SOME COMMENTS ON THE THE FLUTE SCALES, THE DIAPHONIC CYCLES, AND THE HELIXSONG (revised 2/2018)
These three papers illustrate three subtle variations in approaching the combinination of two or more harmonic or subharmonic segments. From there they become the basis of extracting subsets beginning with both pentatonic and tetrachordal scales or any subset of interest. Wilson found them also useful in imitating other scales such as pelog as if it was made of two subharmonic sulings for examble. While Wilson presented these papers, dependent on the instrument design, with either a harmonic or subharmonic context, but he thought of all these scales as invertable.
The flute scales represent a single subharmonic scales most often with an exit hole tuned to a 3/2 or 4/3 from one of its subharmonics. This is a practice he noticed in his collection of flutes from South America.The possibility of combined flutes are shown to play some subharmonic versions of the Helixsong scales. It was one of these flutes he gave to Harry Partch which he used in "Delusion of the Fury."
The Diaphonic cycles comprises two subharmonic series originally conceived to be tuned upon at least a two stringed instrument with parallel bridges equally spaced apart. The simplest possibilities are on page 2 [which have been rotated on page 5 to read easier]. On page 12 of the diaphonic set Wilson shows the series including the underlying subharmonic series whose factors at the meeting points represent the 'fundamental' of the two series or divisable by 2 or 3. In the second example on that page, the point where 12 and 18 meet the underlying series is 6 and where 8 and 12 interset it is 4.
John Chalmers’ The Division of the Tetrachord devotes a section to these scales [page159] http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/chapter8.pdf
The Helixsong is a simple instrument designed orginally for metal tubes combining two harmonic series. Each series starts and stops on different shared tones found in its middle row. The first instrument provides alternative ways to use different sections of each series together to form both pentatonic and tetrachordal scales. These represent another pattern, that of combined diaphonic series in their harmonic form.
The 11 limit Helixsong has embedded within it a 5 and 7 tone diaphonic scale, while the 17 limit has a 7 and 10 tone scale, and the the next example has 12 and 17 tone scales. Todd Manley helped Wilson to construct the first 11 limit Helixsong out of 2” aluminum tubing for which he, Lydia Ayers, and David Rosenthal wrote compositions. The Helixsong offers a gateway into many tetrachoral scales. It also contains the harmonic inversions of many of the diaphonic cycles (see Diaphonic Cycles paper).
The overlaps and interaction of these threee are interesting and musically useful. Each Helixsong contains at least two diaphonic cycles but oriented harmonically instead of subharmonically. The 11 limit contains the first two we find on page 1 of the diaphonic cycles with the second 17-limit one encompasses the third. The series has not been taken any further that i know of and worthy of investigation. In one paper elsewhere Wilson takes the simplest diaphonic and by going through the common tone modulations constructs a diamond with it to show how just one possible popint of departure the music maker can make.
~Comments and Questions Welcome~