18edo
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<span style="text-align: right;">[[18平均律|日本語]] </span> =18 Equal Divisions of the Octave= AKA The Third-Tone System ==Basic Properties== 18-EDO divides the octave into 18 equal parts of ~66.667 cents each. It does not approximate the 3rd harmonic at all, unless a >30¢-error is considered acceptable, and it approximates the 5th and 7th harmonics equally with 12-TET. It does, however, render a most accurate tuning of 9/8, 7/6, 21/16, 15/11, 12/7, 16/9, and 13/7. It is also the smallest EDO to approximate the harmonic series chord 5:6:7 without tempering out 36/35 (and thus without using the same interval to approximate both 6/5 and 7/6). In order to access the excellent consonances actually available, one must take a considerably "non-common-practice" approach, meaning to avoid the usual closed-voice "root-3rd-5th" type of chord and instead use chords which are either more compressed or more stretched out. 18-EDO may be treated as a temperament of the 17-limit [[k*N subgroups|4*18 subgroup]] [[Just intonation subgroups|just intonation subgroup]] 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as 72 does on the full [[17-limit]], and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources. However, less accurate approximations can be used. 18 equal does temper out 28/27, which makes three "fifths" (ie. 3/2) up, a 7/4. Thus 9/8 = a near just 7/6 (and what the relatively accurate 200 cents as 9/8, is in fact 8/7 - what do you make of that? Music.) This treatment applies to the scale generated by the large fifth, known as Father. One, if one really gets into it, can generate scales from the 3/2 and the half octave: with all the sharpness, what's 18e going to hurt? Call 600 cents 11/8 and 866 cents 13/8. Hey it's possible, lots of people like mavila. 18-EDO contains sub-EDOs 2, 3, 6, and 9, and itself is half of 36-EDO and one-fourth of 72-EDO. It bears some similarities to 13-EDO (with its very flat 4ths and nice subminor 3rds), 11-EDO (with its very sharp minor 3rds, two of which span a very flat 5th), 16-EDO (with its sharp 4ths and flat 5ths), and 17-EDO and 19-EDO (with its narrow semitone, three of which comprise a whole-tone). It is an excellent tuning for those seeking a forceful deviation from the common practice. ===Representations of Just Intervals=== || Degree || Cents DMS ||= 5L3s Notation || Nearest Ratio || Error (cents) (DMS) || 17-Limit Ratios* || || 0 || 0 ||= **C** || 1/1 || 0 || **1/1** || || 1 || 66.667 20° ||= Db || 27/26 || +1.329 +23'56" ||> 78/75, 75/72 || || 2 || 133.333 40° ||= C# || 27/25 || +0.096 +1'43" ||> 51/55, 42/39 || || 3 || 200 60° ||= **D** || 9/8 || -3.910 -1°10'23" || **9/8** || || 4 || 266.667 80° ||= Eb || 7/6 || -0.204 -1"50" || **75/64** || || 5 || 333.333 100° ||= D# || 17/14 or 40/33 || -2.796 +0.293 -50'20" +5'16" || **39/32** || || 6 || 400 120° ||= **E** || 5/4 or 44/35 || +13.686 +3.822 +4°6'21" +1°8'47" ||> 64/55 || || 7 || 466.667 140° ||= **F** || 21/16 || -4.114 -1°14'3" || **21/16** || || 8 || 533.333 160° ||= Gb || 15/11 || -3.617 -1°5'7" ||> 102/75 || || 9 || 600 180° ||= F# || 17/12 or 24/17 || -3.000 +3.000 -54' +54' ||> 17/12 || || 10 || 666.667 200° ||= **G** || 22/15 || +3.617 +1°5'7" ||> 75/51 || || 11 || 733.333 220° ||= Hb || 32/21 || +4.114 +1°14'3" ||> 32/21 || || 12 || 800 240° ||= G# || 8/5 or 35/22 || -13.686 -3.8222 -4°6'21" -1°8'47" || **51/32** || || 13 || 866.667 260° ||= **H** || 28/17 or 33/20 || +2.796 -0.293 <span style="line-height: 15.6000003814697px;">+</span>50'20" <span style="line-height: 15.6000003814697px;">-</span><span style="line-height: 1.5;">5'16"</span> ||> 64/39 || || 14 || 933.333 280° ||= **A** || 12/7 || +0.204 +1"50" || **55/32** || || 15 || 1000 300° ||= Bb || 16/9 || +3.910 +1°10'23" ||> 16/9 || || 16 || 1066.667 320° ||= A# || 50/27 || -0.096 -1'43" ||> 39/21 || || 17 || 1133.333 340° ||= **B** || 52/27 || -1.329 -23'56" ||> 75/39 || || 18 || 1200 360° ||= **C** || 2/1 || 0 || **2/1** || *based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament ==<span style="font-size: 1.3em;">Useful Moment-of-Symmetry Scales</span>== Note: This list excludes scales found in 9-EDO. ===<span style="font-size: 1.1em;">Pentatonic:</span>=== 3L2s Father Pentatonic: 4 4 3 4 3 ===<span style="font-size: 1.1em;">Hexatonic:</span>=== 6-Equal Whole-Tone Scale: 3 3 3 3 3 3 4L2s Bicycle: 4 4 1 4 4 1 2L4s Rice Hexatonic: 2 5 2 2 5 2 ===<span style="font-size: 1.1em;">Heptatonic:</span>=== 4L3s Amity/Mish Heptatonic: 3 2 3 2 3 3 2 ===<span style="font-size: 1.1em;">Octatonic:</span>=== 5L3s Father Octatonic: 3 1 3 3 1 3 3 1 2L6s Rice Octatonic: 2 2 3 2 2 2 3 2 ===<span style="font-size: 1.1em;">Decatonic:</span>=== 8L2s Biggie Decatonic: 2 2 1 2 2 2 2 1 2 2 ==<span style="font-size: 1.3em;">Application to Guitar</span>== 18-EDO is an ideal scale for the first-time refretter, because you can retain all the even-number frets from 12-tET--essentially 1/3 of your work is done for you! The "Father Octatonic" scale maps very simply to a 6-string guitar tuned in "reverse-standard" tuning (tune using four 466.667¢ intervals, with one 533.333¢ interval between the 2nd and 3rd strings), making for a softer learning-curve than EDOs like 14, 16, or 21 (all of which are most evenly open-tuned using a series of sharpened 4ths and a minor or neutral 3rd, and whose scales thus often require position-shifting and/or larger stretches of the hand). ==Commas== 18 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] < 18 29 42 51 62 67 |.) ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 || ||= 128/125 || | 7 0 -3 > ||> 41.06 ||= Diesis ||= Augmented Comma || ||= 1212717/1210381 || | 23 6 -14 > ||> 3.34 ||= Vishnuzma ||= Semisuper || ||= 50/49 || | 1 0 2 -2 > ||> 34.98 ||= Tritonic Diesis ||= Jubilisma || ||= 686/675 || | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= || ||= 875/864 || | -5 -3 3 1 > ||> 21.90 ||= Keema ||= || ||= 1728/1715 || | 6 3 -1 -3 > ||> 13.07 ||= Orwellisma ||= Orwell Comma || ||= 16875/16807 || | 0 3 4 -5 > ||> 6.99 ||= Mirkwai ||= || ||= 3136/3125 || | 6 0 -5 2 > ||> 6.08 ||= Hemimean ||= || ||= 99/98 || | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||= || ||= 100/99 || | 2 -2 2 0 -1 > ||> 17.40 ||= Ptolemisma ||= || ||= 65536/65219 || | 16 0 0 -2 -3 > ||> 8.39 ||= Orgonisma ||= || ||= 385/384 || | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||= || ||= 9801/9800 || | -3 4 -2 -2 2 > ||> 0.18 ||= Kalisma ||= Gauss' Comma || ||= 91/90 || | -1 -2 -1 1 1 > ||> 19.13 ||= Superleap ||= || ==Listen== * [[http://www.h-pi.com/mp3/18ETPrelude.mp3|18ETPrelude]] by [[Aaron Andrew Hunt]] * [[http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3|Prelude in 18et]] by [[@http://www.chrisvaisvil.com|Chris Vaisvil]] => [[@http://chrisvaisvil.com/?p=3|composer notes]] * [[http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3|Flippertronics]] by Chris Vaisvil * [[http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3|Gerbils at the Wheel of Government]] by [[@http://chrisvaisvil.com/?p=1402|Chris Vaisvil (in 9 and 18 edo simultaneously)]] * [[http://www.seraph.it/dep/det/DoAndroidsDreamof18ED2.mp3.mp3|Do Androids Dream Of 18ED2?]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/fb0306486b51c270607f90a0c795d531-202.html|blog entry]])
Original HTML content:
<html><head><title>18edo</title></head><body><span style="text-align: right;"><a class="wiki_link" href="/18%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br />
</span><br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x18 Equal Divisions of the Octave"></a><!-- ws:end:WikiTextHeadingRule:0 -->18 Equal Divisions of the Octave</h1>
AKA The Third-Tone System<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x18 Equal Divisions of the Octave-Basic Properties"></a><!-- ws:end:WikiTextHeadingRule:2 -->Basic Properties</h2>
18-EDO divides the octave into 18 equal parts of ~66.667 cents each. It does not approximate the 3rd harmonic at all, unless a >30¢-error is considered acceptable, and it approximates the 5th and 7th harmonics equally with 12-TET. It does, however, render a most accurate tuning of 9/8, 7/6, 21/16, 15/11, 12/7, 16/9, and 13/7. It is also the smallest EDO to approximate the harmonic series chord 5:6:7 without tempering out 36/35 (and thus without using the same interval to approximate both 6/5 and 7/6).<br />
<br />
In order to access the excellent consonances actually available, one must take a considerably "non-common-practice" approach, meaning to avoid the usual closed-voice "root-3rd-5th" type of chord and instead use chords which are either more compressed or more stretched out. 18-EDO may be treated as a temperament of the 17-limit <a class="wiki_link" href="/k%2AN%20subgroups">4*18 subgroup</a> <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a> 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as 72 does on the full <a class="wiki_link" href="/17-limit">17-limit</a>, and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources.<br />
<br />
However, less accurate approximations can be used. 18 equal does temper out 28/27, which makes three "fifths" (ie. 3/2) up, a 7/4. Thus 9/8 = a near just 7/6 (and what the relatively accurate 200 cents as 9/8, is in fact 8/7 - what do you make of that? Music.) This treatment applies to the scale generated by the large fifth, known as Father. One, if one really gets into it, can generate scales from the 3/2 and the half octave: with all the sharpness, what's 18e going to hurt? Call 600 cents 11/8 and 866 cents 13/8. Hey it's possible, lots of people like mavila.<br />
<br />
18-EDO contains sub-EDOs 2, 3, 6, and 9, and itself is half of 36-EDO and one-fourth of 72-EDO. It bears some similarities to 13-EDO (with its very flat 4ths and nice subminor 3rds), 11-EDO (with its very sharp minor 3rds, two of which span a very flat 5th), 16-EDO (with its sharp 4ths and flat 5ths), and 17-EDO and 19-EDO (with its narrow semitone, three of which comprise a whole-tone). It is an excellent tuning for those seeking a forceful deviation from the common practice.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x18 Equal Divisions of the Octave-Basic Properties-Representations of Just Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Representations of Just Intervals</h3>
<table class="wiki_table">
<tr>
<td>Degree<br />
</td>
<td>Cents<br />
DMS<br />
</td>
<td style="text-align: center;">5L3s Notation<br />
</td>
<td>Nearest Ratio<br />
</td>
<td>Error (cents)<br />
(DMS)<br />
</td>
<td>17-Limit Ratios*<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
<td style="text-align: center;"><strong>C</strong><br />
</td>
<td>1/1<br />
</td>
<td>0<br />
</td>
<td><strong>1/1</strong><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>66.667<br />
20°<br />
</td>
<td style="text-align: center;">Db<br />
</td>
<td>27/26<br />
</td>
<td>+1.329<br />
+23'56"<br />
</td>
<td style="text-align: right;">78/75, 75/72<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>133.333<br />
40°<br />
</td>
<td style="text-align: center;">C#<br />
</td>
<td>27/25<br />
</td>
<td>+0.096<br />
+1'43"<br />
</td>
<td style="text-align: right;">51/55, 42/39<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>200<br />
60°<br />
</td>
<td style="text-align: center;"><strong>D</strong><br />
</td>
<td>9/8<br />
</td>
<td>-3.910<br />
-1°10'23"<br />
</td>
<td><strong>9/8</strong><br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>266.667<br />
80°<br />
</td>
<td style="text-align: center;">Eb<br />
</td>
<td>7/6<br />
</td>
<td>-0.204<br />
-1"50"<br />
</td>
<td><strong>75/64</strong><br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>333.333<br />
100°<br />
</td>
<td style="text-align: center;">D#<br />
</td>
<td>17/14 or 40/33<br />
</td>
<td>-2.796 +0.293<br />
-50'20" +5'16"<br />
</td>
<td><strong>39/32</strong><br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>400<br />
120°<br />
</td>
<td style="text-align: center;"><strong>E</strong><br />
</td>
<td>5/4 or 44/35<br />
</td>
<td>+13.686 +3.822<br />
+4°6'21" +1°8'47"<br />
</td>
<td style="text-align: right;">64/55<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>466.667<br />
140°<br />
</td>
<td style="text-align: center;"><strong>F</strong><br />
</td>
<td>21/16<br />
</td>
<td>-4.114<br />
-1°14'3"<br />
</td>
<td><strong>21/16</strong><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>533.333<br />
160°<br />
</td>
<td style="text-align: center;">Gb<br />
</td>
<td>15/11<br />
</td>
<td>-3.617<br />
-1°5'7"<br />
</td>
<td style="text-align: right;">102/75<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>600<br />
180°<br />
</td>
<td style="text-align: center;">F#<br />
</td>
<td>17/12 or 24/17<br />
</td>
<td>-3.000 +3.000<br />
-54' +54'<br />
</td>
<td style="text-align: right;">17/12<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>666.667<br />
200°<br />
</td>
<td style="text-align: center;"><strong>G</strong><br />
</td>
<td>22/15<br />
</td>
<td>+3.617<br />
+1°5'7"<br />
</td>
<td style="text-align: right;">75/51<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>733.333<br />
220°<br />
</td>
<td style="text-align: center;">Hb<br />
</td>
<td>32/21<br />
</td>
<td>+4.114<br />
+1°14'3"<br />
</td>
<td style="text-align: right;">32/21<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>800<br />
240°<br />
</td>
<td style="text-align: center;">G#<br />
</td>
<td>8/5 or 35/22<br />
</td>
<td>-13.686 -3.8222<br />
-4°6'21" -1°8'47"<br />
</td>
<td><strong>51/32</strong><br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>866.667<br />
260°<br />
</td>
<td style="text-align: center;"><strong>H</strong><br />
</td>
<td>28/17 or 33/20<br />
</td>
<td>+2.796 -0.293<br />
<span style="line-height: 15.6000003814697px;">+</span>50'20" <span style="line-height: 15.6000003814697px;">-</span><span style="line-height: 1.5;">5'16"</span><br />
</td>
<td style="text-align: right;">64/39<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>933.333<br />
280°<br />
</td>
<td style="text-align: center;"><strong>A</strong><br />
</td>
<td>12/7<br />
</td>
<td>+0.204<br />
+1"50"<br />
</td>
<td><strong>55/32</strong><br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>1000<br />
300°<br />
</td>
<td style="text-align: center;">Bb<br />
</td>
<td>16/9<br />
</td>
<td>+3.910<br />
+1°10'23"<br />
</td>
<td style="text-align: right;">16/9<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>1066.667<br />
320°<br />
</td>
<td style="text-align: center;">A#<br />
</td>
<td>50/27<br />
</td>
<td>-0.096<br />
-1'43"<br />
</td>
<td style="text-align: right;">39/21<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>1133.333<br />
340°<br />
</td>
<td style="text-align: center;"><strong>B</strong><br />
</td>
<td>52/27<br />
</td>
<td>-1.329<br />
-23'56"<br />
</td>
<td style="text-align: right;">75/39<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>1200<br />
360°<br />
</td>
<td style="text-align: center;"><strong>C</strong><br />
</td>
<td>2/1<br />
</td>
<td>0<br />
</td>
<td><strong>2/1</strong><br />
</td>
</tr>
</table>
*based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x18 Equal Divisions of the Octave-Useful Moment-of-Symmetry Scales"></a><!-- ws:end:WikiTextHeadingRule:6 --><span style="font-size: 1.3em;">Useful Moment-of-Symmetry Scales</span></h2>
Note: This list excludes scales found in 9-EDO.<br />
<!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="x18 Equal Divisions of the Octave-Useful Moment-of-Symmetry Scales-Pentatonic:"></a><!-- ws:end:WikiTextHeadingRule:8 --><span style="font-size: 1.1em;">Pentatonic:</span></h3>
3L2s Father Pentatonic: 4 4 3 4 3<br />
<!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="x18 Equal Divisions of the Octave-Useful Moment-of-Symmetry Scales-Hexatonic:"></a><!-- ws:end:WikiTextHeadingRule:10 --><span style="font-size: 1.1em;">Hexatonic:</span></h3>
6-Equal Whole-Tone Scale: 3 3 3 3 3 3<br />
4L2s Bicycle: 4 4 1 4 4 1<br />
2L4s Rice Hexatonic: 2 5 2 2 5 2<br />
<!-- ws:start:WikiTextHeadingRule:12:<h3> --><h3 id="toc6"><a name="x18 Equal Divisions of the Octave-Useful Moment-of-Symmetry Scales-Heptatonic:"></a><!-- ws:end:WikiTextHeadingRule:12 --><span style="font-size: 1.1em;">Heptatonic:</span></h3>
4L3s Amity/Mish Heptatonic: 3 2 3 2 3 3 2<br />
<!-- ws:start:WikiTextHeadingRule:14:<h3> --><h3 id="toc7"><a name="x18 Equal Divisions of the Octave-Useful Moment-of-Symmetry Scales-Octatonic:"></a><!-- ws:end:WikiTextHeadingRule:14 --><span style="font-size: 1.1em;">Octatonic:</span></h3>
5L3s Father Octatonic: 3 1 3 3 1 3 3 1<br />
2L6s Rice Octatonic: 2 2 3 2 2 2 3 2<br />
<!-- ws:start:WikiTextHeadingRule:16:<h3> --><h3 id="toc8"><a name="x18 Equal Divisions of the Octave-Useful Moment-of-Symmetry Scales-Decatonic:"></a><!-- ws:end:WikiTextHeadingRule:16 --><span style="font-size: 1.1em;">Decatonic:</span></h3>
8L2s Biggie Decatonic: 2 2 1 2 2 2 2 1 2 2<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="x18 Equal Divisions of the Octave-Application to Guitar"></a><!-- ws:end:WikiTextHeadingRule:18 --><span style="font-size: 1.3em;">Application to Guitar</span></h2>
18-EDO is an ideal scale for the first-time refretter, because you can retain all the even-number frets from 12-tET--essentially 1/3 of your work is done for you!<br />
<br />
The "Father Octatonic" scale maps very simply to a 6-string guitar tuned in "reverse-standard" tuning (tune using four 466.667¢ intervals, with one 533.333¢ interval between the 2nd and 3rd strings), making for a softer learning-curve than EDOs like 14, 16, or 21 (all of which are most evenly open-tuned using a series of sharpened 4ths and a minor or neutral 3rd, and whose scales thus often require position-shifting and/or larger stretches of the hand).<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="x18 Equal Divisions of the Octave-Commas"></a><!-- ws:end:WikiTextHeadingRule:20 -->Commas</h2>
18 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> < 18 29 42 51 62 67 |.)<br />
<table class="wiki_table">
<tr>
<th>Comma<br />
</th>
<th>Monzo<br />
</th>
<th>Value (Cents)<br />
</th>
<th>Name 1<br />
</th>
<th>Name 2<br />
</th>
</tr>
<tr>
<td style="text-align: center;">128/125<br />
</td>
<td>| 7 0 -3 ><br />
</td>
<td style="text-align: right;">41.06<br />
</td>
<td style="text-align: center;">Diesis<br />
</td>
<td style="text-align: center;">Augmented Comma<br />
</td>
</tr>
<tr>
<td style="text-align: center;">1212717/1210381<br />
</td>
<td>| 23 6 -14 ><br />
</td>
<td style="text-align: right;">3.34<br />
</td>
<td style="text-align: center;">Vishnuzma<br />
</td>
<td style="text-align: center;">Semisuper<br />
</td>
</tr>
<tr>
<td style="text-align: center;">50/49<br />
</td>
<td>| 1 0 2 -2 ><br />
</td>
<td style="text-align: right;">34.98<br />
</td>
<td style="text-align: center;">Tritonic Diesis<br />
</td>
<td style="text-align: center;">Jubilisma<br />
</td>
</tr>
<tr>
<td style="text-align: center;">686/675<br />
</td>
<td>| 1 -3 -2 3 ><br />
</td>
<td style="text-align: right;">27.99<br />
</td>
<td style="text-align: center;">Senga<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">875/864<br />
</td>
<td>| -5 -3 3 1 ><br />
</td>
<td style="text-align: right;">21.90<br />
</td>
<td style="text-align: center;">Keema<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">1728/1715<br />
</td>
<td>| 6 3 -1 -3 ><br />
</td>
<td style="text-align: right;">13.07<br />
</td>
<td style="text-align: center;">Orwellisma<br />
</td>
<td style="text-align: center;">Orwell Comma<br />
</td>
</tr>
<tr>
<td style="text-align: center;">16875/16807<br />
</td>
<td>| 0 3 4 -5 ><br />
</td>
<td style="text-align: right;">6.99<br />
</td>
<td style="text-align: center;">Mirkwai<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">3136/3125<br />
</td>
<td>| 6 0 -5 2 ><br />
</td>
<td style="text-align: right;">6.08<br />
</td>
<td style="text-align: center;">Hemimean<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">99/98<br />
</td>
<td>| -1 2 0 -2 1 ><br />
</td>
<td style="text-align: right;">17.58<br />
</td>
<td style="text-align: center;">Mothwellsma<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">100/99<br />
</td>
<td>| 2 -2 2 0 -1 ><br />
</td>
<td style="text-align: right;">17.40<br />
</td>
<td style="text-align: center;">Ptolemisma<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">65536/65219<br />
</td>
<td>| 16 0 0 -2 -3 ><br />
</td>
<td style="text-align: right;">8.39<br />
</td>
<td style="text-align: center;">Orgonisma<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">385/384<br />
</td>
<td>| -7 -1 1 1 1 ><br />
</td>
<td style="text-align: right;">4.50<br />
</td>
<td style="text-align: center;">Keenanisma<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">9801/9800<br />
</td>
<td>| -3 4 -2 -2 2 ><br />
</td>
<td style="text-align: right;">0.18<br />
</td>
<td style="text-align: center;">Kalisma<br />
</td>
<td style="text-align: center;">Gauss' Comma<br />
</td>
</tr>
<tr>
<td style="text-align: center;">91/90<br />
</td>
<td>| -1 -2 -1 1 1 ><br />
</td>
<td style="text-align: right;">19.13<br />
</td>
<td style="text-align: center;">Superleap<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="x18 Equal Divisions of the Octave-Listen"></a><!-- ws:end:WikiTextHeadingRule:22 -->Listen</h2>
<ul><li><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/18ETPrelude.mp3" rel="nofollow">18ETPrelude</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3" rel="nofollow">Prelude in 18et</a> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank">Chris Vaisvil</a> => <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=3" rel="nofollow" target="_blank">composer notes</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3" rel="nofollow">Flippertronics</a> by Chris Vaisvil</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3" rel="nofollow">Gerbils at the Wheel of Government</a> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1402" rel="nofollow" target="_blank">Chris Vaisvil (in 9 and 18 edo simultaneously)</a></li><li><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/DoAndroidsDreamof18ED2.mp3.mp3" rel="nofollow">Do Androids Dream Of 18ED2?</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/fb0306486b51c270607f90a0c795d531-202.html" rel="nofollow">blog entry</a>)</li></ul></body></html>