Crossbone tuning
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author joeydinardo2 and made on 2014-07-15 19:46:10 UTC.
- The original revision id was 516324968.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
<span style="background-color: #f6f5f1; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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)</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 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;">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> <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">Because the septave and pentave are not based around the octave, 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.</span> <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">One beautiful alignment of this temperament is that it uses a combination of 17 (pentave) and 19 (septave) tones per sepent. 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.. a sepent spanning a total key range of 3 12-tone octaves, coinciding beautifully with the fact that the natural sepent occurs between the 2nd and 3rd standard octave naturally. 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). I may modify the keyboard graphic in the future to show which octave-range in which the octave-reduced ratios fall.</span> [[image:crossbonepiano.png width="800" height="154"]]
Original HTML content:
<html><head><title>Crossbone Tuning</title></head><body><span style="background-color: #f6f5f1; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px;">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)</span><br /> <br /> <br /> <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;"><em>Background:</em></span><br /> <br /> <br /> <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 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 /> <br /> <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><br /> <br /> <br /> <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 /> <br /> <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">Because the septave and pentave are not based around the octave, 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.</span><br /> <br /> <span style="background-color: #f6f5f1; color: #444444; font-family: 'Open Sans','Helvetica Neue',Arial,Helvetica,sans-serif; font-size: 20px; vertical-align: baseline;">One beautiful alignment of this temperament is that it uses a combination of 17 (pentave) and 19 (septave) tones per sepent. 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.. a sepent spanning a total key range of 3 12-tone octaves, coinciding beautifully with the fact that the natural sepent occurs between the 2nd and 3rd standard octave naturally. 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). I may modify the keyboard graphic in the future to show which octave-range in which the octave-reduced ratios fall.</span><br /> <br /> <br /> <br /> <!-- ws:start:WikiTextLocalImageRule:0:<img src="/file/view/crossbonepiano.png/516324958/800x154/crossbonepiano.png" alt="" title="" style="height: 154px; width: 800px;" /> --><img src="/file/view/crossbonepiano.png/516324958/800x154/crossbonepiano.png" alt="crossbonepiano.png" title="crossbonepiano.png" style="height: 154px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:0 --></body></html>