24edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 602917870 - Original comment: ** |
Wikispaces>TallKite **Imported revision 621461643 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 18:48:08 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>621461643</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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*based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible. | *based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible. | ||
The 11th harmonic, and intervals derived from it, (11:10, 11:9, 11:8, 11:6, 12:11, 15:11, 16:11, 18:11, 20:11) are very well approximated in 24-tone equal temperament. The 24-tone interval of 550 cents is 1.3 cents flatter than 11:8 and is almost indistinguishable from it. In addition, the interval approximating 11:9 is 7 steps which is exactly half the perfect fifth. Some good chords in 24-tET are (the numbers are | Combining ups and downs notation with [[Kite's color notation|color notation]], qualities can be loosely associated with colors: | ||
||~ quality ||~ color ||~ monzo format ||~ examples || | |||
||= downminor ||= blue ||= {a, b, 0, 1} ||= 7/6, 7/4 || | |||
||= minor ||= fourthward white ||= {a, b}, b < -1 ||= 16/9, 32/27 || | |||
||= " ||= green ||= {a, b, -1} ||= 6/5, 9/5 || | |||
||= mid ||= jade ||= {a, b, 0, 0, 1} ||= 11/9, 11/6 || | |||
||= " ||= amber ||= {a, b, 0, 0, -1} ||= 12/11, 18/11 || | |||
||= major ||= yellow ||= {a, b, 1} ||= 5/4, 5/3 || | |||
||= " ||= fifthward white ||= {a, b}, b > 1 ||= 9/8, 27/16 || | |||
||= upmajor ||= red ||= {a, b, 0, -1} ||= 9/7, 12/7 || | |||
The 11th harmonic, and most intervals derived from it, (11:10, 11:9, 11:8, 11:6, 12:11, 15:11, 16:11, 18:11, 20:11) are very well approximated in 24-tone equal temperament. The 24-tone interval of 550 cents is 1.3 cents flatter than 11:8 and is almost indistinguishable from it. In addition, the interval approximating 11:9 is 7 steps which is exactly half the perfect fifth. Some good chords in 24-tET are (the numbers are edosteps, e.g. 4 is a major second, 8 is a major third): | |||
0-4-8-11-14 ("major" chord with a 9:8 and a 11:8 above the root) | 0-4-8-11-14 ("major" chord with a 9:8 and a 11:8 above the root) | ||
| Line 55: | Line 66: | ||
24 EDO tempers out the following commas. (Note: This assumes val < 24 38 56 67 83 89 |.) | 24 EDO tempers out the following commas. (Note: This assumes val < 24 38 56 67 83 89 |.) | ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||
||= 531441/524288 || | -19 12 > || | ||= 531441/524288 ||= | -19 12 > ||= 23.46 ||= Pythagorean Comma ||= ||= || | ||
||= 648/625 || | 3 4 -4 > || | ||= 648/625 ||= | 3 4 -4 > ||= 62.57 ||= Major Diesis ||= Diminished Comma ||= || | ||
||= 128/125 || | 7 0 -3 > || | ||= 128/125 ||= | 7 0 -3 > ||= 41.06 ||= Diesis ||= Augmented Comma ||= || | ||
||= 81/80 || | -4 4 -1 > || | ||= 81/80 ||= | -4 4 -1 > ||= 21.51 ||= Syntonic Comma ||= Didymos Comma ||= Meantone Comma || | ||
||= 2048/2025 || | 11 -4 -2 > || | ||= 2048/2025 ||= | 11 -4 -2 > ||= 19.55 ||= Diaschisma ||= ||= || | ||
||= 5201701/5149091 || | 26 -12 -3 > || | ||= 5201701/5149091 ||= | 26 -12 -3 > ||= 17.60 ||= Misty Comma ||= ||= || | ||
||= 32805/32768 || | -15 8 1 > || | ||= 32805/32768 ||= | -15 8 1 > ||= 1.95 ||= Schisma ||= ||= || | ||
||= 1465155/1465142 || | 161 -84 -12 > || | ||= 1465155/1465142 ||= | 161 -84 -12 > ||= 0.02 ||= Atom ||= ||= || | ||
||= 49/48 || | -4 -1 0 2 > || | ||= 49/48 ||= | -4 -1 0 2 > ||= 35.70 ||= Slendro Diesis ||= ||= || | ||
||= 245/243 || | 0 -5 1 2 > || | ||= 245/243 ||= | 0 -5 1 2 > ||= 14.19 ||= Sensamagic ||= ||= || | ||
||= 19683/19600 || | -4 9 -2 -2 > || | ||= 19683/19600 ||= | -4 9 -2 -2 > ||= 7.32 ||= Cataharry ||= ||= || | ||
||= 6144/6125 || | 11 1 -3 -2 > || | ||= 6144/6125 ||= | 11 1 -3 -2 > ||= 5.36 ||= Porwell ||= ||= || | ||
||= 121/120 || | -3 -1 -1 0 2 > || | ||= 121/120 ||= | -3 -1 -1 0 2 > ||= 14.37 ||= Biyatisma ||= ||= || | ||
||= 176/175 || | 4 0 -2 -1 1 > || | ||= 176/175 ||= | 4 0 -2 -1 1 > ||= 9.86 ||= Valinorsma ||= ||= || | ||
||= 896/891 || | 7 -4 0 1 -1 > || | ||= 896/891 ||= | 7 -4 0 1 -1 > ||= 9.69 ||= Pentacircle ||= ||= || | ||
||= 243/242 || | -1 5 0 0 -2 > || | ||= 243/242 ||= | -1 5 0 0 -2 > ||= 7.14 ||= Rastma ||= ||= || | ||
||= 385/384 || | -7 -1 1 1 1 > || | ||= 385/384 ||= | -7 -1 1 1 1 > ||= 4.50 ||= Keenanisma ||= ||= || | ||
||= 9801/9800 || | -3 4 -2 -2 2 > || | ||= 9801/9800 ||= | -3 4 -2 -2 2 > ||= 0.18 ||= Kalisma ||= Gauss' Comma ||= || | ||
||= 91/90 || | -1 -2 -1 1 0 1 > || | ||= 91/90 ||= | -1 -2 -1 1 0 1 > ||= 19.13 ||= Superleap ||= ||= || | ||
||= 676/675 || | 2 -3 -2 0 0 2 > || | ||= 676/675 ||= | 2 -3 -2 0 0 2 > ||= 2.56 ||= Parizeksma ||= ||= || | ||
=Intervals= | =Intervals= | ||
24 EDO breaks intervals into two sets of five cartegories. Infra - Minor - Neutral - Major - Ultra for seconds, thirds, sixths, and sevenths; and diminished - narrow - perfect - wide - augmented for | 24 EDO breaks intervals into two sets of five cartegories. Infra - Minor - Neutral - Major - Ultra for seconds, thirds, sixths, and sevenths; and diminished - narrow - perfect - wide - augmented for fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth. | ||
fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth. | |||
These are the intervals of 24 EDO that do not exist in 12 EDO: 2 | These are the intervals of 24 EDO that do not exist in 12 EDO: 2 | ||
| Line 231: | Line 241: | ||
Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 | Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 | ||
Alternatively, [[ups and downs notation]] can be used: | Alternatively, [[ups and downs notation]] can be used. Here are the blue, green, jade, yellow and red triads: | ||
0-5-14 = | ||~ color of the 3rd ||~ JI chord ||~ notes as edosteps ||~ notes of C chord ||~ written name ||~ spoken name || | ||
0-6-14 = | ||= blue ||= 6:7:9 ||= 0-5-14 ||= C Ebv G ||= C.vm ||= C downminor || | ||
0-7-14 = | ||= green ||= 10:12:15 ||= 0-6-14 ||= C Eb G ||= Cm ||= C minor || | ||
0-8-14 = | ||= jade ||= 18:22:27 ||= 0-7-14 ||= C Ev G ||= C~ ||= C mid || | ||
0-9-14 = | ||= yellow ||= 4:5:6 ||= 0-8-14 ||= C E G ||= C ||= C major or C || | ||
||= red ||= 14:18:27 ||= 0-9-14 ||= C E^ G ||= C.^ ||= C upmajor or C dot up || | |||
For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | |||
=Rank two temperaments= | =Rank two temperaments= | ||
| Line 813: | Line 824: | ||
*based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible.<br /> | *based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible.<br /> | ||
<br /> | <br /> | ||
Combining ups and downs notation with <a class="wiki_link" href="/Kite%27s%20color%20notation">color notation</a>, qualities can be loosely associated with colors:<br /> | |||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<th> | <th>quality<br /> | ||
</th> | </th> | ||
<th> | <th>color<br /> | ||
</th> | </th> | ||
<th> | <th>monzo format<br /> | ||
</th> | </th> | ||
<th> | <th>examples<br /> | ||
</th> | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">downminor<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">blue<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">{a, b, 0, 1}<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">7/6, 7/4<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">minor<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">fourthward white<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">{a, b}, b &lt; -1<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">16/9, 32/27<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">green<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">{a, b, -1}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">6/5, 9/5<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">mid<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">jade<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">{a, b, 0, 0, 1}<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">11/9, 11/6<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">amber<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">{a, b, 0, 0, -1}<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">12/11, 18/11<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">major<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">yellow<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">{a, b, 1}<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">5/4, 5/3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">fifthward white<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">{a, b}, b &gt; 1<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">9/8, 27/16<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">upmajor<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">red<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">{a, b, 0, -1}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">9/7, 12/7<br /> | ||
</td> | </td> | ||
</tr> | |||
</table> | |||
<br /> | |||
The 11th harmonic, and most intervals derived from it, (11:10, 11:9, 11:8, 11:6, 12:11, 15:11, 16:11, 18:11, 20:11) are very well approximated in 24-tone equal temperament. The 24-tone interval of 550 cents is 1.3 cents flatter than 11:8 and is almost indistinguishable from it. In addition, the interval approximating 11:9 is 7 steps which is exactly half the perfect fifth. Some good chords in 24-tET are (the numbers are edosteps, e.g. 4 is a major second, 8 is a major third):<br /> | |||
<br /> | |||
0-4-8-11-14 (&quot;major&quot; chord with a 9:8 and a 11:8 above the root)<br /> | |||
Its inversion, 0-3-6-10-14 (&quot;minor&quot;)<br /> | |||
0-7-14 (&quot;neutral&quot;)<br /> | |||
0-5-10 (another kind of &quot;neutral&quot;, splitting the fourth in two. The 0-5-10 can be extended into a pentatonic scale, 0-5-10-14-19-24 (<a class="wiki_link" href="/godzilla">godzilla</a>), that is close to equi-pentatonic and also close to several Indonesian slêndros. In a similar way 0-7-14 extends to 0-4-7-11-14-18-21-24 (<a class="wiki_link" href="/mohajira">mohajira</a>), a heptatonic scale close to several Arabic scales.)<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc2"><a name="x24edo as a temperament--Commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->Commas</h3> | |||
24 EDO tempers out the following commas. (Note: This assumes val &lt; 24 38 56 67 83 89 |.)<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> | |||
<th>Name 3<br /> | |||
</th> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">531441/524288<br /> | ||
</td> | </td> | ||
<td>| - | <td style="text-align: center;">| -19 12 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">23.46<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Pythagorean Comma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">648/625<br /> | ||
</td> | |||
<td style="text-align: center;">| 3 4 -4 &gt;<br /> | |||
</td> | </td> | ||
<td | <td style="text-align: center;">62.57<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">Major Diesis<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Diminished Comma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">128/125<br /> | ||
</td> | |||
<td style="text-align: center;">| 7 0 -3 &gt;<br /> | |||
</td> | </td> | ||
<td | <td style="text-align: center;">41.06<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">Diesis<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Augmented Comma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">81/80<br /> | ||
</td> | </td> | ||
<td>| | <td style="text-align: center;">| -4 4 -1 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">21.51<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Syntonic Comma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">Didymos Comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">Meantone Comma<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">2048/2025<br /> | ||
</td> | </td> | ||
<td>| - | <td style="text-align: center;">| 11 -4 -2 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">19.55<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Diaschisma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">5201701/5149091<br /> | ||
</td> | </td> | ||
<td>| | <td style="text-align: center;">| 26 -12 -3 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">17.60<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Misty Comma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">32805/32768<br /> | ||
</td> | </td> | ||
<td>| | <td style="text-align: center;">| -15 8 1 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">1.95<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Schisma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1465155/1465142<br /> | ||
</td> | </td> | ||
<td>| - | <td style="text-align: center;">| 161 -84 -12 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">0.02<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Atom<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">49/48<br /> | ||
</td> | </td> | ||
<td>| - | <td style="text-align: center;">| -4 -1 0 2 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">35.70<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Slendro Diesis<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">245/243<br /> | ||
</td> | </td> | ||
<td>| - | <td style="text-align: center;">| 0 -5 1 2 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">14.19<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Sensamagic<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">19683/19600<br /> | ||
</td> | </td> | ||
<td>| - | <td style="text-align: center;">| -4 9 -2 -2 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">7.32<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Cataharry<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">6144/6125<br /> | ||
</td> | </td> | ||
<td>| | <td style="text-align: center;">| 11 1 -3 -2 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">5.36<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Porwell<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
< | <td style="text-align: center;">121/120<br /> | ||
</ | </td> | ||
< | <td style="text-align: center;">| -3 -1 -1 0 2 &gt;<br /> | ||
</ | </td> | ||
<td style="text-align: center;">14.37<br /> | |||
</td> | |||
<td style="text-align: center;">Biyatisma<br /> | |||
</ | </td> | ||
< | <td style="text-align: center;"><br /> | ||
</ | </td> | ||
< | <td style="text-align: center;"><br /> | ||
</ | </td> | ||
< | |||
</ | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">176/175<br /> | ||
</td> | |||
<td style="text-align: center;">| 4 0 -2 -1 1 &gt;<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">9.86<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Valinorsma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">896/891<br /> | ||
</td> | |||
<td style="text-align: center;">| 7 -4 0 1 -1 &gt;<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">9.69<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Pentacircle<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">243/242<br /> | ||
</td> | |||
<td style="text-align: center;">| -1 5 0 0 -2 &gt;<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">7.14<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Rastma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">385/384<br /> | ||
</td> | |||
<td style="text-align: center;">| -7 -1 1 1 1 &gt;<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">4.50<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Keenanisma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">9801/9800<br /> | ||
</td> | |||
<td style="text-align: center;">| -3 4 -2 -2 2 &gt;<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">0.18<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Kalisma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Gauss' Comma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">91/90<br /> | ||
</td> | |||
<td style="text-align: center;">| -1 -2 -1 1 0 1 &gt;<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">19.13<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Superleap<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">676/675<br /> | ||
</td> | |||
<td style="text-align: center;">| 2 -3 -2 0 0 2 &gt;<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">2.56<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Parizeksma<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:8 -->Intervals</h1> | |||
<br /> | |||
24 EDO breaks intervals into two sets of five cartegories. Infra - Minor - Neutral - Major - Ultra for seconds, thirds, sixths, and sevenths; and diminished - narrow - perfect - wide - augmented for fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth.<br /> | |||
<br /> | |||
These are the intervals of 24 EDO that do not exist in 12 EDO: 2<br /> | |||
<a class="wiki_link" href="/24%20EDO%20Interval%20names%20and%20Harmonies">See full article on 24 Edo intervals.</a><br /> | |||
<table class="wiki_table"> | |||
<tr> | <tr> | ||
<td style="text-align: center;"> | <th colspan="2">The twelve new intervals in 24edo<br /> | ||
</th> | |||
<th colspan="3">some nearby JI intervals<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<th>cents<br /> | |||
</th> | |||
<th>common names<br /> | |||
</th> | |||
<th>frequency ratio<br /> | |||
</th> | |||
<th>cents<br /> | |||
</th> | |||
<th>common name<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">50<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">wide | <td style="text-align: center;">quartertone<br /> | ||
infra second, wide unison<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/ | <td style="text-align: center;"><a class="wiki_link" href="/36_35">36/35</a><br /> | ||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/35_34">35/34</a><br /> | ||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/34_33">34/33</a><br /> | ||
<a class="wiki_link" href="/33_32">33/32</a><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">48.770<br /> | ||
50.184<br /> | |||
51.682<br /> | |||
53.273<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">large septimal quarter-tone (Archytas)<br /> | ||
large 17-limit quartertone<br /> | |||
17-limit | small 17-limit quartertone<br /> | ||
33rd harmonic<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">150<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">neutral | <td style="text-align: center;">neutral second<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/ | <td style="text-align: center;"><a class="wiki_link" href="/12_11">12/11</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">150.637<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">large undecimal neutral second<br /> | ||
undecimal neutral | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">250<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">ultra | <td style="text-align: center;">ultra second<br /> | ||
<span style="line-height: 1.5;">infra third</span><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/ | <td style="text-align: center;"><a class="wiki_link" href="/144_125">144/125</a><br /> | ||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/15_13">15/13</a><br /> | ||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/52_45">52/45</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">244.969<br /> | ||
247.741<br /> | |||
250.304<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">diminished third (6/5 x 24/25)<br /> | ||
..<br /> | ..<br /> | ||
..<br /> | ..<br /> | ||
| Line 1,317: | Line 1,310: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">350<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">neutral | <td style="text-align: center;">neutral third<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/ | <td style="text-align: center;"><a class="wiki_link" href="/11_9">11/9</a><br /> | ||
<a class="wiki_link" href="/27_22">27/22</a><br /> | |||
<a class="wiki_link" href="/16_13">16/13</a><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">347.408<br /> | ||
354.547<br /> | |||
359.472<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">undecimal neutral | <td style="text-align: center;">undecimal neutral third<br /> | ||
..<br /> | |||
tridecimal neutral third<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">450<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">ultra | <td style="text-align: center;">minor fourth, ultra third, narrow fourth<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/ | <td style="text-align: center;"><a class="wiki_link" href="/22_17">22/17</a><br /> | ||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/35_27">35/27</a><br /> | ||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/13_10">13/10</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">446.363<br /> | ||
449.275<br /> | |||
454.214<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">17-limit supermajor third<br /> | ||
..<br /> | ..<br /> | ||
tridecimal subfourth<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">550<br /> | |||
</td> | |||
<td style="text-align: center;">wide fourth<br /> | |||
</td> | |||
<td style="text-align: center;"><a class="wiki_link" href="/11_8">11/8</a><br /> | |||
</td> | |||
<td style="text-align: center;">551.318<br /> | |||
</td> | |||
<td style="text-align: center;">undecimal superfourth, harmonic 11th<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">650<br /> | |||
</td> | |||
<td style="text-align: center;">narrow fifth<br /> | |||
</td> | |||
<td style="text-align: center;"><a class="wiki_link" href="/16_11">16/11</a><br /> | |||
</td> | |||
<td style="text-align: center;">648.682<br /> | |||
</td> | |||
<td style="text-align: center;">undecimal subfifth, 11th subharmonic<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
< | <td style="text-align: center;">750<br /> | ||
</ | </td> | ||
< | <td style="text-align: center;">wide fifth, infra sixth<br /> | ||
</ | </td> | ||
< | <td style="text-align: center;"><a class="wiki_link" href="/20_13">20/13</a><br /> | ||
</ | <a class="wiki_link" href="/54_35">54/35</a><br /> | ||
< | <a class="wiki_link" href="/17_11">17/11</a><br /> | ||
</ | </td> | ||
<td style="text-align: center;">745.786<br /> | |||
750.725<br /> | |||
753.637<br /> | |||
</td> | |||
<td style="text-align: center;">tridecimal superfifth<br /> | |||
..<br /> | |||
17-limit subminor sixth<br /> | |||
</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>neutral<br /> | <td style="text-align: center;">850<br /> | ||
</td> | |||
<td style="text-align: center;">neutral sixth<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;"><a class="wiki_link" href="/13_8">13/8</a><br /> | ||
<a class="wiki_link" href="/44_27">44/27</a><br /> | |||
<a class="wiki_link" href="/18_11">18/11</a><br /> | |||
</td> | </td> | ||
<td>1 v3 5 v7<br /> | <td style="text-align: center;">840.528<br /> | ||
845.453<br /> | |||
852.592<br /> | |||
</td> | |||
<td style="text-align: center;">overtone sixth, 13th harmonic<br /> | |||
..<br /> | |||
undecimal neutral sixth<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">950<br /> | |||
</td> | |||
<td style="text-align: center;">ultra sixth , infra seventh<br /> | |||
</td> | |||
<td style="text-align: center;"><a class="wiki_link" href="/45_26">45/26</a><br /> | |||
<a class="wiki_link" href="/26_15">26/15</a><br /> | |||
<a class="wiki_link" href="/125_72">125/72</a><br /> | |||
</td> | |||
<td style="text-align: center;">949.696<br /> | |||
952.259<br /> | |||
955.031<br /> | |||
</td> | |||
<td style="text-align: center;">..<br /> | |||
..<br /> | |||
..<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">1050<br /> | |||
</td> | |||
<td style="text-align: center;">neutral seventh<br /> | |||
</td> | |||
<td style="text-align: center;"><a class="wiki_link" href="/11_6">11/6</a><br /> | |||
</td> | |||
<td style="text-align: center;">1049.363<br /> | |||
</td> | |||
<td style="text-align: center;">undecimal neutral seventh<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">1150<br /> | |||
</td> | |||
<td style="text-align: center;">ultra seventh, narrow octave<br /> | |||
</td> | |||
<td style="text-align: center;"><a class="wiki_link" href="/31_16">31/16</a><br /> | |||
<a class="wiki_link" href="/33_17">33/17</a><br /> | |||
<a class="wiki_link" href="/35_18">35/18</a><br /> | |||
</td> | |||
<td style="text-align: center;">1145.036<br /> | |||
1148.318<br /> | |||
1151.230<br /> | |||
</td> | |||
<td style="text-align: center;">31st harmonic<br /> | |||
..<br /> | |||
..<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc4"><a name="Notation"></a><!-- ws:end:WikiTextHeadingRule:10 -->Notation</h1> | |||
There have been disputes about disadvantages of various systems for notating quarter tones. Here are some of the few systems along with pros and cons.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc5"><a name="Notation-Mainstream Quartertone Notation"></a><!-- ws:end:WikiTextHeadingRule:12 -->Mainstream Quartertone Notation</h2> | |||
<!-- ws:start:WikiTextRemoteImageRule:1872:&lt;img src=&quot;http://www.wfg.woodwind.org/n/s14_blue.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /><!-- ws:end:WikiTextRemoteImageRule:1872 --> or ^ = quarter-tone sharp or &quot;Jump&quot; or &quot;up&quot;<br /> | |||
<!-- ws:start:WikiTextRemoteImageRule:1873:&lt;img src=&quot;http://www.wfg.woodwind.org/n/s34_blue.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /><!-- ws:end:WikiTextRemoteImageRule:1873 --> or #^ or ^# = three-quarter-tone sharp or &quot;Jump-Sharp&quot; or &quot;upsharp&quot;<br /> | |||
<!-- ws:start:WikiTextRemoteImageRule:1874:&lt;img src=&quot;http://www.wfg.woodwind.org/n/f14_blue.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /><!-- ws:end:WikiTextRemoteImageRule:1874 --> or v = quarter-tone flat or &quot;Drop&quot; or &quot;down&quot;<br /> | |||
<!-- ws:start:WikiTextRemoteImageRule:1875:&lt;img src=&quot;http://www.wfg.woodwind.org/n/f34_blue.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /><!-- ws:end:WikiTextRemoteImageRule:1875 --> or bv or vb = three-quarter-tone flat or &quot;Drop-Flat&quot; or &quot;downflat&quot;<br /> | |||
<br /> | |||
Pros: Familiar, fairly easy to learn<br /> | |||
Cons: Clutters a score easily, can get confusing when sight read at faster paces<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="Notation-Alternate Quartertone Accidentals"></a><!-- ws:end:WikiTextHeadingRule:14 -->Alternate Quartertone Accidentals</h2> | |||
<!-- ws:start:WikiTextRemoteImageRule:1876:&lt;img src=&quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /><!-- ws:end:WikiTextRemoteImageRule:1876 --> = quarter-tone sharp or Jump<br /> | |||
††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp<br /> | |||
<!-- ws:start:WikiTextRemoteImageRule:1877:&lt;img src=&quot;http://www.dolmetsch.com/onequarterflat.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /><!-- ws:end:WikiTextRemoteImageRule:1877 --> = quarter-tone flat or Drop<br /> | |||
<!-- ws:start:WikiTextRemoteImageRule:1878:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /><!-- ws:end:WikiTextRemoteImageRule:1878 --> = three quarter-tones flat or drop-flat<br /> | |||
For example, the scale 0-5-10-15-20 is written as C-D<!-- ws:start:WikiTextRemoteImageRule:1879:&lt;img src=&quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /><!-- ws:end:WikiTextRemoteImageRule:1879 --> (or E<!-- ws:start:WikiTextRemoteImageRule:1880:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /><!-- ws:end:WikiTextRemoteImageRule:1880 -->) F G<!-- ws:start:WikiTextRemoteImageRule:1881:&lt;img src=&quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /><!-- ws:end:WikiTextRemoteImageRule:1881 --> (or A<!-- ws:start:WikiTextRemoteImageRule:1882:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /><!-- ws:end:WikiTextRemoteImageRule:1882 -->) Bb.<br /> | |||
<br /> | |||
Pros: Very easy to distinguish accidentals from one another<br /> | |||
Cons: Not practical, tends to clutter a score<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc7"><a name="Notation-And in Persian music"></a><!-- ws:end:WikiTextHeadingRule:16 --><span style="line-height: 1.5;">And in Persian music</span></h2> | |||
<!-- ws:start:WikiTextRemoteImageRule:1883:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 25px; width: 12px;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png" alt="external image 200px-Koron_sign.svg.png" title="external image 200px-Koron_sign.svg.png" style="height: 25px; width: 12px;" /><!-- ws:end:WikiTextRemoteImageRule:1883 -->Koron (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow">en</a> | <a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow">fa</a>) = quarter-tone flat or Jump<br /> | |||
<!-- ws:start:WikiTextRemoteImageRule:1884:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 25px; width: 15px;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png" alt="external image 200px-Sori_sign.svg.png" title="external image 200px-Sori_sign.svg.png" style="height: 25px; width: 15px;" /><!-- ws:end:WikiTextRemoteImageRule:1884 -->Sori (<a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%28%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C%29" rel="nofollow">fa</a>) = quarter-tone sharp or Drop<br /> | |||
<br /> | |||
Pros: Easy to read<br /> | |||
Cons: Hard to write on a computer, doesn't fit with standard notation well<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc8"><a name="Notation-Sagittal Notation"></a><!-- ws:end:WikiTextHeadingRule:18 -->Sagittal Notation</h2> | |||
<a class="wiki_link" href="/Sagittal%20notation">Sagittal notation</a> works extremely well for 24 Edo notation as well as other systems.<br /> | |||
It's easy on the eyes, easy to recognize the various symbols and keeps a score looking tidy and neat.<br /> | |||
A possibility for the best approach would be to not use traditional sharps and flats altogether and replace them<br /> | |||
with Sagittal signs for sharp and flat.<br /> | |||
<br /> | |||
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<br /> | |||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc9"><a name="Interval Alterations"></a><!-- ws:end:WikiTextHeadingRule:20 -->Interval Alterations</h1> | |||
The special alterations of the intervals and chords of 12 equal can be notated like this:<br /> | |||
<br /> | |||
Supermajor or &quot;<strong>Tendo</strong>&quot; is a major interval raised a quarter tone<br /> | |||
Subminor or &quot;<strong>Arto</strong>&quot; is a minor interval lowered a quarter tone<br /> | |||
Neutral are intervals that exist between the major and minor version of an interval<br /> | |||
The prefix <strong>under</strong> indicates a perfect interval lowered by one quarter tone<br /> | |||
The prefix <strong>over</strong> indicates a perfect interval raised by a quarter tone<br /> | |||
<br /> | |||
The Latin words &quot;tendo&quot; (meaning &quot;expand&quot;) and &quot;arto&quot; (meaning &quot;contract&quot;) can be used to replace the words &quot;supermajor&quot; and &quot;subminor&quot; in order to shorten the names of the intervals.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc10"><a name="Chord Structures"></a><!-- ws:end:WikiTextHeadingRule:22 -->Chord Structures</h1> | |||
24edo features a rich variety on not only new chords, but also alterations that can be used with regular 12 Edo chords. For example, an approximation of the ninth, eleventh, and thirteenth harmonic can be added to a major triad to create a sort of super-extended chord structure of a major chord: 4:5:6:9:11:13.<br /> | |||
<br /> | |||
As for entirely new chords, 24edo features many possibilities for chords. The most obvious is the neutral or mid triad 0-7-14 however there are other options such as<br /> | |||
0-9-14 (Ultra Triad or upmajor triad) and 0-5-14 (Infra Triad or downminor triad), the chord names being based on what kind of third is in the chord.<br /> | |||
These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.<br /> | |||
For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad. 0-14-21-35 <a class="wiki_link" href="/William%20Lynch">William Lynch</a> considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality. 24 edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system.<br /> | |||
<br /> | |||
William Lynch considers these as some possible good tetrads:<br /> | |||
<br /> | |||
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<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>Chord name<br /> | |||
</th> | |||
<th>Degrees of 24edo<br /> | |||
</th> | |||
<th>Chord spelling<br /> | |||
</th> | |||
<th>Audio example<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>neutral<br /> | |||
</td> | |||
<td>0 7 14 21<br /> | |||
</td> | |||
<td>1 v3 5 v7<br /> | |||
</td> | |||
<td><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/Neutral%20Tetrad%20on%20C.mp3?h=30&amp;w=200&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;Neutral Tetrad on C.mp3&amp;quot; width=&amp;quot;200&amp;quot; height=&amp;quot;30&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;30&quot; width=&quot;200&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="200" height="30" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FNeutral%252BTetrad%252Bon%252BC.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=200&height=30"></embed><!-- ws:end:WikiTextMediaRule:0 --><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>arto<br /> | |||
</td> | |||
<td>0 5 14 20<br /> | |||
</td> | |||
<td>1 bv3 5 b7<br /> | |||
</td> | |||
<td><!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/arto%20tetrad%20on%20C.mp3?h=30&amp;w=200&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;arto tetrad on C.mp3&amp;quot; width=&amp;quot;200&amp;quot; height=&amp;quot;30&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;30&quot; width=&quot;200&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="200" height="30" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Farto%252Btetrad%252Bon%252BC.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=200&height=30"></embed><!-- ws:end:WikiTextMediaRule:1 --><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>tendo<br /> | |||
</td> | |||
<td>0 9 14 19<br /> | |||
</td> | |||
<td>1 ^3 5 bv7<br /> | |||
</td> | |||
<td>...<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
Due to convenience, the names Arto and tendo have been changed to Ultra and Infra.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc11"><a name="Naming Chords in 24edo"></a><!-- ws:end:WikiTextHeadingRule:24 -->Naming Chords in 24edo</h1> | |||
Naming chords in 24edo can be achieved by adding a few things to the already [[#|existing]] set of terms that are used to name 12edo chords.<br /> | |||
They are:<br /> | |||
Super + perfect interval such as &quot;perfect fifth&quot; means to raise it by a quarter tone<br /> | |||
Sub + perfect interval means to lower a quarter tone<br /> | |||
Sharp is to raise by one half tone<br /> | |||
Flat is to raise by a half tone<br /> | |||
Neutral, arto and tendo refer to triads or tetrads<br /> | |||
Neutral, arto, or tendo + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively<br /> | |||
<br /> | |||
Examples:<br /> | |||
Neutral Super Eleventh or neut^11 = C neutral 7th chord with a super 11th thrown on top<br /> | |||
Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11<br /> | |||
<br /> | |||
Alternatively, <a class="wiki_link" href="/ups%20and%20downs%20notation">ups and downs notation</a> can be used. Here are the blue, green, jade, yellow and red triads:<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>color of the 3rd<br /> | |||
</th> | |||
<th>JI chord<br /> | |||
</th> | |||
<th>notes as edosteps<br /> | |||
</th> | |||
<th>notes of C chord<br /> | |||
</th> | |||
<th>written name<br /> | |||
</th> | |||
<th>spoken name<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">blue<br /> | |||
</td> | |||
<td style="text-align: center;">6:7:9<br /> | |||
</td> | |||
<td style="text-align: center;">0-5-14<br /> | |||
</td> | |||
<td style="text-align: center;">C Ebv G<br /> | |||
</td> | |||
<td style="text-align: center;">C.vm<br /> | |||
</td> | |||
<td style="text-align: center;">C downminor<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">green<br /> | |||
</td> | |||
<td style="text-align: center;">10:12:15<br /> | |||
</td> | |||
<td style="text-align: center;">0-6-14<br /> | |||
</td> | |||
<td style="text-align: center;">C Eb G<br /> | |||
</td> | |||
<td style="text-align: center;">Cm<br /> | |||
</td> | |||
<td style="text-align: center;">C minor<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">jade<br /> | |||
</td> | |||
<td style="text-align: center;">18:22:27<br /> | |||
</td> | |||
<td style="text-align: center;">0-7-14<br /> | |||
</td> | |||
<td style="text-align: center;">C Ev G<br /> | |||
</td> | |||
<td style="text-align: center;">C~<br /> | |||
</td> | |||
<td style="text-align: center;">C mid<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">yellow<br /> | |||
</td> | |||
<td style="text-align: center;">4:5:6<br /> | |||
</td> | |||
<td style="text-align: center;">0-8-14<br /> | |||
</td> | |||
<td style="text-align: center;">C E G<br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | </td> | ||
<td | <td style="text-align: center;">C major or C<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td | <td style="text-align: center;">red<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">14:18:27<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">0-9-14<br /> | |||
<td> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">C E^ G<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">C.^<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">C upmajor or C dot up<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
For a more complete list, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.<br /> | |||
<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc12"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:26 -->Rank two temperaments</h1> | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc12"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:26 -->Rank two temperaments</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc23"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:48 -->Instruments<!-- ws:start:WikiTextAnchorRule:91:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@instruments&quot; title=&quot;Anchor: instruments&quot;/&gt; --><a name="instruments"></a><!-- ws:end:WikiTextAnchorRule:91 --></h1> | <!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc23"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:48 -->Instruments<!-- ws:start:WikiTextAnchorRule:91:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@instruments&quot; title=&quot;Anchor: instruments&quot;/&gt; --><a name="instruments"></a><!-- ws:end:WikiTextAnchorRule:91 --></h1> | ||
The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This <a class="wiki_link" href="/Microtonal%20Keyboards#twelvenoteoctavescales">&quot;12 note octave scales&quot;</a> approach is used in a wide part of the existing literature - see below.<br /> | The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This <a class="wiki_link" href="/Microtonal%20Keyboards#twelvenoteoctavescales">&quot;12 note octave scales&quot;</a> approach is used in a wide part of the existing literature - see below.<br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1885:&lt;img src=&quot;http://www.swordguitars.com/Sword_quartertone_stratsm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 195px; width: 406px;&quot; /&gt; --><img src="http://www.swordguitars.com/Sword_quartertone_stratsm.jpg" alt="external image Sword_quartertone_stratsm.jpg" title="external image Sword_quartertone_stratsm.jpg" style="height: 195px; width: 406px;" /><!-- ws:end:WikiTextRemoteImageRule:1885 -->24-tone &quot;1/4-tone&quot; Guitar by Ron Sword / Sword guitars<br /> | ||
<br /> | <br /> | ||
Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called <a class="wiki_link" href="/Iceface%20Tuning">Iceface tuning</a>.<br /> | Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called <a class="wiki_link" href="/Iceface%20Tuning">Iceface tuning</a>.<br /> | ||
| Line 2,286: | Line 2,477: | ||
<!-- ws:start:WikiTextHeadingRule:56:&lt;h1&gt; --><h1 id="toc27"><a name="Practical Theory / Books"></a><!-- ws:end:WikiTextHeadingRule:56 -->Practical Theory / Books</h1> | <!-- ws:start:WikiTextHeadingRule:56:&lt;h1&gt; --><h1 id="toc27"><a name="Practical Theory / Books"></a><!-- ws:end:WikiTextHeadingRule:56 -->Practical Theory / Books</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:1886:&lt;img src=&quot;http://ronsword.com/images/24_tet_Coversm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 236px; width: 179px;&quot; /&gt; --><img src="http://ronsword.com/images/24_tet_Coversm.jpg" alt="external image 24_tet_Coversm.jpg" title="external image 24_tet_Coversm.jpg" style="height: 236px; width: 179px;" /><!-- ws:end:WikiTextRemoteImageRule:1886 --><strong>&quot;Icosakaiteraphonic Scales for Guitar&quot;</strong> - A Book for Twenty-Four Equal Divisions of the Octave on guitar, or 'Quarter-tones'. Features a practical approach to understanding the tuning, and over 550 Scale Examples on Nine-String finger board charts, which allows for both symmetrical tuning visualization and standard guitar tuning- helpful for bassists and large range guitarists as well. Includes MOS, DE, and *all* the Scales / Modes from the list above.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc28"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:58 -->External links</h1> | <!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc28"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:58 -->External links</h1> | ||