16edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 602817514 - Original comment: ** |
Wikispaces>TallKite **Imported revision 606393483 - 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>2017-02-15 15:44:49 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>606393483</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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||~ Degree ||~ Cents ||~ Approximate | ||~ Degree ||~ Cents ||~ Approximate | ||
Ratios* ||||~ Melodic names, | Ratios* ||||~ Melodic names, | ||
major wider than minor ||||~ Harmonic names, | major wider than minor ||||~ Harmonic names, | ||
major narrower | major narrower | ||
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||= 0 ||= 0 ||= 1/1 ||= unison ||= D ||= unison ||= D ||= Unison ||= Unison || | ||= 0 ||= 0 ||= 1/1 ||= unison ||= D ||= unison ||= D ||= Unison ||= Unison || | ||
||= 1 ||= 75 ||= 28/27, 27/26 ||= aug 1, dim 2nd ||= D#, Eb ||= dim 1, aug 2nd ||= Db, E# ||= Subminor 2nd ||= Min 2nd || | ||= 1 ||= 75 ||= 28/27, 27/26 ||= aug 1, dim 2nd ||= D#, Eb ||= dim 1, aug 2nd ||= Db, E# ||= Subminor 2nd ||= Min 2nd || | ||
||= 2 ||= 150 ||= 12/11, 35/32 ||= | ||= 2 ||= 150 ||= 12/11, 35/32 ||= minor 2nd ||= E ||= major 2nd ||= E ||= Neutral 2nd ||= Maj 2nd || | ||
||= 3 ||= 225 ||= 8/7 ||= | ||= 3 ||= 225 ||= 8/7 ||= major 2nd ||= E# ||= minor 2nd ||= Eb ||= Supermajor 2nd, | ||
Septimal Whole-Tone ||= Perf 2nd || | Septimal Whole-Tone ||= Perf 2nd || | ||
||= 4 ||= 300 ||= 19/16, 32/27 ||= | ||= 4 ||= 300 ||= 19/16, 32/27 ||= minor 3rd ||= Fb ||= major 3rd ||= F# ||= Minor 3rd ||= Min 3rd || | ||
||= 5 ||= 375 ||= 5/4, 26/21 ||= | ||= 5 ||= 375 ||= 5/4, 26/21 ||= major 3rd ||= F ||= minor 3rd ||= F ||= Major 3rd ||= Maj 3rd || | ||
||= 6 ||= 450 ||= 13/10, 35/27 ||= aug 3rd | ||= 6 ||= 450 ||= 13/10, 35/27 ||= aug 3rd | ||
dim 4th ||= F#, Gb ||= dim 3rd, | |||
aug 4th ||= Fb, G# ||= Sub-4th, | |||
Supermajor 3rd ||= Min 4th || | Supermajor 3rd ||= Min 4th || | ||
||= 7 ||= 525 ||= 27/20, 52/35, 256/189 ||= | ||= 7 ||= 525 ||= 27/20, 52/35, 256/189 ||= perfect 4th ||= G ||= perfect 4th ||= G ||= Wide 4th ||= Maj 4th || | ||
||= 8 ||= 600 ||= 7/5, 10/7 ||= aug 4th | ||= 8 ||= 600 ||= 7/5, 10/7 ||= aug 4th | ||
dim 5th ||= G#, Ab ||= dim 4th, | |||
aug 5th ||= Gb, A# ||= Tritone ||= Aug 4th, | |||
Dim 5th || | Dim 5th || | ||
||= 9 ||= 675 ||= 40/27, 35/26, 189/128 ||= | ||= 9 ||= 675 ||= 40/27, 35/26, 189/128 ||= perfect 5th ||= A ||= perfect 5th ||= A ||= Narrow 5th ||= Min 5th || | ||
||= 10 ||= 750 ||= 20/13, 54/35 ||= aug 5th | ||= 10 ||= 750 ||= 20/13, 54/35 ||= aug 5th | ||
dim 6th ||= A#, Bb ||= dim 5th, aug 6th ||= Ab, B# ||= Super-5th, | |||
Subminor 6th ||= Maj 5th || | Subminor 6th ||= Maj 5th || | ||
||= 11 ||= 825 ||= 8/5, 21/13 ||= | ||= 11 ||= 825 ||= 8/5, 21/13 ||= minor 6th ||= B ||= major 6th ||= B ||= Minor 6th ||= Min 6th || | ||
||= 12 ||= 900 ||= 27/16, 32/19 ||= | ||= 12 ||= 900 ||= 27/16, 32/19 ||= major 6th ||= B# ||= minor 6th ||= Bb ||= Major 6th ||= Maj 6th || | ||
||= 13 ||= 975 ||= 7/4 ||= | ||= 13 ||= 975 ||= 7/4 ||= minor 7th ||= Cb ||= major 7th ||= C# ||= Subminor 7th, | ||
Septimal Minor 7th ||= Perf 7th || | Septimal Minor 7th ||= Perf 7th || | ||
||= 14 ||= 1050 ||= 11/6, 64/35 ||= | ||= 14 ||= 1050 ||= 11/6, 64/35 ||= major 7th ||= C ||= minor 7th ||= C ||= Neutral 7th ||= Min 7th || | ||
||= 15 ||= 1125 ||= 27/14, 52/27 ||= aug 7th | ||= 15 ||= 1125 ||= 27/14, 52/27 ||= aug 7th | ||
dim 8ve ||= C#, Db ||= dim 7th, | |||
aug 8ve ||= Cb, D# ||= Supermajor 7th ||= Maj 7th || | |||
||= 16 ||= 1200 ||= 2/1 ||= 8ve ||= D ||= 8ve ||= D ||= Octave ||= Octave || | ||= 16 ||= 1200 ||= 2/1 ||= 8ve ||= D ||= 8ve ||= D ||= Octave ||= Octave || | ||
*based on treating 16-EDO as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible. | *based on treating 16-EDO as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible. | ||
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Ratios*<br /> | Ratios*<br /> | ||
</th> | </th> | ||
<th colspan="2">Melodic names, <br /> | <th colspan="2">Melodic names,<br /> | ||
major wider than minor<br /> | major wider than minor<br /> | ||
</th> | </th> | ||
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<td style="text-align: center;">12/11, 35/32<br /> | <td style="text-align: center;">12/11, 35/32<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">minor 2nd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E<br /> | <td style="text-align: center;">E<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">major 2nd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E<br /> | <td style="text-align: center;">E<br /> | ||
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<td style="text-align: center;">8/7<br /> | <td style="text-align: center;">8/7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">major 2nd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E#<br /> | <td style="text-align: center;">E#<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">minor 2nd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Eb<br /> | <td style="text-align: center;">Eb<br /> | ||
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<td style="text-align: center;">19/16, 32/27<br /> | <td style="text-align: center;">19/16, 32/27<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">minor 3rd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Fb<br /> | <td style="text-align: center;">Fb<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">major 3rd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">F#<br /> | <td style="text-align: center;">F#<br /> | ||
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<td style="text-align: center;">5/4, 26/21<br /> | <td style="text-align: center;">5/4, 26/21<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">major 3rd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">F<br /> | <td style="text-align: center;">F<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">minor 3rd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">F<br /> | <td style="text-align: center;">F<br /> | ||
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<td style="text-align: center;">13/10, 35/27<br /> | <td style="text-align: center;">13/10, 35/27<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">aug 3rd | <td style="text-align: center;">aug 3rd <br /> | ||
dim 4th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">F#, Gb<br /> | <td style="text-align: center;">F#, Gb<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">dim 3rd, aug 4th<br /> | <td style="text-align: center;">dim 3rd,<br /> | ||
aug 4th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">Fb, G#<br /> | <td style="text-align: center;">Fb, G#<br /> | ||
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<td style="text-align: center;">27/20, 52/35, 256/189<br /> | <td style="text-align: center;">27/20, 52/35, 256/189<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">perfect 4th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">G<br /> | <td style="text-align: center;">G<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">perfect 4th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">G<br /> | <td style="text-align: center;">G<br /> | ||
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<td style="text-align: center;">7/5, 10/7<br /> | <td style="text-align: center;">7/5, 10/7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">aug 4th | <td style="text-align: center;">aug 4th <br /> | ||
dim 5th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">G#, Ab<br /> | <td style="text-align: center;">G#, Ab<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">dim 4th, aug 5th<br /> | <td style="text-align: center;">dim 4th, <br /> | ||
aug 5th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">Gb, A#<br /> | <td style="text-align: center;">Gb, A#<br /> | ||
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<td style="text-align: center;">40/27, 35/26, 189/128<br /> | <td style="text-align: center;">40/27, 35/26, 189/128<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">perfect 5th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A<br /> | <td style="text-align: center;">A<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">perfect 5th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A<br /> | <td style="text-align: center;">A<br /> | ||
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<td style="text-align: center;">20/13, 54/35<br /> | <td style="text-align: center;">20/13, 54/35<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">aug 5th | <td style="text-align: center;">aug 5th <br /> | ||
dim 6th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">A#, Bb<br /> | <td style="text-align: center;">A#, Bb<br /> | ||
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<td style="text-align: center;">8/5, 21/13<br /> | <td style="text-align: center;">8/5, 21/13<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">minor 6th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">B<br /> | <td style="text-align: center;">B<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">major 6th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">B<br /> | <td style="text-align: center;">B<br /> | ||
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<td style="text-align: center;">27/16, 32/19<br /> | <td style="text-align: center;">27/16, 32/19<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">major 6th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">B#<br /> | <td style="text-align: center;">B#<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">minor 6th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Bb<br /> | <td style="text-align: center;">Bb<br /> | ||
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<td style="text-align: center;">7/4<br /> | <td style="text-align: center;">7/4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">minor 7th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Cb<br /> | <td style="text-align: center;">Cb<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">major 7th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C#<br /> | <td style="text-align: center;">C#<br /> | ||
| Line 579: | Line 591: | ||
<td style="text-align: center;">11/6, 64/35<br /> | <td style="text-align: center;">11/6, 64/35<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">major 7th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C<br /> | <td style="text-align: center;">C<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">minor 7th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C<br /> | <td style="text-align: center;">C<br /> | ||
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<td style="text-align: center;">27/14, 52/27<br /> | <td style="text-align: center;">27/14, 52/27<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">aug 7th | <td style="text-align: center;">aug 7th <br /> | ||
dim 8ve<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C#, Db<br /> | <td style="text-align: center;">C#, Db<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">dim 7th, aug 8ve<br /> | <td style="text-align: center;">dim 7th, <br /> | ||
aug 8ve<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">Cb, D#<br /> | <td style="text-align: center;">Cb, D#<br /> | ||