On the Diaphonic Cycles.

On the diaphonic cycles. relavant papers: https://anaphoria.com/diaphonicset.pdf and https://anaphoria.com/diaphonic2.pdf Upon reflection and looking deeper into also a few points others have pointed out, i thought i would add a few comments. It should be noted that indeed Wilson was not completely satisfied with them compared to other material he ended up pursuiting. There is enough to piece together how he saw them though as there are still useful material here. Often he would use them instead of ETs especially in the context of a fretted instrument where what is equal is the fret distances with strings tuned to alternating 3/2 and 4/3 ( for a start). He had commented to me that it enabled one to form tetrachordal scales (which he saw as a different scale building method than MOS for instance). While with the smaller diaphonic cycles, they easily fall into making good scales often even being Constant Structures, Paul Johnson pointed out that this was not always the case. With larger Diaphonic Cycles we can see that Wilson used these less as scales and more as sets in which to extract smaller scales in the same way it is common for people to so with just the harmonic or subharmonic series on its own. Also relating to how as a substitute for an ET where the process of exstracting smaller sets is also quite common. Wilson thought that dual series offered more in terms of many structures such as a diamond where the gaps are often more filled and the same material is capable of being transposed to at least one other position. Even with his CPS structures we find two 1-3-7-9-11-15 eikosanies in his Dallesandro tuning.

Comma ZigZag Patterns

A 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

An unusual 22 tone 7- limit tuning

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.

IN MEMORY: I REMEMBER ERV WILSON

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.

A 22 TONE 11 LIMIT CONSTANT STRUCTURE FORMED FROM A SPECIAL HEXANY STELLATION METHOD

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. 

SOME 5 LIMIT PENTATONICS (1982)

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.

MAKING A DIAMOND SEEDED FROM A SCALE TREE LAYER

In this document novavotreediamond.pdf 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.

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 

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 borrowed from another document. This section of the tree was the focus of Novaro who also played with some triangles that do not repeat at the octave mention in this blog in the past. 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.

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.