Crossbone tuning: 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:joeydinardo2|joeydinardo2]] and made on <tt>2014-07-18 18:34:45 UTC</tt>.

: This revision was by author [[User:joeydinardo2|joeydinardo2]] and made on <tt>2014-07-18 19:17:57 UTC</tt>.

: The original revision id was <tt>~~516564422~~</tt>.

: The original revision id was <tt>516566386</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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[[image:crossbonepiano.png width="993" height="199"]]

__//**Intervals**//__

First Septave: 19EDS

||~ Step # ||~ Cents ||~ Just Approximate ||~ Cents Error ||

||> 0 ||> 0 ||> 1/1 ||> 0 ||

||> 1 ||> 177.31 ||> 71/64 ||> -2.39 ||

||> 2 ||> 354.62 ||> 79/64 ||> -9.92 ||

||> 3 ||> 531.93 ||> 87/64 ||> .4 ||

||> 4 ||> 709.24 ||> 3/2 ||> 7.28 ||

||> 5 ||> 886.55 ||> 5/3 ||> -3.21 ||

||> 6 ||> 1063.86 ||> 59/64 ||> 4.69 ||

||> 7 ||> 1241.17 ||> 128/125 ||> .11 ||

||> 8 ||> 1418.48 ||> 73/64 ||> -9.31 ||

||> 9 ||> 1595.79 ||> 5/4 ||> 9.48 ||

||> 10 ||> 1773.1 ||> 89/64 ||> 2.22 ||

||> 11 ||> 1950.41 ||> 99/64 ||> -4.82 ||

||> 12 ||> 2127.72 ||> 12/7 ||> -5.41 ||

||> 13 ||> 2305.03 ||> 121/64 ||> 2.39 ||

||> 14 ||> 2482.34 ||> 67/64 ||> 3.03 ||

||> 15 ||> 2659.65 ||> 7/6 ||> -7.22 ||

||> 16 ||> 2836.96 ||> 9/7 ||> 1.88 ||

||> 17 ||> 3014.27 ||> 10/7 ||> -3.22 ||

||> 18 ||> 3191.58 ||> 101/64 ||> 1.73 ||

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__//**Crossbone Scale (1st order, 1st sepent):**//__

The Crossbone Scale is an octave-repeating simplified version of the Crossbone Temperament, forcing the intervals found within the sepent into a 12-tone octave-repeating scale. Within the first sepent, when one simply neglects including the harmonic approximations (and the 128/125 anamoly), he is left with 12 just 7-limit ratios between 1/1 and 2/1:

**~~~~•1/1~~~~** - tonic

**•1/1** - tonic

**•16/15** - major 5-limit half-step

•**7/6** - septimal minor third

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Background:

Using a prime number wheel -a face with 24 repeating integers equally spaced over 2pi- the relationship between twin primes separated by 12 is easily visualized. We are familiar with the special relationships prime numbers

<img src="http://xenharmonic.wikispaces.com/file/view/crossbones.png/516326650/crossbones.png" alt="crossbones.png" title="crossbones.png" style="width: 424px;" align="right" /> have to music, and we understand the relationship certain primes share with each other, so it is not unfeasible that prime relationships in communication with one another also share musical significance.

<img src="http://xenharmonic.wikispaces.com/file/view/crossbones.png/516326650/crossbones.png" alt="crossbones.png" title="crossbones.png" style="width: 424px;" align="right" /> have to music, and we understand the relationship certain primes share with each other, so it is not unfeasible that prime relationships in communication with one another also share musical significance.

Crossbone Tuning (1st Order):

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One beautiful alignment of the 1st order of Crossbone is that it uses a combination of 17 and 19 tones. We notice that the standard 12-tone keyboard has 12 keys broken into a grouping of 5 notes and a grouping of 7 notes. This means that Crossbones tuning can be easily realized on any 'standard' keyboard, the first 5 7 5 grouping of keys representing the pentave, the second 7 5 7 grouping of keys representing the septave.. spanning a total key range of 3 12-tone octaves, coinciding beautifully with the fact that the natural septave and pentave naturally occur between the 2nd and 3rd standard octave. Note that below, the intervals represented are octave-reduced, though the true harmonic range of the septave and pentave are true and preserved on the keyboard, representing the absolute pitch approximation I find to be much more intuitive in comparison to the octave-equivalent versions (ex. a twelfth being represented as 3/2 though sounding as a twelfth).

<img src="/file/view/crossbonepiano.png/516324958/993x199/crossbonepiano.png" alt="crossbonepiano.png" title="crossbonepiano.png" style="height: 199px; width: 993px;" />

<img src="/file/view/crossbonepiano.png/516324958/993x199/crossbonepiano.png" alt="crossbonepiano.png" title="crossbonepiano.png" style="height: 199px; width: 993px;" />

Intervals

First Septave: 19EDS

<tr>

<th>Step #

</th>

<th>Cents

</th>

<th>Just Approximate

</th>

<th>Cents Error

</th>

</tr>

<tr>

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

</td>

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

</td>

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

</td>

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

</td>

</tr>

<tr>

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

</td>

<td style="text-align: right;">177.31

</td>

<td style="text-align: right;">71/64

</td>

<td style="text-align: right;">-2.39

</td>

</tr>

<tr>

<td style="text-align: right;">2

</td>

<td style="text-align: right;">354.62

</td>

<td style="text-align: right;">79/64

</td>

<td style="text-align: right;">-9.92

</td>

</tr>

<tr>

<td style="text-align: right;">3

</td>

<td style="text-align: right;">531.93

</td>

<td style="text-align: right;">87/64

</td>

<td style="text-align: right;">.4

</td>

</tr>

<tr>

<td style="text-align: right;">4

</td>

<td style="text-align: right;">709.24

</td>

<td style="text-align: right;">3/2

</td>

<td style="text-align: right;">7.28

</td>

</tr>

<tr>

<td style="text-align: right;">5

</td>

<td style="text-align: right;">886.55

</td>

<td style="text-align: right;">5/3

</td>

<td style="text-align: right;">-3.21

</td>

</tr>

<tr>

<td style="text-align: right;">6

</td>

<td style="text-align: right;">1063.86

</td>

<td style="text-align: right;">59/64

</td>

<td style="text-align: right;">4.69

</td>

</tr>

<tr>

<td style="text-align: right;">7

</td>

<td style="text-align: right;">1241.17

</td>

<td style="text-align: right;">128/125

</td>

<td style="text-align: right;">.11

</td>

</tr>

<tr>

<td style="text-align: right;">8

</td>

<td style="text-align: right;">1418.48

</td>

<td style="text-align: right;">73/64

</td>

<td style="text-align: right;">-9.31

</td>

</tr>

<tr>

<td style="text-align: right;">9

</td>

<td style="text-align: right;">1595.79

</td>

<td style="text-align: right;">5/4

</td>

<td style="text-align: right;">9.48

</td>

</tr>

<tr>

<td style="text-align: right;">10

</td>

<td style="text-align: right;">1773.1

</td>

<td style="text-align: right;">89/64

</td>

<td style="text-align: right;">2.22

</td>

</tr>

<tr>

<td style="text-align: right;">11

</td>

<td style="text-align: right;">1950.41

</td>

<td style="text-align: right;">99/64

</td>

<td style="text-align: right;">-4.82

</td>

</tr>

<tr>

<td style="text-align: right;">12

</td>

<td style="text-align: right;">2127.72

</td>

<td style="text-align: right;">12/7

</td>

<td style="text-align: right;">-5.41

</td>

</tr>

<tr>

<td style="text-align: right;">13

</td>

<td style="text-align: right;">2305.03

</td>

<td style="text-align: right;">121/64

</td>

<td style="text-align: right;">2.39

</td>

</tr>

<tr>

<td style="text-align: right;">14

</td>

<td style="text-align: right;">2482.34

</td>

<td style="text-align: right;">67/64

</td>

<td style="text-align: right;">3.03

</td>

</tr>

<tr>

<td style="text-align: right;">15

</td>

<td style="text-align: right;">2659.65

</td>

<td style="text-align: right;">7/6

</td>

<td style="text-align: right;">-7.22

</td>

</tr>

<tr>

<td style="text-align: right;">16

</td>

<td style="text-align: right;">2836.96

</td>

<td style="text-align: right;">9/7

</td>

<td style="text-align: right;">1.88

</td>

</tr>

<tr>

<td style="text-align: right;">17

</td>

<td style="text-align: right;">3014.27

</td>

<td style="text-align: right;">10/7

</td>

<td style="text-align: right;">-3.22

</td>

</tr>

<tr>

<td style="text-align: right;">18

</td>

<td style="text-align: right;">3191.58

</td>

<td style="text-align: right;">101/64

</td>

<td style="text-align: right;">1.73

</td>

</tr>

</table>

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The Crossbone Lattice is a 4-dimensional lattice generated using the 5-limit, 7-limit, 17-limit, and 19-limit. By not including the 3-limit (but still implying the octave) and skipping over the 11 and 13 limits, we can arrive at very unique and interesting destinations.

Because the lattice is octave-based and generated using the Crossbone primes, represented as harmonics, and doesn't enforce a relationship between them -as in Crossbone Temperament-, the relationship between the lattice and the temperament should be considered tangential, and the usage of the lattice

<img src="/file/view/tessa.png/516325086/tessa.png" alt="tessa.png" title="tessa.png" style="width: 435px;" align="right" />

<img src="/file/view/tessa.png/516325086/tessa.png" alt="tessa.png" title="tessa.png" style="width: 435px;" align="right" />

considered novel. I personally use it simply to add 17 and 19 limit 'spice' to certain intervals generated using my 3rds and 7ths. Arriving at destinations by combination of 3rd and 7ths without piggybacking on the 5th I find to be very satisfying.

Crossbone Scale (1st order, 1st sepent):

The Crossbone Scale is an octave-repeating simplified version of the Crossbone Temperament, forcing the intervals found within the sepent into a 12-tone octave-repeating scale. Within the first sepent, when one simply neglects including the harmonic approximations (and the 128/125 anamoly), he is left with 12 just 7-limit ratios between 1/1 and 2/1:

<strong~~>•1/1~~ - tonic

•1/1 - tonic

•16/15 - major 5-limit half-step

•7/6 - septimal minor third

@@ 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:joeydinardo2|joeydinardo2]] and made on <tt>2014-07-18 18:34:45 UTC</tt>.<br>
+: This revision was by author [[User:joeydinardo2|joeydinardo2]] and made on <tt>2014-07-18 19:17:57 UTC</tt>.<br>
-: The original revision id was <tt>516564422</tt>.<br>
+: The original revision id was <tt>516566386</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 37: / Line 37: @@
 [[image:crossbonepiano.png width="993" height="199"]]
+__//**&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Intervals&lt;/span&gt;**//__
+&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;First Septave: 19EDS&lt;/span&gt;
+||~ Step # ||~ Cents ||~ Just Approximate ||~ Cents Error ||
+||&gt; 0 ||&gt; 0 ||&gt; 1/1 ||&gt; 0 ||
+||&gt; 1 ||&gt; 177.31 ||&gt; 71/64 ||&gt; -2.39 ||
+||&gt; 2 ||&gt; 354.62 ||&gt; 79/64 ||&gt; -9.92 ||
+||&gt; 3 ||&gt; 531.93 ||&gt; 87/64 ||&gt; .4 ||
+||&gt; 4 ||&gt; 709.24 ||&gt; 3/2 ||&gt; 7.28 ||
+||&gt; 5 ||&gt; 886.55 ||&gt; 5/3 ||&gt; -3.21 ||
+||&gt; 6 ||&gt; 1063.86 ||&gt; 59/64 ||&gt; 4.69 ||
+||&gt; 7 ||&gt; 1241.17 ||&gt; 128/125 ||&gt; .11 ||
+||&gt; 8 ||&gt; 1418.48 ||&gt; 73/64 ||&gt; -9.31 ||
+||&gt; 9 ||&gt; 1595.79 ||&gt; 5/4 ||&gt; 9.48 ||
+||&gt; 10 ||&gt; 1773.1 ||&gt; 89/64 ||&gt; 2.22 ||
+||&gt; 11 ||&gt; 1950.41 ||&gt; 99/64 ||&gt; -4.82 ||
+||&gt; 12 ||&gt; 2127.72 ||&gt; 12/7 ||&gt; -5.41 ||
+||&gt; 13 ||&gt; 2305.03 ||&gt; 121/64 ||&gt; 2.39 ||
+||&gt; 14 ||&gt; 2482.34 ||&gt; 67/64 ||&gt; 3.03 ||
+||&gt; 15 ||&gt; 2659.65 ||&gt; 7/6 ||&gt; -7.22 ||
+||&gt; 16 ||&gt; 2836.96 ||&gt; 9/7 ||&gt; 1.88 ||
+||&gt; 17 ||&gt; 3014.27 ||&gt; 10/7 ||&gt; -3.22 ||
+||&gt; 18 ||&gt; 3191.58 ||&gt; 101/64 ||&gt; 1.73 ||
@@ Line 47: / Line 72: @@
 __//**&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Crossbone Scale (1st order, 1st sepent):&lt;/span&gt;**//__
 &lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;The Crossbone Scale is an octave-repeating simplified version of the Crossbone Temperament, forcing the intervals found within the sepent into a 12-tone octave-repeating scale. Within the first sepent, when one simply neglects including the harmonic approximations (and the 128/125 anamoly), he is left with 12 just 7-limit ratios between 1/1 and 2/1:&lt;/span&gt;
-**&lt;span style="line-height: 1.5;"&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;•1/1&lt;/span&gt;&lt;/span&gt;**&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt; - tonic&lt;/span&gt;
+**&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; line-height: 1.5;"&gt;•1/1&lt;/span&gt;**&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt; - tonic&lt;/span&gt;
 **&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;•16/15&lt;/span&gt;**&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt; - major 5-limit half-step&lt;/span&gt;
 &lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;•**7/6** - septimal minor third&lt;/span&gt;
@@ Line 83: / Line 108: @@
 &lt;em&gt;&lt;strong&gt;&lt;u&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Background:&lt;/span&gt;&lt;/u&gt;&lt;/strong&gt;&lt;/em&gt;&lt;br /&gt;
 &lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;"&gt;Using a prime number wheel -a face with 24 repeating integers equally spaced over 2pi- the relationship between twin primes separated by 12 is easily visualized. We are familiar with the special relationships prime numbers&lt;/span&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:0:&amp;lt;img src=&amp;quot;http://xenharmonic.wikispaces.com/file/view/crossbones.png/516326650/crossbones.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;width: 424px;&amp;quot; align=&amp;quot;right&amp;quot; /&amp;gt; --&gt;&lt;img src="http://xenharmonic.wikispaces.com/file/view/crossbones.png/516326650/crossbones.png" alt="crossbones.png" title="crossbones.png" style="width: 424px;" align="right" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:0 --&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; line-height: 1.5;"&gt; have to music, and we understand the relationship certain primes share with each other, so it is not unfeasible that prime relationships in communication with one another also share musical significance.&lt;/span&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:202:&amp;lt;img src=&amp;quot;http://xenharmonic.wikispaces.com/file/view/crossbones.png/516326650/crossbones.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;width: 424px;&amp;quot; align=&amp;quot;right&amp;quot; /&amp;gt; --&gt;&lt;img src="http://xenharmonic.wikispaces.com/file/view/crossbones.png/516326650/crossbones.png" alt="crossbones.png" title="crossbones.png" style="width: 424px;" align="right" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:202 --&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; line-height: 1.5;"&gt; have to music, and we understand the relationship certain primes share with each other, so it is not unfeasible that prime relationships in communication with one another also share musical significance.&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;em&gt;&lt;u&gt;&lt;strong&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Crossbone Tuning (1st Order):&lt;/span&gt;&lt;/strong&gt;&lt;/u&gt;&lt;/em&gt;&lt;br /&gt;
@@ Line 92: / Line 117: @@
 &lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;One beautiful alignment of the 1st order of Crossbone is that it uses a combination of 17 and 19 tones. We notice that the standard 12-tone keyboard has 12 keys broken into a grouping of 5 notes and a grouping of 7 notes. This means that Crossbones tuning can be easily realized on any 'standard' keyboard, the first 5 7 5 grouping of keys representing the pentave, the second 7 5 7 grouping of keys representing the septave.. spanning a total key range of 3 12-tone octaves, coinciding beautifully with the fact that the natural septave and pentave naturally occur between the 2nd and 3rd standard octave. Note that below, the intervals represented are octave-reduced, though the true harmonic range of the septave and pentave are true and preserved on the keyboard, representing the absolute pitch approximation I find to be much more intuitive in comparison to the octave-equivalent versions (ex. a twelfth being represented as 3/2 though sounding as a twelfth).&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:1:&amp;lt;img src=&amp;quot;/file/view/crossbonepiano.png/516324958/993x199/crossbonepiano.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 199px; width: 993px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/crossbonepiano.png/516324958/993x199/crossbonepiano.png" alt="crossbonepiano.png" title="crossbonepiano.png" style="height: 199px; width: 993px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:203:&amp;lt;img src=&amp;quot;/file/view/crossbonepiano.png/516324958/993x199/crossbonepiano.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 199px; width: 993px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/crossbonepiano.png/516324958/993x199/crossbonepiano.png" alt="crossbonepiano.png" title="crossbonepiano.png" style="height: 199px; width: 993px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:203 --&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;br /&gt;
+&lt;u&gt;&lt;em&gt;&lt;strong&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Intervals&lt;/span&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/u&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;First Septave: 19EDS&lt;/span&gt;&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;th&gt;Step #&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Cents&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Just Approximate&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Cents Error&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;1/1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;0&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;177.31&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;71/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;-2.39&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;354.62&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;79/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;-9.92&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;531.93&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;87/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;.4&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;709.24&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;3/2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;7.28&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;886.55&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;5/3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;-3.21&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;1063.86&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;59/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;4.69&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;1241.17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;128/125&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;.11&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;1418.48&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;73/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;-9.31&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;1595.79&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;5/4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;9.48&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;1773.1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;89/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;2.22&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;1950.41&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;99/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;-4.82&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;2127.72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;12/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;-5.41&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;2305.03&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;121/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;2.39&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;2482.34&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;67/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;3.03&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;2659.65&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;7/6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;-7.22&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;16&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;2836.96&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;9/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;1.88&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;3014.27&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;10/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;-3.22&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: right;"&gt;18&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;3191.58&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;101/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;1.73&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;
@@ Line 98: / Line 333: @@
 &lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;The Crossbone Lattice is a 4-dimensional lattice generated using the 5-limit, 7-limit, 17-limit, and 19-limit. By not including the 3-limit (but still implying the octave) and skipping over the 11 and 13 limits, we can arrive at very unique and interesting destinations.&lt;/span&gt;&lt;br /&gt;
 &lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Because the lattice is octave-based and generated using the Crossbone primes, represented as harmonics, and doesn't enforce a relationship between them -as in Crossbone Temperament-, the relationship between the lattice and the temperament should be considered tangential, and the usage of the lattice &lt;/span&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:2:&amp;lt;img src=&amp;quot;/file/view/tessa.png/516325086/tessa.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;width: 435px;&amp;quot; align=&amp;quot;right&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/tessa.png/516325086/tessa.png" alt="tessa.png" title="tessa.png" style="width: 435px;" align="right" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:204:&amp;lt;img src=&amp;quot;/file/view/tessa.png/516325086/tessa.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;width: 435px;&amp;quot; align=&amp;quot;right&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/tessa.png/516325086/tessa.png" alt="tessa.png" title="tessa.png" style="width: 435px;" align="right" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:204 --&gt;&lt;br /&gt;
 &lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;considered &lt;/span&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; line-height: 1.5;"&gt;novel. I personally use it simply to add 17 and 19 limit 'spice' to certain intervals generated using my 3rds and 7ths. Arriving at destinations by combination of 3rd and 7ths without piggybacking on the 5th I find to be very satisfying.&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;u&gt;&lt;em&gt;&lt;strong&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Crossbone Scale (1st order, 1st sepent):&lt;/span&gt;&lt;/strong&gt;&lt;/em&gt;&lt;/u&gt;&lt;br /&gt;
 &lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;The Crossbone Scale is an octave-repeating simplified version of the Crossbone Temperament, forcing the intervals found within the sepent into a 12-tone octave-repeating scale. Within the first sepent, when one simply neglects including the harmonic approximations (and the 128/125 anamoly), he is left with 12 just 7-limit ratios between 1/1 and 2/1:&lt;/span&gt;&lt;br /&gt;
-&lt;strong&gt;&lt;span style="line-height: 1.5;"&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;•1/1&lt;/span&gt;&lt;/span&gt;&lt;/strong&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt; - tonic&lt;/span&gt;&lt;br /&gt;
+&lt;strong&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; line-height: 1.5;"&gt;•1/1&lt;/span&gt;&lt;/strong&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt; - tonic&lt;/span&gt;&lt;br /&gt;
 &lt;strong&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;•16/15&lt;/span&gt;&lt;/strong&gt;&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt; - major 5-limit half-step&lt;/span&gt;&lt;br /&gt;
 &lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;•&lt;strong&gt;7/6&lt;/strong&gt; - septimal minor third&lt;/span&gt;&lt;br /&gt;