An investigation into the compositional properties of prime numbers from Vermont-based electronic musician Greg Davis, New Primes employs custom-written software to translate prime number sequences into a mesmerizing universe of sound. Davis pares his sound materials down to their most basic — a network of pure sine tones — to create a collection of pieces ranging from the almost-tonal to the harmonically alien.

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In summer 2016, greyfade founder Joseph Branciforte found himself at a small record shop in Vermont, stocking up on music for a 6-hour drive back to New York. Among the records he chanced upon that day was a compilation of works composed using just intonation — a system of musical tuning in whole number ratios — which contained a track by electronic musician Greg Davis.

“I kept returning to a particular piece for sine tones, replaying it endlessly, without knowing who or what it was,” says Branciforte. “The harmony was like nothing I had ever heard before.”

That piece was Davis’ Star Primes (For James Tenney), Davis’ first foray into composing using just intonation. ”I began exploring using prime number sets compositionally around 2008,” says Davis. “I was invited by Important Records to contribute a piece for The Harmonic Series compilation and landed on using prime number sets as a way to develop just intonation tuning relationships and intervals. It felt like a unique position for me.”

To realize the piece, Davis developed a custom software system in the Max/MSP environment, using a network of pure sine tones. The software allows various prime number sets to be imported and used to control aspects of the musical composition, from its harmonic relationships and rhythm to its form and spatialization. This same system has been in development since 2008, appearing on Davis’ 2009 recording Primes (Autumn Records) and in its most recent incarnation on New Primes.

”I start by choosing a fundamental frequency for each piece and multiplying that frequency by each of the prime numbers in a given sequence to determine the overtones above the base frequency,” Davis explains. “Most of the overtones are transposed down several octaves to fit within a comfortable 3- or 4-octave audible frequency range. This becomes the ‘scale’ or harmonic space for each piece. The panning, fades, metronome speed and other variables of each overtone are related to its frequency. Rhythmically, each sine tone follows its own beat cycle by stepping through multiple octaves and silent pauses, which create overlapping prime number rhythmic patterns. The lower overtones generally have faster rhythmic cycles and the higher overtones are slower. All of this acts as a way of relating the rhythmic aspects of the piece to the prime number sequences and integrating it with the harmony, while still retaining a musical texture that sounds interesting to me.”

Branciforte and Davis eventually began a correspondence, discussing the musical and software programming details of the project. “Speaking with Greg was a decisive moment in the development of greyfade,” says Branciforte, who, at the time, was toying with the idea of starting a record label focused on generative and process-based music. “This was a blueprint for exactly the kind of music I had imagined releasing. There was so much conceptual integrity to it, but it was still addictively listenable.”

Davis and Branciforte’s conversations led to the first performance of the material in over a decade. “Joseph invited me to rework the Primes project for an 8-channel performance at the Fridman Gallery in New York in 2019,” says Davis. “I kept the basic structure of the original Primes software but worked quite a bit on its rhythmic functions, creating the ability to shorten or elongate the time scales of the various tones, as well as developing a method of crossfading between their octave displacements. Finally, I selected a group of new prime number sets to use as material.”

New Primes documents this latest evolution of Davis’ system, distilling his expansive 2019 multichannel performance into a stereo version designed for home listening. Recorded over two days in October 2020 and mixed live to 2-track by Davis, the music on New Primes ranges from the almost-tonal to the harmonically alien. The titles of the pieces simply refer to the name of the prime number set used.

“The pieces you hear on the finished record are snapshots of an endless generative music that could last for hours, days, or even longer,” says Davis.

Although the music on New Primes suggests mathematical relationships with an otherworldly scope and scale, the material was carefully edited and sequenced with an ear towards its album presentation, capturing both the variety and depth of Davis’ system in LP form.