46edo: Difference between revisions
Wikispaces>TallKite **Imported revision 621435639 - Original comment: ** |
Wikispaces>TallKite **Imported revision 621435931 - 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>2017-11-11 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 04:18:08 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>621435931</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> | ||
| Line 294: | Line 294: | ||
|| 23 || 1\46 || 26.087 || || || || | || 23 || 1\46 || 26.087 || || || || | ||
=Intervals= | =Intervals= | ||
||~ degrees of 46edo ||~ solfege ||~ cents value ||~ approximate ratios in the [[xenharmonic/17-limit|17-limit]] ||||~ [[Ups and Downs Notation|ups and downs notation]] || | ||~ degrees of 46edo ||~ solfege ||~ cents value ||~ approximate ratios | ||
||= 0 ||= do || 0.00 || 1/1 ||= P1 ||= D || | in the [[xenharmonic/17-limit|17-limit]] ||||||~ [[Ups and Downs Notation|ups and downs notation]] || | ||
||= 1 ||= di || 26.087 || ||= ^1 ||= D^ || | ||= 0 ||= do || 0.00 || 1/1 ||= perfect unison ||= P1 ||= D || | ||
||= 2 ||= ro || 52.174 || ||= vm2 ||= Ebv || | ||= 1 ||= di || 26.087 || ||= up unison ||= ^1 ||= D^ || | ||
||= 3 ||= rih || 78.261 || ||= m2 ||= Eb || | ||= 2 ||= ro || 52.174 || ||= downminor 2nd ||= vm2 ||= Ebv || | ||
||= 4 ||= ra || 104.348 || 16/15, 17/16, 18/17 ||= ^m2 ||= Eb^ || | ||= 3 ||= rih || 78.261 || ||= minor 2nd ||= m2 ||= Eb || | ||
||= 5 ||= ru (as in supraminor) || 130.435 || 13/12, 14/13, 15/14 ||= v~2 ||= Eb^^ || | ||= 4 ||= ra || 104.348 || 16/15, 17/16, 18/17 ||= upminor 2nd ||= ^m2 ||= Eb^ || | ||
||= 6 ||= ruh (as in submajor) || 156.522 || 12/11, 11/10 ||= ^~2 ||= Evv || | ||= 5 ||= ru (as in supraminor) || 130.435 || 13/12, 14/13, 15/14 ||= downmid 2nd ||= v~2 ||= Eb^^ || | ||
||= 7 ||= reh || 182.609 || 10/9 ||= vM2 ||= Ev || | ||= 6 ||= ruh (as in submajor) || 156.522 || 12/11, 11/10 ||= upmid 2nd ||= ^~2 ||= Evv || | ||
||= 8 ||= re || 208.696 || 9/8, 17/15 ||= | ||= 7 ||= reh || 182.609 || 10/9 ||= downmajor 2nd ||= vM2 ||= Ev || | ||
||= 9 ||= ri || 234.783 || 8/7, 15/13* ||= ^M2 ||= E^ || | ||= 8 ||= re || 208.696 || 9/8, 17/15 ||= major 2nd ||= M2 ||= E || | ||
||= 10 ||= ma || 260.87 || 7/6, 15/13* ||= vm3 ||= Fv || | ||= 9 ||= ri || 234.783 || 8/7, 15/13* ||= upmajor 2nd ||= ^M2 ||= E^ || | ||
||= 11 ||= meh || 286.957 || 13/11, 20/17 ||= m3 ||= F || | ||= 10 ||= ma || 260.87 || 7/6, 15/13* ||= downminor 3rd ||= vm3 ||= Fv || | ||
||= 12 ||= me || 313.043 || 6/5 ||= ^m3 ||= F^ || | ||= 11 ||= meh || 286.957 || 13/11, 20/17 ||= minor 3rd ||= m3 ||= F || | ||
||= 13 ||= mu || 339.13 || 11/9, 17/14 ||= v~3 ||= F^^ || | ||= 12 ||= me || 313.043 || 6/5 ||= upminor 3rd ||= ^m3 ||= F^ || | ||
||= 14 ||= muh || 365.217 || 16/13 ||= ^~3 ||= F#vv || | ||= 13 ||= mu || 339.13 || 11/9, 17/14 ||= downmid 3rd ||= v~3 ||= F^^ || | ||
||= 15 ||= mi || 391.304 || 5/4 ||= vM3 ||= F#v || | ||= 14 ||= muh || 365.217 || 16/13 ||= upmid 3rd ||= ^~3 ||= F#vv || | ||
||= 16 ||= maa || 417.391 || 14/11 ||= M3 ||= F# || | ||= 15 ||= mi || 391.304 || 5/4 ||= downmajor 3rd ||= vM3 ||= F#v || | ||
||= 17 ||= mo || 443.478 || 9/7, 13/10, 22/17 ||= ^M3 ||= F#^ || | ||= 16 ||= maa || 417.391 || 14/11 ||= major 3rd ||= M3 ||= F# || | ||
||= 18 ||= fe || 469.565 || 17/13 ||= v4 ||= Gv || | ||= 17 ||= mo || 443.478 || 9/7, 13/10, 22/17 ||= upmajor 3rd ||= ^M3 ||= F#^ || | ||
||= 19 ||= fa || 495.652 || 4/3 ||= P4 ||= G || | ||= 18 ||= fe || 469.565 || 17/13 ||= down 4th ||= v4 ||= Gv || | ||
||= 20 ||= fih || 521.739 || ||= ^4 ||= G^ || | ||= 19 ||= fa || 495.652 || 4/3 ||= perfect 4th ||= P4 ||= G || | ||
||= 21 ||= fu || 547.826 || 11/8, 15/11 ||= ^^4 ||= G^^ || | ||= 20 ||= fih || 521.739 || ||= up 4th ||= ^4 ||= G^ || | ||
||= 22 ||= fi || 573.913 || 7/5, 18/13 ||= vvA4 ||= G#vv || | ||= 21 ||= fu || 547.826 || 11/8, 15/11 ||= double-up 4th ||= ^^4 ||= G^^ || | ||
||= 23 ||= seh || 600 || 17/12, 24/17 ||= | ||= 22 ||= fi || 573.913 || 7/5, 18/13 ||= double-down aug 4th, | ||
||= 24 ||= se || 626.087 || 10/7, 13/9 ||= ^^d5 ||= Ab^^ || | dim 5th ||= vvA4, d5 ||= G#vv, Ab || | ||
||= 25 ||= su || 652.174 || 16/11, 22/15 ||= vv5 ||= Avv || | ||= 23 ||= seh || 600 || 17/12, 24/17 ||= downaug 4th, updim 5th ||= vA4, ^d5 ||= G#v, Ab^ || | ||
||= 26 ||= sih || 678.261 || ||= v5 ||= Av || | ||= 24 ||= se || 626.087 || 10/7, 13/9 ||= aug 4th, double-up dim 5th ||= A4, ^^d5 ||= G#, Ab^^ || | ||
||= 27 ||= sol || 704.348 || 3/2 ||= P5 ||= A || | ||= 25 ||= su || 652.174 || 16/11, 22/15 ||= double-down 5th ||= vv5 ||= Avv || | ||
||= 28 ||= si || 730.435 || 26/17 ||= ^5 ||= A^ || | ||= 26 ||= sih || 678.261 || ||= down 5th ||= v5 ||= Av || | ||
||= 29 ||= lo || 756.522 || 14/9, 20/13, 17/11 ||= | ||= 27 ||= sol || 704.348 || 3/2 ||= perfect 5th ||= P5 ||= A || | ||
||= 30 ||= leh || 782.609 || 11/7 ||= m6 ||= Bb || | ||= 28 ||= si || 730.435 || 26/17 ||= up 5th ||= ^5 ||= A^ || | ||
||= 31 ||= le || 808.696 || 8/5 ||= ^m6 ||= Bb^ || | ||= 29 ||= lo || 756.522 || 14/9, 20/13, 17/11 ||= downminor 6th ||= vm6 ||= Bbv || | ||
||= 32 ||= lu || 834.783 || 13/8 ||= v~6 ||= Bb^^ || | ||= 30 ||= leh || 782.609 || 11/7 ||= minor 6th ||= m6 ||= Bb || | ||
||= 33 ||= luh || 860.87 || 18/11, 28/17 ||= ^~6 ||= Bvv || | ||= 31 ||= le || 808.696 || 8/5 ||= upminor 6th ||= ^m6 ||= Bb^ || | ||
||= 34 ||= la || 886.957 || 5/3 ||= vM6 ||= Bv || | ||= 32 ||= lu || 834.783 || 13/8 ||= downmid 6th ||= v~6 ||= Bb^^ || | ||
||= 35 ||= laa || 913.043 || 22/13, 17/10 ||= M6 ||= B || | ||= 33 ||= luh || 860.87 || 18/11, 28/17 ||= upmid 6th ||= ^~6 ||= Bvv || | ||
||= 36 ||= li || 939.13 || 12/7, 26/15* ||= ^M6 ||= B^ || | ||= 34 ||= la || 886.957 || 5/3 ||= downmajor 6th ||= vM6 ||= Bv || | ||
||= 37 ||= ta || 965.217 || 7/4, 26/15* ||= vm7 ||= Cv || | ||= 35 ||= laa || 913.043 || 22/13, 17/10 ||= major 6th ||= M6 ||= B || | ||
||= 38 ||= teh || 991.304 || 16/9, 30/17 ||= m7 ||= C || | ||= 36 ||= li || 939.13 || 12/7, 26/15* ||= upmajor 6th ||= ^M6 ||= B^ || | ||
||= 39 ||= te || 1017.391 || 9/5 ||= ^m7 ||= C^ || | ||= 37 ||= ta || 965.217 || 7/4, 26/15* ||= downminor 7th ||= vm7 ||= Cv || | ||
||= 40 ||= tu || 1043.478 || 11/6, 20/11 ||= v~7 ||= C^^ || | ||= 38 ||= teh || 991.304 || 16/9, 30/17 ||= minor 7th ||= m7 ||= C || | ||
||= 41 ||= tuh || 1069.565 || 24/13, 13/7, 28/15 ||= ^~7 ||= C#vv || | ||= 39 ||= te || 1017.391 || 9/5 ||= upminor 7th ||= ^m7 ||= C^ || | ||
||= 42 ||= ti || 1095.652 || 15/8, 32/17, 17/9 ||= vM7 ||= C#v || | ||= 40 ||= tu || 1043.478 || 11/6, 20/11 ||= downmid 7th ||= v~7 ||= C^^ || | ||
||= 43 ||= taa || 1121.739 || ||= M7 ||= C# || | ||= 41 ||= tuh || 1069.565 || 24/13, 13/7, 28/15 ||= upmid 7th ||= ^~7 ||= C#vv || | ||
||= 44 ||= to || 1147.826 || ||= ^M7 ||= C#^ || | ||= 42 ||= ti || 1095.652 || 15/8, 32/17, 17/9 ||= downmajor 7th ||= vM7 ||= C#v || | ||
||= 45 ||= da || 1173.913 || ||= v8 ||= Dv || | ||= 43 ||= taa || 1121.739 || ||= major 7th ||= M7 ||= C# || | ||
||= 46 ||= do || 1200 || 2/1 ||= P8 ||= D || | ||= 44 ||= to || 1147.826 || ||= upmajor 7th ||= ^M7 ||= C#^ || | ||
||= 45 ||= da || 1173.913 || ||= down 8ve ||= v8 ||= Dv || | |||
||= 46 ||= do || 1200 || 2/1 ||= perfect 8ve ||= P8 ||= D || | |||
*15/13 (and its inversion 26/15) appears twice on the list. 9\46edo is closest to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13. This discrepancy occurs because 46edo is not [[xenharmonic/consistent|consistent]] in the [[xenharmonic/15-limit|15-limit]]. | *15/13 (and its inversion 26/15) appears twice on the list. 9\46edo is closest to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13. This discrepancy occurs because 46edo is not [[xenharmonic/consistent|consistent]] in the [[xenharmonic/15-limit|15-limit]]. | ||
All 46edo chords can be named using ups and downs: | |||
0-10-27 = C Ebv G = C.vm = "C downminor" | |||
0-12-27 = C Eb^ G = C.^m = "C upminor" | |||
0-14-27 = C Evv G = C.^~ = "C upmid" | |||
0-16-27 = C E G = "C major" or "C" | |||
0-17-27 = C E^ G = C.^= "C upmajor" or "C dot up" | |||
etc. | |||
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]]. | |||
=Approximation to Mode 8 of the Harmonic Series= | =Approximation to Mode 8 of the Harmonic Series= | ||
| Line 989: | Line 1,001: | ||
<th>cents value<br /> | <th>cents value<br /> | ||
</th> | </th> | ||
<th>approximate ratios in the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17-limit">17-limit</a><br /> | <th>approximate ratios<br /> | ||
in the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17-limit">17-limit</a><br /> | |||
</th> | </th> | ||
<th colspan=" | <th colspan="3"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs notation</a><br /> | ||
</th> | </th> | ||
</tr> | </tr> | ||
| Line 1,002: | Line 1,015: | ||
</td> | </td> | ||
<td>1/1<br /> | <td>1/1<br /> | ||
</td> | |||
<td style="text-align: center;">perfect unison<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">P1<br /> | <td style="text-align: center;">P1<br /> | ||
| Line 1,016: | Line 1,031: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td style="text-align: center;">up unison<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^1<br /> | <td style="text-align: center;">^1<br /> | ||
| Line 1,030: | Line 1,047: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td style="text-align: center;">downminor 2nd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">vm2<br /> | <td style="text-align: center;">vm2<br /> | ||
| Line 1,044: | Line 1,063: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td style="text-align: center;">minor 2nd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">m2<br /> | <td style="text-align: center;">m2<br /> | ||
| Line 1,058: | Line 1,079: | ||
</td> | </td> | ||
<td>16/15, 17/16, 18/17<br /> | <td>16/15, 17/16, 18/17<br /> | ||
</td> | |||
<td style="text-align: center;">upminor 2nd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^m2<br /> | <td style="text-align: center;">^m2<br /> | ||
| Line 1,072: | Line 1,095: | ||
</td> | </td> | ||
<td>13/12, 14/13, 15/14<br /> | <td>13/12, 14/13, 15/14<br /> | ||
</td> | |||
<td style="text-align: center;">downmid 2nd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">v~2<br /> | <td style="text-align: center;">v~2<br /> | ||
| Line 1,086: | Line 1,111: | ||
</td> | </td> | ||
<td>12/11, 11/10<br /> | <td>12/11, 11/10<br /> | ||
</td> | |||
<td style="text-align: center;">upmid 2nd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^~2<br /> | <td style="text-align: center;">^~2<br /> | ||
| Line 1,100: | Line 1,127: | ||
</td> | </td> | ||
<td>10/9<br /> | <td>10/9<br /> | ||
</td> | |||
<td style="text-align: center;">downmajor 2nd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">vM2<br /> | <td style="text-align: center;">vM2<br /> | ||
| Line 1,114: | Line 1,143: | ||
</td> | </td> | ||
<td>9/8, 17/15<br /> | <td>9/8, 17/15<br /> | ||
</td> | |||
<td style="text-align: center;">major 2nd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">M2<br /> | <td style="text-align: center;">M2<br /> | ||
| Line 1,128: | Line 1,159: | ||
</td> | </td> | ||
<td>8/7, 15/13*<br /> | <td>8/7, 15/13*<br /> | ||
</td> | |||
<td style="text-align: center;">upmajor 2nd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^M2<br /> | <td style="text-align: center;">^M2<br /> | ||
| Line 1,142: | Line 1,175: | ||
</td> | </td> | ||
<td>7/6, 15/13*<br /> | <td>7/6, 15/13*<br /> | ||
</td> | |||
<td style="text-align: center;">downminor 3rd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">vm3<br /> | <td style="text-align: center;">vm3<br /> | ||
| Line 1,156: | Line 1,191: | ||
</td> | </td> | ||
<td>13/11, 20/17<br /> | <td>13/11, 20/17<br /> | ||
</td> | |||
<td style="text-align: center;">minor 3rd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">m3<br /> | <td style="text-align: center;">m3<br /> | ||
| Line 1,170: | Line 1,207: | ||
</td> | </td> | ||
<td>6/5<br /> | <td>6/5<br /> | ||
</td> | |||
<td style="text-align: center;">upminor 3rd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^m3<br /> | <td style="text-align: center;">^m3<br /> | ||
| Line 1,184: | Line 1,223: | ||
</td> | </td> | ||
<td>11/9, 17/14<br /> | <td>11/9, 17/14<br /> | ||
</td> | |||
<td style="text-align: center;">downmid 3rd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">v~3<br /> | <td style="text-align: center;">v~3<br /> | ||
| Line 1,198: | Line 1,239: | ||
</td> | </td> | ||
<td>16/13<br /> | <td>16/13<br /> | ||
</td> | |||
<td style="text-align: center;">upmid 3rd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^~3<br /> | <td style="text-align: center;">^~3<br /> | ||
| Line 1,212: | Line 1,255: | ||
</td> | </td> | ||
<td>5/4<br /> | <td>5/4<br /> | ||
</td> | |||
<td style="text-align: center;">downmajor 3rd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">vM3<br /> | <td style="text-align: center;">vM3<br /> | ||
| Line 1,226: | Line 1,271: | ||
</td> | </td> | ||
<td>14/11<br /> | <td>14/11<br /> | ||
</td> | |||
<td style="text-align: center;">major 3rd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">M3<br /> | <td style="text-align: center;">M3<br /> | ||
| Line 1,240: | Line 1,287: | ||
</td> | </td> | ||
<td>9/7, 13/10, 22/17<br /> | <td>9/7, 13/10, 22/17<br /> | ||
</td> | |||
<td style="text-align: center;">upmajor 3rd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^M3<br /> | <td style="text-align: center;">^M3<br /> | ||
| Line 1,254: | Line 1,303: | ||
</td> | </td> | ||
<td>17/13<br /> | <td>17/13<br /> | ||
</td> | |||
<td style="text-align: center;">down 4th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">v4<br /> | <td style="text-align: center;">v4<br /> | ||
| Line 1,268: | Line 1,319: | ||
</td> | </td> | ||
<td>4/3<br /> | <td>4/3<br /> | ||
</td> | |||
<td style="text-align: center;">perfect 4th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">P4<br /> | <td style="text-align: center;">P4<br /> | ||
| Line 1,282: | Line 1,335: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td style="text-align: center;">up 4th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^4<br /> | <td style="text-align: center;">^4<br /> | ||
| Line 1,296: | Line 1,351: | ||
</td> | </td> | ||
<td>11/8, 15/11<br /> | <td>11/8, 15/11<br /> | ||
</td> | |||
<td style="text-align: center;">double-up 4th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^^4<br /> | <td style="text-align: center;">^^4<br /> | ||
| Line 1,311: | Line 1,368: | ||
<td>7/5, 18/13<br /> | <td>7/5, 18/13<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">double-down aug 4th,<br /> | ||
dim 5th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">G#vv<br /> | <td style="text-align: center;">vvA4, d5<br /> | ||
</td> | |||
<td style="text-align: center;">G#vv, Ab<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,324: | Line 1,384: | ||
</td> | </td> | ||
<td>17/12, 24/17<br /> | <td>17/12, 24/17<br /> | ||
</td> | |||
<td style="text-align: center;">downaug 4th, updim 5th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">vA4, ^d5<br /> | <td style="text-align: center;">vA4, ^d5<br /> | ||
| Line 1,339: | Line 1,401: | ||
<td>10/7, 13/9<br /> | <td>10/7, 13/9<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">aug 4th, double-up dim 5th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Ab^^<br /> | <td style="text-align: center;">A4, ^^d5<br /> | ||
</td> | |||
<td style="text-align: center;">G#, Ab^^<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,352: | Line 1,416: | ||
</td> | </td> | ||
<td>16/11, 22/15<br /> | <td>16/11, 22/15<br /> | ||
</td> | |||
<td style="text-align: center;">double-down 5th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">vv5<br /> | <td style="text-align: center;">vv5<br /> | ||
| Line 1,366: | Line 1,432: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td style="text-align: center;">down 5th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">v5<br /> | <td style="text-align: center;">v5<br /> | ||
| Line 1,380: | Line 1,448: | ||
</td> | </td> | ||
<td>3/2<br /> | <td>3/2<br /> | ||
</td> | |||
<td style="text-align: center;">perfect 5th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">P5<br /> | <td style="text-align: center;">P5<br /> | ||
| Line 1,394: | Line 1,464: | ||
</td> | </td> | ||
<td>26/17<br /> | <td>26/17<br /> | ||
</td> | |||
<td style="text-align: center;">up 5th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^5<br /> | <td style="text-align: center;">^5<br /> | ||
| Line 1,408: | Line 1,480: | ||
</td> | </td> | ||
<td>14/9, 20/13, 17/11<br /> | <td>14/9, 20/13, 17/11<br /> | ||
</td> | |||
<td style="text-align: center;">downminor 6th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">vm6<br /> | <td style="text-align: center;">vm6<br /> | ||
| Line 1,422: | Line 1,496: | ||
</td> | </td> | ||
<td>11/7<br /> | <td>11/7<br /> | ||
</td> | |||
<td style="text-align: center;">minor 6th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">m6<br /> | <td style="text-align: center;">m6<br /> | ||
| Line 1,436: | Line 1,512: | ||
</td> | </td> | ||
<td>8/5<br /> | <td>8/5<br /> | ||
</td> | |||
<td style="text-align: center;">upminor 6th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^m6<br /> | <td style="text-align: center;">^m6<br /> | ||
| Line 1,450: | Line 1,528: | ||
</td> | </td> | ||
<td>13/8<br /> | <td>13/8<br /> | ||
</td> | |||
<td style="text-align: center;">downmid 6th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">v~6<br /> | <td style="text-align: center;">v~6<br /> | ||
| Line 1,464: | Line 1,544: | ||
</td> | </td> | ||
<td>18/11, 28/17<br /> | <td>18/11, 28/17<br /> | ||
</td> | |||
<td style="text-align: center;">upmid 6th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^~6<br /> | <td style="text-align: center;">^~6<br /> | ||
| Line 1,478: | Line 1,560: | ||
</td> | </td> | ||
<td>5/3<br /> | <td>5/3<br /> | ||
</td> | |||
<td style="text-align: center;">downmajor 6th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">vM6<br /> | <td style="text-align: center;">vM6<br /> | ||
| Line 1,492: | Line 1,576: | ||
</td> | </td> | ||
<td>22/13, 17/10<br /> | <td>22/13, 17/10<br /> | ||
</td> | |||
<td style="text-align: center;">major 6th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">M6<br /> | <td style="text-align: center;">M6<br /> | ||
| Line 1,506: | Line 1,592: | ||
</td> | </td> | ||
<td>12/7, 26/15*<br /> | <td>12/7, 26/15*<br /> | ||
</td> | |||
<td style="text-align: center;">upmajor 6th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^M6<br /> | <td style="text-align: center;">^M6<br /> | ||
| Line 1,520: | Line 1,608: | ||
</td> | </td> | ||
<td>7/4, 26/15*<br /> | <td>7/4, 26/15*<br /> | ||
</td> | |||
<td style="text-align: center;">downminor 7th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">vm7<br /> | <td style="text-align: center;">vm7<br /> | ||
| Line 1,534: | Line 1,624: | ||
</td> | </td> | ||
<td>16/9, 30/17<br /> | <td>16/9, 30/17<br /> | ||
</td> | |||
<td style="text-align: center;">minor 7th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">m7<br /> | <td style="text-align: center;">m7<br /> | ||
| Line 1,548: | Line 1,640: | ||
</td> | </td> | ||
<td>9/5<br /> | <td>9/5<br /> | ||
</td> | |||
<td style="text-align: center;">upminor 7th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^m7<br /> | <td style="text-align: center;">^m7<br /> | ||
| Line 1,562: | Line 1,656: | ||
</td> | </td> | ||
<td>11/6, 20/11<br /> | <td>11/6, 20/11<br /> | ||
</td> | |||
<td style="text-align: center;">downmid 7th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">v~7<br /> | <td style="text-align: center;">v~7<br /> | ||
| Line 1,576: | Line 1,672: | ||
</td> | </td> | ||
<td>24/13, 13/7, 28/15<br /> | <td>24/13, 13/7, 28/15<br /> | ||
</td> | |||
<td style="text-align: center;">upmid 7th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^~7<br /> | <td style="text-align: center;">^~7<br /> | ||
| Line 1,590: | Line 1,688: | ||
</td> | </td> | ||
<td>15/8, 32/17, 17/9<br /> | <td>15/8, 32/17, 17/9<br /> | ||
</td> | |||
<td style="text-align: center;">downmajor 7th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">vM7<br /> | <td style="text-align: center;">vM7<br /> | ||
| Line 1,604: | Line 1,704: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td style="text-align: center;">major 7th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">M7<br /> | <td style="text-align: center;">M7<br /> | ||
| Line 1,618: | Line 1,720: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td style="text-align: center;">upmajor 7th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">^M7<br /> | <td style="text-align: center;">^M7<br /> | ||
| Line 1,632: | Line 1,736: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td style="text-align: center;">down 8ve<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">v8<br /> | <td style="text-align: center;">v8<br /> | ||
| Line 1,646: | Line 1,752: | ||
</td> | </td> | ||
<td>2/1<br /> | <td>2/1<br /> | ||
</td> | |||
<td style="text-align: center;">perfect 8ve<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">P8<br /> | <td style="text-align: center;">P8<br /> | ||
| Line 1,655: | Line 1,763: | ||
*15/13 (and its inversion 26/15) appears twice on the list. 9\46edo is closest to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13. This discrepancy occurs because 46edo is not <a class="wiki_link" href="http://xenharmonic.wikispaces.com/consistent">consistent</a> in the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/15-limit">15-limit</a>.<br /> | *15/13 (and its inversion 26/15) appears twice on the list. 9\46edo is closest to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13. This discrepancy occurs because 46edo is not <a class="wiki_link" href="http://xenharmonic.wikispaces.com/consistent">consistent</a> in the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/15-limit">15-limit</a>.<br /> | ||
<br /> | |||
All 46edo chords can be named using ups and downs:<br /> | |||
0-10-27 = C Ebv G = C.vm = &quot;C downminor&quot;<br /> | |||
0-12-27 = C Eb^ G = C.^m = &quot;C upminor&quot;<br /> | |||
0-14-27 = C Evv G = C.^~ = &quot;C upmid&quot;<br /> | |||
0-16-27 = C E G = &quot;C major&quot; or &quot;C&quot;<br /> | |||
0-17-27 = C E^ G = C.^= &quot;C upmajor&quot; or &quot;C dot up&quot;<br /> | |||
etc.<br /> | |||
<br /> | |||
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 /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Approximation to Mode 8 of the Harmonic Series"></a><!-- ws:end:WikiTextHeadingRule:8 -->Approximation to Mode 8 of the Harmonic Series</h1> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Approximation to Mode 8 of the Harmonic Series"></a><!-- ws:end:WikiTextHeadingRule:8 -->Approximation to Mode 8 of the Harmonic Series</h1> | ||