10edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 601330544 - Original comment: ** |
Wikispaces>TallKite **Imported revision 602738066 - 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 03:52:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602738066</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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=[[media type="custom" key="10886138"]]= | =[[media type="custom" key="10886138"]]= | ||
=Intervals= | =Intervals= | ||
|| Degree || Cents | || Degree || Cents || Approximate | ||
Ratios* || Additional Ratios | Ratios* || Additional Ratios | ||
of 3, 5 and 9 || Interval Names ||||||= [[Ups and Downs Notation|ups and downs]] | of 3, 5 and 9 || Interval Names ||||||= [[Ups and Downs Notation|ups and downs]] | ||
[[Ups and Downs Notation|notation]] || | [[Ups and Downs Notation|notation]] || | ||
|| 0 || 0 | || 0 || 0 || 1/1 || 256/243, 50/49, 25/24 || unison || unison ||= P1 ||= D || | ||
|| 1 || 120 | || 1 || 120 || 16/15, 15/14, 13/14 || 10/9, 13/12, 81/80 || small neutral second, | ||
large minor second || mid 2nd ||= ~2 ||= D^, Ev || | large minor second || mid 2nd ||= ~2 ||= D^, Ev || | ||
|| 2 || 240 | || 2 || 240 || 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || maj 2nd, | ||
min 3rd ||= M2,m3 ||= E, F || | min 3rd ||= M2,m3 ||= E, F || | ||
|| 3 || 360 | || 3 || 360 || 16/13 || 5/4 || large neutral third || mid 3rd ||= ~3 ||= F^, Gv || | ||
|| 4 || 480 | || 4 || 480 || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || maj 3rd, | ||
perf 4th ||= M3,P4 ||= F#, G || | perf 4th ||= M3,P4 ||= F#, G || | ||
|| 5 || 600 | || 5 || 600 || 91/64, 128/91, | ||
169/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone || up 4th, | 169/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone || up 4th, | ||
down 5th ||= ^4,v5 ||= G^, Av || | down 5th ||= ^4,v5 ||= G^, Av || | ||
|| 6 || 720 | || 6 || 720 || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || perf 5th, | ||
min 6th ||= P5,m6 ||= A, Bb || | min 6th ||= P5,m6 ||= A, Bb || | ||
|| 7 || 840 | || 7 || 840 || 13/8 || 8/5 || neutral sixth || mid 6th ||= ~6 ||= A^, Bv || | ||
|| 8 || 960 | || 8 || 960 || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || maj 6th, | ||
min 7th ||= M6,m7 ||= B, C || | min 7th ||= M6,m7 ||= B, C || | ||
|| 9 || 1080 | || 9 || 1080 || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || mid 7th ||= ~7 ||= C^, Dv || | ||
|| 10 || 1200 | || 10 || 1200 || 2/1 || 243/128, 49/25, 48/25 || octave || octave ||= P8 ||= D || | ||
*based on treating 10-EDO as a 2.7.13.15 subgroup temperament. | *based on treating 10-EDO as a 2.7.13.15 subgroup temperament. | ||
adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-EDO intervals. | adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-EDO intervals. | ||
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<td>Degree<br /> | <td>Degree<br /> | ||
</td> | </td> | ||
<td>Cents | <td>Cents<br /> | ||
</td> | </td> | ||
<td>Approximate<br /> | <td>Approximate<br /> | ||
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<td>0<br /> | <td>0<br /> | ||
</td> | </td> | ||
<td>0 | <td>0<br /> | ||
</td> | </td> | ||
<td>1/1<br /> | <td>1/1<br /> | ||
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<td>1<br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>120 | <td>120<br /> | ||
</td> | </td> | ||
<td>16/15, 15/14, 13/14<br /> | <td>16/15, 15/14, 13/14<br /> | ||
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<td>2<br /> | <td>2<br /> | ||
</td> | </td> | ||
<td>240 | <td>240<br /> | ||
</td> | </td> | ||
<td>8/7, 15/13, 144/125<br /> | <td>8/7, 15/13, 144/125<br /> | ||
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<td>3<br /> | <td>3<br /> | ||
</td> | </td> | ||
<td>360 | <td>360<br /> | ||
</td> | </td> | ||
<td>16/13<br /> | <td>16/13<br /> | ||
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<td>4<br /> | <td>4<br /> | ||
</td> | </td> | ||
<td>480 | <td>480<br /> | ||
</td> | </td> | ||
<td>64/49, 169/128<br /> | <td>64/49, 169/128<br /> | ||
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<td>5<br /> | <td>5<br /> | ||
</td> | </td> | ||
<td>600 | <td>600<br /> | ||
</td> | </td> | ||
<td>91/64, 128/91,<br /> | <td>91/64, 128/91,<br /> | ||
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<td>6<br /> | <td>6<br /> | ||
</td> | </td> | ||
<td>720 | <td>720<br /> | ||
</td> | </td> | ||
<td>49/32, 256/169<br /> | <td>49/32, 256/169<br /> | ||
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<td>7<br /> | <td>7<br /> | ||
</td> | </td> | ||
<td>840 | <td>840<br /> | ||
</td> | </td> | ||
<td>13/8<br /> | <td>13/8<br /> | ||
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<td>8<br /> | <td>8<br /> | ||
</td> | </td> | ||
<td>960 | <td>960<br /> | ||
</td> | </td> | ||
<td>7/4, 26/15, 125/72<br /> | <td>7/4, 26/15, 125/72<br /> | ||
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<td>9<br /> | <td>9<br /> | ||
</td> | </td> | ||
<td>1080 | <td>1080<br /> | ||
</td> | </td> | ||
<td>15/8, 28/15, 13/7<br /> | <td>15/8, 28/15, 13/7<br /> | ||
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<td>10<br /> | <td>10<br /> | ||
</td> | </td> | ||
<td>1200 | <td>1200<br /> | ||
</td> | </td> | ||
<td>2/1<br /> | <td>2/1<br /> | ||