10edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~TallKite~~|~~TallKite~~]] and made on <tt>2016-12-~~26 00~~:55:15 UTC</tt>.

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 17:02:15 UTC</tt>.

: The original revision id was <tt>~~602810518~~</tt>.

: The original revision id was <tt>602900608</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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=[[media type="custom" key="10886138"]]=

=Intervals=

|| Degree || Cents || Approximate

||~ Degree ||~ Cents ||~ Approximate Ratios* ||~ Additional Ratios*

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]]

|| 0 ||> 0 ||= 1/1 || 256/243, 50/49, 25/24 || unison || unison ||= P1 ||= D ||

~~[[Ups and Downs Notation|~~notation]] ||

|| 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 ||

|| 0 || 0 || 1/1 || 256/243, 50/49, 25/24 || unison || unison ||= P1 ||= D ||

|| 2 ||> 240 ||= 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || maj 2nd, min 3rd ||= M2,m3 ||= E, F ||

|| 1 || 120 || 16/15, 15/14, 13/14 || 10/9, 13/12, 81/80 || small neutral second,

|| 3 ||> 360 ||= 16/13 || 5/4 || large neutral third || mid 3rd ||= ~3 ||= F^, Gv ||

large minor second || mid 2nd ||= ~2 ||= D^, Ev ||

|| 4 ||> 480 ||= 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || maj 3rd, perf 4th ||= M3,P4 ||= F#, G ||

|| 2 || 240 || 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || maj 2nd,

|| 5 ||> 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 ||

min 3rd ||= M2,m3 ||= E, F ||

|| 6 ||> 720 ||= 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || perf 5th, min 6th ||= P5,m6 ||= A, Bb ||

|| 3 || 360 || 16/13 || 5/4 || large neutral third || mid 3rd ||= ~3 ||= F^, Gv ||

|| 7 ||> 840 ||= 13/8 || 8/5 || neutral sixth || mid 6th ||= ~6 ||= A^, Bv ||

|| 4 || 480 || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || maj 3rd,

|| 8 ||> 960 ||= 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || maj 6th, min 7th ||= M6,m7 ||= B, C ||

perf 4th ||= M3,P4 ||= F#, G ||

|| 9 ||> 1080 ||= 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || mid 7th ||= ~7 ||= C^, Dv ||

|| 5 || 600 || 91/64, 128/91,

|| 10 ||> 1200 ||= 2/1 || 243/128, 49/25, 48/25 || octave || octave ||= P8 ||= D ||

169/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone || up 4th,

down 5th ||= ^4,v5 ||= G^, Av ||

|| 6 || 720 || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || perf 5th,

min 6th ||= P5,m6 ||= A, Bb ||

|| 7 || 840 || 13/8 || 8/5 || neutral sixth || mid 6th ||= ~6 ||= A^, Bv ||

|| 8 || 960 || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || maj 6th,

min 7th ||= M6,m7 ||= B, C ||

|| 9 || 1080 || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || mid 7th ||= ~7 ||= C^, Dv ||

|| 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.

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.

For alternative notations, see [[Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Pentatonic%22%20EDOs|Ups and Downs Notation -"Pentatonic" EDOs]] (pentatonic fifth-based) and [[xenharmonic/Ups and Downs Notation#Natural%20Generators|Ups and Downs Notation - Natural Generators]] (heptatonic 3rd-based).

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|| 5 || 1\10 || [[Blackwood]]/[[blacksmith]] ||

=Commas=

10 EDO tempers out the following commas. (Note: This assumes the val < 10 16 23 28 35 37/1 |.)

10 EDO tempers out the following commas. (Note: This assumes the val < 10 16 23 28 35 37 |.)

||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||

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||= 225/224 || | -5 2 2 -1 > ||> 7.71 ||= Septimal Kleisma ||= Marvel Comma || ||

||= 16875/16807 || | 0 3 4 -5 > ||> 6.99 ||= Mirkwai ||= || ||

||= || | 11 -10 -10 10/1 > ||> 5.57 ||= Linus ||= || ||

||= || | 11 -10 -10 10 > ||> 5.57 ||= Linus ||= || ||

||= 2401/2400 || | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||= || ||

||= 243/242 || | -1 5 0 0 -2 > ||> 7.14 ||= Rastma ||= || ||

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<tr>

<td>Degree

<th>Degree

</td>

</th>

<td>Cents

<th>Cents

</td>

</th>

<td>Approximate~~ ~~

<th>Approximate Ratios*

Ratios*

</th>

</td>

<th>Additional Ratios*

<td>Additional Ratios

of 3, 5 and 9

</td>

</th>

<td>Interval Names

<th>Interval Names

</td>

</th>

<td colspan="3~~" style="text-align: center;~~"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs~~</a> ~~

<th colspan="3"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs notation</a>

~~<a class="wiki_link" href="/Ups%20and%20Downs%20Notation">~~notation</a>

</th>

</td>

</tr>

<tr>

<td>0

</td>

<td>0

<td style="text-align: right;">0

</td>

<td>1/1

<td style="text-align: center;">1/1

</td>

<td>256/243, 50/49, 25/24

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<td>1

</td>

<td>120

<td style="text-align: right;">120

</td>

<td>16/15, 15/14, 13/14

<td style="text-align: center;">16/15, 15/14, 13/14

</td>

<td>10/9, 13/12, 81/80

</td>

<td>small neutral second,~~ ~~

<td>small neutral second, large minor second

large minor second

</td>

<td>mid 2nd

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<td>2

</td>

<td>240

<td style="text-align: right;">240

</td>

<td>8/7, 15/13, 144/125

<td style="text-align: center;">8/7, 15/13, 144/125

</td>

<td>9/8, 7/6

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<td>second/third

</td>

<td>maj 2nd,~~ ~~

<td>maj 2nd, min 3rd

min 3rd

</td>

<td style="text-align: center;">M2,m3

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<td>3

</td>

<td>360

<td style="text-align: right;">360

</td>

<td>16/13

<td style="text-align: center;">16/13

</td>

<td>5/4

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<td>4

</td>

<td>480

<td style="text-align: right;">480

</td>

<td>64/49, 169/128

<td style="text-align: center;">64/49, 169/128

</td>

<td>4/3, 9/7, 13/10

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<td>smaller fourth

</td>

<td>maj 3rd,~~ ~~

<td>maj 3rd, perf 4th

perf 4th

</td>

<td style="text-align: center;">M3,P4

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<td>5

</td>

<td>600

<td style="text-align: right;">600

</td>

<td>91/64, 128/91,~~ ~~

<td style="text-align: center;">91/64, 128/91, 169/120, 240/169

169/120, 240/169

</td>

<td>7/5, 10/7, 13/9, 18/13

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<td>tritone

</td>

<td>up 4th,~~ ~~

<td>up 4th, down 5th

down 5th

</td>

<td style="text-align: center;">^4,v5

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<td>6

</td>

<td>720

<td style="text-align: right;">720

</td>

<td>49/32, 256/169

<td style="text-align: center;">49/32, 256/169

</td>

<td>3/2, 14/9, 20/13

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<td>bigger fifth

</td>

<td>perf 5th,~~ ~~

<td>perf 5th, min 6th

min 6th

</td>

<td style="text-align: center;">P5,m6

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<td>7

</td>

<td>840

<td style="text-align: right;">840

</td>

<td>13/8

<td style="text-align: center;">13/8

</td>

<td>8/5

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<td>8

</td>

<td>960

<td style="text-align: right;">960

</td>

<td>7/4, 26/15, 125/72

<td style="text-align: center;">7/4, 26/15, 125/72

</td>

<td>16/9, 12/7

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<td>sixth/seventh

</td>

<td>maj 6th,~~ ~~

<td>maj 6th, min 7th

min 7th

</td>

<td style="text-align: center;">M6,m7

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<td>9

</td>

<td>1080

<td style="text-align: right;">1080

</td>

<td>15/8, 28/15, 13/7

<td style="text-align: center;">15/8, 28/15, 13/7

</td>

<td>9/5, 24/13, 160/81

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<td>10

</td>

<td>1200

<td style="text-align: right;">1200

</td>

<td>2/1

<td style="text-align: center;">2/1

</td>

<td>243/128, 49/25, 48/25

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*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.

adding the ratios of 3, 5 and 9 introduces greater <a class="wiki_link" href="/error">error</a> while giving several more harmonic identities to the 10-EDO intervals.

*adding the ratios of 3, 5 and 9 introduces greater <a class="wiki_link" href="/error">error</a> while giving several more harmonic identities to the 10-EDO intervals.

For alternative notations, see <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Pentatonic%22%20EDOs">Ups and Downs Notation -&quot;Pentatonic&quot; EDOs</a> (pentatonic fifth-based) and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Natural%20Generators">Ups and Downs Notation - Natural Generators</a> (heptatonic 3rd-based).

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<h1 id="toc4"><a name="Commas"></a>Commas</h1>

10 EDO tempers out the following commas. (Note: This assumes the val &lt; 10 16 23 28 35 37/1 |.)

10 EDO tempers out the following commas. (Note: This assumes the val &lt; 10 16 23 28 35 37 |.)

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</td>

<td>| 11 -10 -10 10/1 &gt;

<td>| 11 -10 -10 10 &gt;

</td>

<td style="text-align: right;">5.57

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2016-12-26 00:55:15 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 17:02:15 UTC</tt>.<br>
-: The original revision id was <tt>602810518</tt>.<br>
+: The original revision id was <tt>602900608</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>
@@ Line 15: / Line 15: @@
 =[[media type="custom" key="10886138"]]=
 =Intervals=
-|| Degree || Cents || Approximate
+||~ Degree ||~ Cents ||~ Approximate Ratios* ||~ Additional Ratios*
-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]]
+||  0 ||&gt;    0 ||= 1/1 || 256/243, 50/49, 25/24 || unison || unison ||= P1 ||= D ||
-[[Ups and Downs Notation|notation]] ||
+||  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 ||
-|| 0 || 0 || 1/1 || 256/243, 50/49, 25/24 || unison || unison ||= P1 ||= D ||
+||  2 ||&gt;  240 ||= 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || maj 2nd, min 3rd ||= M2,m3 ||= E, F ||
-|| 1 || 120 || 16/15, 15/14, 13/14 || 10/9, 13/12, 81/80 || small neutral second,
+||  3 ||&gt;  360 ||= 16/13 || 5/4 || large neutral third || mid 3rd ||= ~3 ||= F^, Gv ||
-large minor second || mid 2nd ||= ~2 ||= D^, Ev ||
+||  4 ||&gt;  480 ||= 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || maj 3rd, perf 4th ||= M3,P4 ||= F#, G ||
-|| 2 || 240 || 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || maj 2nd,
+||  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 ||
-min 3rd ||= M2,m3 ||= E, F ||
+||  6 ||&gt;  720 ||= 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || perf 5th, min 6th ||= P5,m6 ||= A, Bb ||
-|| 3 || 360 || 16/13 || 5/4 || large neutral third || mid 3rd ||= ~3 ||= F^, Gv ||
+||  7 ||&gt;  840 ||= 13/8 || 8/5 || neutral sixth || mid 6th ||= ~6 ||= A^, Bv ||
-|| 4 || 480 || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || maj 3rd,
+||  8 ||&gt;  960 ||= 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || maj 6th, min 7th ||= M6,m7 ||= B, C ||
-perf 4th ||= M3,P4 ||= F#, G ||
+||  9 ||&gt; 1080 ||= 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || mid 7th ||= ~7 ||= C^, Dv ||
-|| 5 || 600 || 91/64, 128/91,
+|| 10 ||&gt; 1200 ||= 2/1 || 243/128, 49/25, 48/25 || octave || octave ||= P8 ||= D ||
-/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone || up 4th,
-down 5th ||= ^4,v5 ||= G^, Av ||
-|| 6 || 720 || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || perf 5th,
-min 6th ||= P5,m6 ||= A, Bb ||
-|| 7 || 840 || 13/8 || 8/5 || neutral sixth || mid 6th ||= ~6 ||= A^, Bv ||
-|| 8 || 960 || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || maj 6th,
-min 7th ||= M6,m7 ||= B, C ||
-|| 9 || 1080 || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || mid 7th ||= ~7 ||= C^, Dv ||
-|| 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.
-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.
 For alternative notations, see [[Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Pentatonic%22%20EDOs|Ups and Downs Notation -"Pentatonic" EDOs]] (pentatonic fifth-based) and [[xenharmonic/Ups and Downs Notation#Natural%20Generators|Ups and Downs Notation - Natural Generators]] (heptatonic 3rd-based).
@@ Line 59: / Line 50: @@
 || 5 || 1\10 || [[Blackwood]]/[[blacksmith]] ||
 =Commas=
-EDO tempers out the following commas. (Note: This assumes the val &lt; 10 16 23 28 35 37/1 |.)
+EDO tempers out the following commas. (Note: This assumes the val &lt; 10 16 23 28 35 37 |.)
 ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
@@ Line 76: / Line 67: @@
 ||= 225/224 || | -5 2 2 -1 &gt; ||&gt; 7.71 ||= Septimal Kleisma ||= Marvel Comma ||   ||
 ||= 16875/16807 || | 0 3 4 -5 &gt; ||&gt; 6.99 ||= Mirkwai ||=   ||   ||
-||=   || | 11 -10 -10 10/1 &gt; ||&gt; 5.57 ||= Linus ||=   ||   ||
+||=   || | 11 -10 -10 10 &gt; ||&gt; 5.57 ||= Linus ||=   ||   ||
 ||= 2401/2400 || | -5 -1 -2 4 &gt; ||&gt; 0.72 ||= Breedsma ||=   ||   ||
 ||= 243/242 || | -1 5 0 0 -2 &gt; ||&gt; 7.14 ||= Rastma ||=   ||   ||
@@ Line 130: / Line 121: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;Degree&lt;br /&gt;
+         &lt;th&gt;Degree&lt;br /&gt;
-&lt;/td&gt;
+&lt;/th&gt;
-         &lt;td&gt;Cents&lt;br /&gt;
+         &lt;th&gt;Cents&lt;br /&gt;
-&lt;/td&gt;
+&lt;/th&gt;
-         &lt;td&gt;Approximate&lt;br /&gt;
+         &lt;th&gt;Approximate Ratios*&lt;br /&gt;
-Ratios*&lt;br /&gt;
+&lt;/th&gt;
-&lt;/td&gt;
+         &lt;th&gt;Additional Ratios*&lt;br /&gt;
-         &lt;td&gt;Additional Ratios&lt;br /&gt;
 of 3, 5 and 9&lt;br /&gt;
-&lt;/td&gt;
+&lt;/th&gt;
-         &lt;td&gt;Interval Names&lt;br /&gt;
+         &lt;th&gt;Interval Names&lt;br /&gt;
-&lt;/td&gt;
+&lt;/th&gt;
-         &lt;td colspan="3" style="text-align: center;"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;ups and downs&lt;/a&gt;&lt;br /&gt;
+         &lt;th colspan="3"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;ups and downs notation&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;notation&lt;/a&gt;&lt;br /&gt;
+&lt;/th&gt;
-&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1/1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;256/243, 50/49, 25/24&lt;br /&gt;
@@ Line 167: / Line 156: @@
          &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;120&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;120&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16/15, 15/14, 13/14&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;16/15, 15/14, 13/14&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;10/9, 13/12, 81/80&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;small neutral second,&lt;br /&gt;
+         &lt;td&gt;small neutral second, large minor second&lt;br /&gt;
-large minor second&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;mid 2nd&lt;br /&gt;
@@ Line 186: / Line 174: @@
          &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;240&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;240&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;8/7, 15/13, 144/125&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8/7, 15/13, 144/125&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9/8, 7/6&lt;br /&gt;
@@ Line 194: / Line 182: @@
          &lt;td&gt;second/third&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;maj 2nd,&lt;br /&gt;
+         &lt;td&gt;maj 2nd, min 3rd&lt;br /&gt;
-min 3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;M2,m3&lt;br /&gt;
@@ Line 205: / Line 192: @@
          &lt;td&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;360&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;360&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16/13&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;16/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;5/4&lt;br /&gt;
@@ Line 223: / Line 210: @@
          &lt;td&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;480&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;480&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;64/49, 169/128&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;64/49, 169/128&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;4/3, 9/7, 13/10&lt;br /&gt;
@@ Line 231: / Line 218: @@
          &lt;td&gt;smaller fourth&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;maj 3rd,&lt;br /&gt;
+         &lt;td&gt;maj 3rd, perf 4th&lt;br /&gt;
-perf 4th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;M3,P4&lt;br /&gt;
@@ Line 242: / Line 228: @@
          &lt;td&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;600&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;600&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;91/64, 128/91,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;91/64, 128/91, 169/120, 240/169&lt;br /&gt;
-/120, 240/169&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/5, 10/7, 13/9, 18/13&lt;br /&gt;
@@ Line 251: / Line 236: @@
          &lt;td&gt;tritone&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;up 4th,&lt;br /&gt;
+         &lt;td&gt;up 4th, down 5th&lt;br /&gt;
-down 5th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;^4,v5&lt;br /&gt;
@@ Line 262: / Line 246: @@
          &lt;td&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;720&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;720&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;49/32, 256/169&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;49/32, 256/169&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;3/2, 14/9, 20/13&lt;br /&gt;
@@ Line 270: / Line 254: @@
          &lt;td&gt;bigger fifth&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;perf 5th,&lt;br /&gt;
+         &lt;td&gt;perf 5th, min 6th&lt;br /&gt;
-min 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;P5,m6&lt;br /&gt;
@@ Line 281: / Line 264: @@
          &lt;td&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;840&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;840&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;13/8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13/8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;8/5&lt;br /&gt;
@@ Line 299: / Line 282: @@
          &lt;td&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;960&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;960&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7/4, 26/15, 125/72&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7/4, 26/15, 125/72&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;16/9, 12/7&lt;br /&gt;
@@ Line 307: / Line 290: @@
          &lt;td&gt;sixth/seventh&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;maj 6th,&lt;br /&gt;
+         &lt;td&gt;maj 6th, min 7th&lt;br /&gt;
-min 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;M6,m7&lt;br /&gt;
@@ Line 318: / Line 300: @@
          &lt;td&gt;9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1080&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1080&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;15/8, 28/15, 13/7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;15/8, 28/15, 13/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9/5, 24/13, 160/81&lt;br /&gt;
@@ Line 336: / Line 318: @@
          &lt;td&gt;10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1200&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2/1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;243/128, 49/25, 48/25&lt;br /&gt;
@@ Line 354: / Line 336: @@
 *based on treating 10-EDO as a 2.7.13.15 subgroup temperament.&lt;br /&gt;
-adding the ratios of 3, 5 and 9 introduces greater &lt;a class="wiki_link" href="/error"&gt;error&lt;/a&gt; while giving several more harmonic identities to the 10-EDO intervals.&lt;br /&gt;
+*adding the ratios of 3, 5 and 9 introduces greater &lt;a class="wiki_link" href="/error"&gt;error&lt;/a&gt; while giving several more harmonic identities to the 10-EDO intervals.&lt;br /&gt;
 &lt;br /&gt;
 For alternative notations, see &lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Pentatonic%22%20EDOs"&gt;Ups and Downs Notation -&amp;quot;Pentatonic&amp;quot; EDOs&lt;/a&gt; (pentatonic fifth-based) and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Natural%20Generators"&gt;Ups and Downs Notation - Natural Generators&lt;/a&gt; (heptatonic 3rd-based).&lt;br /&gt;
@@ Line 422: / Line 404: @@
 &lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Commas&lt;/h1&gt;
-EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 10 16 23 28 35 37/1 |.)&lt;br /&gt;
+EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 10 16 23 28 35 37 |.)&lt;br /&gt;
 &lt;br /&gt;
@@ Line 640: / Line 622: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| 11 -10 -10 10/1 &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| 11 -10 -10 10 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;5.57&lt;br /&gt;