[This is an ASCII version of a portion of a post to
the Tuning list regarding the piece _Prelude in Shur
for Erv Wilson_, with thanks to Chris Vaisvil, whose
questions led to the diagrams which follow.]

     C#*  472.3 ---- +230.9 ----   E   703.1
   (704.3)                      (703.1)
     Bb*  138.2 ---- -138.2 ----   A    0.0
   (370.3)                       (0.0)
     F#*  968.0 ---- +232.0 ----   A    0.0

This is a diagram of the final cadence in the piece,
with pitches with respect to the 1/1, here A, shown
following each note name; harmonic or vertical intervals
above the lowest note of a sonority by numbers in
parentheses; and ascending or descending melodic
intervals by positive or negative numbers.

[On the generators of the 24-note O3 temperament]

Apart from the 2/1 octave, the generators are chains of fifths at
703.125 or 704.297 cents (600 or 601 steps of 1024-EDO), plus an
interval of 57.422 cents (49 steps of 1024-EDO) defining the space
between two 12-note chains.

The two chains are identically arranged as follows, with A on the
lower chain as the 1/1 for this piece, and thus for the diagram.
While only 10 notes are actually used for the piece, this is the
bigger picture, with pitch locations in cents with respect to the 1/1
shown below each note name on a chain, and fifth sizes in the spaces
above and between the note names along a given chain.

   704.3   703.1 704.3 703.1  704.3 704.3 703.1 704.3 703.1  704.3  704.3
 Eb*-----Bb*----F*----C*-----G*----D*----A*----E*----B*----F#*----C#*----G#    
634.0  138.2  841.4 345.7 1048.8 553.1  57.4 760.5 264.8 968.0   472.2 1176.6  
                                                                          
   704.3   703.1 704.3 703.1  704.3 704.3 703.1 704.3 703.1  704.3  704.3   
 Eb------Bb-----F-----C------G-----D-----A-----E-----B-----F#-----C#-----G#    
576.5   80.9  784.0 288.3  991.4 495.7  0.0  703.1 207.4  910.5 414.8  1119.1

While these values should be accurate enough to give a good idea of
the O3 system, here are Scala files for the complete O3 temperament;
the ten-note set used for _Prelude in Shur for Erv Wilson_; and the
"Zalzalian 12" set which includes these ten notes in the rotation
making Scala step 7 (704.297 cents) the 1/1.

<http://www.bestII.com/~mschulter/O3-24.scl>
<http://www.bestII.com/~mschulter/prelude_in_shur.scl>
<http://www.bestii.com/~mschulter/O3-zalzalian12_D.scl>

Margo Schulter
mschulter@calweb.com