt;2.9121&lt;br /&gt;
         &lt;td&gt;2.9121&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5*7*17)/(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11)&lt;br /&gt;
         &lt;td&gt;(5*7*17)/(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,151: Line 1,158:
         &lt;td&gt;2.0796&lt;br /&gt;
         &lt;td&gt;2.0796&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;*13)&lt;br /&gt;
         &lt;td&gt;(7&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;6&lt;/span&gt;*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,161: Line 1,168:
         &lt;td&gt;1.8506&lt;br /&gt;
         &lt;td&gt;1.8506&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)/(5*11*17)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13)/(5*11*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,171: Line 1,178:
         &lt;td&gt;1.5905&lt;br /&gt;
         &lt;td&gt;1.5905&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;*17)&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*11&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;6&lt;/span&gt;*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,181: Line 1,188:
         &lt;td&gt;1.4983&lt;br /&gt;
         &lt;td&gt;1.4983&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(3*5*7*11)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(3*5*7*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,191: Line 1,198:
         &lt;td&gt;1.4138&lt;br /&gt;
         &lt;td&gt;1.4138&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
         &lt;td&gt;(5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,201: Line 1,208:
         &lt;td&gt;1.3584&lt;br /&gt;
         &lt;td&gt;1.3584&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/(2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)&lt;br /&gt;
         &lt;td&gt;(3*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)/(2*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,211: Line 1,218:
         &lt;td&gt;1.0181&lt;br /&gt;
         &lt;td&gt;1.0181&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*7)/[(2*5)&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17]&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*7)/[(2*5)&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17]&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,221: Line 1,228:
         &lt;td&gt;0.8414&lt;br /&gt;
         &lt;td&gt;0.8414&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3*7&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(11&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
         &lt;td&gt;(2*3*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;)/(11&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;xenisma&lt;br /&gt;
         &lt;td&gt;xenisma&lt;br /&gt;
Line 1,231: Line 1,238:
         &lt;td&gt;0.7123&lt;br /&gt;
         &lt;td&gt;0.7123&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(11*13*17)/(2*3&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*5)&lt;br /&gt;
         &lt;td&gt;(11*13*17)/(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,241: Line 1,248:
         &lt;td&gt;0.6926&lt;br /&gt;
         &lt;td&gt;0.6926&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;)/(3*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;)/(3*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,251: Line 1,258:
         &lt;td&gt;0.6657&lt;br /&gt;
         &lt;td&gt;0.6657&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,261: Line 1,268:
         &lt;td&gt;0.3523&lt;br /&gt;
         &lt;td&gt;0.3523&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7*13)/(17&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*7*13)/(17&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,271: Line 1,278:
         &lt;td&gt;0.2969&lt;br /&gt;
         &lt;td&gt;0.2969&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;)/(7&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*17)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;6&lt;/span&gt;)/(7&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,281: Line 1,288:
         &lt;td&gt;0.1399&lt;br /&gt;
         &lt;td&gt;0.1399&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7*13*17)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*7*13*17)/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,291: Line 1,298:
         &lt;td&gt;0.1202&lt;br /&gt;
         &lt;td&gt;0.1202&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(7*11&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;6&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(7*11&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,301: Line 1,308:
         &lt;td&gt;0.0606&lt;br /&gt;
         &lt;td&gt;0.0606&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(13&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3*5*7*17)&lt;br /&gt;
         &lt;td&gt;(13&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*3*5*7*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,311: Line 1,318:
         &lt;td&gt;0.0555&lt;br /&gt;
         &lt;td&gt;0.0555&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(7&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*13)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*17&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;(7&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*13)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*17&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,321: Line 1,328:
         &lt;td&gt;0.0466&lt;br /&gt;
         &lt;td&gt;0.0466&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5*11*13&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(3&lt;span style="vertical-align: super;"&gt;7&lt;/span&gt;*17)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5*11*13&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;7&lt;/span&gt;*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,331: Line 1,338:
         &lt;td&gt;0.0089&lt;br /&gt;
         &lt;td&gt;0.0089&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*7&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5*11*13*17)&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*5*11*13*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;scintillisma&lt;br /&gt;
         &lt;td&gt;scintillisma&lt;br /&gt;
Line 1,341: Line 1,348:
         &lt;td&gt;0.0052&lt;br /&gt;
         &lt;td&gt;0.0052&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5*7&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,355: Line 1,362:
         &lt;td&gt;93.603&lt;br /&gt;
         &lt;td&gt;93.603&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;19/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;19/(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;undevicesimal semitone&lt;br /&gt;
         &lt;td&gt;undevicesimal semitone&lt;br /&gt;
Line 1,365: Line 1,372:
         &lt;td&gt;88.801&lt;br /&gt;
         &lt;td&gt;88.801&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/19&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5)/19&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;small undevicesimal semitone&lt;br /&gt;
         &lt;td&gt;small undevicesimal semitone&lt;br /&gt;
Line 1,385: Line 1,392:
         &lt;td&gt;30.642&lt;br /&gt;
         &lt;td&gt;30.642&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*19)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7)&lt;br /&gt;
         &lt;td&gt;(3*19)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,395: Line 1,402:
         &lt;td&gt;22.931&lt;br /&gt;
         &lt;td&gt;22.931&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)/(3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*19)/(3*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,405: Line 1,412:
         &lt;td&gt;22.631&lt;br /&gt;
         &lt;td&gt;22.631&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(7*11)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)&lt;br /&gt;
         &lt;td&gt;(7*11)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*19)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,415: Line 1,422:
         &lt;td&gt;18.128&lt;br /&gt;
         &lt;td&gt;18.128&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3)/(5*19)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*3)/(5*19)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,425: Line 1,432:
         &lt;td&gt;13.066&lt;br /&gt;
         &lt;td&gt;13.066&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(19*7)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*11)&lt;br /&gt;
         &lt;td&gt;(19*7)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,435: Line 1,442:
         &lt;td&gt;11.352&lt;br /&gt;
         &lt;td&gt;11.352&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*19)&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*19)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,445: Line 1,452:
         &lt;td&gt;10.154&lt;br /&gt;
         &lt;td&gt;10.154&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)/(2*5*17)&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*19)/(2*5*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,455: Line 1,462:
         &lt;td&gt;9.1358&lt;br /&gt;
         &lt;td&gt;9.1358&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*5*19)/(3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7)&lt;br /&gt;
         &lt;td&gt;(2*5*19)/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,465: Line 1,472:
         &lt;td&gt;8.3033&lt;br /&gt;
         &lt;td&gt;8.3033&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(11*19)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*13)&lt;br /&gt;
         &lt;td&gt;(11*19)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,495: Line 1,502:
         &lt;td&gt;4.3335&lt;br /&gt;
         &lt;td&gt;4.3335&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(3*7*19)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(3*7*19)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,505: Line 1,512:
         &lt;td&gt;3.8007&lt;br /&gt;
         &lt;td&gt;3.8007&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3*19)/(5*7*13)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3*19)/(5*7*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,515: Line 1,522:
         &lt;td&gt;3.6409&lt;br /&gt;
         &lt;td&gt;3.6409&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7*17)/(5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7*17)/(5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*19)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,525: Line 1,532:
         &lt;td&gt;3.501&lt;br /&gt;
         &lt;td&gt;3.501&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5*11)/(2*13*19)&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5*11)/(2*13*19)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,535: Line 1,542:
         &lt;td&gt;3.378&lt;br /&gt;
         &lt;td&gt;3.378&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;span style="vertical-align: super;"&gt;(3^3*19)/2^9&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*19)/2&lt;span style="vertical-align: super; font-size: 70%;"&gt;9&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;513th harmonic&lt;br /&gt;
         &lt;td&gt;513th harmonic&lt;br /&gt;
Line 1,559: Line 1,566:
         &lt;td&gt;73.681&lt;br /&gt;
         &lt;td&gt;73.681&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3)/23&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3)/23&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,569: Line 1,576:
         &lt;td&gt;38.051&lt;br /&gt;
         &lt;td&gt;38.051&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*23)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)&lt;br /&gt;
         &lt;td&gt;(2*23)/(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,579: Line 1,586:
         &lt;td&gt;25.274&lt;br /&gt;
         &lt;td&gt;25.274&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*23)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
         &lt;td&gt;(3*23)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,599: Line 1,606:
         &lt;td&gt;18.921&lt;br /&gt;
         &lt;td&gt;18.921&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23)/(7*13)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*23)/(7*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,619: Line 1,626:
         &lt;td&gt;10.7865&lt;br /&gt;
         &lt;td&gt;10.7865&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(7*23)/(2^5*5)&lt;br /&gt;
         &lt;td&gt;(7*23)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,629: Line 1,636:
         &lt;td&gt;10.720&lt;br /&gt;
         &lt;td&gt;10.720&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3^4)/(7*23)&lt;br /&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;)/(7*23)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,663: Line 1,670:
         &lt;td&gt;60.751&lt;br /&gt;
         &lt;td&gt;60.751&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;29/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)&lt;br /&gt;
         &lt;td&gt;29/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,693: Line 1,700:
         &lt;td&gt;19.786&lt;br /&gt;
         &lt;td&gt;19.786&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11)/(3*29)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*11)/(3*29)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,717: Line 1,724:
         &lt;td&gt;54.964&lt;br /&gt;
         &lt;td&gt;54.964&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;/31&lt;br /&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;/31&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;31st subharmonic&lt;br /&gt;
         &lt;td&gt;31st subharmonic&lt;br /&gt;
Line 1,727: Line 1,734:
         &lt;td&gt;27.700&lt;br /&gt;
         &lt;td&gt;27.700&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)/(2*31)&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*7)/(2*31)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,737: Line 1,744:
         &lt;td&gt;18.716&lt;br /&gt;
         &lt;td&gt;18.716&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*31)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23)&lt;br /&gt;
         &lt;td&gt;(3*31)/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*23)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,751: Line 1,758:
         &lt;td&gt;47.434&lt;br /&gt;
         &lt;td&gt;47.434&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;37/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;37/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,771: Line 1,778:
         &lt;td&gt;23.238&lt;br /&gt;
         &lt;td&gt;23.238&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(2*37)&lt;br /&gt;
         &lt;td&gt;(3*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/(2*37)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,785: Line 1,792:
         &lt;td&gt;42.749&lt;br /&gt;
         &lt;td&gt;42.749&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;41/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5)&lt;br /&gt;
         &lt;td&gt;41/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,805: Line 1,812:
         &lt;td&gt;21.242&lt;br /&gt;
         &lt;td&gt;21.242&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*41)/3&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(2*41)/3&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,829: Line 1,836:
         &lt;td&gt;39.800&lt;br /&gt;
         &lt;td&gt;39.800&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)/43&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*11)/43&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,873: Line 1,880:
         &lt;td&gt;36.448&lt;br /&gt;
         &lt;td&gt;36.448&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3)/47&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*3)/47&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,907: Line 1,914:
         &lt;td&gt;32.977&lt;br /&gt;
         &lt;td&gt;32.977&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;53/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)&lt;br /&gt;
         &lt;td&gt;53/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,917: Line 1,924:
         &lt;td&gt;32.360&lt;br /&gt;
         &lt;td&gt;32.360&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/53&lt;br /&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;)/53&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,941: Line 1,948:
         &lt;td&gt;29.097&lt;br /&gt;
         &lt;td&gt;29.097&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*5)/59&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3*5)/59&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,955: Line 1,962:
         &lt;td&gt;28.616&lt;br /&gt;
         &lt;td&gt;28.616&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;61/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*5)&lt;br /&gt;
         &lt;td&gt;61/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,989: Line 1,996:
         &lt;td&gt;25.648&lt;br /&gt;
         &lt;td&gt;25.648&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/67&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*17)/67&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 2,013: Line 2,020:
         &lt;td&gt;24.213&lt;br /&gt;
         &lt;td&gt;24.213&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/71&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/71&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 2,027: Line 2,034:
         &lt;td&gt;23.879&lt;br /&gt;
         &lt;td&gt;23.879&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;73/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;73/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 2,061: Line 2,068:
         &lt;td&gt;21.777&lt;br /&gt;
         &lt;td&gt;21.777&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5)/79&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;4&lt;/span&gt;*5)/79&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 2,085: Line 2,092:
         &lt;td&gt;20.734&lt;br /&gt;
         &lt;td&gt;20.734&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*7)/83&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*3*7)/83&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 2,099: Line 2,106:
         &lt;td&gt;19.562&lt;br /&gt;
         &lt;td&gt;19.562&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;89/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11)&lt;br /&gt;
         &lt;td&gt;89/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;3&lt;/span&gt;*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 2,109: Line 2,116:
         &lt;td&gt;19.344&lt;br /&gt;
         &lt;td&gt;19.344&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/89&lt;br /&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5)/89&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 2,123: Line 2,130:
         &lt;td&gt;17.940&lt;br /&gt;
         &lt;td&gt;17.940&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;97/(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3)&lt;br /&gt;
         &lt;td&gt;97/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;5&lt;/span&gt;*3)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 2,133: Line 2,140:
         &lt;td&gt;17.756&lt;br /&gt;
         &lt;td&gt;17.756&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/97&lt;br /&gt;
         &lt;td&gt;(2*7&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)/97&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 2,147: Line 2,154:
         &lt;td&gt;17.226&lt;br /&gt;
         &lt;td&gt;17.226&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;101/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;101/(2&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super; font-size: 70%;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Retrieved from "https://en.xen.wiki/w/List_of_superparticular_intervals"