18edo
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=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. Stick a major third in that "4":6:7 and it's oh so sweet. 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 ||= 5L3s Notation || Nearest Ratio || Error (cents) || 17-Limit Ratios* || || 0 || 0 ||= **C** || 1/1 || 0 || **1/1** || || 1 || 66.667 ||= Db || 27/26 || +1.329 ||> 78/75, 75/72 || || 2 || 133.333 ||= C# || 27/25 || +0.096 ||> 51/55, 42/39 || || 3 || 200 ||= **D** || 9/8 || -3.910 || **9/8** || || 4 || 266.667 ||= Eb || 7/6 || -0.204 || **75/64** || || 5 || 333.333 ||= D# || 17/14 or 40/33 || -2.796 +0.293 || **39/32** || || 6 || 400 ||= **E** || 5/4 or 44/35 || +13.686 +3.822 ||> 64/55 || || 7 || 466.667 ||= **F** || 21/16 || -4.114 || **21/16** || || 8 || 533.333 ||= Gb || 15/11 || -3.617 ||> 102/75 || || 9 || 600 ||= F# || 17/12 or 24/17 || -3.000 +3.000 ||> 17/12 || || 10 || 666.667 ||= **G** || 22/15 || +3.617 ||> 75/51 || || 11 || 733.333 ||= Hb || 32/21 || +4.114 ||> 32/21 || || 12 || 800 ||= G# || 8/5 or 35/22 || -13.686 -3.8222 || **51/32** || || 13 || 866.667 ||= **H** || 28/17 or 33/20 || +2.796 -0.293 ||> 64/39 || || 14 || 933.333 ||= **A** || 12/7 || +0.204 || **55/32** || || 15 || 1000 ||= Bb || 16/9 || +3.910 ||> 16/9 || || 16 || 1066.667 ||= A# || 50/27 || -0.096 ||> 39/21 || || 17 || 1133.333 ||= **B** || 52/27 || -1.329 ||> 75/39 || || 18 || 1200 ||= **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)]]
Original HTML content:
<html><head><title>18edo</title></head><body><!-- 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. Stick a major third in that "4":6:7 and it's oh so sweet. 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 />
</td>
<td style="text-align: center;">5L3s Notation<br />
</td>
<td>Nearest Ratio<br />
</td>
<td>Error (cents)<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 />
</td>
<td style="text-align: center;">Db<br />
</td>
<td>27/26<br />
</td>
<td>+1.329<br />
</td>
<td style="text-align: right;">78/75, 75/72<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>133.333<br />
</td>
<td style="text-align: center;">C#<br />
</td>
<td>27/25<br />
</td>
<td>+0.096<br />
</td>
<td style="text-align: right;">51/55, 42/39<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>200<br />
</td>
<td style="text-align: center;"><strong>D</strong><br />
</td>
<td>9/8<br />
</td>
<td>-3.910<br />
</td>
<td><strong>9/8</strong><br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>266.667<br />
</td>
<td style="text-align: center;">Eb<br />
</td>
<td>7/6<br />
</td>
<td>-0.204<br />
</td>
<td><strong>75/64</strong><br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>333.333<br />
</td>
<td style="text-align: center;">D#<br />
</td>
<td>17/14 or 40/33<br />
</td>
<td>-2.796 +0.293<br />
</td>
<td><strong>39/32</strong><br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>400<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 />
</td>
<td style="text-align: right;">64/55<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>466.667<br />
</td>
<td style="text-align: center;"><strong>F</strong><br />
</td>
<td>21/16<br />
</td>
<td>-4.114<br />
</td>
<td><strong>21/16</strong><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>533.333<br />
</td>
<td style="text-align: center;">Gb<br />
</td>
<td>15/11<br />
</td>
<td>-3.617<br />
</td>
<td style="text-align: right;">102/75<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>600<br />
</td>
<td style="text-align: center;">F#<br />
</td>
<td>17/12 or 24/17<br />
</td>
<td>-3.000 +3.000<br />
</td>
<td style="text-align: right;">17/12<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>666.667<br />
</td>
<td style="text-align: center;"><strong>G</strong><br />
</td>
<td>22/15<br />
</td>
<td>+3.617<br />
</td>
<td style="text-align: right;">75/51<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>733.333<br />
</td>
<td style="text-align: center;">Hb<br />
</td>
<td>32/21<br />
</td>
<td>+4.114<br />
</td>
<td style="text-align: right;">32/21<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>800<br />
</td>
<td style="text-align: center;">G#<br />
</td>
<td>8/5 or 35/22<br />
</td>
<td>-13.686 -3.8222<br />
</td>
<td><strong>51/32</strong><br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>866.667<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 />
</td>
<td style="text-align: right;">64/39<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>933.333<br />
</td>
<td style="text-align: center;"><strong>A</strong><br />
</td>
<td>12/7<br />
</td>
<td>+0.204<br />
</td>
<td><strong>55/32</strong><br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>1000<br />
</td>
<td style="text-align: center;">Bb<br />
</td>
<td>16/9<br />
</td>
<td>+3.910<br />
</td>
<td style="text-align: right;">16/9<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>1066.667<br />
</td>
<td style="text-align: center;">A#<br />
</td>
<td>50/27<br />
</td>
<td>-0.096<br />
</td>
<td style="text-align: right;">39/21<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>1133.333<br />
</td>
<td style="text-align: center;"><strong>B</strong><br />
</td>
<td>52/27<br />
</td>
<td>-1.329<br />
</td>
<td style="text-align: right;">75/39<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>1200<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><em><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/18ETPrelude.mp3" rel="nofollow">18ETPrelude</a></em> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a></li><li><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3" rel="nofollow">Prelude in 18et</a></em> 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><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3" rel="nofollow">Flippertronics</a></em> by Chris Vaisvil</li><li><em><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></em> 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></ul></body></html>