20edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 601339770 - Original comment: ** |
Wikispaces>TallKite **Imported revision 602738788 - 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>2016-12-22 04:28:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602738788</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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=Properties= | =Properties= | ||
==Intervals== | ==Intervals== | ||
|| **Degree** || **Cents | ||= **Degree** ||= **Cents** ||||||= [[Ups and Downs Notation|up/down notation]] ||= **Approximate** | ||
**Ratios** ||= **Nearest** | **Ratios** ||= **Nearest** | ||
**Harmonic** || | **Harmonic** || | ||
|| 0 || 0 || unison || P1 || D ||= 1/1 ||= 1 || | ||= 0 ||= 0 ||= unison ||= P1 ||= D ||= 1/1 ||= 1 || | ||
|| 1 || 60 | ||= 1 ||= 60 ||= upminor 2nd ||= ^m2 ||= D^ ||= 29/28 ||= 33 || | ||
||= 2 ||= 120 ||= mid 2nd ||= ~2 ||= D^^, Evv ||= 14/13, 15/14 ||= 69 || | |||
|| 2 || 120 | ||= 3 ||= 180 ||= downmajor 2nd ||= vM2 ||= Ev ||= 10/9 ||= 71 || | ||
||= 4 ||= 240 ||= major 2nd, minor 3rd ||= M2, m3 ||= E, F ||= 8/7, 15/13 ||= 37 || | |||
|| 3 || 180 | ||= 5 ||= 300 ||= upminor 3rd ||= ^m3 ||= F^ ||= 13/11, 19/16 ||= 19 || | ||
||= 6 ||= 360 ||= mid 3rd ||= ~3 ||= F^^ ||= 16/13, 5/4 ||= 79 || | |||
|| 4 || 240 | ||= 7 ||= 420 ||= downmajor 3rd ||= vM3 ||= F#v ||= [[14_11|14/11]], [[51_40|51/40]] ||= 41 || | ||
||= 8 ||= 480 ||= major 3rd, perfect fourth ||= M3, P4 ||= F#, G ||= 25/19, 4/3 ||= 21 || | |||
minor 3rd || M2, m3 || E, F ||= 8/7, 15/13 ||= 37 || | ||= 9 ||= 540 ||= up-fourth ||= ^4 ||= G^ ||= 15/11, 11/8 ||= 11 || | ||
|| 5 || 300 | ||= 10 ||= 600 ||= double-up fourth, | ||
double-down fifth ||= ^^4, vv5 ||= G^^, Avv ||= 7/5 ||= 91 || | |||
|| 6 || 360 | ||= 11 ||= 660 ||= down-fifth ||= v5 ||= Av ||= 22/15, 16/11 ||= 47 || | ||
||= 12 ||= 720 ||= fifth ||= P5, m6 ||= A ||= 38/25, 3/2 ||= 97 || | |||
|| 7 || 420 | ||= 13 ||= 780 ||= upminor 6th ||= ^m6 ||= A^ ||= 11/7, 25/16 ||= 25 || | ||
||= 14 ||= 840 ||= mid 6th ||= ~6 ||= A^^, Bvv ||= 13/8, 8/5 ||= 13 || | |||
|| 8 || 480 | ||= 15 ||= 900 ||= downmajor 6th ||= vM6 ||= Bv ||= 22/13, 32/19 ||= 27 || | ||
||= 16 ||= 960 ||= major 6th, minor 7th ||= M6, m7 ||= B, C ||= 7/4, 26/15 ||= 7 || | |||
perfect fourth || M3, P4 || F#, G ||= 25/19, 4/3 ||= 21 || | ||= 17 ||= 1020 ||= upminor 7th ||= ^m7 ||= C^ ||= 9/5 ||= 115 || | ||
|| 9 || 540 | ||= 18 ||= 1080 ||= mid 7th ||= ~7 ||= C^^, Dvv ||= 15/8, 13/7 ||= 15 || | ||
||= 19 ||= 1140 ||= downmajor 7th ||= vM7 ||= Dv ||= 56/29 ||= 31 || | |||
|| 10 || 600 | ||= 20 ||= 1200 ||= octave ||= P8 ||= D ||= 2/1 ||= 2 || | ||
double-down fifth || ^^4, vv5 || G^^, Avv ||= 7/5 ||= 91 || | |||
|| 11 || 660 | |||
|| 12 || 720 | |||
|| 13 || 780 | |||
|| 14 || 840 | |||
|| 15 || 900 | |||
|| 16 || 960 | |||
minor 7th || M6, m7 || B, C ||= 7/4, 26/15 ||= 7 || | |||
|| 17 || 1020 | |||
|| 18 || 1080 | |||
|| 19 || 1140 | |||
|| 20 || 1200 | |||
==Modes== | ==Modes== | ||
20 tone equal modes: | 20 tone equal modes: | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td><strong>Degree</strong><br /> | <td style="text-align: center;"><strong>Degree</strong><br /> | ||
</td> | </td> | ||
<td><strong>Cents | <td style="text-align: center;"><strong>Cents</strong><br /> | ||
</td> | </td> | ||
<td colspan="3" style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">up/down notation</a><br /> | <td colspan="3" style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">up/down notation</a><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>0<br /> | <td style="text-align: center;">0<br /> | ||
</td> | </td> | ||
<td>0<br /> | <td style="text-align: center;">0<br /> | ||
</td> | </td> | ||
<td>unison<br /> | <td style="text-align: center;">unison<br /> | ||
</td> | </td> | ||
<td>P1<br /> | <td style="text-align: center;">P1<br /> | ||
</td> | </td> | ||
<td>D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1/1<br /> | <td style="text-align: center;">1/1<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>1<br /> | <td style="text-align: center;">1<br /> | ||
</td> | </td> | ||
<td>60 | <td style="text-align: center;">60<br /> | ||
</td> | </td> | ||
<td>upminor 2nd<br /> | <td style="text-align: center;">upminor 2nd<br /> | ||
</td> | </td> | ||
<td>^m2<br /> | <td style="text-align: center;">^m2<br /> | ||
</td> | </td> | ||
<td>D^<br /> | <td style="text-align: center;">D^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">29/28<br /> | <td style="text-align: center;">29/28<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>2<br /> | <td style="text-align: center;">2<br /> | ||
</td> | </td> | ||
<td>120 | <td style="text-align: center;">120<br /> | ||
</td> | </td> | ||
<td>mid 2nd<br /> | <td style="text-align: center;">mid 2nd<br /> | ||
</td> | </td> | ||
<td>~2<br /> | <td style="text-align: center;">~2<br /> | ||
</td> | </td> | ||
<td>D^^, Evv<br /> | <td style="text-align: center;">D^^, Evv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">14/13, 15/14<br /> | <td style="text-align: center;">14/13, 15/14<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>3<br /> | <td style="text-align: center;">3<br /> | ||
</td> | </td> | ||
<td>180 | <td style="text-align: center;">180<br /> | ||
</td> | </td> | ||
<td>downmajor 2nd<br /> | <td style="text-align: center;">downmajor 2nd<br /> | ||
</td> | </td> | ||
<td>vM2<br /> | <td style="text-align: center;">vM2<br /> | ||
</td> | </td> | ||
<td>Ev<br /> | <td style="text-align: center;">Ev<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">10/9<br /> | <td style="text-align: center;">10/9<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>4<br /> | <td style="text-align: center;">4<br /> | ||
</td> | </td> | ||
<td>240 | <td style="text-align: center;">240<br /> | ||
</td> | </td> | ||
<td>major 2nd, | <td style="text-align: center;">major 2nd, minor 3rd<br /> | ||
minor 3rd<br /> | |||
</td> | </td> | ||
<td>M2, m3<br /> | <td style="text-align: center;">M2, m3<br /> | ||
</td> | </td> | ||
<td>E, F<br /> | <td style="text-align: center;">E, F<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">8/7, 15/13<br /> | <td style="text-align: center;">8/7, 15/13<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>5<br /> | <td style="text-align: center;">5<br /> | ||
</td> | </td> | ||
<td>300 | <td style="text-align: center;">300<br /> | ||
</td> | </td> | ||
<td>upminor 3rd<br /> | <td style="text-align: center;">upminor 3rd<br /> | ||
</td> | </td> | ||
<td>^m3<br /> | <td style="text-align: center;">^m3<br /> | ||
</td> | </td> | ||
<td>F^<br /> | <td style="text-align: center;">F^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">13/11, 19/16<br /> | <td style="text-align: center;">13/11, 19/16<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>6<br /> | <td style="text-align: center;">6<br /> | ||
</td> | </td> | ||
<td>360 | <td style="text-align: center;">360<br /> | ||
</td> | </td> | ||
<td>mid 3rd<br /> | <td style="text-align: center;">mid 3rd<br /> | ||
</td> | </td> | ||
<td>~3<br /> | <td style="text-align: center;">~3<br /> | ||
</td> | </td> | ||
<td>F^^<br /> | <td style="text-align: center;">F^^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">16/13, 5/4<br /> | <td style="text-align: center;">16/13, 5/4<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>7<br /> | <td style="text-align: center;">7<br /> | ||
</td> | </td> | ||
<td>420 | <td style="text-align: center;">420<br /> | ||
</td> | </td> | ||
<td>downmajor 3rd<br /> | <td style="text-align: center;">downmajor 3rd<br /> | ||
</td> | </td> | ||
<td>vM3<br /> | <td style="text-align: center;">vM3<br /> | ||
</td> | </td> | ||
<td>F#v<br /> | <td style="text-align: center;">F#v<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/51_40">51/40</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/51_40">51/40</a><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>8<br /> | <td style="text-align: center;">8<br /> | ||
</td> | </td> | ||
<td>480 | <td style="text-align: center;">480<br /> | ||
</td> | </td> | ||
<td>major 3rd, | <td style="text-align: center;">major 3rd, perfect fourth<br /> | ||
perfect fourth<br /> | |||
</td> | </td> | ||
<td>M3, P4<br /> | <td style="text-align: center;">M3, P4<br /> | ||
</td> | </td> | ||
<td>F#, G<br /> | <td style="text-align: center;">F#, G<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">25/19, 4/3<br /> | <td style="text-align: center;">25/19, 4/3<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>9<br /> | <td style="text-align: center;">9<br /> | ||
</td> | </td> | ||
<td>540 | <td style="text-align: center;">540<br /> | ||
</td> | </td> | ||
<td>up-fourth<br /> | <td style="text-align: center;">up-fourth<br /> | ||
</td> | </td> | ||
<td>^4<br /> | <td style="text-align: center;">^4<br /> | ||
</td> | </td> | ||
<td>G^<br /> | <td style="text-align: center;">G^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">15/11, 11/8<br /> | <td style="text-align: center;">15/11, 11/8<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>10<br /> | <td style="text-align: center;">10<br /> | ||
</td> | </td> | ||
<td>600 | <td style="text-align: center;">600<br /> | ||
</td> | </td> | ||
<td>double-up fourth,<br /> | <td style="text-align: center;">double-up fourth,<br /> | ||
double-down fifth<br /> | double-down fifth<br /> | ||
</td> | </td> | ||
<td>^^4, vv5<br /> | <td style="text-align: center;">^^4, vv5<br /> | ||
</td> | </td> | ||
<td>G^^, Avv<br /> | <td style="text-align: center;">G^^, Avv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">7/5<br /> | <td style="text-align: center;">7/5<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>11<br /> | <td style="text-align: center;">11<br /> | ||
</td> | </td> | ||
<td>660 | <td style="text-align: center;">660<br /> | ||
</td> | </td> | ||
<td>down-fifth<br /> | <td style="text-align: center;">down-fifth<br /> | ||
</td> | </td> | ||
<td>v5<br /> | <td style="text-align: center;">v5<br /> | ||
</td> | </td> | ||
<td>Av<br /> | <td style="text-align: center;">Av<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">22/15, 16/11<br /> | <td style="text-align: center;">22/15, 16/11<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>12<br /> | <td style="text-align: center;">12<br /> | ||
</td> | </td> | ||
<td>720 | <td style="text-align: center;">720<br /> | ||
</td> | </td> | ||
<td>fifth<br /> | <td style="text-align: center;">fifth<br /> | ||
</td> | </td> | ||
<td>P5, m6<br /> | <td style="text-align: center;">P5, m6<br /> | ||
</td> | </td> | ||
<td>A<br /> | <td style="text-align: center;">A<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">38/25, 3/2<br /> | <td style="text-align: center;">38/25, 3/2<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13<br /> | <td style="text-align: center;">13<br /> | ||
</td> | </td> | ||
<td>780 | <td style="text-align: center;">780<br /> | ||
</td> | </td> | ||
<td>upminor 6th<br /> | <td style="text-align: center;">upminor 6th<br /> | ||
</td> | </td> | ||
<td>^m6<br /> | <td style="text-align: center;">^m6<br /> | ||
</td> | </td> | ||
<td>A^<br /> | <td style="text-align: center;">A^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">11/7, 25/16<br /> | <td style="text-align: center;">11/7, 25/16<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>14<br /> | <td style="text-align: center;">14<br /> | ||
</td> | </td> | ||
<td>840 | <td style="text-align: center;">840<br /> | ||
</td> | </td> | ||
<td>mid 6th<br /> | <td style="text-align: center;">mid 6th<br /> | ||
</td> | </td> | ||
<td>~6<br /> | <td style="text-align: center;">~6<br /> | ||
</td> | </td> | ||
<td>A^^, Bvv<br /> | <td style="text-align: center;">A^^, Bvv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">13/8, 8/5<br /> | <td style="text-align: center;">13/8, 8/5<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>15<br /> | <td style="text-align: center;">15<br /> | ||
</td> | </td> | ||
<td>900 | <td style="text-align: center;">900<br /> | ||
</td> | </td> | ||
<td>downmajor 6th<br /> | <td style="text-align: center;">downmajor 6th<br /> | ||
</td> | </td> | ||
<td>vM6<br /> | <td style="text-align: center;">vM6<br /> | ||
</td> | </td> | ||
<td>Bv<br /> | <td style="text-align: center;">Bv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">22/13, 32/19<br /> | <td style="text-align: center;">22/13, 32/19<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>16<br /> | <td style="text-align: center;">16<br /> | ||
</td> | </td> | ||
<td>960 | <td style="text-align: center;">960<br /> | ||
</td> | </td> | ||
<td>major 6th, | <td style="text-align: center;">major 6th, minor 7th<br /> | ||
minor 7th<br /> | |||
</td> | </td> | ||
<td>M6, m7<br /> | <td style="text-align: center;">M6, m7<br /> | ||
</td> | </td> | ||
<td>B, C<br /> | <td style="text-align: center;">B, C<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">7/4, 26/15<br /> | <td style="text-align: center;">7/4, 26/15<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>17<br /> | <td style="text-align: center;">17<br /> | ||
</td> | </td> | ||
<td>1020 | <td style="text-align: center;">1020<br /> | ||
</td> | </td> | ||
<td>upminor 7th<br /> | <td style="text-align: center;">upminor 7th<br /> | ||
</td> | </td> | ||
<td>^m7<br /> | <td style="text-align: center;">^m7<br /> | ||
</td> | </td> | ||
<td>C^<br /> | <td style="text-align: center;">C^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">9/5<br /> | <td style="text-align: center;">9/5<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>18<br /> | <td style="text-align: center;">18<br /> | ||
</td> | </td> | ||
<td>1080 | <td style="text-align: center;">1080<br /> | ||
</td> | </td> | ||
<td>mid 7th<br /> | <td style="text-align: center;">mid 7th<br /> | ||
</td> | </td> | ||
<td>~7<br /> | <td style="text-align: center;">~7<br /> | ||
</td> | </td> | ||
<td>C^^, Dvv<br /> | <td style="text-align: center;">C^^, Dvv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">15/8, 13/7<br /> | <td style="text-align: center;">15/8, 13/7<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>19<br /> | <td style="text-align: center;">19<br /> | ||
</td> | </td> | ||
<td>1140 | <td style="text-align: center;">1140<br /> | ||
</td> | </td> | ||
<td>downmajor 7th<br /> | <td style="text-align: center;">downmajor 7th<br /> | ||
</td> | </td> | ||
<td>vM7<br /> | <td style="text-align: center;">vM7<br /> | ||
</td> | </td> | ||
<td>Dv<br /> | <td style="text-align: center;">Dv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">56/29<br /> | <td style="text-align: center;">56/29<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>20<br /> | <td style="text-align: center;">20<br /> | ||
</td> | </td> | ||
<td>1200 | <td style="text-align: center;">1200<br /> | ||
</td> | </td> | ||
<td>octave<br /> | <td style="text-align: center;">octave<br /> | ||
</td> | </td> | ||
<td>P8<br /> | <td style="text-align: center;">P8<br /> | ||
</td> | </td> | ||
<td>D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">2/1<br /> | <td style="text-align: center;">2/1<br /> | ||