Porcupine intervals: 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:~~phylingual~~|~~phylingual~~]] and made on <tt>2012-07-~~07 20~~:47:23 UTC</tt>.

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-07-19 14:42:20 UTC</tt>.

: The original revision id was <tt>~~351337216~~</tt>.

: The original revision id was <tt>353982584</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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In [[15edo]], on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a **minor** fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo.

||~ Name ||~ Size* ||~ Ratios ||~ Comments ||

||~ Name ||~ Size* ||~ Ratios ||~ # of Porcupine Generators

||||||||~ Unisons ||

(~162.7¢) ||~ Comments ||

|| Perfect unison (P1) || 0 || 1/1 || ||

||||||||~ Unisons ||~ ||

|| Augmented unison (A1) || 61.1 || 81/80~36/35~33/32~25/24 || [[Cluster temperament#porcupine~~(fish)~~|And other ratios, of course]] ||

|| Perfect unison (P1) || 0 || 1/1 || 0 || ||

||||||||~ Seconds ||

|| Augmented unison (A1) || 61.1 || 81/80~36/35~33/32~25/24 || -7 || [[Cluster temperament#porcupine%28fish%29|And other ratios, of course]] ||

|| Diminished second (d2) || 101.6 || 21/20~16/15 || ||

||||||||~ Seconds ||~ ||

|| Minor second (m2) || 162.7 || 12/11~11/10~10/9 || ||

|| Diminished second (d2) || 101.6 || 21/20~16/15 || 8 || ||

|| Major second (M2) || 223.8 || 9/8~8/7 || ||

|| Minor second (m2) || 162.7 || 12/11~11/10~10/9 || 1 || ||

|| Augmented second (A2) || 284.9 || Close to 13/11 || Also "subminor third" ||

|| Major second (M2) || 223.8 || 9/8~8/7 || -6 || ||

||||||||~ Thirds ||

|| Augmented second (A2) || 284.9 || Close to 13/11 || -13 || Also "subminor third" ||

|| Diminished third (d3) || 264.3 || 7/6 || Also "supermajor second" ||

||||||||~ Thirds ||~ ||

|| Minor third (m3) || 325.4 || 6/5~11/9 || Coincidentally familiar ||

|| Diminished third (d3) || 264.3 || 7/6 || 9 || Also "supermajor second" ||

|| Major third (M3) || 386.5 || 5/4 || Coincidentally familiar ||

|| Minor third (m3) || 325.4 || 6/5~11/9 || 2 || Coincidentally familiar ||

|| Augmented third (A3) || 447.6 || 9/7 (close to 13/10) || Also "subminor fourth" ||

|| Major third (M3) || 386.5 || 5/4 || -5 || Coincidentally familiar ||

||||||||~ Fourths ||

|| Augmented third (A3) || 447.6 || 9/7 (close to 13/10) || -12 || Also "subminor fourth" ||

|| Diminished fourth (d4) || 427.0 || 14/11 || Also "supermajor third" ||

||||||||~ Fourths ||~ ||

|| Minor fourth (m4) || 488.1 || 4/3 || Rather than "perfect fourth" ||

|| Diminished fourth (d4) || 427.0 || 14/11 || 10 || Also "supermajor third" ||

|| Major fourth (M4) || 549.2 || 11/8 || ||

|| Minor fourth (m4) || 488.1 || 4/3 || 3 || Rather than "perfect fourth" ||

|| Augmented fourth (A4) || 610.3 || 10/7 || Also "subminor fifth" ||

|| Major fourth (M4) || 549.2 || 11/8 || -4 || ||

||||||||~ Fifths ||

|| Augmented fourth (A4) || 610.3 || 10/7 || -11 || Also "subminor fifth" ||

|| Diminished fifth (d5) || 589.7 || 7/5 || Also "supermajor fourth" ||

||||||||~ Fifths ||~ ||

|| Minor fifth (m5) || 650.8 || 16/11 || ||

|| Diminished fifth (d5) || 589.7 || 7/5 || 11 || Also "supermajor fourth" ||

|| Major fifth (M5) || 711.9 || 3/2 || Rather than "perfect fifth" ||

|| Minor fifth (m5) || 650.8 || 16/11 || 4 || ||

|| Augmented fifth (A5) || 773.0 || 11/7 || Also "subminor sixth" ||

|| Major fifth (M5) || 711.9 || 3/2 || -3 || Rather than "perfect fifth" ||

||||||||~ Sixths ||

|| Augmented fifth (A5) || 773.0 || 11/7 || -10 || Also "subminor sixth" ||

|| Diminished sixth (d6) || 752.4 || 14/9 (close to 20/13) || Also "supermajor fifth" ||

||||||||~ Sixths ||~ ||

|| Minor sixth (m6) || 813.5 || 8/5 || Coincidentally familiar ||

|| Diminished sixth (d6) || 752.4 || 14/9 (close to 20/13) || 12 || Also "supermajor fifth" ||

|| Major sixth (M6) || 874.6 || 5/3 || Coincidentally familiar ||

|| Minor sixth (m6) || 813.5 || 8/5 || 5 || Coincidentally familiar ||

|| Augmented sixth (A6) || 935.7 || 12/7 || Also "subminor seventh" ||

|| Major sixth (M6) || 874.6 || 5/3 || -2 || Coincidentally familiar ||

||||||||~ Sevenths ||

|| Augmented sixth (A6) || 935.7 || 12/7 || -9 || Also "subminor seventh" ||

|| Diminished seventh (d7) || 915.1 || Close to 22/13 || Also "supermajor sixth" ||

||||||||~ Sevenths ||~ ||

|| Minor seventh (m7) || 976.2 || 7/4~16/9 || ||

|| Diminished seventh (d7) || 915.1 || Close to 22/13 || 13 || Also "supermajor sixth" ||

|| Major seventh (M7) || 1037.3 || 9/5~11/6 || ||

|| Minor seventh (m7) || 976.2 || 7/4~16/9 || 6 || ||

|| Augmented seventh (A7) || 1098.4 || 15/8 || ||

|| Major seventh (M7) || 1037.3 || 9/5~11/6 || -3 || ||

||||||||~ Octaves ||

|| Augmented seventh (A7) || 1098.4 || 15/8 || -8 || ||

|| Diminished octave (d8) || 1138.9 || 21/11~35/18~160/81 || ||

||||||||~ Octaves ||~ ||

|| Perfect octave (P8) || 1200 || 2/1 || ||

|| Diminished octave (d8) || 1138.9 || 21/11~35/18~160/81 || 7 || ||

|| Augmented octave (A8) || 1261.1 || 81/40~45/22~33/16~25/12 || ||

|| Perfect octave (P8) || 1200 || 2/1 || 0 || ||

|| Augmented octave (A8) || 1261.1 || 81/40~45/22~33/16~25/12 || -7 || ||

``*`` In POTE 11-limit porcupine</pre></div>

<h4>Original HTML content:</h4>

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</th>

<th>Ratios

</th>

<th><ol><li>of Porcupine Generators</li></ol>(~162.7¢)

</th>

<th>Comments

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<tr>

<th colspan="4">Unisons

</th>

<th>

</th>

</tr>

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</td>

<td>1/1

</td>

<td>0

</td>

<td>

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<td>81/80~36/35~33/32~25/24

</td>

<td><a class="wiki_link" href="/Cluster%20temperament#porcupine~~(fish)~~">And other ratios, of course</a>

<td>-7

</td>

<td><a class="wiki_link" href="/Cluster%20temperament#porcupine%28fish%29">And other ratios, of course</a>

</td>

</tr>

<tr>

<th colspan="4">Seconds

</th>

<th>

</th>

</tr>

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</td>

<td>21/20~16/15

</td>

<td>8

</td>

<td>

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</td>

<td>12/11~11/10~10/9

</td>

<td>1

</td>

<td>

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</td>

<td>9/8~8/7

</td>

<td>-6

</td>

<td>

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</td>

<td>Close to 13/11

</td>

<td>-13

</td>

<td>Also &quot;subminor third&quot;

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<tr>

<th colspan="4">Thirds

</th>

<th>

</th>

</tr>

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</td>

<td>7/6

</td>

<td>9

</td>

<td>Also &quot;supermajor second&quot;

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</td>

<td>6/5~11/9

</td>

<td>2

</td>

<td>Coincidentally familiar

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</td>

<td>5/4

</td>

<td>-5

</td>

<td>Coincidentally familiar

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</td>

<td>9/7 (close to 13/10)

</td>

<td>-12

</td>

<td>Also &quot;subminor fourth&quot;

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<tr>

<th colspan="4">Fourths

</th>

<th>

</th>

</tr>

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</td>

<td>14/11

</td>

<td>10

</td>

<td>Also &quot;supermajor third&quot;

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</td>

<td>4/3

</td>

<td>3

</td>

<td>Rather than &quot;perfect fourth&quot;

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</td>

<td>11/8

</td>

<td>-4

</td>

<td>

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</td>

<td>10/7

</td>

<td>-11

</td>

<td>Also &quot;subminor fifth&quot;

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<tr>

<th colspan="4">Fifths

</th>

<th>

</th>

</tr>

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</td>

<td>7/5

</td>

<td>11

</td>

<td>Also &quot;supermajor fourth&quot;

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</td>

<td>16/11

</td>

<td>4

</td>

<td>

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</td>

<td>3/2

</td>

<td>-3

</td>

<td>Rather than &quot;perfect fifth&quot;

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</td>

<td>11/7

</td>

<td>-10

</td>

<td>Also &quot;subminor sixth&quot;

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<tr>

<th colspan="4">Sixths

</th>

<th>

</th>

</tr>

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</td>

<td>14/9 (close to 20/13)

</td>

<td>12

</td>

<td>Also &quot;supermajor fifth&quot;

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</td>

<td>8/5

</td>

<td>5

</td>

<td>Coincidentally familiar

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</td>

<td>5/3

</td>

<td>-2

</td>

<td>Coincidentally familiar

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</td>

<td>12/7

</td>

<td>-9

</td>

<td>Also &quot;subminor seventh&quot;

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<tr>

<th colspan="4">Sevenths

</th>

<th>

</th>

</tr>

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</td>

<td>Close to 22/13

</td>

<td>13

</td>

<td>Also &quot;supermajor sixth&quot;

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</td>

<td>7/4~16/9

</td>

<td>6

</td>

<td>

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</td>

<td>9/5~11/6

</td>

<td>-3

</td>

<td>

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</td>

<td>15/8

</td>

<td>-8

</td>

<td>

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<tr>

<th colspan="4">Octaves

</th>

<th>

</th>

</tr>

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</td>

<td>21/11~35/18~160/81

</td>

<td>7

</td>

<td>

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</td>

<td>2/1

</td>

<td>0

</td>

<td>

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</td>

<td>81/40~45/22~33/16~25/12

</td>

<td>-7

</td>

<td>

@@ 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:phylingual|phylingual]] and made on <tt>2012-07-07 20:47:23 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-07-19 14:42:20 UTC</tt>.<br>
-: The original revision id was <tt>351337216</tt>.<br>
+: The original revision id was <tt>353982584</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 12: / Line 12: @@
 In [[15edo]], on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a **minor** fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo.
-||~ Name ||~ Size* ||~ Ratios ||~ Comments ||
+||~ Name ||~ Size* ||~ Ratios ||~ # of Porcupine Generators
-||||||||~ Unisons ||
+(~162.7¢) ||~ Comments ||
-|| Perfect unison (P1) || 0 || 1/1 ||   ||
+||||||||~ Unisons ||~   ||
-|| Augmented unison (A1) || 61.1 || 81/80~36/35~33/32~25/24 || [[Cluster temperament#porcupine(fish)|And other ratios, of course]] ||
+|| Perfect unison (P1) || 0 || 1/1 || 0 ||   ||
-||||||||~ Seconds ||
+|| Augmented unison (A1) || 61.1 || 81/80~36/35~33/32~25/24 || -7 || [[Cluster temperament#porcupine%28fish%29|And other ratios, of course]] ||
-|| Diminished second (d2) || 101.6 || 21/20~16/15 ||   ||
+||||||||~ Seconds ||~   ||
-|| Minor second (m2) || 162.7 || 12/11~11/10~10/9 ||   ||
+|| Diminished second (d2) || 101.6 || 21/20~16/15 || 8 ||   ||
-|| Major second (M2) || 223.8 || 9/8~8/7 ||   ||
+|| Minor second (m2) || 162.7 || 12/11~11/10~10/9 || 1 ||   ||
-|| Augmented second (A2) || 284.9 || Close to 13/11 || Also "subminor third" ||
+|| Major second (M2) || 223.8 || 9/8~8/7 || -6 ||   ||
-||||||||~ Thirds ||
+|| Augmented second (A2) || 284.9 || Close to 13/11 || -13 || Also "subminor third" ||
-|| Diminished third (d3) || 264.3 || 7/6 || Also "supermajor second" ||
+||||||||~ Thirds ||~   ||
-|| Minor third (m3) || 325.4 || 6/5~11/9 || Coincidentally familiar ||
+|| Diminished third (d3) || 264.3 || 7/6 || 9 || Also "supermajor second" ||
-|| Major third (M3) || 386.5 || 5/4 || Coincidentally familiar ||
+|| Minor third (m3) || 325.4 || 6/5~11/9 || 2 || Coincidentally familiar ||
-|| Augmented third (A3) || 447.6 || 9/7 (close to 13/10) || Also "subminor fourth" ||
+|| Major third (M3) || 386.5 || 5/4 || -5 || Coincidentally familiar ||
-||||||||~ Fourths ||
+|| Augmented third (A3) || 447.6 || 9/7 (close to 13/10) || -12 || Also "subminor fourth" ||
-|| Diminished fourth (d4) || 427.0 || 14/11 || Also "supermajor third" ||
+||||||||~ Fourths ||~   ||
-|| Minor fourth (m4) || 488.1 || 4/3 || Rather than "perfect fourth" ||
+|| Diminished fourth (d4) || 427.0 || 14/11 || 10 || Also "supermajor third" ||
-|| Major fourth (M4) || 549.2 || 11/8 ||   ||
+|| Minor fourth (m4) || 488.1 || 4/3 || 3 || Rather than "perfect fourth" ||
-|| Augmented fourth (A4) || 610.3 || 10/7 || Also "subminor fifth" ||
+|| Major fourth (M4) || 549.2 || 11/8 || -4 ||   ||
-||||||||~ Fifths ||
+|| Augmented fourth (A4) || 610.3 || 10/7 || -11 || Also "subminor fifth" ||
-|| Diminished fifth (d5) || 589.7 || 7/5 || Also "supermajor fourth" ||
+||||||||~ Fifths ||~   ||
-|| Minor fifth (m5) || 650.8 || 16/11 ||   ||
+|| Diminished fifth (d5) || 589.7 || 7/5 || 11 || Also "supermajor fourth" ||
-|| Major fifth (M5) || 711.9 || 3/2 || Rather than "perfect fifth" ||
+|| Minor fifth (m5) || 650.8 || 16/11 || 4 ||   ||
-|| Augmented fifth (A5) || 773.0 || 11/7 || Also "subminor sixth" ||
+|| Major fifth (M5) || 711.9 || 3/2 || -3 || Rather than "perfect fifth" ||
-||||||||~ Sixths ||
+|| Augmented fifth (A5) || 773.0 || 11/7 || -10 || Also "subminor sixth" ||
-|| Diminished sixth (d6) || 752.4 || 14/9 (close to 20/13) || Also "supermajor fifth" ||
+||||||||~ Sixths ||~   ||
-|| Minor sixth (m6) || 813.5 || 8/5 || Coincidentally familiar ||
+|| Diminished sixth (d6) || 752.4 || 14/9 (close to 20/13) || 12 || Also "supermajor fifth" ||
-|| Major sixth (M6) || 874.6 || 5/3 || Coincidentally familiar ||
+|| Minor sixth (m6) || 813.5 || 8/5 || 5 || Coincidentally familiar ||
-|| Augmented sixth (A6) || 935.7 || 12/7 || Also "subminor seventh" ||
+|| Major sixth (M6) || 874.6 || 5/3 || -2 || Coincidentally familiar ||
-||||||||~ Sevenths ||
+|| Augmented sixth (A6) || 935.7 || 12/7 || -9 || Also "subminor seventh" ||
-|| Diminished seventh (d7) || 915.1 || Close to 22/13 || Also "supermajor sixth" ||
+||||||||~ Sevenths ||~   ||
-|| Minor seventh (m7) || 976.2 || 7/4~16/9 ||   ||
+|| Diminished seventh (d7) || 915.1 || Close to 22/13 || 13 || Also "supermajor sixth" ||
-|| Major seventh (M7) || 1037.3 || 9/5~11/6 ||   ||
+|| Minor seventh (m7) || 976.2 || 7/4~16/9 || 6 ||   ||
-|| Augmented seventh (A7) || 1098.4 || 15/8 ||   ||
+|| Major seventh (M7) || 1037.3 || 9/5~11/6 || -3 ||   ||
-||||||||~ Octaves ||
+|| Augmented seventh (A7) || 1098.4 || 15/8 || -8 ||   ||
-|| Diminished octave (d8) || 1138.9 || 21/11~35/18~160/81 ||   ||
+||||||||~ Octaves ||~   ||
-|| Perfect octave (P8) || 1200 || 2/1 ||   ||
+|| Diminished octave (d8) || 1138.9 || 21/11~35/18~160/81 || 7 ||   ||
-|| Augmented octave (A8) || 1261.1 || 81/40~45/22~33/16~25/12 ||   ||
+|| Perfect octave (P8) || 1200 || 2/1 || 0 ||   ||
+|| Augmented octave (A8) || 1261.1 || 81/40~45/22~33/16~25/12 || -7 ||   ||
 ``*`` In POTE 11-limit porcupine</pre></div>
 <h4>Original HTML content:</h4>
@@ Line 67: / Line 68: @@
 &lt;/th&gt;
          &lt;th&gt;Ratios&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;ol&gt;&lt;li&gt;of Porcupine Generators&lt;/li&gt;&lt;/ol&gt;(~162.7¢)&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;Comments&lt;br /&gt;
@@ Line 73: / Line 76: @@
      &lt;tr&gt;
          &lt;th colspan="4"&gt;Unisons&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 81: / Line 86: @@
 &lt;/td&gt;
          &lt;td&gt;1/1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 92: / Line 99: @@
          &lt;td&gt;81/80~36/35~33/32~25/24&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/Cluster%20temperament#porcupine(fish)"&gt;And other ratios, of course&lt;/a&gt;&lt;br /&gt;
+        &lt;td&gt;-7&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Cluster%20temperament#porcupine%28fish%29"&gt;And other ratios, of course&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;th colspan="4"&gt;Seconds&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 105: / Line 116: @@
 &lt;/td&gt;
          &lt;td&gt;21/20~16/15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 115: / Line 128: @@
 &lt;/td&gt;
          &lt;td&gt;12/11~11/10~10/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 125: / Line 140: @@
 &lt;/td&gt;
          &lt;td&gt;9/8~8/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 135: / Line 152: @@
 &lt;/td&gt;
          &lt;td&gt;Close to 13/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Also &amp;quot;subminor third&amp;quot;&lt;br /&gt;
@@ Line 141: / Line 160: @@
      &lt;tr&gt;
          &lt;th colspan="4"&gt;Thirds&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 149: / Line 170: @@
 &lt;/td&gt;
          &lt;td&gt;7/6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Also &amp;quot;supermajor second&amp;quot;&lt;br /&gt;
@@ Line 159: / Line 182: @@
 &lt;/td&gt;
          &lt;td&gt;6/5~11/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Coincidentally familiar&lt;br /&gt;
@@ Line 169: / Line 194: @@
 &lt;/td&gt;
          &lt;td&gt;5/4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Coincidentally familiar&lt;br /&gt;
@@ Line 179: / Line 206: @@
 &lt;/td&gt;
          &lt;td&gt;9/7 (close to 13/10)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-12&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Also &amp;quot;subminor fourth&amp;quot;&lt;br /&gt;
@@ Line 185: / Line 214: @@
      &lt;tr&gt;
          &lt;th colspan="4"&gt;Fourths&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 193: / Line 224: @@
 &lt;/td&gt;
          &lt;td&gt;14/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Also &amp;quot;supermajor third&amp;quot;&lt;br /&gt;
@@ Line 203: / Line 236: @@
 &lt;/td&gt;
          &lt;td&gt;4/3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Rather than &amp;quot;perfect fourth&amp;quot;&lt;br /&gt;
@@ Line 213: / Line 248: @@
 &lt;/td&gt;
          &lt;td&gt;11/8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 223: / Line 260: @@
 &lt;/td&gt;
          &lt;td&gt;10/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Also &amp;quot;subminor fifth&amp;quot;&lt;br /&gt;
@@ Line 229: / Line 268: @@
      &lt;tr&gt;
          &lt;th colspan="4"&gt;Fifths&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 237: / Line 278: @@
 &lt;/td&gt;
          &lt;td&gt;7/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Also &amp;quot;supermajor fourth&amp;quot;&lt;br /&gt;
@@ Line 247: / Line 290: @@
 &lt;/td&gt;
          &lt;td&gt;16/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 257: / Line 302: @@
 &lt;/td&gt;
          &lt;td&gt;3/2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Rather than &amp;quot;perfect fifth&amp;quot;&lt;br /&gt;
@@ Line 267: / Line 314: @@
 &lt;/td&gt;
          &lt;td&gt;11/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-10&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Also &amp;quot;subminor sixth&amp;quot;&lt;br /&gt;
@@ Line 273: / Line 322: @@
      &lt;tr&gt;
          &lt;th colspan="4"&gt;Sixths&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 281: / Line 332: @@
 &lt;/td&gt;
          &lt;td&gt;14/9 (close to 20/13)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Also &amp;quot;supermajor fifth&amp;quot;&lt;br /&gt;
@@ Line 291: / Line 344: @@
 &lt;/td&gt;
          &lt;td&gt;8/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Coincidentally familiar&lt;br /&gt;
@@ Line 301: / Line 356: @@
 &lt;/td&gt;
          &lt;td&gt;5/3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Coincidentally familiar&lt;br /&gt;
@@ Line 311: / Line 368: @@
 &lt;/td&gt;
          &lt;td&gt;12/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Also &amp;quot;subminor seventh&amp;quot;&lt;br /&gt;
@@ Line 317: / Line 376: @@
      &lt;tr&gt;
          &lt;th colspan="4"&gt;Sevenths&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 325: / Line 386: @@
 &lt;/td&gt;
          &lt;td&gt;Close to 22/13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Also &amp;quot;supermajor sixth&amp;quot;&lt;br /&gt;
@@ Line 335: / Line 398: @@
 &lt;/td&gt;
          &lt;td&gt;7/4~16/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 345: / Line 410: @@
 &lt;/td&gt;
          &lt;td&gt;9/5~11/6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 355: / Line 422: @@
 &lt;/td&gt;
          &lt;td&gt;15/8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 361: / Line 430: @@
      &lt;tr&gt;
          &lt;th colspan="4"&gt;Octaves&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 369: / Line 440: @@
 &lt;/td&gt;
          &lt;td&gt;21/11~35/18~160/81&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 379: / Line 452: @@
 &lt;/td&gt;
          &lt;td&gt;2/1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 389: / Line 464: @@
 &lt;/td&gt;
          &lt;td&gt;81/40~45/22~33/16~25/12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;-7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;