User Manual

10
In the world of synthesizers and electronic
keyboards, we often refer to harmonics
– a series of overtones occurring at
fixed mathematical intervals above the
fundamental pitch that are responsible
for a wave’s shape and timbre. A wave
shape may contain certain harmonics in
a particular pattern of relative strength,
for example. We know that pitch can be
modified by changing the length of an
organ pipe, a guitar string, the column
of air in a trumpet, etc. The remarkable
thing is that the ratio between the original pitch and the altered pitch always follows the same pattern
– the harmonic series. So if we have a guitar string vibrating at a frequency (ƒ) of 440 Hz, and we halve
its length by playing at the 12th fret, the string sounds one octave higher (ƒ*2) at 880 Hz, or double
the original frequency. One-third the length produces the fifth above that (ƒ*3), etc. In every case,
multiplying the original frequency by an integer creates a specific harmonic.
Creating an undertone, or a subharmonic, is more challenging in the physical world. Instead of
multiplying the original frequency by an integer value, we must divide by an integer value. We cannot
simply build a guitar that becomes twice as large in order to play the first subharmonic, one octave
down in pitch at 220 Hz (ƒ/2) from the original pitch (ƒ) of 440 Hz.
Throughout the 1960s and 70s, groundbreaking artists like Herb Deutsch, Wendy Carlos, and Keith
Emerson were looking for new ways to explore electronic sound, and found themselves collaborating
with electronic instrument pioneer Bob Moog to create the instruments of their dreams. If we set our
clocks back to the 1930s, we find a similar situation. Cutting-edge musicians and composers such
as Henry Cowell, Joseph Schillinger, Paul Hindemith, and Oskar Sala were teaming up with the likes
of Leon Theremin (of Theremin fame) and Freidrich Trautwein to create the instruments needed to
bring their musical visions to life. These were heady times for composers, performers, and instrument
creators. Electricity and electrical circuitry held the promise of a mechanical prowess that could
enhance and extend existing compositional and performance abilities.
Freidrich Trautwein’s Trautonium was a vacuum tube electronic instrument that created a rich sawtooth
wave, tamed by a resonant low-pass filter, to create an early model of subtractive synthesis. Oskar Sala
eventually took over development of the Trautonium (later renamed the Mixtur-Trautonium), adding a
series of subharmonic oscillators that generated undertones pitched at fractions of the original pitch
(and not the overtones created at multiples of the original pitch, such as in Laurens Hammond’s tone-
wheel organ). Around the same time, Henry Cowell and Joseph Schillinger collaborated with Leon
Theremin on the Rhythmicon, an instrument capable of sounding up to 16 polyrhythm generators
simultaneously. Schillinger’s theories included combining rhythmic “generators” occurring at integer-
related durations.
Their work contained the seeds of today’s algorithmic composition software. The subharmonic
oscillators of the Mixtur-Trautonium were derived from the oscillator’s initial pitch, while the
Rhythmicon created polyrhythms that were derived from the original tempo. It is these concepts
of subharmonics and polyrhythms that form the historic roots of your Moog Subharmonicon, an
inspiring and innovative semi-modular analog polyrhythmic synthesizer.
INTRODUCTION
A BRIEF HISTORY
UNDERSTANDING SUBHARMONICS