Crossbone tuning: Difference between revisions
Wikispaces>joeydinardo2 **Imported revision 516326664 - Original comment: ** |
Wikispaces>joeydinardo2 **Imported revision 516326894 - 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:joeydinardo2|joeydinardo2]] and made on <tt>2014-07-15 20: | : This revision was by author [[User:joeydinardo2|joeydinardo2]] and made on <tt>2014-07-15 20:13:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>516326894</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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__<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">//**Background**://</span>__ | __<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">//**Background**://</span>__ | ||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">Crossbone Tuning was inspired by the fact that primes share a special relationship when seperated by the integer twelve. Using a prime number wheel -a face with 24 repeating integers equally spaced over 2pi- this special relationship is easily visualized. We are familiar with the special relationships prime numbers have to music, and we understand the relationship certain primes share with each other as just described, so it is not unfeasable that prime relationships in communication with one another also share musical significance.</span> | <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">Crossbone Tuning was inspired by the fact that primes share a special relationship when seperated by the integer twelve. Using a prime number wheel -a face with 24 repeating integers equally spaced over 2pi- this special relationship is easily visualized. We are familiar with the special relationships prime numbers</span>[[image:xenharmonic/crossbones.png width="424" height="1.5; height: 455" align="right"]]<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; line-height: 1.5;"> have to music, and we understand the relationship certain primes share with each other as just described, so it is not unfeasable that prime relationships in communication with one another also share musical significance.</span> | ||
__**<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">//Crossbone Temperament://</span>**__ | __**<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">//Crossbone Temperament://</span>**__ | ||
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__**//<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Lattice:</span>//**__ | __**//<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Lattice:</span>//**__ | ||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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.</span> | <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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.</span> | ||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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 </span> | |||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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 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.</span> | [[image:tessa.png width="435" height="1.5; height: 327" align="right"]] | ||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">considered</span><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; line-height: 1.5;">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.</span> | |||
__**//<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Scale (1st sepent):</span>//**__ | __**//<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Scale (1st sepent):</span>//**__ | ||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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:</span> | <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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:</span> | ||
[[image:crossbonepiano12scale.png width="216" height="202" align=" | [[image:crossbonepiano12scale.png width="216" height="202" align="right"]] | ||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•</span>**<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">1/1</span>**<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"> - tonic </span> | <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•</span>**<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">1/1</span>**<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"> - tonic </span> | ||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•</span>**<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">16/15</span>**<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"> - major 5-limit half-step </span> | <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•</span>**<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">16/15</span>**<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"> - major 5-limit half-step </span> | ||
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<u><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;"><em><strong>Background</strong>:</em></span></u><br /> | <u><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;"><em><strong>Background</strong>:</em></span></u><br /> | ||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">Crossbone Tuning was inspired by the fact that primes share a special relationship when seperated by the integer twelve. Using a prime number wheel -a face with 24 repeating integers equally spaced over 2pi- this special relationship is easily visualized. We are familiar with the special relationships prime numbers | <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">Crossbone Tuning was inspired by the fact that primes share a special relationship when seperated by the integer twelve. Using a prime number wheel -a face with 24 repeating integers equally spaced over 2pi- this special relationship is easily visualized. We are familiar with the special relationships prime numbers</span><!-- ws:start:WikiTextLocalImageRule:0:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/crossbones.png/516326650/crossbones.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;width: 424px;&quot; align=&quot;right&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/crossbones.png/516326650/crossbones.png" alt="crossbones.png" title="crossbones.png" style="width: 424px;" align="right" /><!-- ws:end:WikiTextLocalImageRule:0 --><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; line-height: 1.5;"> have to music, and we understand the relationship certain primes share with each other as just described, so it is not unfeasable that prime relationships in communication with one another also share musical significance.</span><br /> | ||
<!-- ws:start:WikiTextLocalImageRule:0: | <br /> | ||
<u><strong><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;"><em>Crossbone Temperament:</em></span></strong></u><br /> | <u><strong><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;"><em>Crossbone Temperament:</em></span></strong></u><br /> | ||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">It is such that the 19th root of 7 and the 17th root of 5 share a unique correspondence, being both reasonable in harmonic range and distance, the pentave and septave ending between the 2nd and 3rd octave in 17 or 19 steps respectively. Because the temperaments are coordinated in Crossbone, each combination of septave and pentave I refer to as a 'sepent'.</span><br /> | <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">It is such that the 19th root of 7 and the 17th root of 5 share a unique correspondence, being both reasonable in harmonic range and distance, the pentave and septave ending between the 2nd and 3rd octave in 17 or 19 steps respectively. Because the temperaments are coordinated in Crossbone, each combination of septave and pentave I refer to as a 'sepent'.</span><br /> | ||
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<u><strong><em><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Lattice:</span></em></strong></u><br /> | <u><strong><em><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Lattice:</span></em></strong></u><br /> | ||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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.</span><br /> | <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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.</span><br /> | ||
< | <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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 </span><br /> | ||
<!-- ws:start:WikiTextLocalImageRule:2:&lt;img src=&quot;/file/view/tessa.png/516325086/tessa.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;width: 435px;&quot; align=&quot;right&quot; /&gt; --><img src="/file/view/tessa.png/516325086/tessa.png" alt="tessa.png" title="tessa.png" style="width: 435px;" align="right" /><!-- ws:end:WikiTextLocalImageRule:2 --><br /> | |||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">considered</span><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; line-height: 1.5;">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.</span><br /> | |||
<br /> | <br /> | ||
<u><strong><em><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Scale (1st sepent):</span></em></strong></u><br /> | <u><strong><em><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Scale (1st sepent):</span></em></strong></u><br /> | ||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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:</span><br /> | <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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:</span><br /> | ||
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<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•</span><strong><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">1/1</span></strong><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"> - tonic </span><br /> | |||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•</span><strong><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">16/15</span></strong><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"> - major 5-limit half-step </span><br /> | <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•</span><strong><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">16/15</span></strong><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"> - major 5-limit half-step </span><br /> | ||
<span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•</span><strong><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">7/6</span></strong><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"> - septimal minor third </span><br /> | <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•</span><strong><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">7/6</span></strong><span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"> - septimal minor third </span><br /> | ||