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>2014-07-16 ~~14:52~~:56 UTC</tt>.

: This revision was by author [[User:joeydinardo2|joeydinardo2]] and made on <tt>2014-07-18 17:16:15 UTC</tt>.

: The original revision id was <tt>~~516390516~~</tt>.

: The original revision id was <tt>516560104</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.

<h4>Original Wikitext content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Crossbone Tuning is a coordinated tuning (intended to be used simultaneously) ~~using the 19th root~~ of the ~~7th harmonic (septave~~) ~~and~~ the ~~17th root of the 5th harmonic (pentave)~~. Crossbone is ~~expressed through various formats~~: ~~as two coordinated equally divided harmonic intervals~~ (Crossbone ~~Temperament)~~, as a 19-~~limit lattice~~ (~~Crossbone Lattice~~)~~, and as an octave~~-~~repeating~~, ~~singular~~ '~~just~~' 12-~~tone version derived by eliminating~~ the ~~pure harmonic approximations within the first septave~~ and pentave. (~~Crossbone Scale~~)

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Crossbone Tuning is a coordinated tuning (intended to be used simultaneously) system utilizing pairs of twin primes (primes separated by the integer 2) separated by the integer 12. Crossbone is capable of being applied to any set of prime twins separated by this constant, though higher orders often yield less musical results.

//**__Example:__**//

Twin primes (5,7) and (17,19) represent a set of twin primes capable of being Crossbone'd, as both 17-5=12 and 19-17 = 12. Once a pair of permissible twin primes is composed, a temperament is devised by taking each member of the lesser set and raising it to (1/x) where x the corresponding member of the greater set.

For (5,7) and (17,19), the Tuning would utilize both 5^1/17 and 7^1/19, or 17EDP(Equally-divided pentave) and 19EDS(Equally-divided septave).

//**__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

[[image:xenharmonic/crossbones.png width="424" 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 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[[image:xenharmonic/crossbones.png width="424" align="right"]] 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.

//__**Crossbone Temperament (1st Order):**__//

//__**Crossbone Temperament:**__//

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'.

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In the near future it would be wise to create a partner scale to the Crossbone Scale based on the 11-limit 2nd sepent as well as extend the current Crossbone Temperament to a full four sepents (the near limit of human hearing). Currently working on a 'Crossbone Extended' using another subset of the 12 relationship, this form in 31 root 19 and 29 root 17. Language on current Crossbone implementation to be clarified. Also uploading spreadsheet with errors and approximations as well as scala files for Crossbone Temperament, Crossbone Extended, Crossbone Scale.</pre></div>

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Crossbone Tuning</title></head><body>Crossbone Tuning is a coordinated tuning (intended to be used simultaneously) ~~using the 19th root~~ of the ~~7th harmonic (septave~~) ~~and~~ the ~~17th root of the 5th harmonic (pentave)~~. Crossbone is ~~expressed through various formats~~: ~~as two coordinated equally divided harmonic intervals~~ (Crossbone ~~Temperament)~~, as a 19-~~limit lattice~~ (~~Crossbone Lattice~~)~~, and as an octave~~-~~repeating~~, ~~singular~~ '~~just~~' 12-~~tone version derived by eliminating~~ the ~~pure harmonic approximations within the first septave~~ and pentave. (~~Crossbone Scale~~)

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Crossbone Tuning</title></head><body>Crossbone Tuning is a coordinated tuning (intended to be used simultaneously) system utilizing pairs of twin primes (primes separated by the integer 2) separated by the integer 12. Crossbone is capable of being applied to any set of prime twins separated by this constant, though higher orders often yield less musical results.

Example:

Twin primes (5,7) and (17,19) represent a set of twin primes capable of being Crossbone'd, as both 17-5=12 and 19-17 = 12. Once a pair of permissible twin primes is composed, a temperament is devised by taking each member of the lesser set and raising it to (1/x) where x the corresponding member of the greater set.

For (5,7) and (17,19), the Tuning would utilize both 5^1/17 and 7^1/19, or 17EDP(Equally-divided pentave) and 19EDS(Equally-divided septave).

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.

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<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 as just described, so it is not unfeasable that prime relationships in communication with one another also share musical significance.

Crossbone Temperament (1st Order):

~~ ~~

Crossbone Temperament:

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'.

@@ 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>2014-07-16 14:52:56 UTC</tt>.<br>
+: This revision was by author [[User:joeydinardo2|joeydinardo2]] and made on <tt>2014-07-18 17:16:15 UTC</tt>.<br>
-: The original revision id was <tt>516390516</tt>.<br>
+: The original revision id was <tt>516560104</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>
 <h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">&lt;span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Crossbone Tuning is a coordinated tuning (intended to be used simultaneously) using the 19th root of the 7th harmonic (septave) and the 17th root of the 5th harmonic (pentave). Crossbone is expressed through various formats: as two coordinated equally divided harmonic intervals (Crossbone Temperament), as a 19-limit lattice (Crossbone Lattice), and as an octave-repeating, singular 'just' 12-tone version derived by eliminating the pure harmonic approximations within the first septave and pentave. (Crossbone Scale)&lt;/span&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">&lt;span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Crossbone Tuning is a coordinated tuning (intended to be used simultaneously) system utilizing pairs of twin primes (primes separated by the integer 2) separated by the integer 12. Crossbone is capable of being applied to any set of prime twins separated by this constant, though higher orders often yield less musical results.&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;Example:&lt;/span&gt;__**//
+&lt;span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Twin primes (5,7) and (17,19) represent a set of twin primes capable of being Crossbone'd, as both 17-5=12 and 19-17 = 12. Once a pair of permissible twin primes is composed, a temperament is devised by taking each member of the lesser set and raising it to (1/x) where x the corresponding member of the greater set.&lt;/span&gt;
+&lt;span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;For (5,7) and (17,19), the Tuning would utilize both 5^1/17 and 7^1/19, or 17EDP(Equally-divided pentave) and 19EDS(Equally-divided septave).&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;Background:&lt;/span&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;
+[[image:xenharmonic/crossbones.png width="424" align="right"]]&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;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;"&gt;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&lt;/span&gt;[[image:xenharmonic/crossbones.png width="424" align="right"]]&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 as just described, so it is not unfeasable that prime relationships in communication with one another also share musical significance.&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;Crossbone Temperament (1st Order):&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;Crossbone Temperament:&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;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'.&lt;/span&gt;
@@ Line 49: / Line 57: @@
 &lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;In the near future it would be wise to create a partner scale to the Crossbone Scale based on the 11-limit 2nd sepent as well as extend the current Crossbone Temperament to a full four sepents (the near limit of human hearing). Currently working on a 'Crossbone Extended' using another subset of the 12 relationship, this form in 31 root 19 and 29 root 17. Language on current Crossbone implementation to be clarified. Also uploading spreadsheet with errors and approximations as well as scala files for Crossbone Temperament, Crossbone Extended, Crossbone Scale.&lt;/span&gt;</pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Crossbone Tuning&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Crossbone Tuning is a coordinated tuning (intended to be used simultaneously) using the 19th root of the 7th harmonic (septave) and the 17th root of the 5th harmonic (pentave). Crossbone is expressed through various formats: as two coordinated equally divided harmonic intervals (Crossbone Temperament), as a 19-limit lattice (Crossbone Lattice), and as an octave-repeating, singular 'just' 12-tone version derived by eliminating the pure harmonic approximations within the first septave and pentave. (Crossbone Scale)&lt;/span&gt;&lt;br /&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Crossbone Tuning&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Crossbone Tuning is a coordinated tuning (intended to be used simultaneously) system utilizing pairs of twin primes (primes separated by the integer 2) separated by the integer 12. Crossbone is capable of being applied to any set of prime twins separated by this constant, though higher orders often yield less musical results.&lt;/span&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;br /&gt;
+&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;Example:&lt;/span&gt;&lt;/u&gt;&lt;/strong&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;Twin primes (5,7) and (17,19) represent a set of twin primes capable of being Crossbone'd, as both 17-5=12 and 19-17 = 12. Once a pair of permissible twin primes is composed, a temperament is devised by taking each member of the lesser set and raising it to (1/x) where x the corresponding member of the greater set.&lt;/span&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;For (5,7) and (17,19), the Tuning would utilize both 5^1/17 and 7^1/19, or 17EDP(Equally-divided pentave) and 19EDS(Equally-divided septave).&lt;/span&gt;&lt;br /&gt;
+&lt;br /&gt;
 &lt;br /&gt;
 &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;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;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&lt;/span&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 as just described, so it is not unfeasable that prime relationships in communication with one another also share musical significance.&lt;/span&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 Temperament (1st Order):&lt;/span&gt;&lt;/strong&gt;&lt;/u&gt;&lt;/em&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 Temperament:&lt;/span&gt;&lt;/strong&gt;&lt;/u&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;"&gt;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'.&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;