18edo: Difference between revisions
Wikispaces>TallKite **Imported revision 599957202 - Original comment: ** |
Wikispaces>TallKite **Imported revision 599959088 - 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:TallKite|TallKite]] and made on <tt>2016-11-21 06: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-21 06:52:04 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>599959088</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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coarse/fine | coarse/fine | ||
DMS ||= 5L3s Notation ||||||= [[Ups and Downs Notation|up/down ]][[Ups and Downs Notation|notation]] | DMS ||= 5L3s Notation ||||||= [[Ups and Downs Notation|up/down ]][[Ups and Downs Notation|notation]] | ||
based on 18b-edo, with | based on 18b-edo, with | ||
sharp lower than flat || Nearest Ratio || Error (cents | sharp lower than flat || Nearest Ratio || Error (cents | ||
coarse/fine) | coarse/fine) | ||
(DMS) ||< 17-Limit Ratios* || | (DMS) ||< 17-Limit Ratios* || | ||
|| 0 || 0 ||= C ||= C || unison ||= P1 || 1/1 || 0 ||< 1/1 || | || 0 || 0 ||= C ||= C ||= unison ||= P1 || 1/1 || 0 ||< 1/1 || | ||
|| 1 || 66.667 | || 1 || 66.667 | ||
80 | 80 | ||
20° ||= Db ||= C^, | 20° ||= Db ||= C^, Dv ||= up-unison, | ||
Dv || up-unison, | downmajor 2nd ||= ^P1, vM2 || 27/26 || +1.329 | ||
downmajor 2nd ||= ^P1, | |||
vM2 || 27/26 || +1.329 | |||
+1.595 | +1.595 | ||
+23'56" ||< 78/75, 75/72 || | +23'56" ||< 78/75, 75/72 || | ||
|| 2 || 133.333 | || 2 || 133.333 | ||
160 | 160 | ||
40° ||= C# ||= D || major 2nd ||= M2 || 27/25 || +0.096 | 40° ||= C# ||= D ||= major 2nd ||= M2 || 27/25 || +0.096 | ||
+0.115 | +0.115 | ||
+1'43" ||< 51/55, 42/39 || | +1'43" ||< 51/55, 42/39 || | ||
|| 3 || 200 | || 3 || 200 | ||
240 | 240 | ||
60° ||= D ||= D^, | 60° ||= D ||= D^, Ev ||= mid 2nd ||= ~2 || 9/8 || -3.910 | ||
Ev || mid 2nd ||= ~2 || 9/8 || -3.910 | |||
-4.692 | -4.692 | ||
-1°10'23" ||< 9/8 || | -1°10'23" ||< 9/8 || | ||
|| 4 || 266.667 | || 4 || 266.667 | ||
320 | 320 | ||
80° ||= Eb ||= E || minor 2nd, | 80° ||= Eb ||= Db, E ||= minor 2nd, | ||
major 3rd ||= m2, | major 3rd ||= m2, M3 || 7/6 || -0.204 | ||
M3 || 7/6 || -0.204 | |||
-0.245 | -0.245 | ||
-1"50" ||< 75/64 || | -1"50" ||< 75/64 || | ||
|| 5 || 333.333 | || 5 || 333.333 | ||
400 | 400 | ||
100° ||= D# ||= E^ || mid 3rd ||= ~3 || 17/14 or 40/33 || -2.796 +0.293 | 100° ||= D# ||= E^ ||= mid 3rd ||= ~3 || 17/14 or 40/33 || -2.796 +0.293 | ||
-3.355 +0.351 | -3.355 +0.351 | ||
-50'20" +5'16" ||< 39/32 || | -50'20" +5'16" ||< 39/32 || | ||
|| 6 || 400 | || 6 || 400 | ||
480 | 480 | ||
120° ||= E ||= Eb, | 120° ||= E ||= Eb, F# ||= minor 3rd, | ||
F# || minor 3rd, | augmented 4th ||= m3, A4 || 5/4 or 44/35 || +13.686 +3.822 | ||
augmented 4th ||= m3, | |||
A4 || 5/4 or 44/35 || +13.686 +3.822 | |||
+16.4235 +4.586 | +16.4235 +4.586 | ||
+4°6'21" +1°8'47" ||< 64/55 || | +4°6'21" +1°8'47" ||< 64/55 || | ||
|| 7 || 466.667 | || 7 || 466.667 | ||
560 | 560 | ||
140° ||= F ||= Fv || upminor 3rd, | 140° ||= F ||= Fv ||= upminor 3rd, | ||
down-fourth ||= ^m3, | down-fourth ||= ^m3, vP4 || 21/16 || -4.114 | ||
vP4 || 21/16 || -4.114 | |||
-4.937 | -4.937 | ||
-1°14'3" ||< 21/16 || | -1°14'3" ||< 21/16 || | ||
|| 8 || 533.333 | || 8 || 533.333 | ||
640 | 640 | ||
160° ||= Gb ||= F || fourth ||= P4 || 15/11 || -3.617 | 160° ||= Gb ||= F ||= fourth ||= P4 || 15/11 || -3.617 | ||
-4.341 | -4.341 | ||
-1°5'7" ||< 102/75 || | -1°5'7" ||< 102/75 || | ||
|| 9 || 600 | || 9 || 600 | ||
720 | 720 | ||
180° ||= F# ||= F^, | 180° ||= F# ||= F^, Gv ||= upfourth, | ||
Gv || upfourth, | downfifth ||= ^P4, vP5 || 17/12 or 24/17 || -3.000 +3.000 | ||
downfifth ||= ^P4, | |||
vP5 || 17/12 or 24/17 || -3.000 +3.000 | |||
-3.6005 +3.6005 | -3.6005 +3.6005 | ||
-54' +54' ||< 17/12 || | -54' +54' ||< 17/12 || | ||
|| 10 || 666.667 | || 10 || 666.667 | ||
800 | 800 | ||
200° ||= G ||= G || fifthj ||= P5 || 22/15 || +3.617 | 200° ||= G ||= G ||= fifthj ||= P5 || 22/15 || +3.617 | ||
+4.341 | +4.341 | ||
+1°5'7" ||< 75/51 || | +1°5'7" ||< 75/51 || | ||
|| 11 || 733.333 | || 11 || 733.333 | ||
880 | 880 | ||
220° ||= Hb ||= G^ || upfifth, | 220° ||= Hb ||= G^ ||= upfifth, | ||
downmajor 6th ||= ^P5, | downmajor 6th ||= ^P5, vM6 || 32/21 || +4.114 | ||
vM6 || 32/21 || +4.114 | |||
+4.937 | +4.937 | ||
+1°14'3" ||< 32/21 || | +1°14'3" ||< 32/21 || | ||
|| 12 || 800 | || 12 || 800 | ||
960 | 960 | ||
240° ||= G# ||= A || diminished 5th, | 240° ||= G# ||= A ||= diminished 5th, | ||
major 6th ||= d5, | major 6th ||= d5, M6 || 8/5 or 35/22 || -13.686 -3.822 | ||
M6 || 8/5 or 35/22 || -13.686 -3.822 | |||
-16.4235 -4.586 | -16.4235 -4.586 | ||
-4°6'21" -1°8'47" ||< 51/32 || | -4°6'21" -1°8'47" ||< 51/32 || | ||
|| 13 || 866.667 | || 13 || 866.667 | ||
1040 | 1040 | ||
260° ||= H ||= A^, | 260° ||= H ||= A^, Bv ||= mid 6th ||= ~6 || 28/17 or 33/20 || +2.796 -0.293 | ||
Bv || mid 6th ||= ~6 || 28/17 or 33/20 || +2.796 -0.293 | |||
+3.355 -0.351 | +3.355 -0.351 | ||
<span style="line-height: 15.6000003814697px;">+</span>50'20" <span style="line-height: 15.6000003814697px;">-</span><span style="line-height: 1.5;">5'16"</span> ||< 64/39 || | <span style="line-height: 15.6000003814697px;">+</span>50'20" <span style="line-height: 15.6000003814697px;">-</span><span style="line-height: 1.5;">5'16"</span> ||< 64/39 || | ||
|| 14 || 933.333 | || 14 || 933.333 | ||
1120 | 1120 | ||
280° ||= A ||= B || minor 6th, | 280° ||= A ||= B ||= minor 6th, | ||
major 7th ||= m6, | major 7th ||= m6, M7 || 12/7 || +0.204 | ||
M7 || 12/7 || +0.204 | |||
+0.245 | +0.245 | ||
+1"50" ||< 55/32 || | +1"50" ||< 55/32 || | ||
|| 15 || 1000 | || 15 || 1000 | ||
1200 | 1200 | ||
300° ||= Bb ||= B^ || mid 7th ||= ~7 || 16/9 || +3.910 | 300° ||= Bb ||= B^ ||= mid 7th ||= ~7 || 16/9 || +3.910 | ||
+4.692 | +4.692 | ||
+1°10'23" ||< 16/9 || | +1°10'23" ||< 16/9 || | ||
|| 16 || 1066.667 | || 16 || 1066.667 | ||
1280 | 1280 | ||
320° ||= A# ||= Bb, | 320° ||= A# ||= Bb, C# ||= minor 7th ||= m7 || 50/27 || -0.096 | ||
C# || minor 7th ||= m7 || 50/27 || -0.096 | |||
-0.115 | -0.115 | ||
-1'43" ||< 39/21 || | -1'43" ||< 39/21 || | ||
|| 17 || 1133.333 | || 17 || 1133.333 | ||
1360 | 1360 | ||
340° ||= B ||= Cv || upminor 7th, | 340° ||= B ||= Cv ||= upminor 7th, | ||
down-octave ||= ^m7, | down-octave ||= ^m7, vP8 || 52/27 || -1.329 | ||
vP8 || 52/27 || -1.329 | |||
-1.595 | -1.595 | ||
-23'56" ||< 75/39 || | -23'56" ||< 75/39 || | ||
|| 18 || 1200 | || 18 || 1200 | ||
1440 | 1440 | ||
360° ||= C ||= C || octave ||= P8 || 2/1 || 0 ||< 2/1** || | 360° ||= C ||= C ||= octave ||= P8 || 2/1 || 0 ||< 2/1** || | ||
*based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament | *based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament | ||
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</td> | </td> | ||
<td colspan="3" style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">up/down </a><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">notation</a><br /> | <td colspan="3" style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">up/down </a><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">notation</a><br /> | ||
based on 18b-edo, with <br /> | based on 18b-edo, with<br /> | ||
sharp lower than flat<br /> | sharp lower than flat<br /> | ||
</td> | </td> | ||
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<td style="text-align: center;">C<br /> | <td style="text-align: center;">C<br /> | ||
</td> | </td> | ||
<td>unison<br /> | <td style="text-align: center;">unison<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P1<br /> | <td style="text-align: center;">P1<br /> | ||
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<td style="text-align: center;">Db<br /> | <td style="text-align: center;">Db<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C^, | <td style="text-align: center;">C^, Dv<br /> | ||
Dv<br /> | |||
</td> | </td> | ||
<td>up-unison,<br /> | <td style="text-align: center;">up-unison,<br /> | ||
downmajor 2nd<br /> | downmajor 2nd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">^P1, | <td style="text-align: center;">^P1, vM2<br /> | ||
vM2<br /> | |||
</td> | </td> | ||
<td>27/26<br /> | <td>27/26<br /> | ||
| Line 305: | Line 288: | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
<td>major 2nd<br /> | <td style="text-align: center;">major 2nd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">M2<br /> | <td style="text-align: center;">M2<br /> | ||
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<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D^, | <td style="text-align: center;">D^, Ev<br /> | ||
Ev<br /> | |||
</td> | </td> | ||
<td>mid 2nd<br /> | <td style="text-align: center;">mid 2nd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">~2<br /> | <td style="text-align: center;">~2<br /> | ||
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<td style="text-align: center;">Eb<br /> | <td style="text-align: center;">Eb<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E<br /> | <td style="text-align: center;">Db, E<br /> | ||
</td> | </td> | ||
<td>minor 2nd,<br /> | <td style="text-align: center;">minor 2nd,<br /> | ||
major 3rd<br /> | major 3rd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">m2, | <td style="text-align: center;">m2, M3<br /> | ||
M3<br /> | |||
</td> | </td> | ||
<td>7/6<br /> | <td>7/6<br /> | ||
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<td style="text-align: center;">E^<br /> | <td style="text-align: center;">E^<br /> | ||
</td> | </td> | ||
<td>mid 3rd<br /> | <td style="text-align: center;">mid 3rd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">~3<br /> | <td style="text-align: center;">~3<br /> | ||
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<td style="text-align: center;">E<br /> | <td style="text-align: center;">E<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Eb, | <td style="text-align: center;">Eb, F#<br /> | ||
F#<br /> | |||
</td> | </td> | ||
<td>minor 3rd,<br /> | <td style="text-align: center;">minor 3rd,<br /> | ||
augmented 4th<br /> | augmented 4th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">m3, | <td style="text-align: center;">m3, A4<br /> | ||
A4<br /> | |||
</td> | </td> | ||
<td>5/4 or 44/35<br /> | <td>5/4 or 44/35<br /> | ||
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<td style="text-align: center;">Fv<br /> | <td style="text-align: center;">Fv<br /> | ||
</td> | </td> | ||
<td>upminor 3rd,<br /> | <td style="text-align: center;">upminor 3rd,<br /> | ||
down-fourth<br /> | down-fourth<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">^m3, | <td style="text-align: center;">^m3, vP4<br /> | ||
vP4<br /> | |||
</td> | </td> | ||
<td>21/16<br /> | <td>21/16<br /> | ||
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<td style="text-align: center;">F<br /> | <td style="text-align: center;">F<br /> | ||
</td> | </td> | ||
<td>fourth<br /> | <td style="text-align: center;">fourth<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P4<br /> | <td style="text-align: center;">P4<br /> | ||
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<td style="text-align: center;">F#<br /> | <td style="text-align: center;">F#<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">F^, | <td style="text-align: center;">F^, Gv<br /> | ||
Gv<br /> | |||
</td> | </td> | ||
<td>upfourth,<br /> | <td style="text-align: center;">upfourth,<br /> | ||
downfifth<br /> | downfifth<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">^P4, | <td style="text-align: center;">^P4, vP5<br /> | ||
vP5<br /> | |||
</td> | </td> | ||
<td>17/12 or 24/17<br /> | <td>17/12 or 24/17<br /> | ||
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<td style="text-align: center;">G<br /> | <td style="text-align: center;">G<br /> | ||
</td> | </td> | ||
<td>fifthj<br /> | <td style="text-align: center;">fifthj<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P5<br /> | <td style="text-align: center;">P5<br /> | ||
| Line 532: | Line 508: | ||
<td style="text-align: center;">G^<br /> | <td style="text-align: center;">G^<br /> | ||
</td> | </td> | ||
<td>upfifth,<br /> | <td style="text-align: center;">upfifth,<br /> | ||
downmajor 6th<br /> | downmajor 6th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">^P5, | <td style="text-align: center;">^P5, vM6<br /> | ||
vM6<br /> | |||
</td> | </td> | ||
<td>32/21<br /> | <td>32/21<br /> | ||
| Line 558: | Line 533: | ||
<td style="text-align: center;">A<br /> | <td style="text-align: center;">A<br /> | ||
</td> | </td> | ||
<td>diminished 5th,<br /> | <td style="text-align: center;">diminished 5th,<br /> | ||
major 6th<br /> | major 6th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">d5, | <td style="text-align: center;">d5, M6<br /> | ||
M6<br /> | |||
</td> | </td> | ||
<td>8/5 or 35/22<br /> | <td>8/5 or 35/22<br /> | ||
| Line 582: | Line 556: | ||
<td style="text-align: center;">H<br /> | <td style="text-align: center;">H<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A^, | <td style="text-align: center;">A^, Bv<br /> | ||
Bv<br /> | |||
</td> | </td> | ||
<td>mid 6th<br /> | <td style="text-align: center;">mid 6th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">~6<br /> | <td style="text-align: center;">~6<br /> | ||
| Line 609: | Line 582: | ||
<td style="text-align: center;">B<br /> | <td style="text-align: center;">B<br /> | ||
</td> | </td> | ||
<td>minor 6th,<br /> | <td style="text-align: center;">minor 6th,<br /> | ||
major 7th<br /> | major 7th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">m6, | <td style="text-align: center;">m6, M7<br /> | ||
M7<br /> | |||
</td> | </td> | ||
<td>12/7<br /> | <td>12/7<br /> | ||
| Line 635: | Line 607: | ||
<td style="text-align: center;">B^<br /> | <td style="text-align: center;">B^<br /> | ||
</td> | </td> | ||
<td>mid 7th<br /> | <td style="text-align: center;">mid 7th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">~7<br /> | <td style="text-align: center;">~7<br /> | ||
| Line 657: | Line 629: | ||
<td style="text-align: center;">A#<br /> | <td style="text-align: center;">A#<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Bb, | <td style="text-align: center;">Bb, C#<br /> | ||
C#<br /> | |||
</td> | </td> | ||
<td>minor 7th<br /> | <td style="text-align: center;">minor 7th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">m7<br /> | <td style="text-align: center;">m7<br /> | ||
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<td style="text-align: center;">Cv<br /> | <td style="text-align: center;">Cv<br /> | ||
</td> | </td> | ||
<td>upminor 7th,<br /> | <td style="text-align: center;">upminor 7th,<br /> | ||
down-octave<br /> | down-octave<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">^m7, | <td style="text-align: center;">^m7, vP8<br /> | ||
vP8<br /> | |||
</td> | </td> | ||
<td>52/27<br /> | <td>52/27<br /> | ||
| Line 710: | Line 680: | ||
<td style="text-align: center;">C<br /> | <td style="text-align: center;">C<br /> | ||
</td> | </td> | ||
<td>octave<br /> | <td style="text-align: center;">octave<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P8<br /> | <td style="text-align: center;">P8<br /> | ||