tag:blogger.com,1999:blog-24315236374488788452024-03-12T17:37:03.880-07:00Gems from the Wilson ArchivesA presentation of documents of Erv Wilson that don't lend themselves to a separate section in the archives yet are illuminating in their thought or implications.
Often comprised of sketches or notes found among his papersKraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.comBlogger49125tag:blogger.com,1999:blog-2431523637448878845.post-31569710779595433352018-11-12T09:43:00.001-08:002018-11-12T09:43:25.573-08:00Comma ZigZag PatternsA new 4 page file has been added tohttp://anaphoria.com/wilsonscaletree.html entitled Comma ZigZag Patterns which you can see here http://anaphoria.com/CommaZigZags.pdf
Some common comma are used to find their location on the scale tree as an example which could be explanded. Of interest is how the epimores of succeeding zigzags are used to point out the commas inherent in each the scales presented. Also Wilson points out some hidden Epimores in the scale tree. A sample below<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5lUozZLiKBWONEcAv6UKH3RSo2d1EleWcDe4yJWEr26yT7Vu8ePDaSVmBZ-O-wqOcLDagokLcgMkNYUHyfEiuIDFRGJ4F1m_98cxxglSARZnmuLnVwA3m7t-9JrWyMGtex6liS925L1g0/s1600/examplecomma.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5lUozZLiKBWONEcAv6UKH3RSo2d1EleWcDe4yJWEr26yT7Vu8ePDaSVmBZ-O-wqOcLDagokLcgMkNYUHyfEiuIDFRGJ4F1m_98cxxglSARZnmuLnVwA3m7t-9JrWyMGtex6liS925L1g0/s640/examplecomma.jpg" width="494" height="640" data-original-width="1236" data-original-height="1600" /></a></div>Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-39558753007828379212018-03-31T12:09:00.000-07:002019-11-26T03:25:02.427-08:00An unusual 22 tone 7- limit tuning<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2Ejj2H09bbAptzUBJEt9zuAEbfCoksUUOOAZdapinuQOhHSErDThUlNuec_yvntc8UA8E_W7hI1gLl5QbnfhQkmLa4HtO4EQm4A6YGESiSKcpDGAN7jnBH9R4-Az3uoq1_okqkilS8rk/s1600/Pages+from+7limitstructures.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1230" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2Ejj2H09bbAptzUBJEt9zuAEbfCoksUUOOAZdapinuQOhHSErDThUlNuec_yvntc8UA8E_W7hI1gLl5QbnfhQkmLa4HtO4EQm4A6YGESiSKcpDGAN7jnBH9R4-Az3uoq1_okqkilS8rk/s640/Pages+from+7limitstructures.jpg" width="492" /></a></div>
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Today's puzzle is 7 limit 22 tone scale based on a 1 9 15 35 set where the result in the lattice finds each factor is two simple ratio steps from each other. The center tetrad of 0. 3. 4. 20. in 22 tone step units is a 'tetrad' within a hexany whose outer points form two diamonds. The chart in the up left corner reflects Wilson interest in transforming a structure in a given tuning by multiplying the unit sizes, here limited to odd numbers in 22. The choice of units might reflect the all interval sets found in 13 here embedded in 22 as two interlocking diamonds.Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-46454873463149040562016-12-11T16:24:00.000-08:002016-12-11T16:24:03.929-08:00IN MEMORY: I REMEMBER ERV WILSON<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCYbHL8KwaIK34mYa9puYwZcQ2WretWL5LELNG4VVv6fwjJm-cdWxS_6PLXUoh7RuyH-z4qLxqpXbWnsLP5NTktZhJDf4llGf16i7TVmxM_KI3TiFtbQ52kjqZdw3-BZtd7ee4EXSKxyU/s1600/ErvWilson.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCYbHL8KwaIK34mYa9puYwZcQ2WretWL5LELNG4VVv6fwjJm-cdWxS_6PLXUoh7RuyH-z4qLxqpXbWnsLP5NTktZhJDf4llGf16i7TVmxM_KI3TiFtbQ52kjqZdw3-BZtd7ee4EXSKxyU/s320/ErvWilson.jpg" width="320" /></a></div>
Invited are all memories and/or comments in tribute to Erv Wilson. Please post your own recollections below or just share your thoughts in memory of this man.Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com2tag:blogger.com,1999:blog-2431523637448878845.post-30259012285108201452016-06-08T22:52:00.001-07:002016-06-08T22:52:45.673-07:00A 22 TONE 11 LIMIT CONSTANT STRUCTURE FORMED FROM A SPECIAL HEXANY STELLATION METHOD<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUswU0mM7vhnd0s9hbNI-9jphkYHDx9KK810SFMVDO8-TITK3IxFbJIyUbYKHKcs5zK5sqChcVdHzpZb3yu5wf5kgP0GA9UFg77PGeXNNcK2ONxgi4kmnPD14A0jWSfjE-KuwTTe9GJvs/s1600/h-page7finaljpg.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="574" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUswU0mM7vhnd0s9hbNI-9jphkYHDx9KK810SFMVDO8-TITK3IxFbJIyUbYKHKcs5zK5sqChcVdHzpZb3yu5wf5kgP0GA9UFg77PGeXNNcK2ONxgi4kmnPD14A0jWSfjE-KuwTTe9GJvs/s640/h-page7finaljpg.jpg" width="640" /></a></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKAXZ_4JefqyEpG3sRwImMtqm4ADqdsz_w6dRKtHuH1j5KwLL2A_PeAh37qAB88WUfD6VmXjRaHnPsAVccIS-9IysoNfLWKSmYvyIld2wYc3hI1zkk7wcWo7tU9peCBXxdG4zqD3ZNtrA/s1600/stellateexample2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKAXZ_4JefqyEpG3sRwImMtqm4ADqdsz_w6dRKtHuH1j5KwLL2A_PeAh37qAB88WUfD6VmXjRaHnPsAVccIS-9IysoNfLWKSmYvyIld2wYc3hI1zkk7wcWo7tU9peCBXxdG4zqD3ZNtrA/s640/stellateexample2.jpg" width="451" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKAXZ_4JefqyEpG3sRwImMtqm4ADqdsz_w6dRKtHuH1j5KwLL2A_PeAh37qAB88WUfD6VmXjRaHnPsAVccIS-9IysoNfLWKSmYvyIld2wYc3hI1zkk7wcWo7tU9peCBXxdG4zqD3ZNtrA/s1600/stellateexample2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a>This 22 tone scale of Wilson's believed to be from 1967 was found in a series of papers, charts and scales based stellating Hexanies in i have not seen before. One particular method resulted in the example below which seems to form the core of the scale above. Wilson took the 1-3-7-11 hexany and stellated it with 5 and /5 to complete the 8 basic triads found within which results in the 14 tone structure to the left. The result of this type of stellation has unexpected results. for instance 4 other hexanies are formed each which occurs twice. All involve the added 5 plus three factors of the 1,3,7,11 set. Because of the relationship of most of the added pitches to this stellate being 3/2 above and below, to form this 22 tone scale. 4 more hexanies also appear. The result is one of many 22 tone scales that contain a great variety of compact hexany subsets. <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVqsDXYDXTq2kfJdEZDSnGQ4sr-fd_K1npDwhuKDtQ8jcAe2sncc7dM7Mdr6LPTOdYQpmen2TTSMt4LtmLYSJSXIFwlFW2mVPyblF-dRnFOFLBTt90qlpEhPYdG5IsSEPOK9k-YRKma38/s1600/stellateexample2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><br />
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<br />Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-31590476174132217882016-03-01T05:11:00.002-08:002016-06-27T04:42:57.729-07:00SOME 5 LIMIT PENTATONICS (1982)<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjnj01-1Pjc4_l8mysGA-3vngaRciKMNth4j5v4n1hY3sLyBl80P9l4hsirt11CFOqdi6V0oPVojMNoCF-20FZybR8bBu2unur_HLuGNaIj8ehFRkmFWJDWjgflJepX68hVlVkrgBys7Y/s1600/pentatonicpurvi.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjnj01-1Pjc4_l8mysGA-3vngaRciKMNth4j5v4n1hY3sLyBl80P9l4hsirt11CFOqdi6V0oPVojMNoCF-20FZybR8bBu2unur_HLuGNaIj8ehFRkmFWJDWjgflJepX68hVlVkrgBys7Y/s400/pentatonicpurvi.jpg" width="282" /></a></div>
This is an unlabelled set of pentatonic scales in rotation in what first appeared to be a process similar to that used in his Purvi papers but was not in the end. Adjacent pages carry the year 1982. This set of 5 limit scales he has mapped over 53 squares with the whole set comprising 17 different pitches. In 53 unit sizes would be 53232323-53232323-9 implying two tetrachordal like blocks of 4/3 repeated with a 9/8 disjunction. Each interval shift involve the difference of a 25/24. The paper deserves more more attention. Comments and observations are welcome on this one.Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-24672195172250133042015-08-12T18:41:00.000-07:002015-08-12T18:54:44.878-07:00MAKING A DIAMOND SEEDED FROM A SCALE TREE LAYER In this document <a href="http://anaphoria.com/novavotreediamond.pdf" target="_blank">novavotreediamond.pdf</a> an inspection reveals that the sequence of notes is determined by common tone modulations of the top hexad. That is by shifting the hexad over one place at a time similar to going through the modes on a common tonic, a 23- note diamond like structure results illustrated at the bottom.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3X6mNv06-xKHsmnwjoy2SZggDer5u7GuFqe9bisKbB4EEKRkfD4SC6wp7-nFcSKcBIgS0GVjKj3qKDEEi2CAWg9y8ekDBGNlv0JZJNJIU73J5VhzMQdxRclfAE9UVmaPLb0sO91vEEpI/s1600/diamond+of+7limithexad.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="311" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3X6mNv06-xKHsmnwjoy2SZggDer5u7GuFqe9bisKbB4EEKRkfD4SC6wp7-nFcSKcBIgS0GVjKj3qKDEEi2CAWg9y8ekDBGNlv0JZJNJIU73J5VhzMQdxRclfAE9UVmaPLb0sO91vEEpI/s400/diamond+of+7limithexad.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The Lone Page Showing a Unique 7 limit Diamond. The Centerpiece of a File Now illustrating a Diamond Formed From the Scale tree or the Mt. Meru Triangle </td></tr>
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What is unusual is the choice of 6 notes that make up the seed to the process. It turns out this hexad is formed by the scale tree section seeded by 1/1 and 2/1 shown on page 2 and <a href="http://anaphoria.com/lamcoprime.PDF" target="_blank">borrowed from another document</a>. This section of the tree was the focus of Novaro who also played with <a href="http://wilsonarchives.blogspot.com.au/2011/08/lucky-accident-concerning-some-non.html" target="_blank">some triangles that do not repeat at the octave mention in this blog in the past</a>. so i have added an example of what type of result we can expect from that process. Here instead of using the tree a reseeding of the meru triangle is used to show another way one can visualize the sequence. What occurs in on the other side of the 2/1 differs only by commas with the lower set of pitches. This could be used as possibly a layout where one only has rooom for centain notes in each traditional octave space.<br />
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What should not be lost is the unique type of diamond presented here. It is neither a harmonically or melodically based one, but one that is formed by the tree or a descent down Mt. Meru triangle.Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-16411858521186161852015-07-10T15:55:00.001-07:002015-07-10T15:55:33.471-07:00CONSIDER OLYMPOS<a href="http://anaphoria.com/olympospremarwa.pdf">Consider Olympos</a> is a preliminary paper to The Marwa Permutations and augments some details that might not be clear in general. First that a generator of a scale can be thought to be a variable within set limits and also shows how the chain can be used as a sequence to generate larger scales. <table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvzetJdYUhshOqTSO4o3cS2LrrXH8OHUKS7NIDJXU1YmTVJqK-55HXWeknjWw4DZFOd1G6EJuicqdFLEAz5JAEP19Lx8ZfzmqA6x2ou8BFYvOOe7ZIgva-4kciJLW0m-8GLnjAFYTDKEk/s1600/olympospremarwa_Page_1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvzetJdYUhshOqTSO4o3cS2LrrXH8OHUKS7NIDJXU1YmTVJqK-55HXWeknjWw4DZFOd1G6EJuicqdFLEAz5JAEP19Lx8ZfzmqA6x2ou8BFYvOOe7ZIgva-4kciJLW0m-8GLnjAFYTDKEk/s400/olympospremarwa_Page_1.jpg" width="308" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Page one of Consider Olympos-a draft of a paper that would become his Marwa Permutations </td></tr>
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Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-86442751140866754812015-01-09T04:49:00.000-08:002016-07-05T03:05:06.103-07:00WILSON'S BASIC TEMPLATE FOR LATTICING 13-LIMIT HARMONICALLY BASED STRUCTURES<div class="separator" style="clear: both; text-align: center;">
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwimIGdV_jf_0frjshLXiIXePqKYNlkMBJz2GNDWx7EQEJC52ARS39Qn_CTlcRepSJ8uFr8a2yshU-8uMMSo1l3XCBtrHraeYMyXxd3BhViwJz5tazUO65ukO_b3I1seqn_NL5aghBn6Q/s1600/latticetemplate2.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="333" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwimIGdV_jf_0frjshLXiIXePqKYNlkMBJz2GNDWx7EQEJC52ARS39Qn_CTlcRepSJ8uFr8a2yshU-8uMMSo1l3XCBtrHraeYMyXxd3BhViwJz5tazUO65ukO_b3I1seqn_NL5aghBn6Q/s400/latticetemplate2.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The Most Common Generalised Lattice used by Wilson.</td></tr>
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<span lang="EN-US">It is hard to think of a microtonal
theorist who has made more headway with developing lattices than Erv Wilson.
Here the concentration will be on what he nicknamed <span style="mso-spacerun: yes;"> </span>an “Euler“ lattice after where he drew his
inspiration.<o:p></o:p></span></div>
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<span lang="EN-US">By working with a template where each prime
harmonic has a unique spacing , he managed to avoid clashes when generating
lattice of multidimensional harmonically-based structure<o:p></o:p></span></div>
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<span lang="EN-US">There are some other features worth
pointing out.<span style="mso-spacerun: yes;"> </span>For instance harmonically
generated intervals will always appear above the fundamental and the
subharmonics below. With a<span style="mso-spacerun: yes;"> </span>9-limit
system the direction will be both above and to the right , leaving the other
quadrant for more complex ratios with the opposite with the subharmonic. This
makes it quite easy to understand what is being represented. <o:p></o:p></span></div>
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<span lang="EN-US">Commonly he would use a 10 square to the
inch graph paper which explains why he didn’t use a template where all the
numbers where divided by 2. This way he had room to notate both ratios and
often the scale degree. The latter always followed by a period or dot to
separate it from the ratios.<o:p></o:p></span><br />
<span lang="EN-US"><br /></span>
<br />
<span lang="EN-US"><br /></span>
<span lang="EN-US">Lately i have been using the following lattice which seems to overcome a few trouble spots. This was plotted using 20 squares per inch.<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8HWvG-iLVxoUPsOKOxV5Aypya15Lg8uE9ShDXX-jC784yEWIlh0qhoypdK1TV1fMPPY1TUhCzG8mJTX33McslsgWWKj4-Ih4k55GDXNUFzghMbwEQ2V_8B3_BxrWsUDrgD4ZmapmCnAo/s1600/latticetemplatenew.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="315" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8HWvG-iLVxoUPsOKOxV5Aypya15Lg8uE9ShDXX-jC784yEWIlh0qhoypdK1TV1fMPPY1TUhCzG8mJTX33McslsgWWKj4-Ih4k55GDXNUFzghMbwEQ2V_8B3_BxrWsUDrgD4ZmapmCnAo/s640/latticetemplatenew.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Alternative lattice by Kraig Grady in cases of slashes with Wilson's Lattice.</td></tr>
</tbody></table>
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Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-40282630190114965552014-08-23T18:53:00.000-07:002014-08-23T18:58:55.505-07:00Paul BeaverWilson often referred to Paul Beaver, especially in making him aware of Pascal's triangle which might be the most important source for Wilson's work. This is one of the few references I know of Paul's work which until now was unknown to this archivist.<br />
<br />
"Ohio’s Paul Beaver, meanwhile, was an important early proponent of the the synthesized film score, working on soundtracks for The Munsters and My Favourite Martian. A Scientologist and noted eccentric, he played on records by The Monkees and The Byrds, and set up the Moog patch heard on The Doors’ ‘Strange Days’. T<br />
<br />
from<br />
.<a href="http://www.thevinylfactory.com/vinyl-factory-releases/the-greatest-electronic-albums-of-the-1950s-and-1960s-2/" rel="nofollow" style="background-color: white; color: #3b5998; cursor: pointer; font-family: Helvetica, Arial, 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 14px; line-height: 19.31999969482422px; text-decoration: none;" target="_blank">http://www.thevinylfactory.com/vinyl-factory-releases/the-greatest-electronic-albums-of-the-1950s-and-1960s-2/</a><br />
<br />Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-1243156771116021432014-06-10T05:15:00.000-07:002014-06-10T05:16:53.633-07:00 ...More Like a Living Thing, Than an Inert Crystal.......<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvIk-_e-tuz05R87g0Fd9UnqkpZiqtgdX9RFuftxaGRQSxDvBelgUT8MPOlmY7dCWgXXsYyPWrNZpi4TRkGvlWcTenvQ2caPua6UPUaHXdB_0xTYHm9pmGPOj7Nymfg1XeDXFPYOzoESU/s1600/scaleascell.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvIk-_e-tuz05R87g0Fd9UnqkpZiqtgdX9RFuftxaGRQSxDvBelgUT8MPOlmY7dCWgXXsYyPWrNZpi4TRkGvlWcTenvQ2caPua6UPUaHXdB_0xTYHm9pmGPOj7Nymfg1XeDXFPYOzoESU/s1600/scaleascell.jpg" height="640" width="452" /></a></div>
<br />Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-77962368452456805022014-06-04T17:53:00.000-07:002014-06-10T05:16:29.076-07:00Addition To Wilson's Moments Of Symmetry Article A new file has been added to Wilson's Moments of Symmetry paper.<br />
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Either you can download the complete paper here <a href="http://anaphoria.com/mos.pdf">http://anaphoria.com/mos.pdf</a><br />
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<div>
or if you wish, you can upload only the appendix. <a href="http://anaphoria.com/mosgeneral.pdf">http://anaphoria.com/mosgeneral.pdf</a></div>
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Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-43238866200280387402014-05-02T22:25:00.001-07:002014-06-04T18:10:00.998-07:00AN 11- Limit "Centaur" Implied In A Wilson Lattice-Update!<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9gWBRm7D3xpI4Ld5EKIrsC4-d4iSE8OLfNqqCvYh01shhnlQictMbt11kQRN1drbJNZvbdBKbH-PmNk_mYLxXoJMpQD8-rhY_D9O6Zk4bRZJP2eZyQloGjGDNdHu4U8TWt1S7uf-Jkn0/s1600/17tonescale11limit.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9gWBRm7D3xpI4Ld5EKIrsC4-d4iSE8OLfNqqCvYh01shhnlQictMbt11kQRN1drbJNZvbdBKbH-PmNk_mYLxXoJMpQD8-rhY_D9O6Zk4bRZJP2eZyQloGjGDNdHu4U8TWt1S7uf-Jkn0/s1600/17tonescale11limit.jpg" height="456" width="640" /></a></div>
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Thus scale would work quite well as an introduction and ear training scale for those interested in both 11 limit harmonic and subharmonic material with a limited amount of notes.</div>
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The bottom Diagram is a blank Lattice found among Wilson's papers. No copy of him filling it in has so far been found.
Taking how he normally lattices scales it produced an interesting and unusual scale. It contains two full harmonic and subharmonic series up to 11th which enables many tetrachords of both or mixed variety. One of the first things noticed is that the scale develops more in the direction of the 11th than the 7th limit direction which is a bit out of the ordinary. The bar at the bottom shows how well it fills space. </div>
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I cannot but relate this scale to my own "Centaur" Scale as it would function extremely well for what "Centaur" hoped to examine. It explores on an 11 limit level what Centaur did on a 7 limit. If a keyboard would have been available to tune to 17 places , it is exactly this type of scale that would have be sought. Thus this scale would have easily been the very first scale i wished for. Giving access on a sustained instrument a bedrock of material i so desired to hear.<br />
<br />
This scale will be included on the <a href="http://anaphoria.com/centaur.html">Centaur page</a> for the reason sited.<br />
<br />
UPDATE! As fate would have it, look what I found only a few hours after posting. Here is an actual drafting of the scale above by Erv Wilson next to the blank that led to the scale. In this diagram the inversion is contemplated as an alternative which i had not pointed out above.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRSfqsDzWHQ2z387Emud8eQZ4Q7Sl3OWCGVrxYxcOqmWbR5xoOjopU8mKoXONlYwlMGWJgt6e2DBAA5PkPOleKPdBnkdF54YkwkXXjRqkFS0xUPgzkGBDZBldz5jEVpYIBeKVABIViQno/s1600/17tone2.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRSfqsDzWHQ2z387Emud8eQZ4Q7Sl3OWCGVrxYxcOqmWbR5xoOjopU8mKoXONlYwlMGWJgt6e2DBAA5PkPOleKPdBnkdF54YkwkXXjRqkFS0xUPgzkGBDZBldz5jEVpYIBeKVABIViQno/s1600/17tone2.jpg" height="244" width="320" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOZL8VaJpou5dFKUzoLX1Ib5yEowjbqP-GmlkKPoZHyLZBJ8uadlTmxOTIg1MCXpT3x46vNhPs_CFnMxvmL-d0K3y5-20d6jZTj7MozFSVseOu8GJigO2Cmj012LtjGa5gwXCy1UozfyE/s1600/17tonescale.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOZL8VaJpou5dFKUzoLX1Ib5yEowjbqP-GmlkKPoZHyLZBJ8uadlTmxOTIg1MCXpT3x46vNhPs_CFnMxvmL-d0K3y5-20d6jZTj7MozFSVseOu8GJigO2Cmj012LtjGa5gwXCy1UozfyE/s1600/17tonescale.jpg" height="400" width="285" /></a></div>
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Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-43217464505215427202014-03-11T05:41:00.000-07:002014-03-12T20:34:54.227-07:00Wilson / Poole / 21: 22: 27: 28 - A Moment of Convergence in a Tuning's Evolution<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnh7aYLa3DhNY4zonErk5GKmq0qYteqZf5uBTUTKbOZOO0CqB5d91ko-1XITf16KvunUEJDwpFqv9ByGBsJSoufcgs7gZQSEycVWIvFBuldjonEVtKSflnkxk2XtwAh7G4ATJDXx6rNds/s1600/Pages+from+RAST_Page_1.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnh7aYLa3DhNY4zonErk5GKmq0qYteqZf5uBTUTKbOZOO0CqB5d91ko-1XITf16KvunUEJDwpFqv9ByGBsJSoufcgs7gZQSEycVWIvFBuldjonEVtKSflnkxk2XtwAh7G4ATJDXx6rNds/s1600/Pages+from+RAST_Page_1.jpg" height="320" width="248" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Page 1 of Modeled on Baglama Scale</td></tr>
</tbody></table>
<br />
Margo Schulter has noticed a correspondence that had lead to an update of file <a href="http://anaphoria.com/RAST.PDF">RAST.PDF</a><br />
Here is what she has to share:<br />
<br />
<div style="text-align: center;">
-------------------------------------------- </div>
<div style="text-align: center;">
Erv Wilson, Rod Poole, and 21:22:27:28
</div>
<div style="text-align: center;">
A Moment of Convergence in a Tuning's Evolution
</div>
<div style="text-align: center;">
---------------------------------------------</div>
<br />
Erv Wilson's RAST.PDF (p. 17 in the version of 11 March 2014) may have
a connection to the evolution of Rod Poole's 17-note JI guitar tuning.
The direct and obvious "moment of convergence" on this page of
Erv's is the appearance of the conjunct soft diatonic mode 21:22:27:28, or
in other words 1/1-22/21-9/7-4/3-88/63-12/7-16/9-2/1. This same mode
is featured by Rod in a typeset page from a CD insert (December 1996),
made available in JPEG format by Ron Sword and reproduced as p. 18 of
RAST.PDF, focusing on this 21:22:27:28 tetrachord and its conjunct
octave mode as the nucleus of "The Death Adder/December 1996" (see
Examples One and Two).
<br />
<table align="right" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-7tW8SWsqFkjO9nvolLTwQdVe3VkMc0OtWbt5RWqiiBHKRekgnmW5XTLs4ros7YBwI1Uml9NJRufW4MebXaMX7cRAmuloVvghqjgQHzyfB_aXjHnb05WFwBMBHkjG3phVWTxCRKNjSNo/s1600/Pages+from+RAST_Page_2.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-7tW8SWsqFkjO9nvolLTwQdVe3VkMc0OtWbt5RWqiiBHKRekgnmW5XTLs4ros7YBwI1Uml9NJRufW4MebXaMX7cRAmuloVvghqjgQHzyfB_aXjHnb05WFwBMBHkjG3phVWTxCRKNjSNo/s1600/Pages+from+RAST_Page_2.jpg" height="320" width="248" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Page 2 of Modeled on Baglama Scale</td></tr>
</tbody></table>
<br />
Of course, this connection leaves open the question of "Who influenced
whom?" -- a question which may be moot when two artists such as Erv
and Rod enjoy a close association over a period of years, and also
share a strong sense of trusting and following their own ideas and
intuitions. By 10 May 1995, for example, Rod had proposed a 29-note
guitar tuning which <a href="http://anaphoria.com/centaur.html#erv29">Erv mapped to generalized keyboard</a>, including all
the notes in Rod's later 17-note set, plus others, some found in Kraig
Grady's Centaur (21/20, 5/4, 7/5. 5/3, 15/8).
<br />
An intriguing possible further connection is suggested by the sketch
at the bottom of Erv's p. 16, where the diagram of the conjunct
21:22:27:28 mode at the top of the page is connected to a diagram of a
17-note instrument, where it is proposed that this mode should start
on the 7/4 step of the 17-note tuning, or step 14. The initial steps
of this 17-note tuning from the "open string" are shown as 1/1, 33/32,
13/12, 9/8, and 7/6, which matches Rod's 17-note system.
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6QlHYGRLMC-mm3dEjJAWTTA2O1_J9Hy5GsyE3S-W1dR_z0ev1-w4izkk-Mx3VukKGFXZi94m3mRiLfgFQ09wOxNx0SrtBgXFl_aBkveXZwaOrMM3bwWMLQv25oRoZS2hctoyqArd00oU/s1600/Pages+from+RAST_Page_3.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6QlHYGRLMC-mm3dEjJAWTTA2O1_J9Hy5GsyE3S-W1dR_z0ev1-w4izkk-Mx3VukKGFXZi94m3mRiLfgFQ09wOxNx0SrtBgXFl_aBkveXZwaOrMM3bwWMLQv25oRoZS2hctoyqArd00oU/s1600/Pages+from+RAST_Page_3.jpg" height="156" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">liner notes to Dec. 96,Rod Poole CD</td></tr>
</tbody></table>
<br />
----------------------------------<br />
1. Correlating Rod's 13-note tuning to his 17-note system
<br />
----------------------------------<br />
<br />
In Rod's system, this 21:22:27:28 mode indeed appears in its precise
conjunct form at one location: the 7/4 step. The following diagram
shows the mode of interest at the top, and the steps of the 17-note
tuning at the bottom:
<br />
<br />
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</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhH5_bs2IGj34JGw1MSEFlP5fTcvnB-926G3mh94A2DZDvG5diYgF8aG-Hpk77tqVH61WwtLWIxBlnl2-rQG-hvBCPe1oyFivf6h1AhaEkeLXqMjv50OJ2TzCrJgNkBZesstVPiW8_ehhA/s1600/Re-Rast-pg_2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhH5_bs2IGj34JGw1MSEFlP5fTcvnB-926G3mh94A2DZDvG5diYgF8aG-Hpk77tqVH61WwtLWIxBlnl2-rQG-hvBCPe1oyFivf6h1AhaEkeLXqMjv50OJ2TzCrJgNkBZesstVPiW8_ehhA/s1600/Re-Rast-pg_2.jpg" height="113" width="640" /></a></div>
<br />
<br />
Since many of Erv's Rast-Bayyati pages are dated 1992 or 1993, his
interest in Mansur Zalzal, his 27/22 wusta (or wosta) middle finger
fret, and tunings featuring Zalzalian or middle intervals (sometimes
know as "neutral" intervals) may have been a theme that he and Rod
focused on in the early years of their association. By 1995, this
interest had led to Rod's 29-tone guitar concept -- and, by 1996, had
for him focused on the 21:22:27:28 mode as the nucleus of at least one
type of guitar tuning featuring septimal and Zalzalian steps.
<br />
Rod's "13-note expanded scale" of December 1996 growing out of this
mode is interesting to compare to the standard 17-note set. Unlike the
17-note set, it includes some pairs of steps at a comma apart, as does
the 29-note concept of 1995. If we again apply Erv's sketch at the
bottom of his page on the 21:22:27:28 mode and begin it on the 7/4
step of the eventual 17-note tuning, some of the additional steps do
match. Here I compare the lower 4/3 tetrachord of the mode, and then
the upper tetrachord and 9:8 tone completing the octave, with extra
tones of the 13-note set in 1996 show above the modal steps:
<br />
<br />
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</div>
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-GyyZ_94DLNeuURD3af6EFXC1Gj1ZJOuyVROgLMKOrAU_ifBbJK64-yk19IJlBwa5w05OK2vPg7xGJnLkrKK1_q6DHItT7yNmeBv3Pme-jjPvjRpN5N4OCS7GdPipIXEaaZSfwZy81Lo/s1600/Re-Rast-pg_3.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-GyyZ_94DLNeuURD3af6EFXC1Gj1ZJOuyVROgLMKOrAU_ifBbJK64-yk19IJlBwa5w05OK2vPg7xGJnLkrKK1_q6DHItT7yNmeBv3Pme-jjPvjRpN5N4OCS7GdPipIXEaaZSfwZy81Lo/s1600/Re-Rast-pg_3.jpg" height="203" width="640" /></a></div>
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</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div style="text-align: left;">
Three of the extra tones, at 3/2, 11/7, and 27/14, together with the </div>
<div style="text-align: left;">
2/1 octave make possible the option of a disjunct 21:22:27:28 </div>
<div style="text-align: left;">
tetrachord at 3/2-11/7-27/14-2/1, in addition to the conjunct </div>
<div style="text-align: left;">
tetrachords of the basic 7-note mode.<br />
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4wBJgCQ82RHPTnRFze0fDPjL0TuF3BV24vLYUkCt3M9IWgseemnIMwsEvh7zR_Y_qxEsOMGGfxJ1XBp6_zuN6ifcHfdy7IY7Vmnm0Kad8Tl_G79zduiuRDVkj_fLlUBFPHjf7IgGRSdA/s1600/Re-Rast-pg_3b.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4wBJgCQ82RHPTnRFze0fDPjL0TuF3BV24vLYUkCt3M9IWgseemnIMwsEvh7zR_Y_qxEsOMGGfxJ1XBp6_zuN6ifcHfdy7IY7Vmnm0Kad8Tl_G79zduiuRDVkj_fLlUBFPHjf7IgGRSdA/s1600/Re-Rast-pg_3b.jpg" height="160" width="640" /></a></div>
<br />
Of the six extra notes in the 1996 tuning, Rod's 17-note tuning taken
from the 7/4 step incorporates two: 11/7 (at 11/8 from the usual 1/1),
and 27/14 (at 27/16). The 3/2 step of 1996 would map to 21/16, a step
included in the 29-note design of 1995, but not in the 17-note set,
where it would be only a 64:63 comma from the 4/3.
<br />
The 11/9 step in 1996 would make possible another very beautiful
tetrachord from 1/1 to 4/3 in this 13-note tuning: 1/1-22/21-11/9-4/3
or 22:21-7:6-12:11, an exact mirroring of Qutb al-Din al-Shirazi's
Hijaz tetrachord around 1300, 1/1-12/11-14/11-4/3 or 12:11-7:6-22:21.
Both these permutations of Hijaz, which John Chalmers's describes as a
"neochromatic" form with the large interval as the middle step of the
tetrachord, derive from Ptolemy's Intense Chromatic at 22:21-12:11-7:6
or 1/1-22/21-8/7-4/3, with the large interval (7:6) as the upper
step. The 22:21-7:6-12:11 form might also be derived from a rotation
of a mode built from a chromatic of al-Farabi, 28:24:22:21 or
7:6-12:11-22:21, 1/1-7/6-14/11-4/3 (see al-farabi_g7.scl in the Scala
archive).
<br />
In the mapping of the 1/1 in this 1996 tuning to 7/4 of the 17-note
system, however, an 11/9 step would translate to a 77/72 step, at
116.234 cents, at a 78:77 comma below the 13/12 step appearing both in
the 1995 concept and the 17-note tuning. Indeed Ibn Sina's famous `oud
tuning features steps at 273/256 (111.389 cents) and 13/12; his
273/256 (39/32 less 8:7), like a hypothetical 77/72, approximates
16/15. However, in Rod's 17-note tuning, the minimum distance between
notes is 33:32, which I find is a variety of "minimal semitone."
We can, however, find a 22:21-7:6-12:11 tetrachord in this tuning at
21/11-1/1-7/6-14/11.
<br />
The 14/11 step of the 1996 tuning would map from the 7/4 step of the
17-note system to 49/44 or 186.334 cents, a bit wide of 10/9, and
99:98 below 9/8 in this scheme.
<br />
The 56/33 step of 1996 would likewise translate to 49/33 or 684.379
cents, a bit wide of 40/27, and 99:98 below the 3/2 step.
<br />
Rod's 3/2 step of 1996 would translate to 21/16, a step present in the
1995 concept, but in the 17-note system would be a 64:63 comma from
4/3 in a context where steps are at least a 33:32 apart.
<br />
Of course, it is important to bear in mind that Rod's 13-note scheme
of 1996 has its own musical logic, with the 56/33 step for example
very logically placed at a 4:3 fourth above 14/11, although as it
happens not included in either the 29-note tuning of 1995 or the
17-note scheme.
<br />
Erv's page on the 21:22:27:28 mode and its mapping to the 7/4 step of
a 17-note system raises interesting questions. Is this a record of something Erv conceived or was it one of Rod's concepts? Or, not so surprisingly, could it be the result of much mutual dialogue and discovery.<br />
<br />
------------------------------------------------------------------------------------------<br />
<div style="text-align: center;">
2. A note on 21:22:27:28 and the Byzantine Hard Chromatic
</div>
------------------------------------------------------------------------------------------<br />
<br />
On the 21:22:27:28 mode itself, Rod describes it as "an enharmonic,
tetrachordal scale. The tetrachord (a perfect fourth) is two
unevenly-sized, small half-steps, 22:21 and 28:27, separated by a
neutral third, 27:22, the Wosta of Zalzal."
<br />
Interestingly, this type of tetrachord is what students of classic
Greek tuning sometimes describe as a soft chromatic, and modern
Byzantine theory calls the Hard Chromatic. In a more moderate form, it
appears as the form of Byzantine Hard Chromatic recommended by the
Committee on Music in 1881, with a tuning expressed in terms of units
of 36-ed2 as 3-10-2 steps or 100-333-67 cents, with a middle interval
at 333 cents (a small Zalzalian third at around 63/52 or 40/33) and a
third step at 433 cents, very close to Rod's 9/7. Some exponents of
Byzantine music report that the large middle interval is in practice
often around 11/9 or even a bit wider, so that 21:22:27:28 may
reasonably approximate this style of vocal intonation.
<br />
While either the classic "soft chromatic" or the modern Byzantine
"Hard Chromatic" may aptly describe this mode, Rod's "enharmonic"
concept may fit broadly into the Byzantine tradition also. While in
classic Greece it tends to imply a yet wider large interval, somewhere
at least around 5/4 and ranging up to 81/64 or beyond, for Chrysanthos
of Madytos in the earlier 19th century, the mark of the enharmonic was
the presence of a small step which could be viewed as in some sense a
"quartertone."
<br />
For Chrysanthos, 68-ed2 provided a reasonable approximation of the
flexible intervals produced by singers -- a conclusion concurred in by
the Syrian theorist on Arab music, Mikhail Mashaqa, who reported that
the scheme of 24-ed2 he used in his own writing was in fact less
accurate than the Greek system of Chrysanthos. Interestingly,
Chrysanthos used a smaller middle interval than Rod's 27:22 for his
Hard Chromatic, at 7-18-3 steps, or 124-318-53 cents -- but a third
note at 441 cents or actually a bit higher than 9/7, and an upper step
even smaller than Ron's classic 28:27 of Archytas (63 cents), at 53
cents or a near-just 33:32. In 68-ed2, this 53-cent step (3 scale
steps) is literally 1/4 of a regular tone at 212 cents of 12 scale
steps -- identical to the tone at 3 steps of 17-ed2.
<br />
As shown in Erv's diagrams, the 21:22:27:28 tetrachord would map in a
17-note system to 1-5-1 steps. In this context, musicians and
theorists such as George Secor sometimes refer to certain types of
motion by a single step as "enharmonic," which along with the dramatic
contrast between the adjacent steps at 27:22 (355 cents) and 28:27 (63
cents) might well prompt this expressive term.
<br />
Happily, this conjunct 21:22:27:28 mode is indeed available in Rod's
17-note tuning at the 7/4 step indicated in Erv's diagram, and also in
offshoots such as Zeta-20 and Zeta-24 at the same location.
<br />
<br />
<br />
------------------------------------------------------------------------------------------<br />
<div style="text-align: center;">
3. Conclusion
</div>
------------------------------------------------------------------------------------------<br />
<br />
The documentation in 1995 of Rod's 29-note concept for a guitar
tuning, followed by his CD notes describing his 13-note tuning of
December 1996 which "began life" as the 21:22:27:28 mode, and then the
implementation of his 17-note tuning, suggests that this process of
evolution may have been complex and not necessarily linear -- and
likewise the artistic collaboration between him and Erv Wilson, with
Kraig Grady and his Centaur tuning and extensions also intimately
involved in this creative process.
<br />
Rod's notes, which focus not only on the selection of certain notes or
modes but on the practical task of implementing them on a real-world
instrument, suggest that we keep in view all sides of this process.
<br />
What Rod's notes and Erv's page together indicate is that the 13-note
tuning of December 1996, or more specifically the 7 notes of the
conjunct 21:22:27:28 mode plus two of the additional steps (11/7 and
27/14), were mapped to the 7/4 step of the 17-note system partially
sketched out by Erv and later implemented by Rod. Thus while the 1995
scheme for 29 notes might be viewed as one source for this system,
since it includes all 17 notes, the mapping of the 21:22:27:28 mode
that was the nucleus of the 1996 system to the 7/4 step of a 17-note
template may represent another step.
<br />
The "moment of convergence" between Erv's diagram and the portrait we have in Rod's CD insert of a tuning in progress gives us a richer perspective on a most
fruitful and creative collaboration.
<br />
I would also like to thank both Ron Sword and Kraig Grady for their
generosity and untiring diligence in making these materials accessible
to interested musicians and the world at large.
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-8891025631627534832014-03-08T20:02:00.002-08:002014-03-09T05:25:06.493-07:00The Pythagorean Assimilation of Subharmonic Flutes<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaLZ0_cRf_vJ8iBWPmNNCIgM6B-jX_nWpu60GJbhKBO6LIgaZzKoAR2Q10TZd3i1e63iLnnS4tmaH1UJ6r-Kd3g9APm60zGHZIzLHKEYaoNDl6_RzDxqQbTzoUOfnIs0DYLsis13vS5Go/s1600/fluteadd.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaLZ0_cRf_vJ8iBWPmNNCIgM6B-jX_nWpu60GJbhKBO6LIgaZzKoAR2Q10TZd3i1e63iLnnS4tmaH1UJ6r-Kd3g9APm60zGHZIzLHKEYaoNDl6_RzDxqQbTzoUOfnIs0DYLsis13vS5Go/s1600/fluteadd.jpg" height="400" width="285" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Wilson's comparison and guide to transcribing<br />
subharmonic scales to a pythagorean system</td></tr>
</tbody></table>
This stray page found in the records is being added to the archives file called <a href="http://anaphoria.com/FluteNotes.pdf" target="_blank">Flute Notes</a>. Wilson is concerned with the way subharmonic scales and their melodies can be assimilated into a pythagorean tuning array. He entertained the idea that subharmonic flute melodies in India could have found their way into string instruments tuned to a pythagorean chain.<br />
Wilson might be the first to mention the use of tuning the exit hole of a subharmonic flute to either a fourth or fifth of one of the holes, hence these designations in the upper of the two sets of blocks. This practice he observed in the tunings found within his large collection of South American flutes. The ratios in between the blocks show the difference between the two sets of scales. The chart is one way we might transcribe subharmonic scales and pythagorean scales and melodies into each other. Unsigned or labeled, it was a document the archivist received from him by at least 1978.Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-69379705881662344592014-02-25T12:44:00.000-08:002014-06-10T05:30:45.068-07:00Evangelina- Maybe Wilson's favorite<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQT6mKbuCVuldi4J9vL2S75eMD9CcOXkiR_8JihqYuqDJiSJulljPk_Thz9p11-AVybVXTBxDyWtq_OxyGh3mxrIAcuMMnr9RB0LVGW2u4tLlGn7xHCdehOBDhfrooCiCAXHGmvJNSNZA/s1600/Pages+from+22tonescales.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQT6mKbuCVuldi4J9vL2S75eMD9CcOXkiR_8JihqYuqDJiSJulljPk_Thz9p11-AVybVXTBxDyWtq_OxyGh3mxrIAcuMMnr9RB0LVGW2u4tLlGn7xHCdehOBDhfrooCiCAXHGmvJNSNZA/s1600/Pages+from+22tonescales.jpg" height="310" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Evangelina-Wilson's 'Personal' Scale</td></tr>
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Erv Wilson stated "The Evangelina tuning commemorates the work done by Evangelina Villegas and Surinder K. Vasal with quality protein maize in Mexico, Africa, India, Japan and China". It strongly resembles a 22 tone harmonic version of his diaphonic cycles. It might be thought of as his adaptation of the 22 shruti system of India as well as an expansion on Boomsliter and Creel's work on "extended reference". Wilson over time replaced the 5 and 7 limit intervals with the colored harmonics listed. Often these are within a cent or two. This was one of the scales he maybe played the most at home and once when a pair of Mormon missionaries descended upon his abode, he used the opportunity to have them sing pieces from the Mormon hymn book in this tuning which went on for months. In this diagram, I have taken his pencil notes and colorized them to accent the 3 harmonic series contained within. The diagram has been inserted into <a href="http://anaphoria.com/22tonescales.pdf">http://anaphoria.com/22tonescales.pdf</a> where one can compare first his diagram of the 22 shrutis with other related scales he developed. The 7 limit one was used by a Los Angeles band 'Cypher' in the mid 80s on instruments built for guitarist Jose Garcia.Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-84384909156568714322013-12-19T15:29:00.000-08:002014-03-11T21:20:51.247-07:00Diatonic, Chromatic, Tri-Chromatic, and Enharmonic Forms of MixolydianHere is a method of deriving some tetrachordal like shapes starting with the sub 7-14 series borrowing Schlesinger designation for Mixolydian. It is interesting to note that to derive each form, there is a shift up the subhamonic series by multipling by 2, 3, or 4 times shifting the series to 14-28, 21-42 and 28-56 respectfully to derive a class of scale. The term Tri-Chromatic (formed by multiplying by 3 the 7-14 series) is invented here to designate a new scale type in between the chromatic and enharmonic. In each set of four a different interval acts as a disjunction like interval and greatly expands the range of what a disjunction might be. These being in order 8/7, 11/10, 14/13 then these are repeated in the next three to construct tetrachordal shapes where the large interval is at the bottom as opposed to the top. It was an idea Wilson left unexplored past this page it appears. The other tetrachordal permutations are left unexplored.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglQ5qHqWDg02H-83QcgTaJ-7DUxpSVvcTV7-Xky9gDC0TtiCzmmjFqYbh7twkjLrFfmrTHzdIzl9eAp-Atnzyywr9acnMqn-YNKwdzd2WrHEI7dDcKhHrnjpWhXcYnEKBoJ_tlzkDKznI/s1600/mixolydianforms.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglQ5qHqWDg02H-83QcgTaJ-7DUxpSVvcTV7-Xky9gDC0TtiCzmmjFqYbh7twkjLrFfmrTHzdIzl9eAp-Atnzyywr9acnMqn-YNKwdzd2WrHEI7dDcKhHrnjpWhXcYnEKBoJ_tlzkDKznI/s320/mixolydianforms.jpg" height="497" width="640" /></a></div>
Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-72776848890500944002013-08-17T20:22:00.000-07:002017-07-18T22:04:49.868-07:00Orson Tuning found by Wilson as early as 1997This tuning was later called Orson. This page is excepted from of<span style="font-size: x-small;"> <a href="http://anaphoria.com/wilsonthree.PDF" target="_blank">EXTENDED DIAGONALS AND VARIOUS PRIMARY AND SECONDARY RECURRENT SERIES</a>. </span>Wilson would often mark those places where a recurrent sequence would be close to an Equal temperament scale with an arrow or an exclamation point if it was negligible as can be seen in the zig zag pattern. for more information on these body of scales, please look at <a href="http://anaphoria.com/wilsonmeru.html" target="_blank">http://anaphoria.com/wilsonmeru.html </a><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVjeYtck3y_vGnW5SQYhvxlRJiSHIpjxwt6rCI45YHCK7XGINmstVI39t6A3T5-fOZBsH8EqP1gTs465gv9w-O-1XUsm05Sd7Lu9sQ2fD18yb0__4BdseBUMyoldUelZsK-JtmAagiDmg/s1600/ORWELLfrommeruthree.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVjeYtck3y_vGnW5SQYhvxlRJiSHIpjxwt6rCI45YHCK7XGINmstVI39t6A3T5-fOZBsH8EqP1gTs465gv9w-O-1XUsm05Sd7Lu9sQ2fD18yb0__4BdseBUMyoldUelZsK-JtmAagiDmg/s400/ORWELLfrommeruthree.jpg" width="305" /></a></div>
<br />Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-10624364922142751752013-07-22T14:56:00.000-07:002013-07-22T15:06:25.242-07:00Largest Tolerance over Average<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimceSQwR5-typyXFOOP6mLxrJwNqZFSBpuz_Pz46WMBbzN-7KKRj1wBycq0dXMBfllap-Rskm-fxh31xiGHoNSUn-FMVY8OOodptLCIXO8O6mCcXYnpUBTgNjDgdhQ5D0jM724X8fGquw/s1600/R-letter.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimceSQwR5-typyXFOOP6mLxrJwNqZFSBpuz_Pz46WMBbzN-7KKRj1wBycq0dXMBfllap-Rskm-fxh31xiGHoNSUn-FMVY8OOodptLCIXO8O6mCcXYnpUBTgNjDgdhQ5D0jM724X8fGquw/s640/R-letter.jpg" width="492" /></a></div>
In this sketch of a letter to a peer, Wilson points out his preference for evaluating temperaments by finding largest tolerance in the scale as opposed to averaging out. This focus on he worse case scenario of tuning makes sense in that the averaging of the others will not diminsh what stands outs. Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-73662266723314150222013-07-18T05:50:00.002-07:002016-12-11T00:29:42.768-08:00Triplet Sets From The Basic Scale Tree.<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCfRtaC7XMpYU6F4BvSXbtJBFxWtVls9veg7JQ5OJ-NKvgqb6KsCYpbdmwZnK_owdB13praYAflCMRKKjTzRPzmPktZt3jz1l3EKrwCGw1Z-J4R1bgVmlWsXd2dgKQ3QRb-oCJhU0EgyM/s1600/tetrachordaltree1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCfRtaC7XMpYU6F4BvSXbtJBFxWtVls9veg7JQ5OJ-NKvgqb6KsCYpbdmwZnK_owdB13praYAflCMRKKjTzRPzmPktZt3jz1l3EKrwCGw1Z-J4R1bgVmlWsXd2dgKQ3QRb-oCJhU0EgyM/s640/tetrachordaltree1.jpg" width="489" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">TETRACHORAL TREE</td><td class="tr-caption" style="text-align: center;"></td><td class="tr-caption" style="text-align: center;"><br /></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtBre-VwwXPbs68UiCvNh7ycWmwfb-dcv0wrDkwUaQpHfZTkvFcMmGBXuMWVmVOVWxuXgFFbOhugPdgykq8IDvwt7X1JaceAenAmwaw42LokIfyXU-MmW28BfOT0XDq4ivpyc1j4DY05g/s1600/tetrachordaltree.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="398" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtBre-VwwXPbs68UiCvNh7ycWmwfb-dcv0wrDkwUaQpHfZTkvFcMmGBXuMWVmVOVWxuXgFFbOhugPdgykq8IDvwt7X1JaceAenAmwaw42LokIfyXU-MmW28BfOT0XDq4ivpyc1j4DY05g/s400/tetrachordaltree.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><u>TRIPLET SETS FROM THE SCALE TREE</u></td></tr>
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This top diagram has been a part of the 'tres.pdf' document for years but it was only after finding the second in his notes do certain aspects become clear. Wilson has taken a trio of terms found in the scale tree and proceeds to multiply them to where they can be easily used to generate a scale tree contained within a 4/3. The beginning set is formed by an outer pair of fractions with the medient being the third term. The top diagram is an example of the first formula realized. In the bottom half we see he also adds up the diagonals which give us different terms to the classic fibonacci series generated by the classic tree. The method in which he determines what ratio each side converges on is unknown. It is possible he might have figured it out just by hand.Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-54013340694413211872013-05-31T18:23:00.001-07:002013-05-31T18:23:48.836-07:00Stretched Pelog<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-_cj7g7L1IZnUgUg4f9FNPDKq4zwRUbBrWxV2zhndiBiKFIYVs2TiYgZaLJepSerVXMdWCF3QRGkeeKTTkel9yQXAFJtJt2fn4KUt4-75zKEFH11Z8hGMKXi1Ed4t795k3i0N394QbIQ/s1600/stretchedpelog.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-_cj7g7L1IZnUgUg4f9FNPDKq4zwRUbBrWxV2zhndiBiKFIYVs2TiYgZaLJepSerVXMdWCF3QRGkeeKTTkel9yQXAFJtJt2fn4KUt4-75zKEFH11Z8hGMKXi1Ed4t795k3i0N394QbIQ/s640/stretchedpelog.jpg" width="587" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Wilson's stretched Pelog tuning</td><td class="tr-caption" style="text-align: center;"><br /></td></tr>
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Here is a Stretched Pelog Tuning found in one of Wilson's notebooks. While not dated, it occurs between pages dated from late 1993. It seems to go through areas that others later have explored.<br />
<br />Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-78075934925388279252012-11-30T15:40:00.003-08:002014-06-10T05:22:11.488-07:00George Secor's mapping of Partch's Scale<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8pW6wvJHoBBnQ8Y1nOKouBr1wlN-7FMHBqu8dYrwbMoWvpy-hP4Q9o1UOkneEfIP-L2Zs14bmieHllJ_9-g5Tn8Rc_E0WZ_wc_8v5vSbut8CCdtd4MX-cxg5MEogCfdd2HDM5EWIl-CA/s1600/SecorPartchmapping.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8pW6wvJHoBBnQ8Y1nOKouBr1wlN-7FMHBqu8dYrwbMoWvpy-hP4Q9o1UOkneEfIP-L2Zs14bmieHllJ_9-g5Tn8Rc_E0WZ_wc_8v5vSbut8CCdtd4MX-cxg5MEogCfdd2HDM5EWIl-CA/s400/SecorPartchmapping.jpg" height="242" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">George Secor's mapping on Partch's scale drawn by Erv Wilson</td></tr>
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While not added to the Archives directly, The document <b>Mapping Of Partch's Scale on Secor's Keyboard</b> has been added to Secor's section of the Main Library. <a href="http://anaphoria.com/secor.html">http://anaphoria.com/secor.html</a> I provide this page as it includes related documents of which this keyboard drawings by Wilson provide an open door to how Partch's scale could be expanded to 72 or even how this layout provides a uniform fingering of Partch's scale. Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-10856327056098176372012-11-27T17:51:00.002-08:002012-11-27T17:51:56.532-08:00Constant Structures<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikz6rm8pz2XI-rzC34j2nBmXXzkwMqLhakEBfOy93iXWs5hVilke86tXHkiyARSa_BEhVFHqTGeHvVQ3fS3jaGvVhRDBG-NuGdcpIx5p7Z1wLc8yc8lP5H141D141PGsHWQ8pqkEhDFb0/s1600/CONSTANTSTRUCTURE.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="492" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikz6rm8pz2XI-rzC34j2nBmXXzkwMqLhakEBfOy93iXWs5hVilke86tXHkiyARSa_BEhVFHqTGeHvVQ3fS3jaGvVhRDBG-NuGdcpIx5p7Z1wLc8yc8lP5H141D141PGsHWQ8pqkEhDFb0/s640/CONSTANTSTRUCTURE.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Wilson's note on Constant Structures to John Chalmers 1965</td></tr>
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Here is one of Wilson's earliest mention of the subject of Constant Structures. This page is apart of a document looking at 3 22 tones scales. Thanks to John Chalmers for making this available sometime back from his collection that is still being archived. Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-12825783466256955332012-11-18T16:03:00.000-08:002012-11-18T16:09:30.755-08:00Meta-Ptolemy [Some Collected Papers}<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhr1uq4qbheRpHGbFbBut3SpsYdltfBRsf8qJsSIWMvdPzOje74fUHA0On2O7OUfPyluynQyc4c-wuwz2jRi-Ce5Dxjl8VidPPyYrtt1QaQ3YKUHIVwHE-dqNzDGBqIdvwwoZH0WCStCUk/s1600/metaptolemy24chart.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhr1uq4qbheRpHGbFbBut3SpsYdltfBRsf8qJsSIWMvdPzOje74fUHA0On2O7OUfPyluynQyc4c-wuwz2jRi-Ce5Dxjl8VidPPyYrtt1QaQ3YKUHIVwHE-dqNzDGBqIdvwwoZH0WCStCUk/s320/metaptolemy24chart.jpg" width="316" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Chain of 7 tone scales within the 24 tone array in Wilson's Meta-Ptolemy</td></tr>
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Wilson collected his papers on Meta-Ptolemy together. This is what is done here with some added notes<a href="http://anaphoria.com/metaptolemy.pdf"> http://anaphoria.com/metaptolemy.pdf</a> The scale offers an interesting chain of 7 tones scales not unlike those we find on various African Ballophones and offer an exploration into like territory. Composer Stephen Taylor has used this scale here. <a href="http://www.thesonicsky.com/music/microtonal-cartoon-cues/">http://www.thesonicsky.com/music/microtonal-cartoon-cues/</a>Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-21414524928278343912012-09-26T03:18:00.002-07:002015-08-19T19:27:21.609-07:00Two Papers on Partch's Tuning Erv is responsible for showing Partch the possibility of inverting the Diamond of what later became the Quadrangularis Reversum. He also helped Partch construct this Marimba. Erv's drawings is a constant contribution throughout the second edition of Partch's <i>Genesis of a Music</i> . Something one used to his style of drawing becomes easy to pick out. A rare double flute from Bolivia found by Erv's brother was another gift he bestowed upon Harry which he used prominently in <i>Delusion of the Fury</i>.<br />
Here are two documents just a few years later commenting on first Partch's use of 392 that he felt too much was being made of, and provides an explanation here. The second paper shows a comparison of Partch's 43 tone scale to a 41 tone space. Like a similar example also found with Novaro's 7 limit diamond [1927] this lead to reinforce his observations of Moments of Symmetry and Constant Structures as "naturally occurring' tendencies in how people construct scales. The latter he defined as when any interval occurs in a tuning it will always be the same number of steps. He found Partch and Novaro both taking their Diamond structures and intuitively filling the space with as close of a constant structure solution possible. He spoke on more than one occasion how he observed Partch following his ear using many near pitches to simpler ratios rather than sacrifice a musical inspiration or inclination. <br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgp-1olQU9Bxkfi0R1EEYm5uR0bzXNktvj_9CFmYgXjJfMBaQ5oDg4RYlaoYWpdVMWCQHoGI89DwE0QEGUFlkpTARCTwtVNc5BeJxbZc97lmJIeOdlg_T7NLGfNwnu9TYczdO75oMyeSPA/s1600/partch-pitches1.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgp-1olQU9Bxkfi0R1EEYm5uR0bzXNktvj_9CFmYgXjJfMBaQ5oDg4RYlaoYWpdVMWCQHoGI89DwE0QEGUFlkpTARCTwtVNc5BeJxbZc97lmJIeOdlg_T7NLGfNwnu9TYczdO75oMyeSPA/s400/partch-pitches1.jpg" width="325" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Wilson-On Partch's Use of G 392</td><td class="tr-caption" style="text-align: center;"><br /></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgARAxtBPq8bmTYW6rlbPxVCEeG7kCssfdCoBry4aCNczWbqWVPrHjgPTn3fh7lBQXv-_gnctQCLjrCu6KIl-jRmtHKlCsG35GVRnU-pt9487V6roSQkCXKcvB7vYnYyfUBZn28REUcC4E/s1600/partch-pitches2.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="" border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgARAxtBPq8bmTYW6rlbPxVCEeG7kCssfdCoBry4aCNczWbqWVPrHjgPTn3fh7lBQXv-_gnctQCLjrCu6KIl-jRmtHKlCsG35GVRnU-pt9487V6roSQkCXKcvB7vYnYyfUBZn28REUcC4E/s400/partch-pitches2.jpg" title="" width="297" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Wilson's comparison of Partch's scale with 41 ET</td></tr>
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Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0tag:blogger.com,1999:blog-2431523637448878845.post-39793315432496382092012-08-12T02:53:00.002-07:002012-08-12T02:55:03.575-07:00The Harmonic and Subharmonic Ogdoads with 12 Tones<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikD97xGaaInLXjpxdQsbL6BqB5VHY9OKgJ-lPdjTr5AGq46GmzHQ4p-1W9I1opBX4DXYE9bMmrmpkuyQpiC9n2YFtGdOjBLGLoT_xJEG98DgrOMd6anD09qze2qQjlASXmhS-_reyA9Bg/s1600/12toneharmsub.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikD97xGaaInLXjpxdQsbL6BqB5VHY9OKgJ-lPdjTr5AGq46GmzHQ4p-1W9I1opBX4DXYE9bMmrmpkuyQpiC9n2YFtGdOjBLGLoT_xJEG98DgrOMd6anD09qze2qQjlASXmhS-_reyA9Bg/s400/12toneharmsub.jpg" width="281" /></a></div>
This quick note written between other papers dated from 1996 shows the possibility of placing a the 13 limit with the harmonic and subharmonic series within a single 12 tone series. Placed at the distance of the 15 means that both series also have the 15th of their series. The idea of placing these two series apart like this can be seen on page 15 of <a href="http://anaphoria.com/earlylattices12-.pdf">http://anaphoria.com/earlylattices12-.pdf</a><br />
That scale of Gary David illustrates 2 harmonic and 2 subharmonic 9 limit pentads with 12 tones. He was the first to point out the use of the 15 as a mirror point with 12 tone scales which here we can see is applied in a slightly different way.Kraig Gradyhttp://www.blogger.com/profile/04234783065045199904noreply@blogger.com0