Gallery of just intervals
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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 || || [[36_35|36/35]] || 48.770 || septimal quarter tone || || [[33_32|33/32]] || 53.273 || unidecimal quarter tone, unidecimal 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 (Al Farabi) || || [[10_9|10/9]] || 182.404 || classic (whole) tone, classic major second, minor whole tone || || [[9_8|9/8]] || 203.910 || (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced) || || [[17_15|17/15]] || 216.687 || septendecimal whole tone || || [[8_7|8/7]] || 231.174 || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic || || [[15_13|15/13]] || 247.741 || semifourth || || [[7_6|7/6]] || 266.871 || (septimal) 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, 27th subharmonic (octave reduced) || || [[6_5|6/5]] || 315.641 || (classic) minor third || || [[17_14|17/14]] || 336.130 || septendecimal supraminor third || || [[11_9|11/9]] || 347.408 || (undecimal) neutral third || || [[16_13|16/13]] || 359.472 || tridecimal neutral third || || [[5_4|5/4]] || 386.314 || (classic) major third, 5th harmonic (octave reduced) || || [[14_11|14/11]] || 417.508 || (undecimal) supermajor third, undecimal major third, (undecimal) diminished fourth || || [[9_7|9/7]] || 435.084 || (septimal) supermajor third, septimal major third, BP third, (septimal) 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 || || [[17_13|17/13]] || 464.428 || septendecimal sub-fourth || || [[21_16|21/16]] || 470.781 || sub-fourth, narrow fourth, augmented third, 21st harmonic or septimal 11th (octave reduced) || || [[4_3|4/3]] || 498.045 || perfect fourth, 3rd subharmonic (octave reduced), diatessaron || || [[27_20|27/20]] || 519.551 || 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, 11th harmonic or harmonic 11th (octave reduced) || || [[18_13|18/13]] || 563.382 || tridecimal augmented fourth || || [[7_5|7/5]] || 582.512 || augmented fourth, septimal tritone, Huygen's tritone, BP fourth, subdiminished fifth || || [[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 || || [[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 || || [[40_27|40/27]] || 680.449 || grave fifth || || [[Just perfect fifth|3/2]] || 701.955 || [[perfect fifth]], 3rd harmonic (octave reduced), diapente || || [[32_21|32/21]] || 729.219 || super-fifth, wide fifth, diminished sixth, 21st subharmonic (octave reduced) || || [[26_17|26/17]] || 735.572 || septendecimal super-fifth || || [[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 || (septimal) subminor sixth, septimal minor sixth, augmented fifth || || [[11_7|11/7]] || 782.492 || (undecimal) subminor sixth, undecimal augmented fifth || || [[8_5|8/5]] || 813.686 || (classic) minor sixth, 5th subharmonic (octave reduced) || || [[13_8|13/8]] || 840.528 || tridecimal neutral sixth || || [[18_11|18/11]] || 852.592 || (undecimal) neutral sixth || || [[28_17|28/17]] || 863.870 || septendecimal submajor sixth || || [[5_3|5/3]] || 884.359 || (classic) major sixth || || [[27_16|27/16]] || 905.865 || Pythagorean major sixth, 27th harmonic (octave reduced) || || [[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 || (septimal) supermajor sixth, septimal major sixth, diminished seventh || || [[26_15|26/15]] || 952.259 || semitwelfth || || [[7_4|7/4]] || 968.826 || (septimal) subminor seventh, harmonic seventh, augmented sixth, 7th harmonic (octave reduced) || || [[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, 9th subharmonic (octave reduced) || || [[9_5|9/5]] || 1017.596 || (classic) minor seventh, just minor seventh, BP seventh || || [[20_11|20/11]] || 1034.996 || (small) undecimal neutral seventh, large minor seventh || || [[11_6|11/6]] || 1049.363 || (large) (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 || (classic) major seventh, 15th harmonic (octave reduced) || || [[32_17|32/17]] || 1095.045 || small septendecimal major seventh, 17th subharmonic (octave-reduced) || || [[17_9|17/9]] || 1101.045 || large septendecimal major seventh || || [[243_128|243/128]] || 1109.775 || || || [[40_21|40/21]] || 1115.533 || acute major seventh || || [[64_33|64/33]] || 1146.727 || 33rd subharmonic (octave reduced) || || [[160_81|160/81]] || 1178.494 || octave minus syntonic comma || || [[Octave|2/1]] || 1200.000 || octave, diapason || =Articles= [[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt|Regions of the Interval Spectrum]] by Margo Schulter [[http://www.webcitation.org/5xeoz4zmC|Permalink]]
Original HTML content:
<html><head><title>Gallery of Just Intervals</title></head><body><!-- ws:start:WikiTextTocRule:6:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- 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="#Articles">Articles</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: -->
<!-- ws:end:WikiTextTocRule:10 --><hr />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><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 "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.<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 "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.<br />
<br />
<hr />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><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="/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>unidecimal quarter tone, unidecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/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 (Al Farabi)<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/10_9">10/9</a><br />
</td>
<td>182.404<br />
</td>
<td>classic (whole) tone, classic major second, minor whole tone<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/9_8">9/8</a><br />
</td>
<td>203.910<br />
</td>
<td>(Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/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>(septimal) 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>(septimal) 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, 27th subharmonic (octave reduced)<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/6_5">6/5</a><br />
</td>
<td>315.641<br />
</td>
<td>(classic) 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="/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="/5_4">5/4</a><br />
</td>
<td>386.314<br />
</td>
<td>(classic) major third, 5th harmonic (octave reduced)<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/14_11">14/11</a><br />
</td>
<td>417.508<br />
</td>
<td>(undecimal) supermajor third, undecimal major third, (undecimal) 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>(septimal) supermajor third, septimal major third, BP third, (septimal) 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="/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, 21st harmonic or septimal 11th (octave reduced)<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="/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, 11th harmonic or harmonic 11th (octave reduced)<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="/7_5">7/5</a><br />
</td>
<td>582.512<br />
</td>
<td>augmented fourth, septimal tritone, Huygen's tritone, BP fourth, subdiminished fifth<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="/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="/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>, 3rd harmonic (octave reduced), 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, 21st subharmonic (octave reduced)<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="/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>(septimal) subminor sixth, septimal minor sixth, augmented fifth<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>(classic) minor sixth, 5th subharmonic (octave reduced)<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="/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>(classic) major sixth<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, 27th harmonic (octave reduced)<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>(septimal) 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>(septimal) subminor seventh, harmonic seventh, augmented sixth, 7th harmonic (octave reduced)<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, 9th subharmonic (octave reduced)<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/9_5">9/5</a><br />
</td>
<td>1017.596<br />
</td>
<td>(classic) minor seventh, just minor seventh, BP seventh<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/20_11">20/11</a><br />
</td>
<td>1034.996<br />
</td>
<td>(small) undecimal neutral seventh, large minor seventh<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/11_6">11/6</a><br />
</td>
<td>1049.363<br />
</td>
<td>(large) (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>(classic) major seventh, 15th harmonic (octave reduced)<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, 17th subharmonic (octave-reduced)<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><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="/64_33">64/33</a><br />
</td>
<td>1146.727<br />
</td>
<td>33rd subharmonic (octave reduced)<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 />
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<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></body></html>