Saw Soloist: Dale Stuckenbruck
Divination by Mirrors is a roughly ten-minute work
featuring the bowed saw, accompanied by a string orchestra
that is divided into two groups of players tuned 1/4 step
apart and occupying opposite sides of the stage. The piece
has eight Sections, each named for a different kind of
divination --foretelling the future by means of the occult.
The unifying compositional idea is an exploration of the
myriad possibilities of musical symmetry. These include
pitch and time mirrors of various sorts, counter-balancing
journeys into the two different pitch "universes" of the
oppositely-tuned halves of the orchestra, and extensive use
of the architectural concept of "dynamic symmetry" in
defining durations of Sections, sub-sections, and tempi.
Section 1: Pyromancy (Divination By Sacrificial Fire) 50bpm; 55 beats plus pause; 67 sec (1m 7s) [for clarity it may be 100bpm/110 beats].
As noted above, much of the material of Divination by Mirrors is generated by the four super-imposed triads—and their 1/4 step sharper counterparts—heard in the opening moments of the piece. From the bottom, the triads are C major, G# minor, D minor, and Gb major. The rhythmic patterns in this Section are Fibonacci number groupings (8,5,3,2,1) which correspond with a gradual change of pitch range from extremities to the middle of the keyboard, ending with a single note. The saw is tacet.
Section 2: Aeromancy (Divination By Appearances in the Air) 80bpm; 144 beats (plus 2 pickup beats); 108sec (1m 48s) The saw introduces the main theme, consisting of a row divided into two descending augmented scales. The first scale (C,B,G#,G,E,D#) is presented in pairs of ascending major sevenths, the second scale (Db,Bb,A,Gb,F,D) in pairs of ascending major sixths. At any given time, the accompaniment derives from which ever half-row is being played by the melody. The second, 1/4 step higher-pitched group begins playing on the "bridge" of the melody, which occurs 89 beats into the piece —a Fibonacci number and a golden mean division of 144, which is the total number of beats in the section.
Section 3: Psychomancy (Divination By Ghosts)
130bpm; 144 beats; 67 sec (1m 7s)
This is a quartertone mirror with notes in Fibonacci-length groups (5,8,13,21). The saw plays a much slower version of the mirror beginning with no vibrato and employing a multi- phonic gliss at a key moment. This Section is divided into golden mean sections, with each of them subdivided by traditional (equal) symmetry.
Section 4: Oneiromancy (Divination By Dreams
80bpm; 144 beats; 108 sec (1m 48s)
A second theme is introduced with a cello solo. A diatonic mirror based on C major, it consists of a series of 7-6
suspensions —a nod toward the main theme's use of 7ths and
6ths. It modulates up a quartertone at the golden mean
division of the Section (89 beats).
Section 5: Sciomancy (Divination By Shadows)
130bpm; 144 beats; 67 sec (1m 7s)
Pizzicato! Back to the augmented scales, the saw plays a variation on the main theme. Symmetrical division of time.
Section 6: Meteoromancy (Divination By Winds)
160bpm; 110 beats; 41 sec
Hocketed mirrors between high and low strings with upper playing C Phrygian and lower C Ionian modes. Phrases are Fibonacci groups of sixteenth notes beginning with 1 and 2 (1,2,3,5,8,13,21)followed, after the first note, by rests one Fibonacci member lower in duration (1,1,2,3,5,8,13). Later, the quartertone higher group fills in the rests with a quasi-canon. Saw plays melody based on opening triads.
Section 7: Catoptromancy (Divination By Mirrors) Cadenza—it should ideally take 1m 7sec. Variations on the two themes and the quartertone mirror.
Section 8: Tephramancy (Divination By Writings in Ashes) 50bpm; 34 beats; 40 sec [for clarity it may be 100bpm/68 beats] The first Section in retrograde and compressed by a ratio of 1/1.618, with added saw playing the opening motif in retrograde.