composer
WINGATE: THE IRRATIONALS TRILOGY
Symphony No. 3
String Quartet No. 2
Piano Sonata No. 1
NOTES ON THE TRILOGY:
Wingate’s Irrationals Trilogy comprises three of his works that were composed using irrational numbers to generate the notes used in the pieces. The irrational numbers pi, phi, and Euler’s number were transformed by Wingate into music by taking their digits and using them as a series of pitch class integers, such that 0=C, 1=C#, 2=D, etc. This resulted in the Symphony No. 3 (2020), the String Quartet No. 2 (2022), and the Piano Sonata No. 1 (2023) respectively. The manifestation of this numeral-to-note process can be seen in the example below from the opening of the String Quartet No. 2, with the digits of the irrational number phi denoted in the score sample.
The number Phi (φ), as delineated in the contrapuntal opening of the String Quartet No. 2.
With this procedure effectively having taken out of the creative equation the usual compositional choice of which note comes next, the creation of these works became a refreshing study in arranging notes whose order was already given (i.e.unchangeable). And instead of this being an weighty creative burden, the composer found it to be a liberation into hitherto-unknown artistic freedoms.
These three pieces, while variously clothed in the raiments of rather disparate instrumentations, nevertheless ended up sharing many sonic qualities. Firstly, none of them has a single instance of the notes B-flat or B-natural, since the twelve tones of the musical scale can only be represented up to A natural by the ten digits from the realm of number: 0 through 9. Secondly, they share a complete lack of chords with more than one pitch sounded in any attack, and any perceived chordal sonorities must be built inside the ear as temporal agglomerations. This often results in many moments of the open sonorities characteristic of the octave and the monad. And thirdly, since these pieces are all built from very long series of, as it were, random sequences of notes, they seem to tentatively ask a fundamental question about the nature of art music, namely: how much does the order of pitch in music actually matter?
Mathematics and music have had a long, somewhat tumultuous, but very rich relationship, perhaps all the way from the time of Pythagoras in the 6th century B.C.E. with his proportions of vibrating strings, to its arguable apex in the twelve-tone system of Schönberg in the early 20th century. The mathematician and classical music lover Eli Maor in his 2020 book Music by the Numbers, illuminates this often surprisingly two-way relationship in its vicissitudes over the centuries. The pieces forming Wingate’s Irrationals Trilogy seek to continue the dialog between these bedfellows of the quadrivium in productive and meaningful ways. And they also contain surprising moments of emotive beauty which serve to defy our prejudices concerning the imagined calculatory coldness of mathematics and logic.