43edo: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 578826585 - Original comment: ** |
Wikispaces>TallKite **Imported revision 602956062 - 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>2017-01-02 06:20:11 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602956062</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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==Intervals== | ==Intervals== | ||
|| Degrees | ||= Degrees ||= Cents value ||< Approximate 13-limit Ratios ||||||= [[xenharmonic/Ups and Downs Notation|ups and downs notation]] || | ||
|| 0 || 0 || | ||= 0 ||= 0 ||< 1/1 ||= P1 ||= perfect unison ||= D || | ||
|| 1 || 27.907 || || | ||= 1 ||= 27.907 ||< ||= ^1, d2 ||= up unison, dim 2nd ||= D^, Ebb || | ||
|| 2 || 55.814 || || | ||= 2 ||= 55.814 ||< ||= vA1, ^d2 ||= downaug unison, updim 2nd ||= D#v, Ebb^ || | ||
|| 3 || 83.721 || || | ||= 3 ||= 83.721 ||< ||= vm2 ||= downminor 2nd ||= Ebv || | ||
|| 4 || 111.628 || 17/16, 16/15, 15/14 || | ||= 4 ||= 111.628 ||< 17/16, 16/15, 15/14 ||= m2 ||= minor 2nd ||= Eb || | ||
|| 5 || 139.535 || 12/11, 13/12, 14/13 || | ||= 5 ||= 139.535 ||< 12/11, 13/12, 14/13 ||= ^m2 ||= upminor 2nd ||= Eb^ || | ||
|| 6 || 167.442 || 11/10 || | ||= 6 ||= 167.442 ||< 11/10 ||= vM2 ||= downmajor 2nd ||= Ev || | ||
|| 7 || 195.349 || 9/8, 10/9 || | ||= 7 ||= 195.349 ||< 9/8, 10/9 ||= M2 ||= major 2nd ||= E || | ||
|| 8 || 223.256 || 8/7 || | ||= 8 ||= 223.256 ||< 8/7 ||= ^M2 ||= upmajor 2nd ||= E^ || | ||
|| 9 || 251.163 || 15/13 || | ||= 9 ||= 251.163 ||< 15/13 ||= vA2, ^d3 ||= downaug 2nd, updim 3rd ||= E#v, Fb^ || | ||
|| 10 || 279.07 || 7/6, 13/11 || | ||= 10 ||= 279.07 ||< 7/6, 13/11 ||= vm3 ||= downminor 3rd ||= Fv || | ||
|| 11 || 306.977 || 6/5 || | ||= 11 ||= 306.977 ||< 6/5 ||= m3 ||= minor 3rd ||= F || | ||
|| 12 || 334.884 || 17/14, 39/32 || | ||= 12 ||= 334.884 ||< 17/14, 39/32 ||= ^m3 ||= upminor 3rd ||= F^ || | ||
|| 13 || 362.791 || 11/9, 16/13 || | ||= 13 ||= 362.791 ||< 11/9, 16/13 ||= vM3 ||= downmajor 3rd ||= F#v || | ||
|| 14 || 390.698 || 5/4 || | ||= 14 ||= 390.698 ||< 5/4 ||= M3 ||= major 3rd ||= F# || | ||
|| 15 || 418.605 || 9/7, 14/11 || | ||= 15 ||= 418.605 ||< 9/7, 14/11 ||= ^M3 ||= upmajor 3rd ||= F#^ || | ||
|| 16 || 446.512 || 13/10 || | ||= 16 ||= 446.512 ||< 13/10 ||= vA3, ^d4 ||= downaug 3rd, updim 4th ||= Fxv, Gb^ || | ||
|| 17 || 474.419 || 21/16 || | ||= 17 ||= 474.419 ||< 21/16 ||= v4 ||= down 4th ||= Gv || | ||
|| 18 || 502.326 || 4/3 || | ||= 18 ||= 502.326 ||< 4/3 ||= P4 ||= perfect 4th ||= G || | ||
|| 19 || 530.233 || 15/11 || | ||= 19 ||= 530.233 ||< 15/11 ||= ^4 ||= up 4th ||= G^ || | ||
|| 20 || 558.139 || 11/8, 18/13 || | ||= 20 ||= 558.139 ||< 11/8, 18/13 ||= vA4 ||= downaug 4th ||= G#v || | ||
|| 21 || 586.046 || 7/5 || | ||= 21 ||= 586.046 ||< 7/5 ||= A4, vd5 ||= aug 4th, downdim 5th ||= G#, Abv || | ||
|| 22 || 613.953 || 10/7 || | ||= 22 ||= 613.953 ||< 10/7 ||= ^A4, d5 ||= upaug 4th, dim 5th ||= G#^, Ab || | ||
|| 23 || 641.86 || 16/11, 13/9 || | ||= 23 ||= 641.86 ||< 16/11, 13/9 ||= ^d5 ||= updim 5th ||= Ab^ || | ||
|| 24 || 669.767 || 22/15 || | ||= 24 ||= 669.767 ||< 22/15 ||= v5 ||= down 5th ||= Av || | ||
|| 25 || 697.674 || 3/2 || | ||= 25 ||= 697.674 ||< 3/2 ||= P5 ||= perfect 5th ||= A || | ||
|| 26 || 725.581 || 32/21 || | ||= 26 ||= 725.581 ||< 32/21 ||= ^5 ||= up 5th ||= A^ || | ||
|| 27 || 753.488 || 20/13 || | ||= 27 ||= 753.488 ||< 20/13 ||= vA5, ^d6 ||= downaug 5th, updim 6th ||= A#v, Bbb^ || | ||
|| 28 || 781.395 || 14/9, 11/7 || | ||= 28 ||= 781.395 ||< 14/9, 11/7 ||= vm6 ||= downminor 6th ||= Bbv || | ||
|| 29 || 809.302 || 8/5 || | ||= 29 ||= 809.302 ||< 8/5 ||= m6 ||= minor 6th ||= Bb || | ||
|| 30 || 837.209 || 18/11, 13/8 || | ||= 30 ||= 837.209 ||< 18/11, 13/8 ||= ^m6 ||= upminor 6th ||= Bb^ || | ||
|| 31 || 865.116 || || | ||= 31 ||= 865.116 ||< ||= vM6 ||= downmajor 6th ||= Bv || | ||
|| 32 || 893.023 || 5/3 || | ||= 32 ||= 893.023 ||< 5/3 ||= M6 ||= major 6th ||= B || | ||
|| 33 || 920.93 || 12/7 || | ||= 33 ||= 920.93 ||< 12/7 ||= ^M6 ||= upmajor 6th ||= B^ || | ||
|| 34 || 948.837 || 26/15 || | ||= 34 ||= 948.837 ||< 26/15 ||= vA6, ^d7 ||= downaug 6th, updim 7th ||= B#v, Cb^ || | ||
|| 35 || 976.744 || 7/4 || | ||= 35 ||= 976.744 ||< 7/4 ||= vm7 ||= downminor 7th ||= Cv || | ||
|| 36 || 1004.651 || 16/9, 9/5 || | ||= 36 ||= 1004.651 ||< 16/9, 9/5 ||= m7 ||= minor 7th ||= C || | ||
|| 37 || 1032.558 || 20/11 || | ||= 37 ||= 1032.558 ||< 20/11 ||= ^m7 ||= upminor 7th ||= C^ || | ||
|| 38 || 1060.465 || 11/6, 24/13, 13/7 || | ||= 38 ||= 1060.465 ||< 11/6, 24/13, 13/7 ||= vM7 ||= downmajor 7th ||= C#v || | ||
|| 39 || 1088.372 || 15/8, 28/15 || | ||= 39 ||= 1088.372 ||< 15/8, 28/15 ||= M7 ||= major 7th ||= C# || | ||
|| 40 || 1116.279 || || | ||= 40 ||= 1116.279 ||< ||= ^M7 ||= upmajor 7th ||= C#^ || | ||
|| 41 || 1144.186 || || | ||= 41 ||= 1144.186 ||< ||= vA7, ^d8 ||= downaug 7th, updim 8ve ||= Cxv, Db^ || | ||
|| 42 || 1172.093 || || | ||= 42 ||= 1172.093 ||< ||= A7, v8 ||= aug 7th, down 8ve ||= Cx, Dv || | ||
||= 43 ||= 1200 ||< 2/1 ||= P8 ||= perfect 8ve ||= D || | |||
The distance from C to C# is 3 keys or frets or EDOsteps. Thus one up equals one third of a sharp. Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | |||
==Notation of 43edo== | ==Notation of 43edo== | ||
| Line 69: | Line 71: | ||
Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A# and Bb are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use "third-sharps", "two-thirds-sharps", "third-flats", and "two-thirds-flats" to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly. | Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A# and Bb are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use "third-sharps", "two-thirds-sharps", "third-flats", and "two-thirds-flats" to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly. | ||
Alternatively, a red-note/blue-note system (similar to that proposed for sixth-tones/[[36edo]]) can be used. Now we have the following sequence of notes, each separated by one meride: A, red A, blue A#, A#, Bb, red Bb, blue B, B. (Note that there are red flats and blue sharps, but no red sharps or blue flats, because the latter are enharmonically equivalent to simpler notes: blue Bb is actually just A#, for instance). | Alternatively, a red-note/blue-note system (similar to that proposed for sixth-tones/[[36edo]]) can be used. (This is a different use of color than Kite's [[xenharmonic/Kite's color notation|color notation]].) Now we have the following sequence of notes, each separated by one meride: A, red A, blue A#, A#, Bb, red Bb, blue B, B. (Note that there are red flats and blue sharps, but no red sharps or blue flats, because the latter are enharmonically equivalent to simpler notes: blue Bb is actually just A#, for instance). | ||
The diatonic semitone is four steps, so for the region between B and C (or, E and F), we can use: B, Cb, red Cb/blue B# (//they are enharmonic equivalents//), B#, and C. All of the notes in 43edo therefore have unambiguous names except for two: red Cb/blue B#, and red Fb/blue E#. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter). | The diatonic semitone is four steps, so for the region between B and C (or, E and F), we can use: B, Cb, red Cb/blue B# (//they are enharmonic equivalents//), B#, and C. All of the notes in 43edo therefore have unambiguous names except for two: red Cb/blue B#, and red Fb/blue E#. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter). | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td>Degrees | <td style="text-align: center;">Degrees<br /> | ||
</td> | </td> | ||
<td>Cents value<br /> | <td style="text-align: center;">Cents value<br /> | ||
</td> | </td> | ||
<td>Approximate 13-limit Ratios<br /> | <td style="text-align: left;">Approximate 13-limit Ratios<br /> | ||
</td> | |||
<td colspan="3" style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">ups and downs notation</a><br /> | |||
</td> | </td> | ||
</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><br /> | <td style="text-align: left;">1/1<br /> | ||
</td> | |||
<td style="text-align: center;">P1<br /> | |||
</td> | |||
<td style="text-align: center;">perfect unison<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>1<br /> | <td style="text-align: center;">1<br /> | ||
</td> | </td> | ||
<td>27.907<br /> | <td style="text-align: center;">27.907<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: left;"><br /> | ||
</td> | |||
<td style="text-align: center;">^1, d2<br /> | |||
</td> | |||
<td style="text-align: center;">up unison, dim 2nd<br /> | |||
</td> | |||
<td style="text-align: center;">D^, Ebb<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>2<br /> | <td style="text-align: center;">2<br /> | ||
</td> | |||
<td style="text-align: center;">55.814<br /> | |||
</td> | |||
<td style="text-align: left;"><br /> | |||
</td> | |||
<td style="text-align: center;">vA1, ^d2<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">downaug unison, updim 2nd<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">D#v, Ebb^<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>3<br /> | <td style="text-align: center;">3<br /> | ||
</td> | </td> | ||
<td>83.721<br /> | <td style="text-align: center;">83.721<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: left;"><br /> | ||
</td> | |||
<td style="text-align: center;">vm2<br /> | |||
</td> | |||
<td style="text-align: center;">downminor 2nd<br /> | |||
</td> | |||
<td style="text-align: center;">Ebv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>4<br /> | <td style="text-align: center;">4<br /> | ||
</td> | </td> | ||
<td>111.628<br /> | <td style="text-align: center;">111.628<br /> | ||
</td> | </td> | ||
<td>17/16, 16/15, 15/14<br /> | <td style="text-align: left;">17/16, 16/15, 15/14<br /> | ||
</td> | |||
<td style="text-align: center;">m2<br /> | |||
</td> | |||
<td style="text-align: center;">minor 2nd<br /> | |||
</td> | |||
<td style="text-align: center;">Eb<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>5<br /> | <td style="text-align: center;">5<br /> | ||
</td> | |||
<td style="text-align: center;">139.535<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: left;">12/11, 13/12, 14/13<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">^m2<br /> | ||
</td> | |||
<td style="text-align: center;">upminor 2nd<br /> | |||
</td> | |||
<td style="text-align: center;">Eb^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>6<br /> | <td style="text-align: center;">6<br /> | ||
</td> | </td> | ||
<td>167.442<br /> | <td style="text-align: center;">167.442<br /> | ||
</td> | </td> | ||
<td>11/10<br /> | <td style="text-align: left;">11/10<br /> | ||
</td> | |||
<td style="text-align: center;">vM2<br /> | |||
</td> | |||
<td style="text-align: center;">downmajor 2nd<br /> | |||
</td> | |||
<td style="text-align: center;">Ev<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>7<br /> | <td style="text-align: center;">7<br /> | ||
</td> | </td> | ||
<td>195.349<br /> | <td style="text-align: center;">195.349<br /> | ||
</td> | </td> | ||
<td>9/8, 10/9<br /> | <td style="text-align: left;">9/8, 10/9<br /> | ||
</td> | |||
<td style="text-align: center;">M2<br /> | |||
</td> | |||
<td style="text-align: center;">major 2nd<br /> | |||
</td> | |||
<td style="text-align: center;">E<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>8<br /> | <td style="text-align: center;">8<br /> | ||
</td> | |||
<td style="text-align: center;">223.256<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: left;">8/7<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">^M2<br /> | ||
</td> | |||
<td style="text-align: center;">upmajor 2nd<br /> | |||
</td> | |||
<td style="text-align: center;">E^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>9<br /> | <td style="text-align: center;">9<br /> | ||
</td> | |||
<td style="text-align: center;">251.163<br /> | |||
</td> | |||
<td style="text-align: left;">15/13<br /> | |||
</td> | |||
<td style="text-align: center;">vA2, ^d3<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">downaug 2nd, updim 3rd<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">E#v, Fb^<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>10<br /> | <td style="text-align: center;">10<br /> | ||
</td> | |||
<td style="text-align: center;">279.07<br /> | |||
</td> | |||
<td style="text-align: left;">7/6, 13/11<br /> | |||
</td> | |||
<td style="text-align: center;">vm3<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">downminor 3rd<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Fv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>11<br /> | <td style="text-align: center;">11<br /> | ||
</td> | </td> | ||
<td>306.977<br /> | <td style="text-align: center;">306.977<br /> | ||
</td> | </td> | ||
<td>6/5<br /> | <td style="text-align: left;">6/5<br /> | ||
</td> | |||
<td style="text-align: center;">m3<br /> | |||
</td> | |||
<td style="text-align: center;">minor 3rd<br /> | |||
</td> | |||
<td style="text-align: center;">F<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>12<br /> | <td style="text-align: center;">12<br /> | ||
</td> | </td> | ||
<td>334.884<br /> | <td style="text-align: center;">334.884<br /> | ||
</td> | </td> | ||
<td>17/14, 39/32<br /> | <td style="text-align: left;">17/14, 39/32<br /> | ||
</td> | |||
<td style="text-align: center;">^m3<br /> | |||
</td> | |||
<td style="text-align: center;">upminor 3rd<br /> | |||
</td> | |||
<td style="text-align: center;">F^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13<br /> | <td style="text-align: center;">13<br /> | ||
</td> | </td> | ||
<td>362.791<br /> | <td style="text-align: center;">362.791<br /> | ||
</td> | </td> | ||
<td>11/9, 16/13<br /> | <td style="text-align: left;">11/9, 16/13<br /> | ||
</td> | |||
<td style="text-align: center;">vM3<br /> | |||
</td> | |||
<td style="text-align: center;">downmajor 3rd<br /> | |||
</td> | |||
<td style="text-align: center;">F#v<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>14<br /> | <td style="text-align: center;">14<br /> | ||
</td> | |||
<td style="text-align: center;">390.698<br /> | |||
</td> | |||
<td style="text-align: left;">5/4<br /> | |||
</td> | |||
<td style="text-align: center;">M3<br /> | |||
</td> | |||
<td style="text-align: center;">major 3rd<br /> | |||
</td> | |||
<td style="text-align: center;">F#<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">15<br /> | |||
</td> | |||
<td style="text-align: center;">418.605<br /> | |||
</td> | |||
<td style="text-align: left;">9/7, 14/11<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">^M3<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">upmajor 3rd<br /> | ||
</td> | |||
<td style="text-align: center;">F#^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">16<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">446.512<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: left;">13/10<br /> | ||
</td> | |||
<td style="text-align: center;">vA3, ^d4<br /> | |||
</td> | |||
<td style="text-align: center;">downaug 3rd, updim 4th<br /> | |||
</td> | |||
<td style="text-align: center;">Fxv, Gb^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">17<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">474.419<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: left;">21/16<br /> | ||
</td> | |||
<td style="text-align: center;">v4<br /> | |||
</td> | |||
<td style="text-align: center;">down 4th<br /> | |||
</td> | |||
<td style="text-align: center;">Gv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">18<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">502.326<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: left;">4/3<br /> | ||
</td> | |||
<td style="text-align: center;">P4<br /> | |||
</td> | |||
<td style="text-align: center;">perfect 4th<br /> | |||
</td> | |||
<td style="text-align: center;">G<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">19<br /> | ||
</td> | |||
<td style="text-align: center;">530.233<br /> | |||
</td> | |||
<td style="text-align: left;">15/11<br /> | |||
</td> | |||
<td style="text-align: center;">^4<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">up 4th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">G^<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">20<br /> | ||
</td> | |||
<td style="text-align: center;">558.139<br /> | |||
</td> | |||
<td style="text-align: left;">11/8, 18/13<br /> | |||
</td> | |||
<td style="text-align: center;">vA4<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">downaug 4th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">G#v<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">21<br /> | ||
</td> | |||
<td style="text-align: center;">586.046<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: left;">7/5<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">A4, vd5<br /> | ||
</td> | |||
<td style="text-align: center;">aug 4th, downdim 5th<br /> | |||
</td> | |||
<td style="text-align: center;">G#, Abv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">22<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">613.953<br /> | ||
</td> | </td> | ||
<td>7/ | <td style="text-align: left;">10/7<br /> | ||
</td> | |||
<td style="text-align: center;">^A4, d5<br /> | |||
</td> | |||
<td style="text-align: center;">upaug 4th, dim 5th<br /> | |||
</td> | |||
<td style="text-align: center;">G#^, Ab<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">23<br /> | ||
</td> | |||
<td style="text-align: center;">641.86<br /> | |||
</td> | |||
<td style="text-align: left;">16/11, 13/9<br /> | |||
</td> | |||
<td style="text-align: center;">^d5<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">updim 5th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Ab^<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">24<br /> | ||
</td> | |||
<td style="text-align: center;">669.767<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: left;">22/15<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">v5<br /> | ||
</td> | |||
<td style="text-align: center;">down 5th<br /> | |||
</td> | |||
<td style="text-align: center;">Av<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">25<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">697.674<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: left;">3/2<br /> | ||
</td> | |||
<td style="text-align: center;">P5<br /> | |||
</td> | |||
<td style="text-align: center;">perfect 5th<br /> | |||
</td> | |||
<td style="text-align: center;">A<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">26<br /> | ||
</td> | |||
<td style="text-align: center;">725.581<br /> | |||
</td> | |||
<td style="text-align: left;">32/21<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">^5<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">up 5th<br /> | ||
</td> | |||
<td style="text-align: center;">A^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">27<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">753.488<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: left;">20/13<br /> | ||
</td> | |||
<td style="text-align: center;">vA5, ^d6<br /> | |||
</td> | |||
<td style="text-align: center;">downaug 5th, updim 6th<br /> | |||
</td> | |||
<td style="text-align: center;">A#v, Bbb^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">28<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">781.395<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: left;">14/9, 11/7<br /> | ||
</td> | |||
<td style="text-align: center;">vm6<br /> | |||
</td> | |||
<td style="text-align: center;">downminor 6th<br /> | |||
</td> | |||
<td style="text-align: center;">Bbv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">29<br /> | ||
</td> | |||
<td style="text-align: center;">809.302<br /> | |||
</td> | |||
<td style="text-align: left;">8/5<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">m6<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">minor 6th<br /> | ||
</td> | |||
<td style="text-align: center;">Bb<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">30<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">837.209<br /> | ||
</td> | </td> | ||
<td>8/ | <td style="text-align: left;">18/11, 13/8<br /> | ||
</td> | |||
<td style="text-align: center;">^m6<br /> | |||
</td> | |||
<td style="text-align: center;">upminor 6th<br /> | |||
</td> | |||
<td style="text-align: center;">Bb^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">31<br /> | ||
</td> | |||
<td style="text-align: center;">865.116<br /> | |||
</td> | |||
<td style="text-align: left;"><br /> | |||
</td> | |||
<td style="text-align: center;">vM6<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">downmajor 6th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Bv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">32<br /> | ||
</td> | |||
<td style="text-align: center;">893.023<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: left;">5/3<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">M6<br /> | ||
</td> | |||
<td style="text-align: center;">major 6th<br /> | |||
</td> | |||
<td style="text-align: center;">B<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">33<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">920.93<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: left;">12/7<br /> | ||
</td> | |||
<td style="text-align: center;">^M6<br /> | |||
</td> | |||
<td style="text-align: center;">upmajor 6th<br /> | |||
</td> | |||
<td style="text-align: center;">B^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">34<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">948.837<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: left;">26/15<br /> | ||
</td> | |||
<td style="text-align: center;">vA6, ^d7<br /> | |||
</td> | |||
<td style="text-align: center;">downaug 6th, updim 7th<br /> | |||
</td> | |||
<td style="text-align: center;">B#v, Cb^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">35<br /> | ||
</td> | |||
<td style="text-align: center;">976.744<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: left;">7/4<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">vm7<br /> | ||
</td> | |||
<td style="text-align: center;">downminor 7th<br /> | |||
</td> | |||
<td style="text-align: center;">Cv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">36<br /> | ||
</td> | |||
<td style="text-align: center;">1004.651<br /> | |||
</td> | |||
<td style="text-align: left;">16/9, 9/5<br /> | |||
</td> | |||
<td style="text-align: center;">m7<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">minor 7th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">C<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">37<br /> | ||
</td> | |||
<td style="text-align: center;">1032.558<br /> | |||
</td> | |||
<td style="text-align: left;">20/11<br /> | |||
</td> | |||
<td style="text-align: center;">^m7<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">upminor 7th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">C^<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">38<br /> | ||
</td> | |||
<td style="text-align: center;">1060.465<br /> | |||
</td> | |||
<td style="text-align: left;">11/6, 24/13, 13/7<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">vM7<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">downmajor 7th<br /> | ||
</td> | |||
<td style="text-align: center;">C#v<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">39<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">1088.372<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: left;">15/8, 28/15<br /> | ||
</td> | |||
<td style="text-align: center;">M7<br /> | |||
</td> | |||
<td style="text-align: center;">major 7th<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">40<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">1116.279<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: left;"><br /> | ||
</td> | |||
<td style="text-align: center;">^M7<br /> | |||
</td> | |||
<td style="text-align: center;">upmajor 7th<br /> | |||
</td> | |||
<td style="text-align: center;">C#^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">41<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">1144.186<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: left;"><br /> | ||
</td> | |||
<td style="text-align: center;">vA7, ^d8<br /> | |||
</td> | |||
<td style="text-align: center;">downaug 7th, updim 8ve<br /> | |||
</td> | |||
<td style="text-align: center;">Cxv, Db^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">42<br /> | ||
</td> | |||
<td style="text-align: center;">1172.093<br /> | |||
</td> | |||
<td style="text-align: left;"><br /> | |||
</td> | |||
<td style="text-align: center;">A7, v8<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">aug 7th, down 8ve<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">Cx, Dv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;">43<br /> | ||
</td> | |||
<td style="text-align: center;">1200<br /> | |||
</td> | |||
<td style="text-align: left;">2/1<br /> | |||
</td> | |||
<td style="text-align: center;">P8<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">perfect 8ve<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
The distance from C to C# is 3 keys or frets or EDOsteps. Thus one up equals one third of a sharp. Chords can be named using ups and downs as C upminor, D downmajor seven, etc. 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 /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x43 tone equal temperament-Notation of 43edo"></a><!-- ws:end:WikiTextHeadingRule:6 -->Notation of 43edo</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x43 tone equal temperament-Notation of 43edo"></a><!-- ws:end:WikiTextHeadingRule:6 -->Notation of 43edo</h2> | ||
| Line 453: | Line 730: | ||
Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A# and Bb are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use &quot;third-sharps&quot;, &quot;two-thirds-sharps&quot;, &quot;third-flats&quot;, and &quot;two-thirds-flats&quot; to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly.<br /> | Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A# and Bb are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use &quot;third-sharps&quot;, &quot;two-thirds-sharps&quot;, &quot;third-flats&quot;, and &quot;two-thirds-flats&quot; to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly.<br /> | ||
<br /> | <br /> | ||
Alternatively, a red-note/blue-note system (similar to that proposed for sixth-tones/<a class="wiki_link" href="/36edo">36edo</a>) can be used. Now we have the following sequence of notes, each separated by one meride: A, red A, blue A#, A#, Bb, red Bb, blue B, B. (Note that there are red flats and blue sharps, but no red sharps or blue flats, because the latter are enharmonically equivalent to simpler notes: blue Bb is actually just A#, for instance).<br /> | Alternatively, a red-note/blue-note system (similar to that proposed for sixth-tones/<a class="wiki_link" href="/36edo">36edo</a>) can be used. (This is a different use of color than Kite's <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kite%27s%20color%20notation">color notation</a>.) Now we have the following sequence of notes, each separated by one meride: A, red A, blue A#, A#, Bb, red Bb, blue B, B. (Note that there are red flats and blue sharps, but no red sharps or blue flats, because the latter are enharmonically equivalent to simpler notes: blue Bb is actually just A#, for instance).<br /> | ||
<br /> | <br /> | ||
The diatonic semitone is four steps, so for the region between B and C (or, E and F), we can use: B, Cb, red Cb/blue B# (<em>they are enharmonic equivalents</em>), B#, and C. All of the notes in 43edo therefore have unambiguous names except for two: red Cb/blue B#, and red Fb/blue E#. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter).<br /> | The diatonic semitone is four steps, so for the region between B and C (or, E and F), we can use: B, Cb, red Cb/blue B# (<em>they are enharmonic equivalents</em>), B#, and C. All of the notes in 43edo therefore have unambiguous names except for two: red Cb/blue B#, and red Fb/blue E#. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter).<br /> | ||