Gallery of just intervals: Difference between revisions

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[[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 (three decimal places) ||~ some common names ||
|| [[1_1|1/1]] || 0.000 || (perfect) unison, unity, perfect prime, tonic ||
|| [[32805_32768|32805/32768]] || 1.954 || schisma ||
|| [[100_99|100/99]] || 17.344 || Ptolemy's comma ||
|| [[81_80|81/80]] || 21.506 || syntonic comma, Didymus comma ||
|| [[531441_524288|531441/524288]] || 23.460 || Pythagorean comma, ditonic comma ||
|| [[65_64|65/64]] || 26.841 || 13th-partial chroma ||
|| [[64_63|64/63]] || 27.264 || septimal comma, Archytas' comma ||
|| [[50_49|50/49]] || 34.976 || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis ||
|| [[49_48|49/48]] || 35.697 || large septimal diesis, slendro diesis ||
|| [[45_44|45/44]] || 38.906 || undecimal 1/5th tone ||
|| [[525_512|525/512]] || 43.408 || Avicenna's enharmonic diesis ||
|| [[36_35|36/35]] || 48.770 || septimal quarter tone ||
|| [[33_32|33/32]] || 53.273 || undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced) ||
|| [[28_27|28/27]] || 62.961 || septimal chroma, small septimal chromatic semitone ||
|| [[25_24|25/24]] || 70.672 || chroma, chromatic semitone, Zarlinian semitone ||
|| [[22_21|22/21]] || 80.537 || undecimal minor semitone ||
|| [[21_20|21/20]] || 84.467 || minor semitone, large septimal chromatic semitone ||
|| [[256_243|256/243]] || 90.225 || Pythagorean limma, Pythagorean minor second ||
|| [[135_128|135/128]] || 92.179 || major limma ||
|| [[18_17|18/17]] || 98.955 || small septendecimal semitone, Arabic lute index finger ||
|| [[17_16|17/16]] || 104.955 || large septendecimal semitone, 17th harmonic (octave reduced) ||
|| [[16_15|16/15]] || 111.713 || diatonic semitone, classic minor second, 15th subharmonic (octave reduced) ||
|| [[2187_2048|2187/2048]] || 113.685 || apotome ||
|| [[15_14|15/14]] || 119.443 || septimal diatonic semitone ||
|| [[14_13|14/13]] || 128.298 || 2/3-tone, trienthird ||
|| [[27_25|27/25]] || 133.238 || large limma ||
|| [[13_12|13/12]] || 138.573 || tridecimal 2/3-tone ||
|| [[12_11|12/11]] || 150.637 || small undecimal neutral second, 3/4-tone ||
|| [[35_32|35/32]] || 155.14 || septimal neutral second ||
|| [[11_10|11/10]] || 165.004 || large undecimal neutral second, 4/5-tone, Ptolemy's second ||
|| [[54_49|54/49]] || 168.213 || Zalzal's mujannab ||
|| [[10_9|10/9]] || 182.404 || minor whole tone ||
|| [[28_25|28/25]] || 196.198 || middle second ||
|| [[9_8|9/8]] || 203.910 || major whole tone, Pythagorean tone, octave reduced 9th harmonic ||
|| [[17_15|17/15]] || 216.687 || septendecimal whole tone ||
|| [[8_7|8/7]] || 231.174 || supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
|| [[15_13|15/13]] || 247.741 || semifourth ||
|| [[7_6|7/6]] || 266.871 || subminor third, septimal minor third, augmented second ||
|| [[20_17|20/17]] || 281.358 || septendecimal augmented second, septendecimal minor third ||
|| [[13_11|13/11]] || 289.210 || tridecimal minor third ||
|| [[32_27|32/27]] || 294.135 || Pythagorean minor third, octave reduced 27th subharmonic ||
|| [[25_21|25/21]] || 301.847 || quasi-tempered minor third ||
|| [[6_5|6/5]] || 315.641 || minor third ||
|| [[17_14|17/14]] || 336.130 || septendecimal supraminor third ||
|| [[11_9|11/9]] || 347.408 || undecimal neutral third ||
|| [[60_49|60/49]] || 350.617 || smaller septimal neutral third ||
|| [[49_40|49/40]] || 351.338 || larger septimal neutral third ||
|| [[16_13|16/13]] || 359.472 || tridecimal neutral third ||
|| [[56_45|56/45]] || 378.602 || narrow perde segah ||
|| [[5_4|5/4]] || 386.314 || major third, octave reduced 5th harmonic ||
|| [[14_11|14/11]] || 417.508 || undecimal major third, undecimal diminished fourth ||
|| [[32_25|32/25]] || 427.373 || classic diminished fourth ||
|| [[9_7|9/7]] || 435.084 || supermajor third, septimal major third, diminished fourth ||
|| [[22_17|22/17]] || 446.363 || septendecimal supermajor third ||
|| [[13_10|13/10]] || 454.214 || Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramajor third ||
|| [[64_49|64/49]] || 462.348 || septatonic major third ||
|| [[17_13|17/13]] || 464.428 || septendecimal sub-fourth ||
|| [[21_16|21/16]] || 470.781 || sub-fourth, narrow fourth, augmented third, octave reduced 21st harmonic ||
|| [[4_3|4/3]] || 498.045 || perfect fourth, 3rd subharmonic (octave reduced), diatessaron ||
|| [[27_20|27/20]] || 519.551 || acute fourth ||
|| [[49_36|49/36]] || 533.742 || Arabic lute acute fourth ||
|| [[15_11|15/11]] || 536.591 || undecimal augmented fourth, subaugmented fourth ||
|| [[48_35|48/35]] || 546.815 || septimal super-fourth ||
|| [[11_8|11/8]] || 551.318 || super-fourth, undecimal semi-augmented fourth, octave reduced 11th harmonic or harmonic 11th ||
|| [[18_13|18/13]] || 563.382 || tridecimal augmented fourth ||
|| [[25_18|25/18]] || 568.717 || classic augmented fourth ||
|| [[7_5|7/5]] || 582.512 || augmented fourth, septimal tritone, Huygen's tritone ||
|| [[24_17|24/17]] || 597.000 || 1st septendecimal tritone ||
|| [[17_12|17/12]] || 603.000 || 2nd septendecimal tritone ||
|| [[10_7|10/7]] || 617.488 || diminished fifth, Euler's tritone, superaugmented fourth ||
|| [[36_25|36/25]] || 631.283 || ||
|| [[13_9|13/9]] || 636.618 || tridecimal diminished fifth ||
|| [[16_11|16/11]] || 648.682 || sub-fifth, undecimal semi-diminished fifth, 11th subharmonic (octave reduced) ||
|| [[35_24|35/24]] || 653.185 || septimal sub-fifth ||
|| [[22_15|22/15]] || 663.049 || undecimal diminished fifth, semidiminished fifth ||
|| [[72_49|72/49]] || 666.258 || ||
|| [[40_27|40/27]] || 680.449 || grave fifth ||
|| [[Just perfect fifth|3/2]] || 701.955 || [[perfect fifth]], octave reduced 3rd harmonic, diapente ||
|| [[32_21|32/21]] || 729.219 || super-fifth, wide fifth, diminished sixth, octave reduced 21st subharmonic ||
|| [[26_17|26/17]] || 735.572 || septendecimal super-fifth ||
|| [[49_32|49/32]] || 737.652 || ||
|| [[20_13|20/13]] || 745.786 || Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth, tridecimal ultraminor sixth ||
|| [[17_11|17/11]] || 753.637 || septendecimal subminor sixth ||
|| [[14_9|14/9]] || 764.916 || subminor sixth, septimal minor sixth, augmented fifth ||
|| [[25_16|25/16]] || 772.627 || ||
|| [[11_7|11/7]] || 782.492 || undecimal subminor sixth, undecimal augmented fifth ||
|| [[8_5|8/5]] || 813.686 || minor sixth, octave reduced 5th subharmonic ||
|| [[13_8|13/8]] || 840.528 || tridecimal neutral sixth ||
|| [[80_49|80/49]] || 848.662 || ||
|| [[49_30|49/30]] || 849.383 || ||
|| [[18_11|18/11]] || 852.592 || undecimal neutral sixth ||
|| [[28_17|28/17]] || 863.870 || septendecimal submajor sixth ||
|| [[5_3|5/3]] || 884.359 || major sixth ||
|| [[42_25|42/25]] || 898.153 || ||
|| [[27_16|27/16]] || 905.865 || Pythagorean major sixth, octave reduced 27th harmonic ||
|| [[22_13|22/13]] || 910.790 || tridecimal major sixth ||
|| [[17_10|17/10]] || 918.642 || septendecimal diminished seventh, septendecimal major sixth ||
|| [[12_7|12/7]] || 933.129 || supermajor sixth, septimal major sixth, diminished seventh ||
|| [[26_15|26/15]] || 952.259 || semitwelfth ||
|| [[7_4|7/4]] || 968.826 || subminor seventh, harmonic seventh, augmented sixth, octave reduced 7th harmonic ||
|| [[225_128|225/128]] || 976.537 || marvel five-limit harmonic seventh ||
|| [[30_17|30/17]] || 983.313 || septendecimal minor seventh ||
|| [[16_9|16/9]] || 996.090 || Pythagorean minor seventh, small minor seventh, octave reduced 9th subharmonic ||
|| [[25_14|25/14]] || 1003.802 || ||
|| [[9_5|9/5]] || 1017.596 || minor seventh, large minor seventh ||
|| [[20_11|20/11]] || 1034.996 || undecimal minor seventh, small undecimal neutral seventh ||
|| [[64_35|64/35]] || 1044.860 || ||
|| [[11_6|11/6]] || 1049.363 || undecimal neutral seventh, 21/4-tone ||
|| [[24_13|24/13]] || 1061.427 || tridecimal neutral seventh ||
|| [[13_7|13/7]] || 1071.702 || 16/3-tone ||
|| [[28_15|28/15]] || 1080.557 || grave major seventh ||
|| [[15_8|15/8]] || 1088.269 || major seventh, just major seventh, octave reduced 15th harmonic ||
|| [[32_17|32/17]] || 1095.045 || small septendecimal major seventh, octave-reduced 17th subharmonic ||
|| [[17_9|17/9]] || 1101.045 || large septendecimal major seventh ||
|| [[243_128|243/128]] || 1109.775 || Pythagorean major seventh ||
|| [[40_21|40/21]] || 1115.533 || acute major seventh ||
|| [[48_25|48/25]] || 1129.328 || ||
|| [[64_33|64/33]] || 1146.727 || octave reduced 33rd subharmonic ||
|| [[35_18|35/18]] || 1151.230 || ||
|| [[96_49|96/49]] || 1164.303 || ||
|| [[49_25|49/25]] || 1165.024 || ||
|| [[160_81|160/81]] || 1178.494 || octave minus syntonic comma ||
|| [[Octave|2/1]] || 1200.000 || 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]]

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 (three 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>0.000<br />
</td>
        <td>(perfect) unison, unity, perfect prime, tonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/32805_32768">32805/32768</a><br />
</td>
        <td>1.954<br />
</td>
        <td>schisma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/100_99">100/99</a><br />
</td>
        <td>17.344<br />
</td>
        <td>Ptolemy's comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/81_80">81/80</a><br />
</td>
        <td>21.506<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>23.460<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>26.841<br />
</td>
        <td>13th-partial chroma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/64_63">64/63</a><br />
</td>
        <td>27.264<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>34.976<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>35.697<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>38.906<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>43.408<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>48.770<br />
</td>
        <td>septimal quarter tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/33_32">33/32</a><br />
</td>
        <td>53.273<br />
</td>
        <td>undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/28_27">28/27</a><br />
</td>
        <td>62.961<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>70.672<br />
</td>
        <td>chroma, chromatic semitone, Zarlinian semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/22_21">22/21</a><br />
</td>
        <td>80.537<br />
</td>
        <td>undecimal minor semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/21_20">21/20</a><br />
</td>
        <td>84.467<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>90.225<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>92.179<br />
</td>
        <td>major limma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/18_17">18/17</a><br />
</td>
        <td>98.955<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>104.955<br />
</td>
        <td>large septendecimal semitone, 17th harmonic (octave reduced)<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/16_15">16/15</a><br />
</td>
        <td>111.713<br />
</td>
        <td>diatonic semitone, classic minor second, 15th subharmonic (octave reduced)<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/2187_2048">2187/2048</a><br />
</td>
        <td>113.685<br />
</td>
        <td>apotome<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/15_14">15/14</a><br />
</td>
        <td>119.443<br />
</td>
        <td>septimal diatonic semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/14_13">14/13</a><br />
</td>
        <td>128.298<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>133.238<br />
</td>
        <td>large limma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13_12">13/12</a><br />
</td>
        <td>138.573<br />
</td>
        <td>tridecimal 2/3-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/12_11">12/11</a><br />
</td>
        <td>150.637<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>155.14<br />
</td>
        <td>septimal neutral second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_10">11/10</a><br />
</td>
        <td>165.004<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>168.213<br />
</td>
        <td>Zalzal's mujannab<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/10_9">10/9</a><br />
</td>
        <td>182.404<br />
</td>
        <td>minor whole tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/28_25">28/25</a><br />
</td>
        <td>196.198<br />
</td>
        <td>middle second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/9_8">9/8</a><br />
</td>
        <td>203.910<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>216.687<br />
</td>
        <td>septendecimal whole tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/8_7">8/7</a><br />
</td>
        <td>231.174<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>247.741<br />
</td>
        <td>semifourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/7_6">7/6</a><br />
</td>
        <td>266.871<br />
</td>
        <td>subminor third, septimal minor third, augmented second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/20_17">20/17</a><br />
</td>
        <td>281.358<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>289.210<br />
</td>
        <td>tridecimal minor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/32_27">32/27</a><br />
</td>
        <td>294.135<br />
</td>
        <td>Pythagorean minor third, octave reduced 27th subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/25_21">25/21</a><br />
</td>
        <td>301.847<br />
</td>
        <td>quasi-tempered minor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/6_5">6/5</a><br />
</td>
        <td>315.641<br />
</td>
        <td>minor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_14">17/14</a><br />
</td>
        <td>336.130<br />
</td>
        <td>septendecimal supraminor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_9">11/9</a><br />
</td>
        <td>347.408<br />
</td>
        <td>undecimal neutral third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/60_49">60/49</a><br />
</td>
        <td>350.617<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>351.338<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>359.472<br />
</td>
        <td>tridecimal neutral third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/56_45">56/45</a><br />
</td>
        <td>378.602<br />
</td>
        <td>narrow perde segah<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/5_4">5/4</a><br />
</td>
        <td>386.314<br />
</td>
        <td>major third, octave reduced 5th harmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/14_11">14/11</a><br />
</td>
        <td>417.508<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>427.373<br />
</td>
        <td>classic diminished fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/9_7">9/7</a><br />
</td>
        <td>435.084<br />
</td>
        <td>supermajor third, septimal major third, diminished fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/22_17">22/17</a><br />
</td>
        <td>446.363<br />
</td>
        <td>septendecimal supermajor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13_10">13/10</a><br />
</td>
        <td>454.214<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>462.348<br />
</td>
        <td>septatonic major third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_13">17/13</a><br />
</td>
        <td>464.428<br />
</td>
        <td>septendecimal sub-fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/21_16">21/16</a><br />
</td>
        <td>470.781<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>498.045<br />
</td>
        <td>perfect fourth, 3rd subharmonic (octave reduced), diatessaron<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/27_20">27/20</a><br />
</td>
        <td>519.551<br />
</td>
        <td>acute fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49_36">49/36</a><br />
</td>
        <td>533.742<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>536.591<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>546.815<br />
</td>
        <td>septimal super-fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_8">11/8</a><br />
</td>
        <td>551.318<br />
</td>
        <td>super-fourth, undecimal semi-augmented fourth, octave reduced 11th harmonic or harmonic 11th<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/18_13">18/13</a><br />
</td>
        <td>563.382<br />
</td>
        <td>tridecimal augmented fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/25_18">25/18</a><br />
</td>
        <td>568.717<br />
</td>
        <td>classic augmented fourth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/7_5">7/5</a><br />
</td>
        <td>582.512<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>597.000<br />
</td>
        <td>1st septendecimal tritone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_12">17/12</a><br />
</td>
        <td>603.000<br />
</td>
        <td>2nd septendecimal tritone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/10_7">10/7</a><br />
</td>
        <td>617.488<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>631.283<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13_9">13/9</a><br />
</td>
        <td>636.618<br />
</td>
        <td>tridecimal diminished fifth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/16_11">16/11</a><br />
</td>
        <td>648.682<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>653.185<br />
</td>
        <td>septimal sub-fifth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/22_15">22/15</a><br />
</td>
        <td>663.049<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>666.258<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/40_27">40/27</a><br />
</td>
        <td>680.449<br />
</td>
        <td>grave fifth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/Just%20perfect%20fifth">3/2</a><br />
</td>
        <td>701.955<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>729.219<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>735.572<br />
</td>
        <td>septendecimal super-fifth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49_32">49/32</a><br />
</td>
        <td>737.652<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/20_13">20/13</a><br />
</td>
        <td>745.786<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>753.637<br />
</td>
        <td>septendecimal subminor sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/14_9">14/9</a><br />
</td>
        <td>764.916<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>772.627<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_7">11/7</a><br />
</td>
        <td>782.492<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>813.686<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>840.528<br />
</td>
        <td>tridecimal neutral sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/80_49">80/49</a><br />
</td>
        <td>848.662<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49_30">49/30</a><br />
</td>
        <td>849.383<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/18_11">18/11</a><br />
</td>
        <td>852.592<br />
</td>
        <td>undecimal neutral sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/28_17">28/17</a><br />
</td>
        <td>863.870<br />
</td>
        <td>septendecimal submajor sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/5_3">5/3</a><br />
</td>
        <td>884.359<br />
</td>
        <td>major sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/42_25">42/25</a><br />
</td>
        <td>898.153<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/27_16">27/16</a><br />
</td>
        <td>905.865<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>910.790<br />
</td>
        <td>tridecimal major sixth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_10">17/10</a><br />
</td>
        <td>918.642<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>933.129<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>952.259<br />
</td>
        <td>semitwelfth<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/7_4">7/4</a><br />
</td>
        <td>968.826<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>976.537<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>983.313<br />
</td>
        <td>septendecimal minor seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/16_9">16/9</a><br />
</td>
        <td>996.090<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>1003.802<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/9_5">9/5</a><br />
</td>
        <td>1017.596<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>1034.996<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>1044.860<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_6">11/6</a><br />
</td>
        <td>1049.363<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>1061.427<br />
</td>
        <td>tridecimal neutral seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13_7">13/7</a><br />
</td>
        <td>1071.702<br />
</td>
        <td>16/3-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/28_15">28/15</a><br />
</td>
        <td>1080.557<br />
</td>
        <td>grave major seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/15_8">15/8</a><br />
</td>
        <td>1088.269<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>1095.045<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>1101.045<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>1109.775<br />
</td>
        <td>Pythagorean major seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/40_21">40/21</a><br />
</td>
        <td>1115.533<br />
</td>
        <td>acute major seventh<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/48_25">48/25</a><br />
</td>
        <td>1129.328<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/64_33">64/33</a><br />
</td>
        <td>1146.727<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>1151.230<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/96_49">96/49</a><br />
</td>
        <td>1164.303<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49_25">49/25</a><br />
</td>
        <td>1165.024<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/160_81">160/81</a><br />
</td>
        <td>1178.494<br />
</td>
        <td>octave minus syntonic comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/Octave">2/1</a><br />
</td>
        <td>1200.000<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></body></html>

Gallery of just intervals: Difference between revisions

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