Gallery of just intervals: Difference between revisions

Revision as of 20:40, 6 July 2012

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author JosephRuhf and made on 2012-07-06 20:40:15 UTC.

The original revision id was 350984630.

The revision comment was:

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

Original Wikitext content:

[[toc|flat]]
----
=Introduction= 

In [[JustIntonation|Just Intonation]], a musical interval is specified as a ratio of two frequencies.. When two (or more) pitches are sounded that are in simple proportions to one another, there is a "fusing" quality to the sound which is often described as pleasing; hence the interest in tuning the pitches of musical systems according to such proportions. There is much debate as to what "consonance" means in a musical system, but in Just Intonation, it is generally assumed that lower numbers in frequency ratios lead to greater consonance. In the actual performance of a piece of music, the number of factors involved are enormous, and it is not often helpful to reduce a musical experience to a one-dimensional description of "consonance versus dissonance." Hence the need for this gallery, to give life to conversation about what an interval means beyond the numerical description: "5/3" or "21/16" or what have you.

What follows is a Gallery of Just Intervals in ascending order from 1/1 to 2/1 and beyond. No such list could possibly be complete (as there are infinite possible ratios), so please add intervals of interest as you see fit. Any rational interval is welcome, as long as the wiki author has some interest in it. Contributions to an interval's lore could include: descriptions of common usage, technical notes, poetry, links, reservations, complaints, chords or compositions that feature it, edos that approximate it, intervals that are functionally (or emotionally) related to it, nicknames, love letters, fan art, etc. If your contribution is unconventional, feel free to sign your name to it.

This page lists links to dedicated pages for each interval. Wiki page names are formatted "n_d" (where n is the numerator and d is the denominator of the interval) because both colons and slashes cannot be part of page names on wikispaces, but the links as they appear on the page are in the form n/d.

----

=Gallery of Just Intervals= 

See also [[List of Superparticular Intervals]] and [[http://www.huygens-fokker.org/docs/intervals.html|List of intervals (Huygens-Fokker foundation)]]

||~ frequency ratio ||~ cents value 
(six decimal places) ||~ some common names ||
|| [[1_1|1/1]] || 0 || unison, unity, perfect prime, tonic ||
|| [[32805_32768|32805/32768]] || 1.95372 || schisma ||
|| [[100_99|100/99]] || 17.399484 || Ptolemy's comma ||
|| [[81_80|81/80]] || 21.506286 || syntonic comma, Didymus comma ||
|| [[531441_524288|531441/524288]] || 23.46001 || Pythagorean comma, ditonic comma ||
|| [[65_64|65/64]] || 26.841376 || 13th-partial chroma ||
|| [[64_63|64/63]] || 27.264092 || septimal comma, Archytas' comma ||
|| [[50_49|50/49]] || 34.975615 || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis ||
|| [[49_48|49/48]] || 35.696812 || large septimal diesis, slendro diesis ||
|| [[45_44|45/44]] || 38.905773 || undecimal 1/5th tone ||
|| [[525_512|525/512]] || 43.408335 || Avicenna's enharmonic diesis ||
|| [[36_35|36/35]] || 48.770381 || septimal quarter tone ||
|| [[100_97|100/97]] || 52.732017 || shrutar quarter tone ||
|| [[33_32|33/32]] || 53.272943 || undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, octave reduced 33rd harmonic ||
|| [[28_27|28/27]] || 62.960904 || septimal chroma, small septimal chromatic semitone ||
|| [[25_24|25/24]] || 70.672427 || chroma, chromatic semitone, Zarlinian semitone ||
|| [[68_65|68/65]] || 78.114034 || valentine semitone ||
|| [[22_21|22/21]] || 80.537035 || undecimal minor semitone ||
|| [[64_61|64/61]] || 83.115195 || harry minor semitone ||
|| [[21_20|21/20]] || 84.467193 || minor semitone, large septimal chromatic semitone ||
|| [[256_243|256/243]] || 90.224996 || Pythagorean limma, Pythagorean minor second ||
|| [[135_128|135/128]] || 92.178716 || major limma ||
|| [[18_17|18/17]] || 98.954592 || small septendecimal semitone, Arabic lute index finger ||
|| [[17_16|17/16]] || 104.95541 || large septendecimal semitone, octave reduced 17th harmonic ||
|| [[16_15|16/15]] || 111.731285 || diatonic semitone, classic minor second, octave reduced 15th subharmonic ||
|| [[2187_2048|2187/2048]] || 113.685006 || apotome ||
|| [[15_14|15/14]] || 119.442808 || septimal diatonic semitone ||
|| [[14_13|14/13]] || 128.298245 || 2/3-tone, trienthird ||
|| [[27_25|27/25]] || 133.237575 || large limma ||
|| [[13_12|13/12]] || 138.572661 || tridecimal 2/3-tone ||
|| [[243_224|243/224]] || 140.949098 || septimal chromatic 7/6-tone ||
|| [[12_11|12/11]] || 150.637059 || small undecimal neutral second, 3/4-tone ||
|| [[35_32|35/32]] || 155.13962 || septimal neutral second ||
|| [[78_71|78/71]] || 162.786119 || porcupine neutral second ||
|| [[11_10|11/10]] || 165.004228 || large undecimal neutral second, 4/5-tone, Ptolemy's second ||
|| [[54_49|54/49]] || 168.21319 || Zalzal's mujannab ||
|| [[10_9|10/9]] || 182.403712 || minor whole tone ||
|| [[28_25|28/25]] || 196.198479 || middle second ||
|| [[9_8|9/8]] || 203.910002 || major whole tone, Pythagorean tone, octave reduced 9th harmonic ||
|| [[17_15|17/15]] || 216.686695 || septendecimal whole tone ||
|| [[8_7|8/7]] || 231.174094 || supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
|| [[15_13|15/13]] || 247.741053 || semifourth ||
|| [[22_19|22/19]] || 253.804926 || minimal minor third, godzilla third ||
|| [[7_6|7/6]] || 266.870906 || subminor third, septimal minor third, augmented second ||
|| [[62_53|62/53]] || 271.531027 || orwell subminor third ||
|| [[20_17|20/17]] || 281.358304 || septendecimal augmented second, septendecimal minor third ||
|| [[13_11|13/11]] || 289.209179 || tridecimal minor third ||
|| [[32_27|32/27]] || 294.134997 || Pythagorean minor third, octave reduced 27th subharmonic ||
|| [[19_16|19/16]] || 297.513016 || otonal minor third, octave reduced 19th harmonic ||
|| [[25_21|25/21]] || 301.84652 || quasi-tempered minor third ||
|| [[61_51|61/51]] || 309.974395 || myna third ||
|| [[6_5|6/5]] || 315.641287 || minor third ||
|| [[35_29|35/29]] || 325.562426 || doublewide minor third ||
|| [[17_14|17/14]] || 336.129503 || septendecimal supraminor third ||
|| [[73_60|73/60]] || 339.520756 || amity supraminor third ||
|| [[11_9|11/9]] || 347.40794 || undecimal neutral third ||
|| [[60_49|60/49]] || 350.616902 || smaller septimal neutral third ||
|| [[49_40|49/40]] || 351.338099 || larger septimal neutral third ||
|| [[16_13|16/13]] || 359.472338 || tridecimal neutral third ||
|| [[56_45|56/45]] || 378.602191 || narrow perde segah ||
|| [[71_57|71/57]] || 380.228526 || witchcraft major third ||
|| [[76_61|76/61]] || 380.628211 || magic major third ||
|| [[5_4|5/4]] || 386.313714 || major third, octave reduced 5th harmonic ||
|| [[81_64|81/64]] || 407.820003 || Pythagorean major third, octave reduced 81st harmonic ||
|| [[14_11|14/11]] || 417.507964 || undecimal major third, undecimal diminished fourth ||
|| [[32_25|32/25]] || 427.372572 || classic diminished fourth ||
|| [[9_7|9/7]] || 435.084095 || supermajor third, septimal major third, diminished fourth ||
|| [[31_24|31/24]] || 443.080572 || sensi supermajor third ||
|| [[22_17|22/17]] || 446.362533 || septendecimal supermajor third ||
|| [[35_27|35/27]] || 449.274618 || semi-diminished fourth ||
|| [[13_10|13/10]] || 454.213948 || Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramajor third ||
|| [[64_49|64/49]] || 462.348187 || septatonic major third ||
|| [[17_13|17/13]] || 464.427748 || septendecimal sub-fourth ||
|| [[21_16|21/16]] || 470.780907 || sub-fourth, narrow fourth, augmented third, octave reduced 21st harmonic ||
|| [[4_3|4/3]] || 498.044999 || perfect fourth, octave reduced 3rd subharmonic, diatessaron ||
|| [[27_20|27/20]] || 519.551289 || acute fourth ||
|| [[49_36|49/36]] || 533.741811 || Arabic lute acute fourth ||
|| [[15_11|15/11]] || 536.950772 || undecimal augmented fourth, subaugmented fourth ||
|| [[48_35|48/35]] || 546.815381 || septimal super-fourth ||
|| [[11_8|11/8]] || 551.317942 || super-fourth, undecimal semi-augmented fourth, octave reduced 11th harmonic or harmonic 11th, Alphorn-Fa ||
|| [[18_13|18/13]] || 563.38234 || tridecimal augmented fourth ||
|| [[25_18|25/18]] || 568.717426 || classic augmented fourth, pental augmented fourth ||
|| [[7_5|7/5]] || 582.512193 || augmented fourth, septimal tritone, Huygen's tritone ||
|| [[24_17|24/17]] || 596.999591 || smaller septendecimal tritone ||
|| [[17_12|17/12]] || 603.000409 || larger septendecimal tritone ||
|| [[10_7|10/7]] || 617.487807 || diminished fifth, Euler's tritone, superaugmented fourth ||
|| [[36_25|36/25]] || 631.282574 || pental augmented fifth, classic augmented fifth ||
|| [[13_9|13/9]] || 636.61766 || tridecimal diminished fifth ||
|| [[16_11|16/11]] || 648.682058 || sub-fifth, undecimal semi-diminished fifth, 11th subharmonic (octave reduced) ||
|| [[35_24|35/24]] || 653.184619 || septimal sub-fifth ||
|| [[22_15|22/15]] || 663.049228 || undecimal diminished fifth, semidiminished fifth ||
|| [[72_49|72/49]] || 666.258889 ||   ||
|| [[40_27|40/27]] || 680.448711 || grave fifth ||
|| [[Just perfect fifth|3/2]] || 701.955001 || [[perfect fifth]], octave reduced 3rd harmonic, diapente ||
|| [[32_21|32/21]] || 729.219093 || super-fifth, wide fifth, diminished sixth, octave reduced 21st subharmonic ||
|| [[26_17|26/17]] || 735.572252 || septendecimal super-fifth ||
|| [[49_32|49/32]] || 737.651813 ||   ||
|| [[20_13|20/13]] || 745.786052 || Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth, tridecimal ultraminor sixth ||
|| [[17_11|17/11]] || 753.637467 || septendecimal subminor sixth ||
|| [[14_9|14/9]] || 764.915905 || subminor sixth, septimal minor sixth, augmented fifth ||
|| [[25_16|25/16]] || 772.627428 ||   ||
|| [[11_7|11/7]] || 782.492036 || undecimal subminor sixth, undecimal augmented fifth ||
|| [[8_5|8/5]] || 813.686286 || minor sixth, octave reduced 5th subharmonic ||
|| [[13_8|13/8]] || 840.527662 || tridecimal neutral sixth ||
|| [[80_49|80/49]] || 848.661901 ||   ||
|| [[49_30|49/30]] || 849.383198 ||   ||
|| [[18_11|18/11]] || 852.59216 || undecimal neutral sixth ||
|| [[28_17|28/17]] || 863.870497 || septendecimal submajor sixth ||
|| [[5_3|5/3]] || 884.358713 || major sixth ||
|| [[42_25|42/25]] || 898.15348 ||   ||
|| [[27_16|27/16]] || 905.865003 || Pythagorean major sixth, octave reduced 27th harmonic ||
|| [[22_13|22/13]] || 910.790821 || tridecimal major sixth ||
|| [[17_10|17/10]] || 918.641696 || septendecimal diminished seventh, septendecimal major sixth ||
|| [[12_7|12/7]] || 933.129094 || supermajor sixth, septimal major sixth, diminished seventh ||
|| [[26_15|26/15]] || 952.258947 || semitwelfth ||
|| [[7_4|7/4]] || 968.825906 || subminor seventh, harmonic seventh, augmented sixth, octave reduced 7th harmonic ||
|| [[225_128|225/128]] || 976.537429 || marvel five-limit harmonic seventh ||
|| [[30_17|30/17]] || 983.313305 || septendecimal minor seventh ||
|| [[16_9|16/9]] || 996.089998 || Pythagorean minor seventh, small minor seventh, octave reduced 9th subharmonic ||
|| [[25_14|25/14]] || 1003.801521 ||   ||
|| [[9_5|9/5]] || 1017.596288 || minor seventh, large minor seventh ||
|| [[20_11|20/11]] || 1034.995772 || undecimal minor seventh, small undecimal neutral seventh ||
|| [[64_35|64/35]] || 1044.86038 ||   ||
|| [[11_6|11/6]] || 1049.362941 || undecimal neutral seventh, 21/4-tone ||
|| [[24_13|24/13]] || 1061.427339 || tridecimal neutral seventh ||
|| [[13_7|13/7]] || 1071.701755 || 16/3-tone ||
|| [[28_15|28/15]] || 1080.557192 || grave major seventh ||
|| [[15_8|15/8]] || 1088.268715 || major seventh, just major seventh, octave reduced 15th harmonic ||
|| [[32_17|32/17]] || 1095.04459 || small septendecimal major seventh, octave-reduced 17th subharmonic ||
|| [[17_9|17/9]] || 1101.045408 || large septendecimal major seventh ||
|| [[243_128|243/128]] || 1109.775004 || Pythagorean major seventh ||
|| [[40_21|40/21]] || 1115.532907 || acute major seventh ||
|| [[61_32|61/32]] || 1116.884905 || octave reduced 61st harmonic ||
|| [[48_25|48/25]] || 1129.327573 ||   ||
|| [[64_33|64/33]] || 1146.727057 || octave reduced 33rd subharmonic ||
|| [[35_18|35/18]] || 1151.239619 ||   ||
|| [[96_49|96/49]] || 1164.303188 ||   ||
|| [[49_25|49/25]] || 1165.024385 ||   ||
|| [[160_81|160/81]] || 1178.493814 || octave minus syntonic comma ||
|| [[Octave|2/1]] || 1200 || octave, diapason ||

=Links= 
[[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt|Regions of the Interval Spectrum]] by Margo Schulter [[http://www.webcitation.org/5xeoz4zmC|Permalink]]
[[http://www.huygens-fokker.org/docs/intervals.html|Manuel Op de Coul interval list]]
[[http://www.kylegann.com/Octave.html|Anantomy of an Octave]] by Kyle Gann
<span style="display: block; height: 1px; left: 0px; overflow-x: hidden; overflow-y: hidden; position: absolute; top: 1754px; width: 1px;">1.9537207879341594002771772863067</span>

Original HTML content:

<html><head><title>Gallery of Just Intervals</title></head><body><!-- ws:start:WikiTextTocRule:6:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#Introduction">Introduction</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Gallery of Just Intervals">Gallery of Just Intervals</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#Links">Links</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: -->
<!-- ws:end:WikiTextTocRule:10 --><hr />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:0 -->Introduction</h1>
 <br />
In <a class="wiki_link" href="/JustIntonation">Just Intonation</a>, a musical interval is specified as a ratio of two frequencies.. When two (or more) pitches are sounded that are in simple proportions to one another, there is a &quot;fusing&quot; quality to the sound which is often described as pleasing; hence the interest in tuning the pitches of musical systems according to such proportions. There is much debate as to what &quot;consonance&quot; means in a musical system, but in Just Intonation, it is generally assumed that lower numbers in frequency ratios lead to greater consonance. In the actual performance of a piece of music, the number of factors involved are enormous, and it is not often helpful to reduce a musical experience to a one-dimensional description of &quot;consonance versus dissonance.&quot; Hence the need for this gallery, to give life to conversation about what an interval means beyond the numerical description: &quot;5/3&quot; or &quot;21/16&quot; or what have you.<br />
<br />
What follows is a Gallery of Just Intervals in ascending order from 1/1 to 2/1 and beyond. No such list could possibly be complete (as there are infinite possible ratios), so please add intervals of interest as you see fit. Any rational interval is welcome, as long as the wiki author has some interest in it. Contributions to an interval's lore could include: descriptions of common usage, technical notes, poetry, links, reservations, complaints, chords or compositions that feature it, edos that approximate it, intervals that are functionally (or emotionally) related to it, nicknames, love letters, fan art, etc. If your contribution is unconventional, feel free to sign your name to it.<br />
<br />
This page lists links to dedicated pages for each interval. Wiki page names are formatted &quot;n_d&quot; (where n is the numerator and d is the denominator of the interval) because both colons and slashes cannot be part of page names on wikispaces, but the links as they appear on the page are in the form n/d.<br />
<br />
<hr />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Gallery of Just Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Gallery of Just Intervals</h1>
 <br />
See also <a class="wiki_link" href="/List%20of%20Superparticular%20Intervals">List of Superparticular Intervals</a> and <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/intervals.html" rel="nofollow">List of intervals (Huygens-Fokker foundation)</a><br />
<br />


<table class="wiki_table">
    <tr>
        <th>frequency ratio<br />
</th>
        <th>cents value <br />
(six decimal places)<br />
</th>
        <th>some common names<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/1_1">1/1</a><br />
</td>
        <td>0<br />
</td>
        <td>unison, unity, perfect prime, tonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/32805_32768">32805/32768</a><br />
</td>
        <td>1.95372<br />
</td>
        <td>schisma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/100_99">100/99</a><br />
</td>
        <td>17.399484<br />
</td>
        <td>Ptolemy's comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/81_80">81/80</a><br />
</td>
        <td>21.506286<br />
</td>
        <td>syntonic comma, Didymus comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/531441_524288">531441/524288</a><br />
</td>
        <td>23.46001<br />
</td>
        <td>Pythagorean comma, ditonic comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/65_64">65/64</a><br />
</td>
        <td>26.841376<br />
</td>
        <td>13th-partial chroma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/64_63">64/63</a><br />
</td>
        <td>27.264092<br />
</td>
        <td>septimal comma, Archytas' comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/50_49">50/49</a><br />
</td>
        <td>34.975615<br />
</td>
        <td>septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49_48">49/48</a><br />
</td>
        <td>35.696812<br />
</td>
        <td>large septimal diesis, slendro diesis<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/45_44">45/44</a><br />
</td>
        <td>38.905773<br />
</td>
        <td>undecimal 1/5th tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/525_512">525/512</a><br />
</td>
        <td>43.408335<br />
</td>
        <td>Avicenna's enharmonic diesis<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/36_35">36/35</a><br />
</td>
        <td>48.770381<br />
</td>
        <td>septimal quarter tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/100_97">100/97</a><br />
</td>
        <td>52.732017<br />
</td>
        <td>shrutar quarter tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/33_32">33/32</a><br />
</td>
        <td>53.272943<br />
</td>
        <td>undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, octave reduced 33rd harmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/28_27">28/27</a><br />
</td>
        <td>62.960904<br />
</td>
        <td>septimal chroma, small septimal chromatic semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/25_24">25/24</a><br />
</td>
        <td>70.672427<br />
</td>
        <td>chroma, chromatic semitone, Zarlinian semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/68_65">68/65</a><br />
</td>
        <td>78.114034<br />
</td>
        <td>valentine semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/22_21">22/21</a><br />
</td>
        <td>80.537035<br />
</td>
        <td>undecimal minor semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/64_61">64/61</a><br />
</td>
        <td>83.115195<br />
</td>
        <td>harry minor semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/21_20">21/20</a><br />
</td>
        <td>84.467193<br />
</td>
        <td>minor semitone, large septimal chromatic semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/256_243">256/243</a><br />
</td>
        <td>90.224996<br />
</td>
        <td>Pythagorean limma, Pythagorean minor second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/135_128">135/128</a><br />
</td>
        <td>92.178716<br />
</td>
        <td>major limma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/18_17">18/17</a><br />
</td>
        <td>98.954592<br />
</td>
        <td>small septendecimal semitone, Arabic lute index finger<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_16">17/16</a><br />
</td>
        <td>104.95541<br />
</td>
        <td>large septendecimal semitone, octave reduced 17th harmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/16_15">16/15</a><br />
</td>
        <td>111.731285<br />
</td>
        <td>diatonic semitone, classic minor second, octave reduced 15th subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/2187_2048">2187/2048</a><br />
</td>
        <td>113.685006<br />
</td>
        <td>apotome<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/15_14">15/14</a><br />
</td>
        <td>119.442808<br />
</td>
        <td>septimal diatonic semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/14_13">14/13</a><br />
</td>
        <td>128.298245<br />
</td>
        <td>2/3-tone, trienthird<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/27_25">27/25</a><br />
</td>
        <td>133.237575<br />
</td>
        <td>large limma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13_12">13/12</a><br />
</td>
        <td>138.572661<br />
</td>
        <td>tridecimal 2/3-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/243_224">243/224</a><br />
</td>
        <td>140.949098<br />
</td>
        <td>septimal chromatic 7/6-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/12_11">12/11</a><br />
</td>
        <td>150.637059<br />
</td>
        <td>small undecimal neutral second, 3/4-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/35_32">35/32</a><br />
</td>
        <td>155.13962<br />
</td>
        <td>septimal neutral second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/78_71">78/71</a><br />
</td>
        <td>162.786119<br />
</td>
        <td>porcupine neutral second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_10">11/10</a><br />
</td>
        <td>165.004228<br />
</td>
        <td>large undecimal neutral second, 4/5-tone, Ptolemy's second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/54_49">54/49</a><br />
</td>
        <td>168.21319<br />
</td>
        <td>Zalzal's mujannab<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/10_9">10/9</a><br />
</td>
        <td>182.403712<br />
</td>
        <td>minor whole tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/28_25">28/25</a><br />
</td>
        <td>196.198479<br />
</td>
        <td>middle second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/9_8">9/8</a><br />
</td>
        <td>203.910002<br />
</td>
        <td>major whole tone, Pythagorean tone, octave reduced 9th harmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_15">17/15</a><br />
</td>
        <td>216.686695<br />
</td>
        <td>septendecimal whole tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/8_7">8/7</a><br />
</td>
        <td>231.174094<br />
</td>
        <td>supermajor second, septimal whole tone, diminished third, 7th subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/15_13">15/13</a><br />
</td>
        <td>247.741053<br />
</td>
        <td>semifourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/22_19">22/19</a><br />
</td>
        <td>253.804926<br />
</td>
        <td>minimal minor third, godzilla third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/7_6">7/6</a><br />
</td>
        <td>266.870906<br />
</td>
        <td>subminor third, septimal minor third, augmented second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/62_53">62/53</a><br />
</td>
        <td>271.531027<br />
</td>
        <td>orwell subminor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/20_17">20/17</a><br />
</td>
        <td>281.358304<br />
</td>
        <td>septendecimal augmented second, septendecimal minor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13_11">13/11</a><br />
</td>
        <td>289.209179<br />
</td>
        <td>tridecimal minor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/32_27">32/27</a><br />
</td>
        <td>294.134997<br />
</td>
        <td>Pythagorean minor third, octave reduced 27th subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/19_16">19/16</a><br />
</td>
        <td>297.513016<br />
</td>
        <td>otonal minor third, octave reduced 19th harmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/25_21">25/21</a><br />
</td>
        <td>301.84652<br />
</td>
        <td>quasi-tempered minor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/61_51">61/51</a><br />
</td>
        <td>309.974395<br />
</td>
        <td>myna third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/6_5">6/5</a><br />
</td>
        <td>315.641287<br />
</td>
        <td>minor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/35_29">35/29</a><br />
</td>
        <td>325.562426<br />
</td>
        <td>doublewide minor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_14">17/14</a><br />
</td>
        <td>336.129503<br />
</td>
        <td>septendecimal supraminor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/73_60">73/60</a><br />
</td>
        <td>339.520756<br />
</td>
        <td>amity supraminor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_9">11/9</a><br />
</td>
        <td>347.40794<br />
</td>
        <td>undecimal neutral third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/60_49">60/49</a><br />
</td>
        <td>350.616902<br />
</td>
        <td>smaller septimal neutral third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49_40">49/40</a><br />
</td>
        <td>351.338099<br />
</td>
        <td>larger septimal neutral third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/16_13">16/13</a><br />
</td>
        <td>359.472338<br />
</td>
        <td>tridecimal neutral third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/56_45">56/45</a><br />
</td>
        <td>378.602191<br />
</td>
        <td>narrow perde segah<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/71_57">71/57</a><br />
</td>
        <td>380.228526<br />
</td>
        <td>witchcraft major third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/76_61">76/61</a><br />
</td>
        <td>380.628211<br />
</td>
        <td>magic major third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/5_4">5/4</a><br />
</td>
        <td>386.313714<br />
</td>
        <td>major third, octave reduced 5th harmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/81_64">81/64</a><br />
</td>
        <td>407.820003<br />
</td>
        <td>Pythagorean major third, octave reduced 81st harmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/14_11">14/11</a><br />
</td>
        <td>417.507964<br />
</td>
        <td>undecimal major third, undecimal diminished fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/32_25">32/25</a><br />
</td>
        <td>427.372572<br />
</td>
        <td>classic diminished fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/9_7">9/7</a><br />
</td>
        <td>435.084095<br />
</td>
        <td>supermajor third, septimal major third, diminished fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/31_24">31/24</a><br />
</td>
        <td>443.080572<br />
</td>
        <td>sensi supermajor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/22_17">22/17</a><br />
</td>
        <td>446.362533<br />
</td>
        <td>septendecimal supermajor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/35_27">35/27</a><br />
</td>
        <td>449.274618<br />
</td>
        <td>semi-diminished fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13_10">13/10</a><br />
</td>
        <td>454.213948<br />
</td>
        <td>Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramajor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/64_49">64/49</a><br />
</td>
        <td>462.348187<br />
</td>
        <td>septatonic major third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_13">17/13</a><br />
</td>
        <td>464.427748<br />
</td>
        <td>septendecimal sub-fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/21_16">21/16</a><br />
</td>
        <td>470.780907<br />
</td>
        <td>sub-fourth, narrow fourth, augmented third, octave reduced 21st harmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/4_3">4/3</a><br />
</td>
        <td>498.044999<br />
</td>
        <td>perfect fourth, octave reduced 3rd subharmonic, diatessaron<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/27_20">27/20</a><br />
</td>
        <td>519.551289<br />
</td>
        <td>acute fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49_36">49/36</a><br />
</td>
        <td>533.741811<br />
</td>
        <td>Arabic lute acute fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/15_11">15/11</a><br />
</td>
        <td>536.950772<br />
</td>
        <td>undecimal augmented fourth, subaugmented fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/48_35">48/35</a><br />
</td>
        <td>546.815381<br />
</td>
        <td>septimal super-fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_8">11/8</a><br />
</td>
        <td>551.317942<br />
</td>
        <td>super-fourth, undecimal semi-augmented fourth, octave reduced 11th harmonic or harmonic 11th, Alphorn-Fa<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/18_13">18/13</a><br />
</td>
        <td>563.38234<br />
</td>
        <td>tridecimal augmented fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/25_18">25/18</a><br />
</td>
        <td>568.717426<br />
</td>
        <td>classic augmented fourth, pental augmented fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/7_5">7/5</a><br />
</td>
        <td>582.512193<br />
</td>
        <td>augmented fourth, septimal tritone, Huygen's tritone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/24_17">24/17</a><br />
</td>
        <td>596.999591<br />
</td>
        <td>smaller septendecimal tritone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_12">17/12</a><br />
</td>
        <td>603.000409<br />
</td>
        <td>larger septendecimal tritone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/10_7">10/7</a><br />
</td>
        <td>617.487807<br />
</td>
        <td>diminished fifth, Euler's tritone, superaugmented fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/36_25">36/25</a><br />
</td>
        <td>631.282574<br />
</td>
        <td>pental augmented fifth, classic augmented fifth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13_9">13/9</a><br />
</td>
        <td>636.61766<br />
</td>
        <td>tridecimal diminished fifth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/16_11">16/11</a><br />
</td>
        <td>648.682058<br />
</td>
        <td>sub-fifth, undecimal semi-diminished fifth, 11th subharmonic (octave reduced)<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/35_24">35/24</a><br />
</td>
        <td>653.184619<br />
</td>
        <td>septimal sub-fifth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/22_15">22/15</a><br />
</td>
        <td>663.049228<br />
</td>
        <td>undecimal diminished fifth, semidiminished fifth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/72_49">72/49</a><br />
</td>
        <td>666.258889<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/40_27">40/27</a><br />
</td>
        <td>680.448711<br />
</td>
        <td>grave fifth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/Just%20perfect%20fifth">3/2</a><br />
</td>
        <td>701.955001<br />
</td>
        <td><a class="wiki_link" href="/perfect%20fifth">perfect fifth</a>, octave reduced 3rd harmonic, diapente<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/32_21">32/21</a><br />
</td>
        <td>729.219093<br />
</td>
        <td>super-fifth, wide fifth, diminished sixth, octave reduced 21st subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/26_17">26/17</a><br />
</td>
        <td>735.572252<br />
</td>
        <td>septendecimal super-fifth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49_32">49/32</a><br />
</td>
        <td>737.651813<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/20_13">20/13</a><br />
</td>
        <td>745.786052<br />
</td>
        <td>Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth, tridecimal ultraminor sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_11">17/11</a><br />
</td>
        <td>753.637467<br />
</td>
        <td>septendecimal subminor sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/14_9">14/9</a><br />
</td>
        <td>764.915905<br />
</td>
        <td>subminor sixth, septimal minor sixth, augmented fifth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/25_16">25/16</a><br />
</td>
        <td>772.627428<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_7">11/7</a><br />
</td>
        <td>782.492036<br />
</td>
        <td>undecimal subminor sixth, undecimal augmented fifth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/8_5">8/5</a><br />
</td>
        <td>813.686286<br />
</td>
        <td>minor sixth, octave reduced 5th subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13_8">13/8</a><br />
</td>
        <td>840.527662<br />
</td>
        <td>tridecimal neutral sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/80_49">80/49</a><br />
</td>
        <td>848.661901<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49_30">49/30</a><br />
</td>
        <td>849.383198<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/18_11">18/11</a><br />
</td>
        <td>852.59216<br />
</td>
        <td>undecimal neutral sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/28_17">28/17</a><br />
</td>
        <td>863.870497<br />
</td>
        <td>septendecimal submajor sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/5_3">5/3</a><br />
</td>
        <td>884.358713<br />
</td>
        <td>major sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/42_25">42/25</a><br />
</td>
        <td>898.15348<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/27_16">27/16</a><br />
</td>
        <td>905.865003<br />
</td>
        <td>Pythagorean major sixth, octave reduced 27th harmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/22_13">22/13</a><br />
</td>
        <td>910.790821<br />
</td>
        <td>tridecimal major sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_10">17/10</a><br />
</td>
        <td>918.641696<br />
</td>
        <td>septendecimal diminished seventh, septendecimal major sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/12_7">12/7</a><br />
</td>
        <td>933.129094<br />
</td>
        <td>supermajor sixth, septimal major sixth, diminished seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/26_15">26/15</a><br />
</td>
        <td>952.258947<br />
</td>
        <td>semitwelfth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/7_4">7/4</a><br />
</td>
        <td>968.825906<br />
</td>
        <td>subminor seventh, harmonic seventh, augmented sixth, octave reduced 7th harmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/225_128">225/128</a><br />
</td>
        <td>976.537429<br />
</td>
        <td>marvel five-limit harmonic seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/30_17">30/17</a><br />
</td>
        <td>983.313305<br />
</td>
        <td>septendecimal minor seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/16_9">16/9</a><br />
</td>
        <td>996.089998<br />
</td>
        <td>Pythagorean minor seventh, small minor seventh, octave reduced 9th subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/25_14">25/14</a><br />
</td>
        <td>1003.801521<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/9_5">9/5</a><br />
</td>
        <td>1017.596288<br />
</td>
        <td>minor seventh, large minor seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/20_11">20/11</a><br />
</td>
        <td>1034.995772<br />
</td>
        <td>undecimal minor seventh, small undecimal neutral seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/64_35">64/35</a><br />
</td>
        <td>1044.86038<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_6">11/6</a><br />
</td>
        <td>1049.362941<br />
</td>
        <td>undecimal neutral seventh, 21/4-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/24_13">24/13</a><br />
</td>
        <td>1061.427339<br />
</td>
        <td>tridecimal neutral seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13_7">13/7</a><br />
</td>
        <td>1071.701755<br />
</td>
        <td>16/3-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/28_15">28/15</a><br />
</td>
        <td>1080.557192<br />
</td>
        <td>grave major seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/15_8">15/8</a><br />
</td>
        <td>1088.268715<br />
</td>
        <td>major seventh, just major seventh, octave reduced 15th harmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/32_17">32/17</a><br />
</td>
        <td>1095.04459<br />
</td>
        <td>small septendecimal major seventh, octave-reduced 17th subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_9">17/9</a><br />
</td>
        <td>1101.045408<br />
</td>
        <td>large septendecimal major seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/243_128">243/128</a><br />
</td>
        <td>1109.775004<br />
</td>
        <td>Pythagorean major seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/40_21">40/21</a><br />
</td>
        <td>1115.532907<br />
</td>
        <td>acute major seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/61_32">61/32</a><br />
</td>
        <td>1116.884905<br />
</td>
        <td>octave reduced 61st harmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/48_25">48/25</a><br />
</td>
        <td>1129.327573<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/64_33">64/33</a><br />
</td>
        <td>1146.727057<br />
</td>
        <td>octave reduced 33rd subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/35_18">35/18</a><br />
</td>
        <td>1151.239619<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/96_49">96/49</a><br />
</td>
        <td>1164.303188<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49_25">49/25</a><br />
</td>
        <td>1165.024385<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/160_81">160/81</a><br />
</td>
        <td>1178.493814<br />
</td>
        <td>octave minus syntonic comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/Octave">2/1</a><br />
</td>
        <td>1200<br />
</td>
        <td>octave, diapason<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:4 -->Links</h1>
 <a class="wiki_link_ext" href="http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt" rel="nofollow">Regions of the Interval Spectrum</a> by Margo Schulter <a class="wiki_link_ext" href="http://www.webcitation.org/5xeoz4zmC" rel="nofollow">Permalink</a><br />
<a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/intervals.html" rel="nofollow">Manuel Op de Coul interval list</a><br />
<a class="wiki_link_ext" href="http://www.kylegann.com/Octave.html" rel="nofollow">Anantomy of an Octave</a> by Kyle Gann<br />
<span style="display: block; height: 1px; left: 0px; overflow-x: hidden; overflow-y: hidden; position: absolute; top: 1754px; width: 1px;">1.9537207879341594002771772863067</span></body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-06 19:30:31 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-07-06 20:40:15 UTC</tt>.<br>
-: The original revision id was <tt>350977166</tt>.<br>
+: The original revision id was <tt>350984630</tt>.<br>
-: The revision comment was: <tt>Reverted to Jun 28, 2012 8:39 am: Change is uglier and less informative</tt><br>
+: The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
@@ Line 22: / Line 22: @@
 See also [[List of Superparticular Intervals]] and [[http://www.huygens-fokker.org/docs/intervals.html|List of intervals (Huygens-Fokker foundation)]]
-||~ frequency ratio ||~ cents value (three decimal places) ||~ some common names ||
+||~ frequency ratio ||~ cents value
-|| [[1_1|1/1]] || 0.000 || unison, unity, perfect prime, tonic ||
+(six decimal places) ||~ some common names ||
-|| [[32805_32768|32805/32768]] || 1.954 || schisma ||
+|| [[1_1|1/1]] || 0 || unison, unity, perfect prime, tonic ||
-|| [[100_99|100/99]] || 17.344 || Ptolemy's comma ||
+|| [[32805_32768|32805/32768]] || 1.95372 || schisma ||
-|| [[81_80|81/80]] || 21.506 || syntonic comma, Didymus comma ||
+|| [[100_99|100/99]] || 17.399484 || Ptolemy's comma ||
-|| [[531441_524288|531441/524288]] || 23.460 || Pythagorean comma, ditonic comma ||
+|| [[81_80|81/80]] || 21.506286 || syntonic comma, Didymus comma ||
-|| [[65_64|65/64]] || 26.841 || 13th-partial chroma ||
+|| [[531441_524288|531441/524288]] || 23.46001 || Pythagorean comma, ditonic comma ||
-|| [[64_63|64/63]] || 27.264 || septimal comma, Archytas' comma ||
+|| [[65_64|65/64]] || 26.841376 || 13th-partial chroma ||
-|| [[50_49|50/49]] || 34.976 || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis ||
+|| [[64_63|64/63]] || 27.264092 || septimal comma, Archytas' comma ||
-|| [[49_48|49/48]] || 35.697 || large septimal diesis, slendro diesis ||
+|| [[50_49|50/49]] || 34.975615 || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis ||
-|| [[45_44|45/44]] || 38.906 || undecimal 1/5th tone ||
+|| [[49_48|49/48]] || 35.696812 || large septimal diesis, slendro diesis ||
-|| [[525_512|525/512]] || 43.408 || Avicenna's enharmonic diesis ||
+|| [[45_44|45/44]] || 38.905773 || undecimal 1/5th tone ||
-|| [[36_35|36/35]] || 48.770 || septimal quarter tone ||
+|| [[525_512|525/512]] || 43.408335 || Avicenna's enharmonic diesis ||
-|| [[100_97|100/97]] || 52.732 ||  shrutar quarter tone ||
+|| [[36_35|36/35]] || 48.770381 || septimal quarter tone ||
-|| [[33_32|33/32]] || 53.273 || undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, octave reduced 33rd harmonic ||
+|| [[100_97|100/97]] || 52.732017 || shrutar quarter tone ||
-|| [[28_27|28/27]] || 62.961 || septimal chroma, small septimal chromatic semitone ||
+|| [[33_32|33/32]] || 53.272943 || undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, octave reduced 33rd harmonic ||
-|| [[25_24|25/24]] || 70.672 || chroma, chromatic semitone, Zarlinian semitone ||
+|| [[28_27|28/27]] || 62.960904 || septimal chroma, small septimal chromatic semitone ||
-|| [[68_65|68/65]] || 78.114 || valentine semitone ||
+|| [[25_24|25/24]] || 70.672427 || chroma, chromatic semitone, Zarlinian semitone ||
-|| [[22_21|22/21]] || 80.537 || undecimal minor semitone ||
+|| [[68_65|68/65]] || 78.114034 || valentine semitone ||
-|| [[64_61|64/61]] || 83.115 || harry minor semitone ||
+|| [[22_21|22/21]] || 80.537035 || undecimal minor semitone ||
-|| [[21_20|21/20]] || 84.467 || minor semitone, large septimal chromatic semitone ||
+|| [[64_61|64/61]] || 83.115195 || harry minor semitone ||
-|| [[256_243|256/243]] || 90.225 || Pythagorean limma, Pythagorean minor second ||
+|| [[21_20|21/20]] || 84.467193 || minor semitone, large septimal chromatic semitone ||
-|| [[135_128|135/128]] || 92.179 || major limma ||
+|| [[256_243|256/243]] || 90.224996 || Pythagorean limma, Pythagorean minor second ||
-|| [[18_17|18/17]] || 98.955 || small septendecimal semitone, Arabic lute index finger ||
+|| [[135_128|135/128]] || 92.178716 || major limma ||
-|| [[17_16|17/16]] || 104.955 || large septendecimal semitone, octave reduced 17th harmonic ||
+|| [[18_17|18/17]] || 98.954592 || small septendecimal semitone, Arabic lute index finger ||
-|| [[16_15|16/15]] || 111.713 || diatonic semitone, classic minor second, octave reduced 15th subharmonic ||
+|| [[17_16|17/16]] || 104.95541 || large septendecimal semitone, octave reduced 17th harmonic ||
-|| [[2187_2048|2187/2048]] || 113.685 || apotome ||
+|| [[16_15|16/15]] || 111.731285 || diatonic semitone, classic minor second, octave reduced 15th subharmonic ||
-|| [[15_14|15/14]] || 119.443 || septimal diatonic semitone ||
+|| [[2187_2048|2187/2048]] || 113.685006 || apotome ||
-|| [[14_13|14/13]] || 128.298 || 2/3-tone, trienthird ||
+|| [[15_14|15/14]] || 119.442808 || septimal diatonic semitone ||
-|| [[27_25|27/25]] || 133.238 || large limma ||
+|| [[14_13|14/13]] || 128.298245 || 2/3-tone, trienthird ||
-|| [[13_12|13/12]] || 138.573 || tridecimal 2/3-tone ||
+|| [[27_25|27/25]] || 133.237575 || large limma ||
-|| [[243_224|243/224]] || 140.949 || septimal chromatic semitone ||
+|| [[13_12|13/12]] || 138.572661 || tridecimal 2/3-tone ||
-|| [[12_11|12/11]] || 150.637 || small undecimal neutral second, 3/4-tone ||
+|| [[243_224|243/224]] || 140.949098 || septimal chromatic 7/6-tone ||
-|| [[35_32|35/32]] || 155.140 || septimal neutral second ||
+|| [[12_11|12/11]] || 150.637059 || small undecimal neutral second, 3/4-tone ||
-|| [[78_71|78/71]] || 162.786 || porcupine neutral second ||
+|| [[35_32|35/32]] || 155.13962 || septimal neutral second ||
-|| [[11_10|11/10]] || 165.004 || large undecimal neutral second, 4/5-tone, Ptolemy's second ||
+|| [[78_71|78/71]] || 162.786119 || porcupine neutral second ||
-|| [[54_49|54/49]] || 168.213 || Zalzal's mujannab ||
+|| [[11_10|11/10]] || 165.004228 || large undecimal neutral second, 4/5-tone, Ptolemy's second ||
-|| [[10_9|10/9]] || 182.404 || minor whole tone ||
+|| [[54_49|54/49]] || 168.21319 || Zalzal's mujannab ||
-|| [[28_25|28/25]] || 196.198 || middle second ||
+|| [[10_9|10/9]] || 182.403712 || minor whole tone ||
-|| [[9_8|9/8]] || 203.910 || major whole tone, Pythagorean tone, octave reduced 9th harmonic ||
+|| [[28_25|28/25]] || 196.198479 || middle second ||
-|| [[17_15|17/15]] || 216.687 || septendecimal whole tone ||
+|| [[9_8|9/8]] || 203.910002 || major whole tone, Pythagorean tone, octave reduced 9th harmonic ||
-|| [[8_7|8/7]] || 231.174 || supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
+|| [[17_15|17/15]] || 216.686695 || septendecimal whole tone ||
-|| [[15_13|15/13]] || 247.741 || semifourth ||
+|| [[8_7|8/7]] || 231.174094 || supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
-|| [[22_19|22/19]] || 253.805 || minimal minor third, godzilla third ||
+|| [[15_13|15/13]] || 247.741053 || semifourth ||
-|| [[7_6|7/6]] || 266.871 || subminor third, septimal minor third, augmented second ||
+|| [[22_19|22/19]] || 253.804926 || minimal minor third, godzilla third ||
-|| [[62_53|62/53]] || 271.531 || orwell subminor third ||
+|| [[7_6|7/6]] || 266.870906 || subminor third, septimal minor third, augmented second ||
-|| [[20_17|20/17]] || 281.358 || septendecimal augmented second, septendecimal minor third ||
+|| [[62_53|62/53]] || 271.531027 || orwell subminor third ||
-|| [[13_11|13/11]] || 289.210 || tridecimal minor third ||
+|| [[20_17|20/17]] || 281.358304 || septendecimal augmented second, septendecimal minor third ||
-|| [[32_27|32/27]] || 294.135 || Pythagorean minor third, octave reduced 27th subharmonic ||
+|| [[13_11|13/11]] || 289.209179 || tridecimal minor third ||
-|| [[19_16|19/16]] || 297.513 || otonal minor third, octave reduced 19th harmonic ||
+|| [[32_27|32/27]] || 294.134997 || Pythagorean minor third, octave reduced 27th subharmonic ||
-|| [[25_21|25/21]] || 301.847 || quasi-tempered minor third ||
+|| [[19_16|19/16]] || 297.513016 || otonal minor third, octave reduced 19th harmonic ||
-|| [[61_51|61/51]] || 309.974 || myna third ||
+|| [[25_21|25/21]] || 301.84652 || quasi-tempered minor third ||
-|| [[6_5|6/5]] || 315.641 || minor third ||
+|| [[61_51|61/51]] || 309.974395 || myna third ||
-|| [[35_29|35/29]] || 325.562 || doublewide minor third ||
+|| [[6_5|6/5]] || 315.641287 || minor third ||
-|| [[17_14|17/14]] || 336.130 || septendecimal supraminor third ||
+|| [[35_29|35/29]] || 325.562426 || doublewide minor third ||
-|| [[73_60|73/60]] || 339.521 || amity supraminor third ||
+|| [[17_14|17/14]] || 336.129503 || septendecimal supraminor third ||
-|| [[11_9|11/9]] || 347.408 || undecimal neutral third ||
+|| [[73_60|73/60]] || 339.520756 || amity supraminor third ||
-|| [[60_49|60/49]] || 350.617 || smaller septimal neutral third ||
+|| [[11_9|11/9]] || 347.40794 || undecimal neutral third ||
-|| [[49_40|49/40]] || 351.338 || larger septimal neutral third ||
+|| [[60_49|60/49]] || 350.616902 || smaller septimal neutral third ||
-|| [[16_13|16/13]] || 359.472 || tridecimal neutral third ||
+|| [[49_40|49/40]] || 351.338099 || larger septimal neutral third ||
-|| [[56_45|56/45]] || 378.602 || narrow perde segah ||
+|| [[16_13|16/13]] || 359.472338 || tridecimal neutral third ||
-|| [[71_57|71/57]] || 380.229 || witchcraft major third ||
+|| [[56_45|56/45]] || 378.602191 || narrow perde segah ||
-|| [[76_61|76/61]] || 380.628 || magic major third ||
+|| [[71_57|71/57]] || 380.228526 || witchcraft major third ||
-|| [[5_4|5/4]] || 386.314 || major third, octave reduced 5th harmonic ||
+|| [[76_61|76/61]] || 380.628211 || magic major third ||
-|| [[81_64|81/64]] || 407.820 || Pythagorean major third, octave reduced 81st harmonic ||
+|| [[5_4|5/4]] || 386.313714 || major third, octave reduced 5th harmonic ||
-|| [[14_11|14/11]] || 417.508 || undecimal major third, undecimal diminished fourth ||
+|| [[81_64|81/64]] || 407.820003 || Pythagorean major third, octave reduced 81st harmonic ||
-|| [[32_25|32/25]] || 427.373 || classic diminished fourth ||
+|| [[14_11|14/11]] || 417.507964 || undecimal major third, undecimal diminished fourth ||
-|| [[9_7|9/7]] || 435.084 || supermajor third, septimal major third, diminished fourth ||
+|| [[32_25|32/25]] || 427.372572 || classic diminished fourth ||
-|| [[31_24|31/24]] || 443.081 || sensi supermajor third ||
+|| [[9_7|9/7]] || 435.084095 || supermajor third, septimal major third, diminished fourth ||
-|| [[22_17|22/17]] || 446.363 || septendecimal supermajor third ||
+|| [[31_24|31/24]] || 443.080572 || sensi supermajor third ||
-|| [[35_27|35/27]] || 449.275 || semi-diminished fourth ||
+|| [[22_17|22/17]] || 446.362533 || septendecimal supermajor third ||
-|| [[13_10|13/10]] || 454.214 || Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramajor third ||
+|| [[35_27|35/27]] || 449.274618 || semi-diminished fourth ||
-|| [[64_49|64/49]] || 462.348 || septatonic major third ||
+|| [[13_10|13/10]] || 454.213948 || Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramajor third ||
-|| [[17_13|17/13]] || 464.428 || septendecimal sub-fourth ||
+|| [[64_49|64/49]] || 462.348187 || septatonic major third ||
-|| [[21_16|21/16]] || 470.781 || sub-fourth, narrow fourth, augmented third, octave reduced 21st harmonic ||
+|| [[17_13|17/13]] || 464.427748 || septendecimal sub-fourth ||
-|| [[4_3|4/3]] || 498.045 || perfect fourth, octave reduced 3rd subharmonic, diatessaron ||
+|| [[21_16|21/16]] || 470.780907 || sub-fourth, narrow fourth, augmented third, octave reduced 21st harmonic ||
-|| [[27_20|27/20]] || 519.551 || acute fourth ||
+|| [[4_3|4/3]] || 498.044999 || perfect fourth, octave reduced 3rd subharmonic, diatessaron ||
-|| [[49_36|49/36]] || 533.742 || Arabic lute acute fourth ||
+|| [[27_20|27/20]] || 519.551289 || acute fourth ||
-|| [[15_11|15/11]] || 536.591 || undecimal augmented fourth, subaugmented fourth ||
+|| [[49_36|49/36]] || 533.741811 || Arabic lute acute fourth ||
-|| [[48_35|48/35]] || 546.815 || septimal super-fourth ||
+|| [[15_11|15/11]] || 536.950772 || undecimal augmented fourth, subaugmented fourth ||
-|| [[11_8|11/8]] || 551.318 || super-fourth, undecimal semi-augmented fourth, octave reduced 11th harmonic or harmonic 11th, Alphorn-Fa ||
+|| [[48_35|48/35]] || 546.815381 || septimal super-fourth ||
-|| [[18_13|18/13]] || 563.382 || tridecimal augmented fourth ||
+|| [[11_8|11/8]] || 551.317942 || super-fourth, undecimal semi-augmented fourth, octave reduced 11th harmonic or harmonic 11th, Alphorn-Fa ||
-|| [[25_18|25/18]] || 568.717 || classic augmented fourth, pental augmented fourth ||
+|| [[18_13|18/13]] || 563.38234 || tridecimal augmented fourth ||
-|| [[7_5|7/5]] || 582.512 || augmented fourth, septimal tritone, Huygen's tritone ||
+|| [[25_18|25/18]] || 568.717426 || classic augmented fourth, pental augmented fourth ||
-|| [[24_17|24/17]] || 597.000 || smaller septendecimal tritone ||
+|| [[7_5|7/5]] || 582.512193 || augmented fourth, septimal tritone, Huygen's tritone ||
-|| [[17_12|17/12]] || 603.000 || larger septendecimal tritone ||
+|| [[24_17|24/17]] || 596.999591 || smaller septendecimal tritone ||
-|| [[10_7|10/7]] || 617.488 || diminished fifth, Euler's tritone, superaugmented fourth ||
+|| [[17_12|17/12]] || 603.000409 || larger septendecimal tritone ||
-|| [[36_25|36/25]] || 631.283 ||  pental augmented fifth, classic augmented fifth ||
+|| [[10_7|10/7]] || 617.487807 || diminished fifth, Euler's tritone, superaugmented fourth ||
-|| [[13_9|13/9]] || 636.618 || tridecimal diminished fifth ||
+|| [[36_25|36/25]] || 631.282574 || pental augmented fifth, classic augmented fifth ||
-|| [[16_11|16/11]] || 648.682 || sub-fifth, undecimal semi-diminished fifth, 11th subharmonic (octave reduced) ||
+|| [[13_9|13/9]] || 636.61766 || tridecimal diminished fifth ||
-|| [[35_24|35/24]] || 653.185 || septimal sub-fifth ||
+|| [[16_11|16/11]] || 648.682058 || sub-fifth, undecimal semi-diminished fifth, 11th subharmonic (octave reduced) ||
-|| [[22_15|22/15]] || 663.049 || undecimal diminished fifth, semidiminished fifth ||
+|| [[35_24|35/24]] || 653.184619 || septimal sub-fifth ||
-|| [[72_49|72/49]] || 666.258 ||   ||
+|| [[22_15|22/15]] || 663.049228 || undecimal diminished fifth, semidiminished fifth ||
-|| [[40_27|40/27]] || 680.449 || grave fifth ||
+|| [[72_49|72/49]] || 666.258889 ||   ||
-|| [[Just perfect fifth|3/2]] || 701.955 || [[perfect fifth]], octave reduced 3rd harmonic, diapente ||
+|| [[40_27|40/27]] || 680.448711 || grave fifth ||
-|| [[32_21|32/21]] || 729.219 || super-fifth, wide fifth, diminished sixth, octave reduced 21st subharmonic ||
+|| [[Just perfect fifth|3/2]] || 701.955001 || [[perfect fifth]], octave reduced 3rd harmonic, diapente ||
-|| [[26_17|26/17]] || 735.572 || septendecimal super-fifth ||
+|| [[32_21|32/21]] || 729.219093 || super-fifth, wide fifth, diminished sixth, octave reduced 21st subharmonic ||
-|| [[49_32|49/32]] || 737.652 ||   ||
+|| [[26_17|26/17]] || 735.572252 || septendecimal super-fifth ||
-|| [[20_13|20/13]] || 745.786 || Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth, tridecimal ultraminor sixth ||
+|| [[49_32|49/32]] || 737.651813 ||   ||
-|| [[17_11|17/11]] || 753.637 || septendecimal subminor sixth ||
+|| [[20_13|20/13]] || 745.786052 || Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth, tridecimal ultraminor sixth ||
-|| [[14_9|14/9]] || 764.916 || subminor sixth, septimal minor sixth, augmented fifth ||
+|| [[17_11|17/11]] || 753.637467 || septendecimal subminor sixth ||
-|| [[25_16|25/16]] || 772.627 ||   ||
+|| [[14_9|14/9]] || 764.915905 || subminor sixth, septimal minor sixth, augmented fifth ||
-|| [[11_7|11/7]] || 782.492 || undecimal subminor sixth, undecimal augmented fifth ||
+|| [[25_16|25/16]] || 772.627428 ||   ||
-|| [[8_5|8/5]] || 813.686 || minor sixth, octave reduced 5th subharmonic ||
+|| [[11_7|11/7]] || 782.492036 || undecimal subminor sixth, undecimal augmented fifth ||
-|| [[13_8|13/8]] || 840.528 || tridecimal neutral sixth ||
+|| [[8_5|8/5]] || 813.686286 || minor sixth, octave reduced 5th subharmonic ||
-|| [[80_49|80/49]] || 848.662 ||   ||
+|| [[13_8|13/8]] || 840.527662 || tridecimal neutral sixth ||
-|| [[49_30|49/30]] || 849.383 ||   ||
+|| [[80_49|80/49]] || 848.661901 ||   ||
-|| [[18_11|18/11]] || 852.592 || undecimal neutral sixth ||
+|| [[49_30|49/30]] || 849.383198 ||   ||
-|| [[28_17|28/17]] || 863.870 || septendecimal submajor sixth ||
+|| [[18_11|18/11]] || 852.59216 || undecimal neutral sixth ||
-|| [[5_3|5/3]] || 884.359 || major sixth ||
+|| [[28_17|28/17]] || 863.870497 || septendecimal submajor sixth ||
-|| [[42_25|42/25]] || 898.153 ||   ||
+|| [[5_3|5/3]] || 884.358713 || major sixth ||
-|| [[27_16|27/16]] || 905.865 || Pythagorean major sixth, octave reduced 27th harmonic ||
+|| [[42_25|42/25]] || 898.15348 ||   ||
-|| [[22_13|22/13]] || 910.790 || tridecimal major sixth ||
+|| [[27_16|27/16]] || 905.865003 || Pythagorean major sixth, octave reduced 27th harmonic ||
-|| [[17_10|17/10]] || 918.642 || septendecimal diminished seventh, septendecimal major sixth ||
+|| [[22_13|22/13]] || 910.790821 || tridecimal major sixth ||
-|| [[12_7|12/7]] || 933.129 || supermajor sixth, septimal major sixth, diminished seventh ||
+|| [[17_10|17/10]] || 918.641696 || septendecimal diminished seventh, septendecimal major sixth ||
-|| [[26_15|26/15]] || 952.259 || semitwelfth ||
+|| [[12_7|12/7]] || 933.129094 || supermajor sixth, septimal major sixth, diminished seventh ||
-|| [[7_4|7/4]] || 968.826 || subminor seventh, harmonic seventh, augmented sixth, octave reduced 7th harmonic ||
+|| [[26_15|26/15]] || 952.258947 || semitwelfth ||
-|| [[225_128|225/128]] || 976.537 || marvel five-limit harmonic seventh ||
+|| [[7_4|7/4]] || 968.825906 || subminor seventh, harmonic seventh, augmented sixth, octave reduced 7th harmonic ||
-|| [[30_17|30/17]] || 983.313 || septendecimal minor seventh ||
+|| [[225_128|225/128]] || 976.537429 || marvel five-limit harmonic seventh ||
-|| [[16_9|16/9]] || 996.090 || Pythagorean minor seventh, small minor seventh, octave reduced 9th subharmonic ||
+|| [[30_17|30/17]] || 983.313305 || septendecimal minor seventh ||
-|| [[25_14|25/14]] || 1003.802 ||   ||
+|| [[16_9|16/9]] || 996.089998 || Pythagorean minor seventh, small minor seventh, octave reduced 9th subharmonic ||
-|| [[9_5|9/5]] || 1017.596 || minor seventh, large minor seventh ||
+|| [[25_14|25/14]] || 1003.801521 ||   ||
-|| [[20_11|20/11]] || 1034.996 || undecimal minor seventh, small undecimal neutral seventh ||
+|| [[9_5|9/5]] || 1017.596288 || minor seventh, large minor seventh ||
-|| [[64_35|64/35]] || 1044.860 ||   ||
+|| [[20_11|20/11]] || 1034.995772 || undecimal minor seventh, small undecimal neutral seventh ||
-|| [[11_6|11/6]] || 1049.363 || undecimal neutral seventh, 21/4-tone ||
+|| [[64_35|64/35]] || 1044.86038 ||   ||
-|| [[24_13|24/13]] || 1061.427 || tridecimal neutral seventh ||
+|| [[11_6|11/6]] || 1049.362941 || undecimal neutral seventh, 21/4-tone ||
-|| [[13_7|13/7]] || 1071.702 || 16/3-tone ||
+|| [[24_13|24/13]] || 1061.427339 || tridecimal neutral seventh ||
-|| [[28_15|28/15]] || 1080.557 || grave major seventh ||
+|| [[13_7|13/7]] || 1071.701755 || 16/3-tone ||
-|| [[15_8|15/8]] || 1088.269 || major seventh, just major seventh, octave reduced 15th harmonic ||
+|| [[28_15|28/15]] || 1080.557192 || grave major seventh ||
-|| [[32_17|32/17]] || 1095.045 || small septendecimal major seventh, octave-reduced 17th subharmonic ||
+|| [[15_8|15/8]] || 1088.268715 || major seventh, just major seventh, octave reduced 15th harmonic ||
-|| [[17_9|17/9]] || 1101.045 || large septendecimal major seventh ||
+|| [[32_17|32/17]] || 1095.04459 || small septendecimal major seventh, octave-reduced 17th subharmonic ||
-|| [[243_128|243/128]] || 1109.775 || Pythagorean major seventh ||
+|| [[17_9|17/9]] || 1101.045408 || large septendecimal major seventh ||
-|| [[40_21|40/21]] || 1115.533 || acute major seventh ||
+|| [[243_128|243/128]] || 1109.775004 || Pythagorean major seventh ||
-|| [[61_32|61/32]] || 1116.885 || octave reduced 61st harmonic ||
+|| [[40_21|40/21]] || 1115.532907 || acute major seventh ||
-|| [[48_25|48/25]] || 1129.328 ||   ||
+|| [[61_32|61/32]] || 1116.884905 || octave reduced 61st harmonic ||
-|| [[64_33|64/33]] || 1146.727 || octave reduced 33rd subharmonic ||
+|| [[48_25|48/25]] || 1129.327573 ||   ||
-|| [[35_18|35/18]] || 1151.230 ||   ||
+|| [[64_33|64/33]] || 1146.727057 || octave reduced 33rd subharmonic ||
-|| [[96_49|96/49]] || 1164.303 ||   ||
+|| [[35_18|35/18]] || 1151.239619 ||   ||
-|| [[49_25|49/25]] || 1165.024 ||   ||
+|| [[96_49|96/49]] || 1164.303188 ||   ||
-|| [[160_81|160/81]] || 1178.494 || octave minus syntonic comma ||
+|| [[49_25|49/25]] || 1165.024385 ||   ||
-|| [[Octave|2/1]] || 1200.000 || octave, diapason ||
+|| [[160_81|160/81]] || 1178.493814 || octave minus syntonic comma ||
+|| [[Octave|2/1]] || 1200 || octave, diapason ||
 =Links=
 [[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt|Regions of the Interval Spectrum]] by Margo Schulter [[http://www.webcitation.org/5xeoz4zmC|Permalink]]
 [[http://www.huygens-fokker.org/docs/intervals.html|Manuel Op de Coul interval list]]
-[[http://www.kylegann.com/Octave.html|Anantomy of an Octave]] by Kyle Gann</pre></div>
+[[http://www.kylegann.com/Octave.html|Anantomy of an Octave]] by Kyle Gann
+&lt;span style="display: block; height: 1px; left: 0px; overflow-x: hidden; overflow-y: hidden; position: absolute; top: 1754px; width: 1px;"&gt;1.9537207879341594002771772863067&lt;/span&gt;</pre></div>
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Gallery of Just Intervals&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:6:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;a href="#Introduction"&gt;Introduction&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt; | &lt;a href="#Gallery of Just Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt; | &lt;a href="#Links"&gt;Links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
@@ Line 191: / Line 193: @@
          &lt;th&gt;frequency ratio&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;cents value (three decimal places)&lt;br /&gt;
+         &lt;th&gt;cents value &lt;br /&gt;
+(six decimal places)&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;some common names&lt;br /&gt;
@@ Line 199: / Line 202: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/1_1"&gt;1/1&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0.000&lt;br /&gt;
+         &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;unison, unity, perfect prime, tonic&lt;br /&gt;
@@ Line 207: / Line 210: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/32805_32768"&gt;32805/32768&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1.954&lt;br /&gt;
+         &lt;td&gt;1.95372&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;schisma&lt;br /&gt;
@@ Line 215: / Line 218: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/100_99"&gt;100/99&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;17.344&lt;br /&gt;
+         &lt;td&gt;17.399484&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Ptolemy's comma&lt;br /&gt;
@@ Line 223: / Line 226: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;21.506&lt;br /&gt;
+         &lt;td&gt;21.506286&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;syntonic comma, Didymus comma&lt;br /&gt;
@@ Line 231: / Line 234: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/531441_524288"&gt;531441/524288&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;23.460&lt;br /&gt;
+         &lt;td&gt;23.46001&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Pythagorean comma, ditonic comma&lt;br /&gt;
@@ Line 239: / Line 242: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/65_64"&gt;65/64&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;26.841&lt;br /&gt;
+         &lt;td&gt;26.841376&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;13th-partial chroma&lt;br /&gt;
@@ Line 247: / Line 250: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;27.264&lt;br /&gt;
+         &lt;td&gt;27.264092&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septimal comma, Archytas' comma&lt;br /&gt;
@@ Line 255: / Line 258: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;34.976&lt;br /&gt;
+         &lt;td&gt;34.975615&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis&lt;br /&gt;
@@ Line 263: / Line 266: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/49_48"&gt;49/48&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;35.697&lt;br /&gt;
+         &lt;td&gt;35.696812&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;large septimal diesis, slendro diesis&lt;br /&gt;
@@ Line 271: / Line 274: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/45_44"&gt;45/44&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;38.906&lt;br /&gt;
+         &lt;td&gt;38.905773&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;undecimal 1/5th tone&lt;br /&gt;
@@ Line 279: / Line 282: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/525_512"&gt;525/512&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;43.408&lt;br /&gt;
+         &lt;td&gt;43.408335&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Avicenna's enharmonic diesis&lt;br /&gt;
@@ Line 287: / Line 290: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/36_35"&gt;36/35&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;48.770&lt;br /&gt;
+         &lt;td&gt;48.770381&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septimal quarter tone&lt;br /&gt;
@@ Line 295: / Line 298: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/100_97"&gt;100/97&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;52.732&lt;br /&gt;
+         &lt;td&gt;52.732017&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;shrutar quarter tone&lt;br /&gt;
@@ Line 303: / Line 306: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/33_32"&gt;33/32&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;53.273&lt;br /&gt;
+         &lt;td&gt;53.272943&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, octave reduced 33rd harmonic&lt;br /&gt;
@@ Line 311: / Line 314: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/28_27"&gt;28/27&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;62.961&lt;br /&gt;
+         &lt;td&gt;62.960904&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septimal chroma, small septimal chromatic semitone&lt;br /&gt;
@@ Line 319: / Line 322: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/25_24"&gt;25/24&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;70.672&lt;br /&gt;
+         &lt;td&gt;70.672427&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;chroma, chromatic semitone, Zarlinian semitone&lt;br /&gt;
@@ Line 327: / Line 330: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/68_65"&gt;68/65&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;78.114&lt;br /&gt;
+         &lt;td&gt;78.114034&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;valentine semitone&lt;br /&gt;
@@ Line 335: / Line 338: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/22_21"&gt;22/21&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;80.537&lt;br /&gt;
+         &lt;td&gt;80.537035&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;undecimal minor semitone&lt;br /&gt;
@@ Line 343: / Line 346: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/64_61"&gt;64/61&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;83.115&lt;br /&gt;
+         &lt;td&gt;83.115195&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;harry minor semitone&lt;br /&gt;
@@ Line 351: / Line 354: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/21_20"&gt;21/20&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;84.467&lt;br /&gt;
+         &lt;td&gt;84.467193&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;minor semitone, large septimal chromatic semitone&lt;br /&gt;
@@ Line 359: / Line 362: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/256_243"&gt;256/243&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;90.225&lt;br /&gt;
+         &lt;td&gt;90.224996&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Pythagorean limma, Pythagorean minor second&lt;br /&gt;
@@ Line 367: / Line 370: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/135_128"&gt;135/128&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;92.179&lt;br /&gt;
+         &lt;td&gt;92.178716&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;major limma&lt;br /&gt;
@@ Line 375: / Line 378: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/18_17"&gt;18/17&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;98.955&lt;br /&gt;
+         &lt;td&gt;98.954592&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;small septendecimal semitone, Arabic lute index finger&lt;br /&gt;
@@ Line 383: / Line 386: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/17_16"&gt;17/16&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;104.955&lt;br /&gt;
+         &lt;td&gt;104.95541&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;large septendecimal semitone, octave reduced 17th harmonic&lt;br /&gt;
@@ Line 391: / Line 394: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/16_15"&gt;16/15&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;111.713&lt;br /&gt;
+         &lt;td&gt;111.731285&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;diatonic semitone, classic minor second, octave reduced 15th subharmonic&lt;br /&gt;
@@ Line 399: / Line 402: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/2187_2048"&gt;2187/2048&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;113.685&lt;br /&gt;
+         &lt;td&gt;113.685006&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;apotome&lt;br /&gt;
@@ Line 407: / Line 410: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/15_14"&gt;15/14&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;119.443&lt;br /&gt;
+         &lt;td&gt;119.442808&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septimal diatonic semitone&lt;br /&gt;
@@ Line 415: / Line 418: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/14_13"&gt;14/13&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;128.298&lt;br /&gt;
+         &lt;td&gt;128.298245&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;2/3-tone, trienthird&lt;br /&gt;
@@ Line 423: / Line 426: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/27_25"&gt;27/25&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;133.238&lt;br /&gt;
+         &lt;td&gt;133.237575&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;large limma&lt;br /&gt;
@@ Line 431: / Line 434: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/13_12"&gt;13/12&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;138.573&lt;br /&gt;
+         &lt;td&gt;138.572661&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;tridecimal 2/3-tone&lt;br /&gt;
@@ Line 439: / Line 442: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/243_224"&gt;243/224&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;140.949&lt;br /&gt;
+         &lt;td&gt;140.949098&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;septimal chromatic semitone&lt;br /&gt;
+         &lt;td&gt;septimal chromatic 7/6-tone&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 447: / Line 450: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/12_11"&gt;12/11&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;150.637&lt;br /&gt;
+         &lt;td&gt;150.637059&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;small undecimal neutral second, 3/4-tone&lt;br /&gt;
@@ Line 455: / Line 458: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/35_32"&gt;35/32&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;155.140&lt;br /&gt;
+         &lt;td&gt;155.13962&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septimal neutral second&lt;br /&gt;
@@ Line 463: / Line 466: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/78_71"&gt;78/71&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;162.786&lt;br /&gt;
+         &lt;td&gt;162.786119&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;porcupine neutral second&lt;br /&gt;
@@ Line 471: / Line 474: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/11_10"&gt;11/10&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;165.004&lt;br /&gt;
+         &lt;td&gt;165.004228&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;large undecimal neutral second, 4/5-tone, Ptolemy's second&lt;br /&gt;
@@ Line 479: / Line 482: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/54_49"&gt;54/49&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;168.213&lt;br /&gt;
+         &lt;td&gt;168.21319&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Zalzal's mujannab&lt;br /&gt;
@@ Line 487: / Line 490: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;182.404&lt;br /&gt;
+         &lt;td&gt;182.403712&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;minor whole tone&lt;br /&gt;
@@ Line 495: / Line 498: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/28_25"&gt;28/25&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;196.198&lt;br /&gt;
+         &lt;td&gt;196.198479&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;middle second&lt;br /&gt;
@@ Line 503: / Line 506: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;203.910&lt;br /&gt;
+         &lt;td&gt;203.910002&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;major whole tone, Pythagorean tone, octave reduced 9th harmonic&lt;br /&gt;
@@ Line 511: / Line 514: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/17_15"&gt;17/15&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;216.687&lt;br /&gt;
+         &lt;td&gt;216.686695&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septendecimal whole tone&lt;br /&gt;
@@ Line 519: / Line 522: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;231.174&lt;br /&gt;
+         &lt;td&gt;231.174094&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;supermajor second, septimal whole tone, diminished third, 7th subharmonic&lt;br /&gt;
@@ Line 527: / Line 530: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/15_13"&gt;15/13&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;247.741&lt;br /&gt;
+         &lt;td&gt;247.741053&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;semifourth&lt;br /&gt;
@@ Line 535: / Line 538: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/22_19"&gt;22/19&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;253.805&lt;br /&gt;
+         &lt;td&gt;253.804926&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;minimal minor third, godzilla third&lt;br /&gt;
@@ Line 543: / Line 546: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;266.871&lt;br /&gt;
+         &lt;td&gt;266.870906&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;subminor third, septimal minor third, augmented second&lt;br /&gt;
@@ Line 551: / Line 554: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/62_53"&gt;62/53&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;271.531&lt;br /&gt;
+         &lt;td&gt;271.531027&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;orwell subminor third&lt;br /&gt;
@@ Line 559: / Line 562: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/20_17"&gt;20/17&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;281.358&lt;br /&gt;
+         &lt;td&gt;281.358304&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septendecimal augmented second, septendecimal minor third&lt;br /&gt;
@@ Line 567: / Line 570: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/13_11"&gt;13/11&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;289.210&lt;br /&gt;
+         &lt;td&gt;289.209179&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;tridecimal minor third&lt;br /&gt;
@@ Line 575: / Line 578: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/32_27"&gt;32/27&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;294.135&lt;br /&gt;
+         &lt;td&gt;294.134997&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Pythagorean minor third, octave reduced 27th subharmonic&lt;br /&gt;
@@ Line 583: / Line 586: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/19_16"&gt;19/16&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;297.513&lt;br /&gt;
+         &lt;td&gt;297.513016&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;otonal minor third, octave reduced 19th harmonic&lt;br /&gt;
@@ Line 591: / Line 594: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/25_21"&gt;25/21&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;301.847&lt;br /&gt;
+         &lt;td&gt;301.84652&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;quasi-tempered minor third&lt;br /&gt;
@@ Line 599: / Line 602: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/61_51"&gt;61/51&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;309.974&lt;br /&gt;
+         &lt;td&gt;309.974395&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;myna third&lt;br /&gt;
@@ Line 607: / Line 610: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;315.641&lt;br /&gt;
+         &lt;td&gt;315.641287&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;minor third&lt;br /&gt;
@@ Line 615: / Line 618: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/35_29"&gt;35/29&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;325.562&lt;br /&gt;
+         &lt;td&gt;325.562426&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;doublewide minor third&lt;br /&gt;
@@ Line 623: / Line 626: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/17_14"&gt;17/14&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;336.130&lt;br /&gt;
+         &lt;td&gt;336.129503&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septendecimal supraminor third&lt;br /&gt;
@@ Line 631: / Line 634: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/73_60"&gt;73/60&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;339.521&lt;br /&gt;
+         &lt;td&gt;339.520756&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;amity supraminor third&lt;br /&gt;
@@ Line 639: / Line 642: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/11_9"&gt;11/9&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;347.408&lt;br /&gt;
+         &lt;td&gt;347.40794&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;undecimal neutral third&lt;br /&gt;
@@ Line 647: / Line 650: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/60_49"&gt;60/49&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;350.617&lt;br /&gt;
+         &lt;td&gt;350.616902&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;smaller septimal neutral third&lt;br /&gt;
@@ Line 655: / Line 658: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/49_40"&gt;49/40&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;351.338&lt;br /&gt;
+         &lt;td&gt;351.338099&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;larger septimal neutral third&lt;br /&gt;
@@ Line 663: / Line 666: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/16_13"&gt;16/13&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;359.472&lt;br /&gt;
+         &lt;td&gt;359.472338&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;tridecimal neutral third&lt;br /&gt;
@@ Line 671: / Line 674: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/56_45"&gt;56/45&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;378.602&lt;br /&gt;
+         &lt;td&gt;378.602191&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;narrow perde segah&lt;br /&gt;
@@ Line 679: / Line 682: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/71_57"&gt;71/57&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;380.229&lt;br /&gt;
+         &lt;td&gt;380.228526&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;witchcraft major third&lt;br /&gt;
@@ Line 687: / Line 690: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/76_61"&gt;76/61&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;380.628&lt;br /&gt;
+         &lt;td&gt;380.628211&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;magic major third&lt;br /&gt;
@@ Line 695: / Line 698: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;386.314&lt;br /&gt;
+         &lt;td&gt;386.313714&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;major third, octave reduced 5th harmonic&lt;br /&gt;
@@ Line 703: / Line 706: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/81_64"&gt;81/64&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;407.820&lt;br /&gt;
+         &lt;td&gt;407.820003&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Pythagorean major third, octave reduced 81st harmonic&lt;br /&gt;
@@ Line 711: / Line 714: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/14_11"&gt;14/11&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;417.508&lt;br /&gt;
+         &lt;td&gt;417.507964&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;undecimal major third, undecimal diminished fourth&lt;br /&gt;
@@ Line 719: / Line 722: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/32_25"&gt;32/25&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;427.373&lt;br /&gt;
+         &lt;td&gt;427.372572&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;classic diminished fourth&lt;br /&gt;
@@ Line 727: / Line 730: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;435.084&lt;br /&gt;
+         &lt;td&gt;435.084095&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;supermajor third, septimal major third, diminished fourth&lt;br /&gt;
@@ Line 735: / Line 738: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/31_24"&gt;31/24&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;443.081&lt;br /&gt;
+         &lt;td&gt;443.080572&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;sensi supermajor third&lt;br /&gt;
@@ Line 743: / Line 746: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/22_17"&gt;22/17&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;446.363&lt;br /&gt;
+         &lt;td&gt;446.362533&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septendecimal supermajor third&lt;br /&gt;
@@ Line 751: / Line 754: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/35_27"&gt;35/27&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;449.275&lt;br /&gt;
+         &lt;td&gt;449.274618&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;semi-diminished fourth&lt;br /&gt;
@@ Line 759: / Line 762: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;454.214&lt;br /&gt;
+         &lt;td&gt;454.213948&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramajor third&lt;br /&gt;
@@ Line 767: / Line 770: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/64_49"&gt;64/49&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;462.348&lt;br /&gt;
+         &lt;td&gt;462.348187&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septatonic major third&lt;br /&gt;
@@ Line 775: / Line 778: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/17_13"&gt;17/13&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;464.428&lt;br /&gt;
+         &lt;td&gt;464.427748&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septendecimal sub-fourth&lt;br /&gt;
@@ Line 783: / Line 786: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/21_16"&gt;21/16&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;470.781&lt;br /&gt;
+         &lt;td&gt;470.780907&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;sub-fourth, narrow fourth, augmented third, octave reduced 21st harmonic&lt;br /&gt;
@@ Line 791: / Line 794: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;498.045&lt;br /&gt;
+         &lt;td&gt;498.044999&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;perfect fourth, octave reduced 3rd subharmonic, diatessaron&lt;br /&gt;
@@ Line 799: / Line 802: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/27_20"&gt;27/20&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;519.551&lt;br /&gt;
+         &lt;td&gt;519.551289&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;acute fourth&lt;br /&gt;
@@ Line 807: / Line 810: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/49_36"&gt;49/36&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;533.742&lt;br /&gt;
+         &lt;td&gt;533.741811&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Arabic lute acute fourth&lt;br /&gt;
@@ Line 815: / Line 818: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/15_11"&gt;15/11&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;536.591&lt;br /&gt;
+         &lt;td&gt;536.950772&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;undecimal augmented fourth, subaugmented fourth&lt;br /&gt;
@@ Line 823: / Line 826: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/48_35"&gt;48/35&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;546.815&lt;br /&gt;
+         &lt;td&gt;546.815381&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septimal super-fourth&lt;br /&gt;
@@ Line 831: / Line 834: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;551.318&lt;br /&gt;
+         &lt;td&gt;551.317942&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;super-fourth, undecimal semi-augmented fourth, octave reduced 11th harmonic or harmonic 11th, Alphorn-Fa&lt;br /&gt;
@@ Line 839: / Line 842: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/18_13"&gt;18/13&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;563.382&lt;br /&gt;
+         &lt;td&gt;563.38234&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;tridecimal augmented fourth&lt;br /&gt;
@@ Line 847: / Line 850: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/25_18"&gt;25/18&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;568.717&lt;br /&gt;
+         &lt;td&gt;568.717426&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;classic augmented fourth, pental augmented fourth&lt;br /&gt;
@@ Line 855: / Line 858: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;582.512&lt;br /&gt;
+         &lt;td&gt;582.512193&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;augmented fourth, septimal tritone, Huygen's tritone&lt;br /&gt;
@@ Line 863: / Line 866: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/24_17"&gt;24/17&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;597.000&lt;br /&gt;
+         &lt;td&gt;596.999591&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;smaller septendecimal tritone&lt;br /&gt;
@@ Line 871: / Line 874: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/17_12"&gt;17/12&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;603.000&lt;br /&gt;
+         &lt;td&gt;603.000409&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;larger septendecimal tritone&lt;br /&gt;
@@ Line 879: / Line 882: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;617.488&lt;br /&gt;
+         &lt;td&gt;617.487807&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;diminished fifth, Euler's tritone, superaugmented fourth&lt;br /&gt;
@@ Line 887: / Line 890: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/36_25"&gt;36/25&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;631.283&lt;br /&gt;
+         &lt;td&gt;631.282574&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;pental augmented fifth, classic augmented fifth&lt;br /&gt;
@@ Line 895: / Line 898: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/13_9"&gt;13/9&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;636.618&lt;br /&gt;
+         &lt;td&gt;636.61766&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;tridecimal diminished fifth&lt;br /&gt;
@@ Line 903: / Line 906: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/16_11"&gt;16/11&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;648.682&lt;br /&gt;
+         &lt;td&gt;648.682058&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;sub-fifth, undecimal semi-diminished fifth, 11th subharmonic (octave reduced)&lt;br /&gt;
@@ Line 911: / Line 914: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/35_24"&gt;35/24&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;653.185&lt;br /&gt;
+         &lt;td&gt;653.184619&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septimal sub-fifth&lt;br /&gt;
@@ Line 919: / Line 922: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/22_15"&gt;22/15&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;663.049&lt;br /&gt;
+         &lt;td&gt;663.049228&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;undecimal diminished fifth, semidiminished fifth&lt;br /&gt;
@@ Line 927: / Line 930: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/72_49"&gt;72/49&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;666.258&lt;br /&gt;
+         &lt;td&gt;666.258889&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 935: / Line 938: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/40_27"&gt;40/27&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;680.449&lt;br /&gt;
+         &lt;td&gt;680.448711&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;grave fifth&lt;br /&gt;
@@ Line 943: / Line 946: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/Just%20perfect%20fifth"&gt;3/2&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;701.955&lt;br /&gt;
+         &lt;td&gt;701.955001&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;a class="wiki_link" href="/perfect%20fifth"&gt;perfect fifth&lt;/a&gt;, octave reduced 3rd harmonic, diapente&lt;br /&gt;
@@ Line 951: / Line 954: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/32_21"&gt;32/21&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;729.219&lt;br /&gt;
+         &lt;td&gt;729.219093&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;super-fifth, wide fifth, diminished sixth, octave reduced 21st subharmonic&lt;br /&gt;
@@ Line 959: / Line 962: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/26_17"&gt;26/17&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;735.572&lt;br /&gt;
+         &lt;td&gt;735.572252&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septendecimal super-fifth&lt;br /&gt;
@@ Line 967: / Line 970: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/49_32"&gt;49/32&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;737.652&lt;br /&gt;
+         &lt;td&gt;737.651813&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 975: / Line 978: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/20_13"&gt;20/13&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;745.786&lt;br /&gt;
+         &lt;td&gt;745.786052&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth, tridecimal ultraminor sixth&lt;br /&gt;
@@ Line 983: / Line 986: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/17_11"&gt;17/11&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;753.637&lt;br /&gt;
+         &lt;td&gt;753.637467&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septendecimal subminor sixth&lt;br /&gt;
@@ Line 991: / Line 994: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;764.916&lt;br /&gt;
+         &lt;td&gt;764.915905&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;subminor sixth, septimal minor sixth, augmented fifth&lt;br /&gt;
@@ Line 999: / Line 1,002: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/25_16"&gt;25/16&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;772.627&lt;br /&gt;
+         &lt;td&gt;772.627428&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,007: / Line 1,010: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/11_7"&gt;11/7&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;782.492&lt;br /&gt;
+         &lt;td&gt;782.492036&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;undecimal subminor sixth, undecimal augmented fifth&lt;br /&gt;
@@ Line 1,015: / Line 1,018: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;813.686&lt;br /&gt;
+         &lt;td&gt;813.686286&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;minor sixth, octave reduced 5th subharmonic&lt;br /&gt;
@@ Line 1,023: / Line 1,026: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;840.528&lt;br /&gt;
+         &lt;td&gt;840.527662&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;tridecimal neutral sixth&lt;br /&gt;
@@ Line 1,031: / Line 1,034: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/80_49"&gt;80/49&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;848.662&lt;br /&gt;
+         &lt;td&gt;848.661901&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,039: / Line 1,042: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/49_30"&gt;49/30&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;849.383&lt;br /&gt;
+         &lt;td&gt;849.383198&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,047: / Line 1,050: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/18_11"&gt;18/11&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;852.592&lt;br /&gt;
+         &lt;td&gt;852.59216&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;undecimal neutral sixth&lt;br /&gt;
@@ Line 1,055: / Line 1,058: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/28_17"&gt;28/17&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;863.870&lt;br /&gt;
+         &lt;td&gt;863.870497&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septendecimal submajor sixth&lt;br /&gt;
@@ Line 1,063: / Line 1,066: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;884.359&lt;br /&gt;
+         &lt;td&gt;884.358713&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;major sixth&lt;br /&gt;
@@ Line 1,071: / Line 1,074: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/42_25"&gt;42/25&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;898.153&lt;br /&gt;
+         &lt;td&gt;898.15348&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,079: / Line 1,082: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/27_16"&gt;27/16&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;905.865&lt;br /&gt;
+         &lt;td&gt;905.865003&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Pythagorean major sixth, octave reduced 27th harmonic&lt;br /&gt;
@@ Line 1,087: / Line 1,090: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/22_13"&gt;22/13&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;910.790&lt;br /&gt;
+         &lt;td&gt;910.790821&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;tridecimal major sixth&lt;br /&gt;
@@ Line 1,095: / Line 1,098: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/17_10"&gt;17/10&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;918.642&lt;br /&gt;
+         &lt;td&gt;918.641696&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septendecimal diminished seventh, septendecimal major sixth&lt;br /&gt;
@@ Line 1,103: / Line 1,106: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/12_7"&gt;12/7&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;933.129&lt;br /&gt;
+         &lt;td&gt;933.129094&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;supermajor sixth, septimal major sixth, diminished seventh&lt;br /&gt;
@@ Line 1,111: / Line 1,114: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/26_15"&gt;26/15&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;952.259&lt;br /&gt;
+         &lt;td&gt;952.258947&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;semitwelfth&lt;br /&gt;
@@ Line 1,119: / Line 1,122: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;968.826&lt;br /&gt;
+         &lt;td&gt;968.825906&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;subminor seventh, harmonic seventh, augmented sixth, octave reduced 7th harmonic&lt;br /&gt;
@@ Line 1,127: / Line 1,130: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/225_128"&gt;225/128&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;976.537&lt;br /&gt;
+         &lt;td&gt;976.537429&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;marvel five-limit harmonic seventh&lt;br /&gt;
@@ Line 1,135: / Line 1,138: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/30_17"&gt;30/17&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;983.313&lt;br /&gt;
+         &lt;td&gt;983.313305&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;septendecimal minor seventh&lt;br /&gt;
@@ Line 1,143: / Line 1,146: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/16_9"&gt;16/9&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;996.090&lt;br /&gt;
+         &lt;td&gt;996.089998&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Pythagorean minor seventh, small minor seventh, octave reduced 9th subharmonic&lt;br /&gt;
@@ Line 1,151: / Line 1,154: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/25_14"&gt;25/14&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1003.802&lt;br /&gt;
+         &lt;td&gt;1003.801521&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,159: / Line 1,162: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/9_5"&gt;9/5&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1017.596&lt;br /&gt;
+         &lt;td&gt;1017.596288&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;minor seventh, large minor seventh&lt;br /&gt;
@@ Line 1,167: / Line 1,170: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/20_11"&gt;20/11&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1034.996&lt;br /&gt;
+         &lt;td&gt;1034.995772&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;undecimal minor seventh, small undecimal neutral seventh&lt;br /&gt;
@@ Line 1,175: / Line 1,178: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/64_35"&gt;64/35&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1044.860&lt;br /&gt;
+         &lt;td&gt;1044.86038&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,183: / Line 1,186: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/11_6"&gt;11/6&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1049.363&lt;br /&gt;
+         &lt;td&gt;1049.362941&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;undecimal neutral seventh, 21/4-tone&lt;br /&gt;
@@ Line 1,191: / Line 1,194: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/24_13"&gt;24/13&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1061.427&lt;br /&gt;
+         &lt;td&gt;1061.427339&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;tridecimal neutral seventh&lt;br /&gt;
@@ Line 1,199: / Line 1,202: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/13_7"&gt;13/7&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1071.702&lt;br /&gt;
+         &lt;td&gt;1071.701755&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;16/3-tone&lt;br /&gt;
@@ Line 1,207: / Line 1,210: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/28_15"&gt;28/15&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1080.557&lt;br /&gt;
+         &lt;td&gt;1080.557192&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;grave major seventh&lt;br /&gt;
@@ Line 1,215: / Line 1,218: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/15_8"&gt;15/8&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1088.269&lt;br /&gt;
+         &lt;td&gt;1088.268715&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;major seventh, just major seventh, octave reduced 15th harmonic&lt;br /&gt;
@@ Line 1,223: / Line 1,226: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/32_17"&gt;32/17&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1095.045&lt;br /&gt;
+         &lt;td&gt;1095.04459&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;small septendecimal major seventh, octave-reduced 17th subharmonic&lt;br /&gt;
@@ Line 1,231: / Line 1,234: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/17_9"&gt;17/9&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1101.045&lt;br /&gt;
+         &lt;td&gt;1101.045408&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;large septendecimal major seventh&lt;br /&gt;
@@ Line 1,239: / Line 1,242: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/243_128"&gt;243/128&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1109.775&lt;br /&gt;
+         &lt;td&gt;1109.775004&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Pythagorean major seventh&lt;br /&gt;
@@ Line 1,247: / Line 1,250: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/40_21"&gt;40/21&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1115.533&lt;br /&gt;
+         &lt;td&gt;1115.532907&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;acute major seventh&lt;br /&gt;
@@ Line 1,255: / Line 1,258: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/61_32"&gt;61/32&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1116.885&lt;br /&gt;
+         &lt;td&gt;1116.884905&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;octave reduced 61st harmonic&lt;br /&gt;
@@ Line 1,263: / Line 1,266: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/48_25"&gt;48/25&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1129.328&lt;br /&gt;
+         &lt;td&gt;1129.327573&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,271: / Line 1,274: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/64_33"&gt;64/33&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1146.727&lt;br /&gt;
+         &lt;td&gt;1146.727057&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;octave reduced 33rd subharmonic&lt;br /&gt;
@@ Line 1,279: / Line 1,282: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/35_18"&gt;35/18&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1151.230&lt;br /&gt;
+         &lt;td&gt;1151.239619&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,287: / Line 1,290: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/96_49"&gt;96/49&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1164.303&lt;br /&gt;
+         &lt;td&gt;1164.303188&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,295: / Line 1,298: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/49_25"&gt;49/25&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1165.024&lt;br /&gt;
+         &lt;td&gt;1165.024385&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,303: / Line 1,306: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/160_81"&gt;160/81&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1178.494&lt;br /&gt;
+         &lt;td&gt;1178.493814&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;octave minus syntonic comma&lt;br /&gt;
@@ Line 1,311: / Line 1,314: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/Octave"&gt;2/1&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200.000&lt;br /&gt;
+         &lt;td&gt;1200&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;octave, diapason&lt;br /&gt;
@@ Line 1,322: / Line 1,325: @@
   &lt;a class="wiki_link_ext" href="http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt" rel="nofollow"&gt;Regions of the Interval Spectrum&lt;/a&gt; by Margo Schulter &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeoz4zmC" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/intervals.html" rel="nofollow"&gt;Manuel Op de Coul interval list&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://www.kylegann.com/Octave.html" rel="nofollow"&gt;Anantomy of an Octave&lt;/a&gt; by Kyle Gann&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;a class="wiki_link_ext" href="http://www.kylegann.com/Octave.html" rel="nofollow"&gt;Anantomy of an Octave&lt;/a&gt; by Kyle Gann&lt;br /&gt;
+&lt;span style="display: block; height: 1px; left: 0px; overflow-x: hidden; overflow-y: hidden; position: absolute; top: 1754px; width: 1px;"&gt;1.9537207879341594002771772863067&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Gallery of just intervals: Difference between revisions

Revision as of 20:40, 6 July 2012

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

Search