Imaginary Harmony

by Dave Seidel



Imaginary Harmony takes as its raw material a 25-note-per-octave "scale" built by octave-reducing the set of harmonics used by La Monte Young in his 1990 sine wave installation "The Prime Time Twins in The Ranges 576 to 448; 288 to 224; 144 to 112; 72 to 56; 36 to 28; with The Range Limits 576, 448, 288, 224, 144, 56 and 28".

The scale is divided into three segments. Each segment is expressed by a sine-wave that plays a randomly-selected sequence from its segment; each voice proceeds at its own independent pace. Simultaneously with each voice we hear a chord that is mathematically derived from the relationship between the sounding pitch and the scale base frequency of 240 Hz. Underlying all of this is a slowly-pulsing, nearly subliminal 60 Hz binaural pedal tone, where each of three binaural pairs is based on the ratio between a set of high-numbered twin primes.

Part 1 uses harmonies based on multiplication, division, and the Pythagorean means (arithmetic, geometric, and harmonic). Part 2 uses harmonies based on difference and summation tones.

The piece is generative; that is, the specific tone choices from which the chords are generated are selected by a randomized process such that every real-time performance of the piece is unique. Each track is a different rendering and thus they have different tone sequences.

Sine waves are the only sound source. The original sound files were generated by Csound. They were then post-processed (also by Csound) for convolution reverb using an impulse response made at Hamilton Mausoleum in Hamilton, Scotland. Finally, the tracks were normalized in Audacity.


released July 5, 2015

Made by Dave Seidel using Csound and Audacity.

Impulse recording from York University's Open Acoustic Impulse Response (Open AIR) Library project, used under a Creative Commons Attribution Share-Alike 3.0 license. For more information, see

Image by Andreas Cellarius (17th century) [CC BY-SA 3.0 (], via Wikimedia Commons.




Dave Seidel New Hampshire

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