Prime Frequencies
Within all things audible, sine waves are arguably the simplest, yet most fundamental elements. They are comprised of one single frequency and cannot be stripped back any further. On the other hand, as stated in the Fourier theorem, virtually all complex sounds can be broken down to, and expressed as a series of simple sine waves.
Thinking about such fascinating qualities of sine waves directed me to a somewhat similar phenomenon elsewhere: prime numbers. A prime number cannot be divided by any other number (other than 1 and itself). At the same time, any other number can be expressed as a product of a series of prime numbers. Defined based on this seemingly simple premise, prime numbers have been pivotal to many significant mathematical conjectures and theorems for many centuries. Therefore, at their core, just like sine waves, prime numbers are the simplest, yet the most elegant and the most foundational entities within their respective systems.
"Prime Frequencies" explores sonic qualities of different prime number categories through sinusoidal sound waves. The series is structured into 47 pieces that are created using a number of algorithmic and aleatoric compositional techniques developed in the programming language ChucK. Each piece presents the sonification of a specific prime number category and is constructed through the compositional ruleset below:
Rule 1: Each composition derives its material from a specific prime number category.
Rule 2: Prime numbers that are within the conventional audible range (i.e., between 20 and 20000) are used to set the frequency content of each composition. This is done by assigning the numeric value of each prime number to the frequency of a sine wave.
Rule 3: All numeric values used to set temporal aspects of the program of are also chosen from the set of the same prime number category. Where applicable, prime numbers smaller than 20 or great 20000 are also used here.
Rule 4: The time units used in each program may vary between samples, milliseconds, seconds, or minutes. The time unit scale for each composition was chosen on a case-by-case basis, and through experimentation.
Rule 5: All sine oscillators used in a given composition have equal amplitude value in the original code.
Rule 6: The quantity and quality of the prime numbers in a category has determined the style of composition from the following modes:
Mode A (Singular): Prime number category has only one member between 20 and 2000.
Mode B (Stochastic): Prime number category has a few members between 20 and 2000.
Mode C (Additive): Prime number category has a couple of dozens of members between 20 and 2000.
Mode D (Iterative): Prime number category may have a dozen to a hundred members between 20 and 2000.
Mode E (Noise): Prime number category has hundreds of members between 20 and 2000.
Mode F (Emblematic): Number of members between 20 and 2000 may vary, depending on the category.
The code version of the project includes the entire source code developed for the project without any further audio processing and modification. Using a set of basic instructions, the code can be downloaded and compiled using any operating system’s command-line. When compiled, the series can be experienced in an interactive manner, where the listener/user can use keyboard shortcuts to navigate between different pieces or to get information about the specific prime number category that each composition is based on. The code version involves a visual accompaniment consisting of the numeric values of the prime numbers that display the frequencies of active sine waves throughout.
Due to the real-time nature of code execution in this version, pieces that involve aleatoric parameters and generative processes will be generated and experienced partially differently each time they are played. Considering the lack of further audio processing, sonification of prime frequencies in the code version is experienced in its most raw and direct manner. Therefore, in this version, the perceptual capacities of the listener’s auditory system and the audio playback system they use add an important final touch to the final reception of the work.
The album version comprises of a one-off rendering of the code that has gone through some basic audio processing and is intended for more conventional modes of distribution and listening. As the perceived sound pressure level of incoming sound waves changes drastically according to their frequency, this version is meant to provide a more standard listening experience. Considering that the series involves sine waves across the entire audible frequency range, including extremely low and high frequencies, an equalisation that approximates an equal-loudness-level contour was applied to all tracks. Given the varying degrees of frequency content and voice number across different compositions, slight dynamic adjustments were also made to provide a more consistent listening experience throughout the album.
Commissionned by Laboratoire formes•ondes as part of the research-creation project « Towards an Aesthetic of the Sine Wave ». Thanks to Nicolas Bernier for inviting me to produce this work.