'Heterodyne Horizon'

by Dolores Catherino

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This polychromatic composition is an exploration and demonstration of the musical use of interactive harmonics. It is an example of the gestalt principle in the sense that the whole (output harmonics) is greater than the sum of the parts (input notes and harmonics). Aural resolution: 106 pitches per octave.

Heterodyne - an existing concept that is a closest description (not explanation) of this musical phenomena of 'extra' harmonics created in the interaction of two or more notes.

Horizon - in the sense of always evolving boundaries of awareness, exploration and understanding.

Music theory describes harmonics 'vertically', in relation to a fundamental pitch. This composition demonstrates that 'horizontal' cross-interaction occurs, creating new harmonics and unique musical textures.

Note in the middle of the composition, I am playing only 2 notes, one static and the other moving melodically. The thing to notice is that a (higher pitched) harmonic is following the melody line NOT in the same direction (high/low), as traditional harmonics do (because they are a subcomponent of the pitch), but in the OPPOSITE direction.

Next, notice a second (lower pitched) interactive harmonic, which moves in the same direction as the melody (just as traditional 'primary' harmonics do). Try also, to hear additional subtle harmonics and a further harmonic blending as the melody becomes polyphonic.

An intriguing question would be whether these interactive harmonics are measurable with an audio spectrum analyzer. More deeply, are these interactive harmonics created in a quantifiable dimension or are they a purely perceptual phenomenon; Qualia; technologically immeasurable?

Video performance available on YouTube. Polychromatic score and audio files are available for download on my website.

more information: dolorescatherino.com

- Contextual information on known phenomena:

HETERODYNE FREQUENCIES (electronics, communications engineering) and COMBINATION TONES (acoustics, psychophysics) are comprised of sum and difference tones.

SUM TONES (f1+ f2) can create a frequency octave(s) above/greater than the lower frequency (f1):
220 Hz (A3) + 293.66 Hz (D3) = 513.66 Hz (C4)

DIFFERENCE TONES (f2- f1) can create a frequency octave(s) below/less than the lower frequency (f1):
293.66 Hz (D3) - 220 Hz (A3) = 73.66 Hz (D1)

INTERACTIVE HARMONICS (music), as demonstrated here, can create other frequency intervals which are neither sum nor difference tones.


released December 23, 2014




Dolores Catherino Alaska

Dolores Catherino is a microtonal composer and multi-instrumentalist exploring the frontiers of the electronic avant- garde.

Her TEDx talk on Music of the Future:

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