10edo: Difference between revisions

Wikispaces>xenwolf
**Imported revision 602900664 - Original comment: **
Wikispaces>diagonalia
**Imported revision 603051974 - Original comment: **
Line 1: Line 1:
<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:xenwolf|xenwolf]] and made on <tt>2016-12-29 17:05:37 UTC</tt>.<br>
: This revision was by author [[User:diagonalia|diagonalia]] and made on <tt>2017-01-03 20:34:07 UTC</tt>.<br>
: The original revision id was <tt>602900664</tt>.<br>
: The original revision id was <tt>603051974</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 17: Line 17:
||~ Degree ||~ Cents ||~ Approximate Ratios* ||~ Additional Ratios*
||~ Degree ||~ Cents ||~ Approximate Ratios* ||~ Additional Ratios*
of 3, 5 and 9 ||~ Interval Names ||||||~ [[Ups and Downs Notation|ups and downs notation]] ||
of 3, 5 and 9 ||~ Interval Names ||||||~ [[Ups and Downs Notation|ups and downs notation]] ||
|| 0 ||&gt;   0 ||= 1/1 || 256/243, 50/49, 25/24 || unison || unison ||= P1 ||= D ||
|| 0 ||&gt; 0 ||= 1/1 || 256/243, 50/49, 25/24 || unison || unison, min 2nd ||= P1, m2 ||= D. Eb ||
|| 1 ||&gt; 120 ||= 16/15, 15/14, 13/14 || 10/9, 13/12, 81/80 || small neutral second, large minor second || mid 2nd ||= ~2 ||= D^, Ev ||
|| 1 ||&gt; 120 ||= 16/15, 15/14, 13/14 || 10/9, 13/12, 81/80 || small neutral second, large minor second || mid 2nd ||= ~2 ||= D^, Ev ||
|| 2 ||&gt; 240 ||= 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || maj 2nd, min 3rd ||= M2,m3 ||= E, F ||
|| 2 ||&gt; 240 ||= 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || maj 2nd, min 3rd ||= M2,m3 ||= E, F ||
|| 3 ||&gt; 360 ||= 16/13 || 5/4 || large neutral third || mid 3rd ||= ~3 ||= F^, Gv ||
|| 3 ||&gt; 360 ||= 16/13 || 5/4 || large neutral third || mid 3rd ||= ~3 ||= F^, Gv ||
|| 4 ||&gt; 480 ||= 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || maj 3rd, perf 4th ||= M3,P4 ||= F#, G ||
|| 4 ||&gt; 480 ||= 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || maj 3rd, perf 4th ||= M3,P4 ||= F#, G ||
|| 5 ||&gt; 600 ||= 91/64, 128/91, 169/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone || up 4th, down 5th ||= ^4,v5 ||= G^, Av ||
|| 5 ||&gt; 600 ||= 91/64, 128/91, 169/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone || up 4th, down 5th ||= ^4,v5 ||= G^, Av ||
|| 6 ||&gt; 720 ||= 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || perf 5th, min 6th ||= P5,m6 ||= A, Bb ||
|| 6 ||&gt; 720 ||= 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || perf 5th, min 6th ||= P5,m6 ||= A, Bb ||
|| 7 ||&gt; 840 ||= 13/8 || 8/5 || neutral sixth || mid 6th ||= ~6 ||= A^, Bv ||
|| 7 ||&gt; 840 ||= 13/8 || 8/5 || neutral sixth || mid 6th ||= ~6 ||= A^, Bv ||
|| 8 ||&gt; 960 ||= 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || maj 6th, min 7th ||= M6,m7 ||= B, C ||
|| 8 ||&gt; 960 ||= 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || maj 6th, min 7th ||= M6,m7 ||= B, C ||
|| 9 ||&gt; 1080 ||= 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || mid 7th ||= ~7 ||= C^, Dv ||
|| 9 ||&gt; 1080 ||= 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || mid 7th ||= ~7 ||= C^, Dv ||
|| 10 ||&gt; 1200 ||= 2/1 || 243/128, 49/25, 48/25 || octave || octave ||= P8 ||= D ||
|| 10 ||&gt; 1200 ||= 2/1 || 243/128, 49/25, 48/25 || octave || maj 7th, octave ||= P8 ||= C#, 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.
Line 146: Line 146:
         &lt;td&gt;unison&lt;br /&gt;
         &lt;td&gt;unison&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;unison&lt;br /&gt;
         &lt;td&gt;unison, min 2nd&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;P1, m2&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;D. Eb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 326: Line 326:
         &lt;td&gt;octave&lt;br /&gt;
         &lt;td&gt;octave&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;octave&lt;br /&gt;
         &lt;td&gt;maj 7th, octave&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;C#, D&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;