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List of superparticular intervals

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=<span style="color: #800080;">List of Superparticular Intervals</span>= 

[[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.

In addition to names and cents values, the list below includes the factorization of each superparticular ratio as well as the largest prime involved. This is relevant when considering which intervals are characteristic of which [[harmonic limit]]s. [[36_35|36/35]], for instance, is an interval of the [[7-limit]], as it factors to (2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">2</span>)/(5*7), while 37/36 would belong to the 37-limit.

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

||~ Ratio ||~ Cents Value ||~ Factorization ||~ Prime Limit ||~ Name(s) ||
|| [[2_1|2/1]] || 1200.000 || 2/1 || 2 || (perfect) unison, unity, perfect prime, tonic, duple ||
|| [[3_2|3/2]] || 701.995 || 3/2 || 3 || [[perfect fifth]], 3rd harmonic (octave reduced), diapente ||
|| [[4_3|4/3]] || 498.045 || 2<span style="vertical-align: super;">2</span>/3 || 3 || perfect fourth, 3rd subharmonic (octave reduced), diatessaron ||
|| [[5_4|5/4]] || 386.314 || 5/2<span style="vertical-align: super;">2</span> || 5 || (classic) (5-limit) major third, 5th harmonic (octave reduced) ||
|| [[6_5|6/5]] || 315.641 || (2*3)/5 || 5 || (classic) (5-limit) minor third ||
|| [[7_6|7/6]] || 266.871 || 7/(2*3) || 7 || (septimal) subminor third, septimal minor third, augmented second ||
|| [[8_7|8/7]] || 231.174 || 2<span style="vertical-align: super;">3</span>/7 || 7 || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
|| [[9_8|9/8]] || 203.910 || 3<span style="vertical-align: super;">2</span>/2<span style="vertical-align: super;">3</span> || 3 || (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced) ||
|| [[10_9|10/9]] || 182.404 || (2*5)/3<span style="vertical-align: super;">2</span> || 5 || classic (whole) tone, classic major second, minor whole tone ||
|| [[11_10|11/10]] || 165.004 || 11/(2*5) || 11 || (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second ||
|| [[12_11|12/11]] || 150.637 || (2<span style="vertical-align: super;">2</span>*3)/11 || 11 || (small) (undecimal) neutral second, 3/4-tone ||
|| [[13_12|13/12]] || 138.573 || 13/(2<span style="vertical-align: super;">2</span>*3) || 13 || tridecimal 2/3-tone ||
|| [[14_13|14/13]] || 128.298 || (2*7)/13 || 13 || 2/3-tone, trienthird ||
|| [[15_14|15/14]] || 119.443 || (3*5)/(2*7) || 7 || septimal diatonic semitone ||
|| [[16_15|16/15]] || 111.713 || 2<span style="vertical-align: super;">4</span>/(3*5) || 5 || minor diatonic semitone, 15th subharmonic ||
|| [[17_16|17/16]] || 104.955 || 17/2<span style="vertical-align: super;">4</span> || 17 || 17th harmonic (octave reduced) ||
|| [[18_17|18/17]] || 98.955 || (2*3<span style="vertical-align: super;">2</span>)/17 || 17 || Arabic lute index finger ||
|| [[19_18|19/18]] || 93.603 || 19/(2*3<span style="vertical-align: super;">2</span>) || 19 || undevicesimal semitone ||
|| [[20_19|20/19]] || 88.801 || (2<span style="vertical-align: super;">2</span>*5)/19 || 19 || small undevicesimal semitone ||
|| [[21_20|21/20]] || 84.467 || (3*7)/(2<span style="vertical-align: super;">2</span>*5) || 7 || minor semitone, large septimal chromatic semitone ||
|| [[22_21|22/21]] || 80.537 || (2*11)/(3*7) || 11 || undecimal minor semitone ||
|| [[23_22|23/22]] || 76.956 || 23/(2*11) || 23 ||   ||
|| [[24_23|24/23]] || 73.681 || (2<span style="vertical-align: super;">3</span>*3)/23 || 23 ||   ||
|| [[25_24|25/24]] || 70.672 || 5<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">3</span>*3) || 5 || chroma, (classic) chromatic semitone, Zarlinian semitone ||
|| [[26_25|26/25]] || 67.900 || (2*13)/5<span style="vertical-align: super;">2</span> || 13 || tridecimal 1/3-tone ||
|| [[27_26|27/26]] || 65.337 || 3<span style="vertical-align: super;">3</span>/(2*13) || 13 || tridecimal comma ||
|| [[28_27|28/27]] || 62.961 || (2<span style="vertical-align: super;">2</span>*7)/3<span style="vertical-align: super;">3</span> || 7 || septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone ||
|| [[29_28|29/28]] || 60.751 || 29/(2<span style="vertical-align: super;">2</span>*7) || 29 ||   ||
|| [[30_29|30/29]] || 58.692 || (2*3*5)/29 || 29 ||   ||
|| [[31_30|31/30]] || 56.767 || 31/(2*3*5) || 31 ||   ||
|| [[32_31|32/31]] || 54.964 || 2<span style="vertical-align: super;">5</span>/31 || 31 || 31st subharmonic ||
|| [[33_32|33/32]] || 53.273 || (3*11)/2<span style="vertical-align: super;">5</span> || 11 || unidecimal quarter tone, unidecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced) ||
|| [[34_33|34/33]] || 51.682 || (2*17)/(3*33) || 17 ||   ||
|| [[35_34|35/34]] || 50.184 || (5*7)/(2*17) || 17 || septendecimal 1/4-tone ||
|| [[36_35|36/35]] || 48.770 || (2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">3</span>)/(5*7) || 7 || septimal quarter tone, septimal diesis ||
|| [[37_36|37/36]] || 47.434 || 37/(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">2</span>) || 37 ||   ||
|| [[38_37|38/37]] || 46.169 || (2*19)/37 || 37 ||   ||
|| [[39_38|39/38]] || 44.970 || (3*13)/(2*19) || 19 ||   ||
|| [[40_39|40/39]] || 43.831 || (2<span style="vertical-align: super;">3</span>*5)/(3*13) || 13 || tridecimal minor diesis ||
|| [[41_40|41/40]] || 42.749 || 41/(2<span style="vertical-align: super;">3</span>*5) || 41 ||   ||
|| [[42_41|42/41]] || 41.719 || (2*3*7)/41 || 41 ||   ||
|| [[43_42|43/42]] || 40.737 || 43/(2*3*7) || 43 ||   ||
|| [[44_43|44/43]] || 39.800 || (2<span style="vertical-align: super;">2</span>*11)/43 || 43 ||   ||
|| [[45_44|45/44]] || 38.906 || (3<span style="vertical-align: super;">2</span>*5)/(2<span style="vertical-align: super;">2</span>*11) || 11 || 1/5-tone ||
|| [[46_45|46/45]] || 38.051 || (2*23)/(3<span style="vertical-align: super;">2</span>*5) || 23 ||   ||
|| [[47_46|47/46]] || 37.232 || 47/(2*23) || 47 ||   ||
|| [[48_47|48/47]] || 36.448 || (2<span style="vertical-align: super;">4</span>*3)/47 || 47 ||   ||
|| [[49_48|49/48]] || 35.697 || 7<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">4</span>*3) || 7 || large septimal diesis, slendro diesis, septimal 1/6-tone ||
|| [[50_49|50/49]] || 34.976 || (2*5<span style="vertical-align: super;">2</span>)/7<span style="vertical-align: super;">2</span> || 7 || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma ||
|| [[51_50|51/50]] || 34.283 || (3*17)/(2*5<span style="vertical-align: super;">2</span>) || 17 || 17th-partial chroma ||
|| [[52_51|52/51]] || 33.617 || (2<span style="vertical-align: super;">2</span>*13)/(3*17) || 17 ||   ||
|| [[53_52|53/52]] || 32.977 || 53/(2<span style="vertical-align: super;">2</span>*13) || 53 ||   ||
|| [[54_53|54/53]] || 32.360 || (2*3<span style="vertical-align: super;">3</span>)/53 || 53 ||   ||
|| [[55_54|55/54]] || 31.767 || (5*11)/(2*3<span style="vertical-align: super;">3</span>) || 11 ||   ||
|| [[56_55|56/55]] || 31.194 || (2<span style="vertical-align: super;">3</span>*7)/(5*11) || 11 ||   ||
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Original HTML content:

<html><head><title>List of Superparticular Intervals</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="List of Superparticular Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #800080;">List of Superparticular Intervals</span></h1>
 <br />
<a class="wiki_link" href="/Superparticular">Superparticular</a> 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 <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a> and <a class="wiki_link" href="/OverToneSeries">Harmonic Series</a> music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio <a class="wiki_link" href="/21_20">21/20</a>. 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 <a class="wiki_link" href="/comma">comma</a>s are superparticular ratios.<br />
<br />
In addition to names and cents values, the list below includes the factorization of each superparticular ratio as well as the largest prime involved. This is relevant when considering which intervals are characteristic of which <a class="wiki_link" href="/harmonic%20limit">harmonic limit</a>s. <a class="wiki_link" href="/36_35">36/35</a>, for instance, is an interval of the <a class="wiki_link" href="/7-limit">7-limit</a>, as it factors to (2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">2</span>)/(5*7), while 37/36 would belong to the 37-limit.<br />
<br />
See also: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a>. Many of the names below come from <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/intervals.html" rel="nofollow">here</a>.<br />
<br />


<table class="wiki_table">
    <tr>
        <th>Ratio<br />
</th>
        <th>Cents Value<br />
</th>
        <th>Factorization<br />
</th>
        <th>Prime Limit<br />
</th>
        <th>Name(s)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/2_1">2/1</a><br />
</td>
        <td>1200.000<br />
</td>
        <td>2/1<br />
</td>
        <td>2<br />
</td>
        <td>(perfect) unison, unity, perfect prime, tonic, duple<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/3_2">3/2</a><br />
</td>
        <td>701.995<br />
</td>
        <td>3/2<br />
</td>
        <td>3<br />
</td>
        <td><a class="wiki_link" href="/perfect%20fifth">perfect fifth</a>, 3rd harmonic (octave reduced), diapente<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/4_3">4/3</a><br />
</td>
        <td>498.045<br />
</td>
        <td>2<span style="vertical-align: super;">2</span>/3<br />
</td>
        <td>3<br />
</td>
        <td>perfect fourth, 3rd subharmonic (octave reduced), diatessaron<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/5_4">5/4</a><br />
</td>
        <td>386.314<br />
</td>
        <td>5/2<span style="vertical-align: super;">2</span><br />
</td>
        <td>5<br />
</td>
        <td>(classic) (5-limit) major third, 5th harmonic (octave reduced)<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/6_5">6/5</a><br />
</td>
        <td>315.641<br />
</td>
        <td>(2*3)/5<br />
</td>
        <td>5<br />
</td>
        <td>(classic) (5-limit) minor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/7_6">7/6</a><br />
</td>
        <td>266.871<br />
</td>
        <td>7/(2*3)<br />
</td>
        <td>7<br />
</td>
        <td>(septimal) subminor third, septimal minor third, augmented second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/8_7">8/7</a><br />
</td>
        <td>231.174<br />
</td>
        <td>2<span style="vertical-align: super;">3</span>/7<br />
</td>
        <td>7<br />
</td>
        <td>(septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/9_8">9/8</a><br />
</td>
        <td>203.910<br />
</td>
        <td>3<span style="vertical-align: super;">2</span>/2<span style="vertical-align: super;">3</span><br />
</td>
        <td>3<br />
</td>
        <td>(Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/10_9">10/9</a><br />
</td>
        <td>182.404<br />
</td>
        <td>(2*5)/3<span style="vertical-align: super;">2</span><br />
</td>
        <td>5<br />
</td>
        <td>classic (whole) tone, classic major second, minor whole tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_10">11/10</a><br />
</td>
        <td>165.004<br />
</td>
        <td>11/(2*5)<br />
</td>
        <td>11<br />
</td>
        <td>(large) (undecimal) neutral second, 4/5-tone, Ptolemy's second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/12_11">12/11</a><br />
</td>
        <td>150.637<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*3)/11<br />
</td>
        <td>11<br />
</td>
        <td>(small) (undecimal) neutral second, 3/4-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13_12">13/12</a><br />
</td>
        <td>138.573<br />
</td>
        <td>13/(2<span style="vertical-align: super;">2</span>*3)<br />
</td>
        <td>13<br />
</td>
        <td>tridecimal 2/3-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/14_13">14/13</a><br />
</td>
        <td>128.298<br />
</td>
        <td>(2*7)/13<br />
</td>
        <td>13<br />
</td>
        <td>2/3-tone, trienthird<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/15_14">15/14</a><br />
</td>
        <td>119.443<br />
</td>
        <td>(3*5)/(2*7)<br />
</td>
        <td>7<br />
</td>
        <td>septimal diatonic semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/16_15">16/15</a><br />
</td>
        <td>111.713<br />
</td>
        <td>2<span style="vertical-align: super;">4</span>/(3*5)<br />
</td>
        <td>5<br />
</td>
        <td>minor diatonic semitone, 15th subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_16">17/16</a><br />
</td>
        <td>104.955<br />
</td>
        <td>17/2<span style="vertical-align: super;">4</span><br />
</td>
        <td>17<br />
</td>
        <td>17th harmonic (octave reduced)<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/18_17">18/17</a><br />
</td>
        <td>98.955<br />
</td>
        <td>(2*3<span style="vertical-align: super;">2</span>)/17<br />
</td>
        <td>17<br />
</td>
        <td>Arabic lute index finger<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/19_18">19/18</a><br />
</td>
        <td>93.603<br />
</td>
        <td>19/(2*3<span style="vertical-align: super;">2</span>)<br />
</td>
        <td>19<br />
</td>
        <td>undevicesimal semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/20_19">20/19</a><br />
</td>
        <td>88.801<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*5)/19<br />
</td>
        <td>19<br />
</td>
        <td>small undevicesimal semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/21_20">21/20</a><br />
</td>
        <td>84.467<br />
</td>
        <td>(3*7)/(2<span style="vertical-align: super;">2</span>*5)<br />
</td>
        <td>7<br />
</td>
        <td>minor semitone, large septimal chromatic semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/22_21">22/21</a><br />
</td>
        <td>80.537<br />
</td>
        <td>(2*11)/(3*7)<br />
</td>
        <td>11<br />
</td>
        <td>undecimal minor semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/23_22">23/22</a><br />
</td>
        <td>76.956<br />
</td>
        <td>23/(2*11)<br />
</td>
        <td>23<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/24_23">24/23</a><br />
</td>
        <td>73.681<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*3)/23<br />
</td>
        <td>23<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/25_24">25/24</a><br />
</td>
        <td>70.672<br />
</td>
        <td>5<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">3</span>*3)<br />
</td>
        <td>5<br />
</td>
        <td>chroma, (classic) chromatic semitone, Zarlinian semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/26_25">26/25</a><br />
</td>
        <td>67.900<br />
</td>
        <td>(2*13)/5<span style="vertical-align: super;">2</span><br />
</td>
        <td>13<br />
</td>
        <td>tridecimal 1/3-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/27_26">27/26</a><br />
</td>
        <td>65.337<br />
</td>
        <td>3<span style="vertical-align: super;">3</span>/(2*13)<br />
</td>
        <td>13<br />
</td>
        <td>tridecimal comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/28_27">28/27</a><br />
</td>
        <td>62.961<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*7)/3<span style="vertical-align: super;">3</span><br />
</td>
        <td>7<br />
</td>
        <td>septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/29_28">29/28</a><br />
</td>
        <td>60.751<br />
</td>
        <td>29/(2<span style="vertical-align: super;">2</span>*7)<br />
</td>
        <td>29<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/30_29">30/29</a><br />
</td>
        <td>58.692<br />
</td>
        <td>(2*3*5)/29<br />
</td>
        <td>29<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/31_30">31/30</a><br />
</td>
        <td>56.767<br />
</td>
        <td>31/(2*3*5)<br />
</td>
        <td>31<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/32_31">32/31</a><br />
</td>
        <td>54.964<br />
</td>
        <td>2<span style="vertical-align: super;">5</span>/31<br />
</td>
        <td>31<br />
</td>
        <td>31st subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/33_32">33/32</a><br />
</td>
        <td>53.273<br />
</td>
        <td>(3*11)/2<span style="vertical-align: super;">5</span><br />
</td>
        <td>11<br />
</td>
        <td>unidecimal quarter tone, unidecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/34_33">34/33</a><br />
</td>
        <td>51.682<br />
</td>
        <td>(2*17)/(3*33)<br />
</td>
        <td>17<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/35_34">35/34</a><br />
</td>
        <td>50.184<br />
</td>
        <td>(5*7)/(2*17)<br />
</td>
        <td>17<br />
</td>
        <td>septendecimal 1/4-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/36_35">36/35</a><br />
</td>
        <td>48.770<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">3</span>)/(5*7)<br />
</td>
        <td>7<br />
</td>
        <td>septimal quarter tone, septimal diesis<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/37_36">37/36</a><br />
</td>
        <td>47.434<br />
</td>
        <td>37/(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">2</span>)<br />
</td>
        <td>37<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/38_37">38/37</a><br />
</td>
        <td>46.169<br />
</td>
        <td>(2*19)/37<br />
</td>
        <td>37<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/39_38">39/38</a><br />
</td>
        <td>44.970<br />
</td>
        <td>(3*13)/(2*19)<br />
</td>
        <td>19<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/40_39">40/39</a><br />
</td>
        <td>43.831<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*5)/(3*13)<br />
</td>
        <td>13<br />
</td>
        <td>tridecimal minor diesis<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/41_40">41/40</a><br />
</td>
        <td>42.749<br />
</td>
        <td>41/(2<span style="vertical-align: super;">3</span>*5)<br />
</td>
        <td>41<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/42_41">42/41</a><br />
</td>
        <td>41.719<br />
</td>
        <td>(2*3*7)/41<br />
</td>
        <td>41<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/43_42">43/42</a><br />
</td>
        <td>40.737<br />
</td>
        <td>43/(2*3*7)<br />
</td>
        <td>43<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/44_43">44/43</a><br />
</td>
        <td>39.800<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*11)/43<br />
</td>
        <td>43<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/45_44">45/44</a><br />
</td>
        <td>38.906<br />
</td>
        <td>(3<span style="vertical-align: super;">2</span>*5)/(2<span style="vertical-align: super;">2</span>*11)<br />
</td>
        <td>11<br />
</td>
        <td>1/5-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/46_45">46/45</a><br />
</td>
        <td>38.051<br />
</td>
        <td>(2*23)/(3<span style="vertical-align: super;">2</span>*5)<br />
</td>
        <td>23<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/47_46">47/46</a><br />
</td>
        <td>37.232<br />
</td>
        <td>47/(2*23)<br />
</td>
        <td>47<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/48_47">48/47</a><br />
</td>
        <td>36.448<br />
</td>
        <td>(2<span style="vertical-align: super;">4</span>*3)/47<br />
</td>
        <td>47<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49_48">49/48</a><br />
</td>
        <td>35.697<br />
</td>
        <td>7<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">4</span>*3)<br />
</td>
        <td>7<br />
</td>
        <td>large septimal diesis, slendro diesis, septimal 1/6-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/50_49">50/49</a><br />
</td>
        <td>34.976<br />
</td>
        <td>(2*5<span style="vertical-align: super;">2</span>)/7<span style="vertical-align: super;">2</span><br />
</td>
        <td>7<br />
</td>
        <td>septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/51_50">51/50</a><br />
</td>
        <td>34.283<br />
</td>
        <td>(3*17)/(2*5<span style="vertical-align: super;">2</span>)<br />
</td>
        <td>17<br />
</td>
        <td>17th-partial chroma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/52_51">52/51</a><br />
</td>
        <td>33.617<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*13)/(3*17)<br />
</td>
        <td>17<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/53_52">53/52</a><br />
</td>
        <td>32.977<br />
</td>
        <td>53/(2<span style="vertical-align: super;">2</span>*13)<br />
</td>
        <td>53<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/54_53">54/53</a><br />
</td>
        <td>32.360<br />
</td>
        <td>(2*3<span style="vertical-align: super;">3</span>)/53<br />
</td>
        <td>53<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/55_54">55/54</a><br />
</td>
        <td>31.767<br />
</td>
        <td>(5*11)/(2*3<span style="vertical-align: super;">3</span>)<br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/56_55">56/55</a><br />
</td>
        <td>31.194<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*7)/(5*11)<br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
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        <td><br />
</td>
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</td>
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</td>
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</td>
        <td><br />
</td>
    </tr>
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        <td><br />
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        <td><br />
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        <td><br />
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        <td><br />
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</table>

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