Crossbone tuning: Difference between revisions

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<span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Tuning is a coordinated tuning (two separate tunings 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.</span>


//**__<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Example:</span>__**//
<span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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, two temperaments are devised by taking each member of the lesser set and dividing it into x equi-distant intervals</span>
<span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">where x is the corresponding member of the greater set and each interval having a distance of the corresponding lesser member raised by (1/x).</span>

<span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">For {5,7} and {17,19}, the yielded Crossbone Tuning would utilize both 5^1/17 and 7^1/19, or 17EDP(Equally-divided pentave) and 19EDS(Equally-divided septave).</span>

//__**<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Ordering:</span>**__//
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Because Crossbone is, at heart, a system for deriving tunings, Crossbone'd sets are described by 'orders'.</span>

<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Order is determined by the numerical indexing of valid prime sets suitable for Crossbone.</span>
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">{5,7}|{17,19} is of order 1.</span>
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">{17,19}|{29,31} is of order 2.</span>
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">and so on.</span>

<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">There is currently no conjecture detailing the total possible number of orderings.</span>

//**__<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Background:</span>__**//
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">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</span>
[[image:xenharmonic/crossbones.png width="424" align="right"]]<span style="background-color: #ffffff; 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, so it is not unfeasible that prime relationships in communication with one another also share musical significance.</span>

//__**<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Tuning (1st Order):</span>**__//
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">The first order of the Crossbone Tuning encompasses the first pair of twin pair of twin primes separated by 12, the set {5,7}|{17,19}.</span>

<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">The septave and pentave are not based around the octave, thus each individual septave and pentave will be completely unique and be found to approximate different intervals. Notice below that many of the intervals approximated happen to be harmonics! Those which are not harmonics happen to be readily usable just intervals no greater than 7-limit in the first sepent and 11-limit in the second sepent. -the sepent refers to the total keyspace represented by the pentave followed by the septave</span>

<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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).</span>

[[image:crossbonepiano.png width="993" height="199"]]


__//**<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Intervals</span>**//__
**<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">First Septave: 19EDS</span>**
||~ 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 ||
**<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">First Septave: 17EDP</span>**
||~ Step # ||~ Cents ||~ Just Approximate ||~ Cents Error ||
||> 0 ||> 0 ||> 1/1 ||> 0 ||
||> 1 ||> 163.9 ||> 35/32 ||> 8.76 ||
||> 2 ||> 327.8 ||> 77/64 ||> 7.66 ||
||> 3 ||> 491.7 ||> 85/64 ||> .43 ||
||> 4 ||> 655.6 ||> 93/64 ||> 8.61 ||
||> 5 ||> 819.5 ||> 103/64 ||> -4.3 ||
||> 6 ||> 983.4 ||> 113/64 ||> -.82 ||
||> 7 ||> 1147.3 ||> 31/16 ||> 2.26 ||
||> 8 ||> 1311.2 ||> 16/15 ||> -.53 ||
||> 9 ||> 1475.1 ||> 7/6 ||> 8.23 ||
||> 10 ||> 1639 ||> 9/7 ||> 3.92 ||
||> 11 ||> 1802.9 ||> 91/64 ||> -6.45 ||
||> 12 ||> 1966.8 ||> 14/9 ||> .88 ||
||> 13 ||> 2130.7 ||> 12/7 ||> -2.43 ||
||> 14 ||> 2294.6 ||> 15/8 ||> 6.33 ||
||> 15 ||> 2458.5 ||> 33/32 ||> 5.23 ||
||> 16 ||> 2622.4 ||> 73/64 ||> -5.39 ||




__//**<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">1st order Crossbone Lattice:</span>**//__
<span style="background-color: #ffffff; 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: #ffffff; 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>
[[image:tessa.png width="435" align="right"]]
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">considered </span><span style="background-color: #ffffff; 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: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Scale (1st order, 1st sepent):</span>**//__
<span style="background-color: #ffffff; 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: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; line-height: 1.5;">•1/1</span>**<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"> - tonic</span>
**<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•16/15</span>**<span style="background-color: #ffffff; 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: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•**7/6** - septimal minor third</span>
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•**5/4** - 5-limit major third</span>
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•**9/7** - septimal major third</span>
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•**10/7** - septimal tritone</span>
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•**3/2** - perfect fifth</span>
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•**14/9** - septimal minor sixth</span>
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•**5/3** - 5-limit major sixth</span>
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•**12/7** - septimal major sixth</span>
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•**7/4** - septimal minor seventh</span>
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•**15/8** - 5-limit major seventh</span>

<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Because the scale is octave-repeating (though derived from the sepent), all sorts of 7-limit inversional fun can be had, and because it is 12-tone, it can be played on a standard keyboard.</span>

Original HTML content:

<html><head><title>Crossbone Tuning</title></head><body><span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Tuning is a coordinated tuning (two separate tunings 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.</span><br />
<br />
<br />
<em><strong><u><span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Example:</span></u></strong></em><br />
<span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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, two temperaments are devised by taking each member of the lesser set and dividing it into x equi-distant intervals</span><br />
<span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">where x is the corresponding member of the greater set and each interval having a distance of the corresponding lesser member raised by (1/x).</span><br />
<br />
<span style="background-color: #ffffff; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">For {5,7} and {17,19}, the yielded Crossbone Tuning would utilize both 5^1/17 and 7^1/19, or 17EDP(Equally-divided pentave) and 19EDS(Equally-divided septave).</span><br />
<br />
<em><u><strong><span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Ordering:</span></strong></u></em><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Because Crossbone is, at heart, a system for deriving tunings, Crossbone'd sets are described by 'orders'.</span><br />
<br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Order is determined by the numerical indexing of valid prime sets suitable for Crossbone.</span><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">{5,7}|{17,19} is of order 1.</span><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">{17,19}|{29,31} is of order 2.</span><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">and so on.</span><br />
<br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">There is currently no conjecture detailing the total possible number of orderings.</span><br />
<br />
<em><strong><u><span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Background:</span></u></strong></em><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">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</span><br />
<!-- ws:start:WikiTextLocalImageRule:384:&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:384 --><span style="background-color: #ffffff; 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, so it is not unfeasible that prime relationships in communication with one another also share musical significance.</span><br />
<br />
<em><u><strong><span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Tuning (1st Order):</span></strong></u></em><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">The first order of the Crossbone Tuning encompasses the first pair of twin pair of twin primes separated by 12, the set {5,7}|{17,19}.</span><br />
<br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">The septave and pentave are not based around the octave, thus each individual septave and pentave will be completely unique and be found to approximate different intervals. Notice below that many of the intervals approximated happen to be harmonics! Those which are not harmonics happen to be readily usable just intervals no greater than 7-limit in the first sepent and 11-limit in the second sepent. -the sepent refers to the total keyspace represented by the pentave followed by the septave</span><br />
<br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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).</span><br />
<br />
<!-- ws:start:WikiTextLocalImageRule:385:&lt;img src=&quot;/file/view/crossbonepiano.png/516324958/993x199/crossbonepiano.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 199px; width: 993px;&quot; /&gt; --><img src="/file/view/crossbonepiano.png/516324958/993x199/crossbonepiano.png" alt="crossbonepiano.png" title="crossbonepiano.png" style="height: 199px; width: 993px;" /><!-- ws:end:WikiTextLocalImageRule:385 --><br />
<br />
<br />
<u><em><strong><span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Intervals</span></strong></em></u><br />
<strong><span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">First Septave: 19EDS</span></strong><br />


<table class="wiki_table">
    <tr>
        <th>Step #<br />
</th>
        <th>Cents<br />
</th>
        <th>Just Approximate<br />
</th>
        <th>Cents Error<br />
</th>
    </tr>
    <tr>
        <td style="text-align: right;">0<br />
</td>
        <td style="text-align: right;">0<br />
</td>
        <td style="text-align: right;">1/1<br />
</td>
        <td style="text-align: right;">0<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">177.31<br />
</td>
        <td style="text-align: right;">71/64<br />
</td>
        <td style="text-align: right;">-2.39<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">2<br />
</td>
        <td style="text-align: right;">354.62<br />
</td>
        <td style="text-align: right;">79/64<br />
</td>
        <td style="text-align: right;">-9.92<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">3<br />
</td>
        <td style="text-align: right;">531.93<br />
</td>
        <td style="text-align: right;">87/64<br />
</td>
        <td style="text-align: right;">.4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">4<br />
</td>
        <td style="text-align: right;">709.24<br />
</td>
        <td style="text-align: right;">3/2<br />
</td>
        <td style="text-align: right;">7.28<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">5<br />
</td>
        <td style="text-align: right;">886.55<br />
</td>
        <td style="text-align: right;">5/3<br />
</td>
        <td style="text-align: right;">-3.21<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">6<br />
</td>
        <td style="text-align: right;">1063.86<br />
</td>
        <td style="text-align: right;">59/64<br />
</td>
        <td style="text-align: right;">4.69<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">7<br />
</td>
        <td style="text-align: right;">1241.17<br />
</td>
        <td style="text-align: right;">128/125<br />
</td>
        <td style="text-align: right;">.11<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">8<br />
</td>
        <td style="text-align: right;">1418.48<br />
</td>
        <td style="text-align: right;">73/64<br />
</td>
        <td style="text-align: right;">-9.31<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">9<br />
</td>
        <td style="text-align: right;">1595.79<br />
</td>
        <td style="text-align: right;">5/4<br />
</td>
        <td style="text-align: right;">9.48<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">10<br />
</td>
        <td style="text-align: right;">1773.1<br />
</td>
        <td style="text-align: right;">89/64<br />
</td>
        <td style="text-align: right;">2.22<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">11<br />
</td>
        <td style="text-align: right;">1950.41<br />
</td>
        <td style="text-align: right;">99/64<br />
</td>
        <td style="text-align: right;">-4.82<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">12<br />
</td>
        <td style="text-align: right;">2127.72<br />
</td>
        <td style="text-align: right;">12/7<br />
</td>
        <td style="text-align: right;">-5.41<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">13<br />
</td>
        <td style="text-align: right;">2305.03<br />
</td>
        <td style="text-align: right;">121/64<br />
</td>
        <td style="text-align: right;">2.39<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">14<br />
</td>
        <td style="text-align: right;">2482.34<br />
</td>
        <td style="text-align: right;">67/64<br />
</td>
        <td style="text-align: right;">3.03<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">15<br />
</td>
        <td style="text-align: right;">2659.65<br />
</td>
        <td style="text-align: right;">7/6<br />
</td>
        <td style="text-align: right;">-7.22<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">16<br />
</td>
        <td style="text-align: right;">2836.96<br />
</td>
        <td style="text-align: right;">9/7<br />
</td>
        <td style="text-align: right;">1.88<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">17<br />
</td>
        <td style="text-align: right;">3014.27<br />
</td>
        <td style="text-align: right;">10/7<br />
</td>
        <td style="text-align: right;">-3.22<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">18<br />
</td>
        <td style="text-align: right;">3191.58<br />
</td>
        <td style="text-align: right;">101/64<br />
</td>
        <td style="text-align: right;">1.73<br />
</td>
    </tr>
</table>

<strong><span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">First Septave: 17EDP</span></strong><br />


<table class="wiki_table">
    <tr>
        <th>Step #<br />
</th>
        <th>Cents<br />
</th>
        <th>Just Approximate<br />
</th>
        <th>Cents Error<br />
</th>
    </tr>
    <tr>
        <td style="text-align: right;">0<br />
</td>
        <td style="text-align: right;">0<br />
</td>
        <td style="text-align: right;">1/1<br />
</td>
        <td style="text-align: right;">0<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">163.9<br />
</td>
        <td style="text-align: right;">35/32<br />
</td>
        <td style="text-align: right;">8.76<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">2<br />
</td>
        <td style="text-align: right;">327.8<br />
</td>
        <td style="text-align: right;">77/64<br />
</td>
        <td style="text-align: right;">7.66<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">3<br />
</td>
        <td style="text-align: right;">491.7<br />
</td>
        <td style="text-align: right;">85/64<br />
</td>
        <td style="text-align: right;">.43<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">4<br />
</td>
        <td style="text-align: right;">655.6<br />
</td>
        <td style="text-align: right;">93/64<br />
</td>
        <td style="text-align: right;">8.61<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">5<br />
</td>
        <td style="text-align: right;">819.5<br />
</td>
        <td style="text-align: right;">103/64<br />
</td>
        <td style="text-align: right;">-4.3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">6<br />
</td>
        <td style="text-align: right;">983.4<br />
</td>
        <td style="text-align: right;">113/64<br />
</td>
        <td style="text-align: right;">-.82<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">7<br />
</td>
        <td style="text-align: right;">1147.3<br />
</td>
        <td style="text-align: right;">31/16<br />
</td>
        <td style="text-align: right;">2.26<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">8<br />
</td>
        <td style="text-align: right;">1311.2<br />
</td>
        <td style="text-align: right;">16/15<br />
</td>
        <td style="text-align: right;">-.53<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">9<br />
</td>
        <td style="text-align: right;">1475.1<br />
</td>
        <td style="text-align: right;">7/6<br />
</td>
        <td style="text-align: right;">8.23<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">10<br />
</td>
        <td style="text-align: right;">1639<br />
</td>
        <td style="text-align: right;">9/7<br />
</td>
        <td style="text-align: right;">3.92<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">11<br />
</td>
        <td style="text-align: right;">1802.9<br />
</td>
        <td style="text-align: right;">91/64<br />
</td>
        <td style="text-align: right;">-6.45<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">12<br />
</td>
        <td style="text-align: right;">1966.8<br />
</td>
        <td style="text-align: right;">14/9<br />
</td>
        <td style="text-align: right;">.88<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">13<br />
</td>
        <td style="text-align: right;">2130.7<br />
</td>
        <td style="text-align: right;">12/7<br />
</td>
        <td style="text-align: right;">-2.43<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">14<br />
</td>
        <td style="text-align: right;">2294.6<br />
</td>
        <td style="text-align: right;">15/8<br />
</td>
        <td style="text-align: right;">6.33<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">15<br />
</td>
        <td style="text-align: right;">2458.5<br />
</td>
        <td style="text-align: right;">33/32<br />
</td>
        <td style="text-align: right;">5.23<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">16<br />
</td>
        <td style="text-align: right;">2622.4<br />
</td>
        <td style="text-align: right;">73/64<br />
</td>
        <td style="text-align: right;">-5.39<br />
</td>
    </tr>
</table>

<br />
<br />
<br />
<br />
<u><em><strong><span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">1st order Crossbone Lattice:</span></strong></em></u><br />
<span style="background-color: #ffffff; 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: #ffffff; 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:386:&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:386 --><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">considered </span><span style="background-color: #ffffff; 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 />
<u><em><strong><span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Crossbone Scale (1st order, 1st sepent):</span></strong></em></u><br />
<span style="background-color: #ffffff; 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 />
<strong><span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; line-height: 1.5;">•1/1</span></strong><span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"> - tonic</span><br />
<strong><span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•16/15</span></strong><span style="background-color: #ffffff; 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: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•<strong>7/6</strong> - septimal minor third</span><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•<strong>5/4</strong> - 5-limit major third</span><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•<strong>9/7</strong> - septimal major third</span><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•<strong>10/7</strong> - septimal tritone</span><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•<strong>3/2</strong> - perfect fifth</span><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•<strong>14/9</strong> - septimal minor sixth</span><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•<strong>5/3</strong> - 5-limit major sixth</span><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•<strong>12/7</strong> - septimal major sixth</span><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•<strong>7/4</strong> - septimal minor seventh</span><br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">•<strong>15/8</strong> - 5-limit major seventh</span><br />
<br />
<span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">Because the scale is octave-repeating (though derived from the sepent), all sorts of 7-limit inversional fun can be had, and because it is 12-tone, it can be played on a standard keyboard.</span></body></html>

@@ 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 19:17:57 UTC</tt>.<br>
+: This revision was by author [[User:joeydinardo2|joeydinardo2]] and made on <tt>2014-07-18 19:24:21 UTC</tt>.<br>
-: The original revision id was <tt>516566386</tt>.<br>
+: The original revision id was <tt>516566910</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 40: / Line 40: @@
 __//**&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;
+**&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 ||
@@ Line 61: / Line 61: @@
 ||&gt; 17 ||&gt; 3014.27 ||&gt; 10/7 ||&gt; -3.22 ||
 ||&gt; 18 ||&gt; 3191.58 ||&gt; 101/64 ||&gt; 1.73 ||
+**&lt;span style="background-color: #ffffff; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;"&gt;First Septave: 17EDP&lt;/span&gt;**
+||~ Step # ||~ Cents ||~ Just Approximate ||~ Cents Error ||
+||&gt; 0 ||&gt; 0 ||&gt; 1/1 ||&gt; 0 ||
+||&gt; 1 ||&gt; 163.9 ||&gt; 35/32 ||&gt; 8.76 ||
+||&gt; 2 ||&gt; 327.8 ||&gt; 77/64 ||&gt; 7.66 ||
+||&gt; 3 ||&gt; 491.7 ||&gt; 85/64 ||&gt; .43 ||
+||&gt; 4 ||&gt; 655.6 ||&gt; 93/64 ||&gt; 8.61 ||
+||&gt; 5 ||&gt; 819.5 ||&gt; 103/64 ||&gt; -4.3 ||
+||&gt; 6 ||&gt; 983.4 ||&gt; 113/64 ||&gt; -.82 ||
+||&gt; 7 ||&gt; 1147.3 ||&gt; 31/16 ||&gt; 2.26 ||
+||&gt; 8 ||&gt; 1311.2 ||&gt; 16/15 ||&gt; -.53 ||
+||&gt; 9 ||&gt; 1475.1 ||&gt; 7/6 ||&gt; 8.23 ||
+||&gt; 10 ||&gt; 1639 ||&gt; 9/7 ||&gt; 3.92 ||
+||&gt; 11 ||&gt; 1802.9 ||&gt; 91/64 ||&gt; -6.45 ||
+||&gt; 12 ||&gt; 1966.8 ||&gt; 14/9 ||&gt; .88 ||
+||&gt; 13 ||&gt; 2130.7 ||&gt; 12/7 ||&gt; -2.43 ||
+||&gt; 14 ||&gt; 2294.6 ||&gt; 15/8 ||&gt; 6.33 ||
+||&gt; 15 ||&gt; 2458.5 ||&gt; 33/32 ||&gt; 5.23 ||
+||&gt; 16 ||&gt; 2622.4 ||&gt; 73/64 ||&gt; -5.39 ||
@@ Line 108: / Line 128: @@
 &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: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;!-- ws:start:WikiTextLocalImageRule:384:&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:384 --&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 117: / Line 137: @@
 &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: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;!-- ws:start:WikiTextLocalImageRule:385:&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:385 --&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;strong&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;/strong&gt;&lt;br /&gt;
@@ Line 327: / Line 347: @@
 &lt;/table&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;First Septave: 17EDP&lt;/span&gt;&lt;/strong&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;163.9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;35/32&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;8.76&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;327.8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;77/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;7.66&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;491.7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;85/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;.43&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;655.6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;93/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;8.61&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;819.5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;103/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;-4.3&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;983.4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;113/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;-.82&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;1147.3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;31/16&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;2.26&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;1311.2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;16/15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;-.53&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;1475.1&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;8.23&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;1639&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;3.92&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;1802.9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;91/64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;-6.45&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;1966.8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;14/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;.88&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;2130.7&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;-2.43&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;2294.6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;15/8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;6.33&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;2458.5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;33/32&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: right;"&gt;5.23&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;2622.4&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;-5.39&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;
@@ Line 333: / Line 540: @@
 &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: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;!-- ws:start:WikiTextLocalImageRule:386:&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:386 --&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;

Crossbone tuning: Difference between revisions

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