WINGATE: SYMPHONY NO. 3 
“Pi” (“π”)

Movements:
I. Sacred Geometries (Digits 1-1000)
II. Dialogue of the Radii (Digits 1001-1250)
III. Scherzo of the Irrationals (Digits 1251-2000)
IV. Spheromachy (Digits 2001-3000)

Date:
Score dated 5th September, 2020

Instrumentation:
3 Fl, 2 Ob (2=English Horn), 3 Cl (1=Clarinet in E-flat, 3=Bass Clarinet in B-flat), 2 Bsn (2=Contrabassoon), 4 Hrn, 3 Trpt (1=Piccolo Trumpet in B-flat), 3 Trbn (1=Tenor Trombone, 2=Bass Trombone, 3=Contrabass Trombone), 1 Tba, 1 Timp, 3 perc (Bass Drum, Crotales, Tub. Bells, Vibraphone), 1 Cel, 1 Harp, and Strings

Duration:
23'

Notes:
What does the number ‘Pi’ sound like? One possible answer is Wingate’s Third Symphony. Composed using the first 3000 digits of Pi as ‘notes’ (i.e. 0 is C, 1 is C#, 2 is D, 3 is E-flat, etc.), the whole symphony is essentially an ordered series of these 3000 numerically-derived pitch events, divided into four movements. So, for example, the opening of the first movement, following Pi’s first three digits (3.14), is E-flat, C-sharp, E-natural, with a bass drum representing the decimal point (and this, incidentally, is the only note of indefinite pitch in the entire piece). This ‘3-1-4’ motive (with some variation) is conspicuously taken by the horns every time it happens to occur in the numerical proceedings of the symphony.
 
To keep the digits of Pi flowing as a succession of notes, the symphony has no ‘chords’ in which different pitches start together, which means any choral structures must be built via conglomeration. The composer’s set of rules for the creation of the piece allowed any pitch to be played by any instrument or combination of instruments, in any octave or octaves, and allowed any pitch to be prolonged as long as desired, or not prolonged at all. This in turn enabled melodies to be ‘picked out’ of the series while it progressed in other instrument lines, and permitted collisions between subsequent tones to form interesting simultaneities. The doublings sometimes partially or totally drop away, causing a sense of musical motion via the subtraction of tones from the texture. 
 
One notable side effect of using the ten digits (0 to 9) to create pitches for the piece is that there are actually twelve pitches in the Western chromatic scale, so two must here be left out. This means that there is not a single B-flat (pitch 10) or B-natural (pitch 11) in the entire piece. 
 
Partially inspired by the terrifying freedom of the first words of Persichetti's Twentieth Century Harmony textbook*: “Any tone can succeed any other tone . . .” Wingate's Third Symphony initially came about from a thought experiment: What if the selection of pitch for an entire piece were left, as it were, to chance, or to a pre-determined order, but arranged in such a way as to seem ‘intentional’? Unlike the aleatorically-composed music of John Cage (like his famous 1951 work Music of Changes), which seems to defy and even mock our expectations of musical meaning, the Pi Symphony attempts to weave musical meaning and a sense of inevitability from its mathematically-determined materials. The result is a symphony that lives in traditional forms (like multiple movements of contrasting tempo and mood), but never quite feels at home in them, instead abiding in a uneasy restlessness all the way to its final (three-thousandth) note.

* Persichetti, V. (1961). Twentieth Century Harmony: Creative Aspects and Practice. New York:  W. W. Norton & Company.