Moog Subharmonicon | An Introduction to Polyrhythm & Subharmonics

Understanding Subharmonics

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.  

Fortunately, electronic circuits can create subharmonics quite easily. Regardless of whether the initial frequency (ƒ) is being multiplied by an integer to create an overtone, or divided by an integer to create a subharmonic undertone, the ratios and intervals will remain the same, as in the following examples: 

Understanding Polyrhythms

Polyrhythms employ multiple rhythms playing at once to create complex, interweaving phrases. In the same way that a subharmonic oscillator uses an integer value to modify the initial pitch (ƒ) of an oscillator to create a musically related subharmonic, each Subharmonicon rhythm generator uses an integer value to divide the current clock value (t) to create a new rhythm. These individual rhythm generators are used to drive one or both of the Subharmonicon’s sequencers. Once you engage more than one rhythm generator, you will hear how the different clock divisions can play off or against one another to synthesize a polyrhythm. Because each rhythm generator references the same clock, they will eventually re-sync to the same downbeat, causing the overarching polyrhythm to finally repeat. In this way, you can think of the rhythm generators as combining to create one larger, cyclic pattern. Rhythm generators can be switched on and off and assigned to different sequencers as you perform, creating complex polyrhythmic content – as well as some truly unique phrasing and grooves.