The Harmonic Shift Oscillator (HSO) by New Systems Instruments is a Eurorack module that allows for the generation of both harmonic and inharmonic spectra. Unlike traditional oscillators, the HSO synthesizes sound using abstract parameters, giving users deep control over the spectral content of their audio output.
Understanding the Harmonic Shift Oscillator
At its core, the HSO generates sound through a combination of angular frequency (ω), harmonic level (L), and harmonic stride (S). These parameters control the characteristics of the output waveforms, which can be either harmonic or inharmonic depending on how they are configured.
Harmonic spectra
When the spectrum contains only integer multiples of a fundamental frequency, it is considered harmonic. This creates sounds that are familiar and musical.
Inharmonic spectra
When these multiples are not integers, the spectrum becomes inharmonic, resulting in more abstract and complex sounds. The HSO excels at creating both types of spectra, making it a versatile tool for sound design.
Interface and controls
The HSO features an intuitive interface designed for both precision and experimentation:
- Coarse frequency (ω)
This knob adjusts the primary frequency, ranging from 7Hz to 50kHz, setting the foundation for the generated waveform. - Fine frequency
Allows for slight adjustments around the frequency set by the Coarse knob, enabling precise tuning within a smaller range. - Harmonic level (L)
Controls the brightness of the sound by adjusting the amplitude of the harmonics. A higher L value results in a brighter sound with more high-frequency content. - Harmonic stride (S)
Determines the spacing between each harmonic. When S is an integer, the spectrum is harmonic; otherwise, it becomes inharmonic. - Frequency modulation (FM) input and attenuator
The FM input modulates the fundamental frequency, while the attenuator controls the intensity of this modulation, allowing for dynamic frequency shifts. - Harmonic stride modulation (HS) input and attenuator
Modulates the harmonic spacing (S), creating complex, evolving spectra when combined with other controls. - Harmonic level modulation (HL) input and attenuator
Modulates the brightness (L) of the spectrum, adding dynamism and texture to the sound. - V/Octave input
Standard V/Oct input for controlling the fundamental frequency in a predictable, musical manner. - Outputs
The HSO provides two outputs: the cosine (real) component () and the sine (imaginary) component (_), each offering unique phase characteristics.
Using the Harmonic Shift Oscillator
The HSO is a powerful tool with a wide range of possibilities. Here's a guide to help you start exploring:
Harmonic sounds
To generate harmonic spectra, set the Harmonic Stride (S) to an integer. For instance, setting S to 1 with the STRIDE knob in the vertical position creates a rich, “normal” waveform. As you increase S to 2 or 4, the sound becomes progressively more hollow or sparse.
Inharmonic sounds
Position the STRIDE knob between harmonic values to explore inharmonic spectra. Modulating S while adjusting the fundamental frequency (ω) can yield complex, evolving soundscapes.
Modulation tips
The HSO’s parameters can all be modulated to create dynamic and percussive tones. Modulating the Harmonic Stride (S) can produce unique rhythmic effects, while modulating the Harmonic Level (L) can dramatically alter the texture of the sound.
Harmonic and inharmonic spectra deep dive
All sounds can be understood as the sum of simpler waveforms, typically sine waves. The relationship between these waveforms’ frequencies and amplitudes forms the sound's spectrum. When frequencies are integer multiples of a fundamental, the spectrum is harmonic, producing familiar musical tones. In contrast, non-integer multiples result in inharmonic spectra, leading to more complex, less predictable sounds.
Constructive and destructive interference
When two waves interact, they create interference patterns, either amplifying (constructive) or reducing (destructive) each other. This interaction can produce beat frequencies, where the perceived frequency is the difference between the interacting frequencies. This concept is central to the HSO’s ability to generate complex inharmonic sounds.
Phase and outputs
The HSO’s two outputs are phase-shifted by 90°, offering unique possibilities for spatialization and stereo effects. The different phases result in distinct saturation characteristics and can produce out-of-phase beat frequencies, enriching the sound's texture.
Natural spectra and tuning
While the HSO is not designed to mimic natural sounds, its ability to generate slightly inharmonic spectra aligns with natural acoustic phenomena. For example, instruments like strings and drums often produce spectra that are not perfectly harmonic, contributing to their “liveliness.” The HSO can emulate this effect, making it sound more organic and dynamic.
Two-dimensional resonators
The HSO can approximate the vibratory modes of two-dimensional resonators, like drumheads, by carefully tuning the Harmonic Stride (S) and Level (L). This allows for the creation of complex, natural-sounding spectra that evolve over time.
Integration with subtractive synthesis
While the HSO can generate complex waveforms on its own, it is also designed to complement traditional subtractive synthesis techniques. By generating specific harmonic content directly, the HSO can simplify or enhance the subtractive process, offering new possibilities for sound design.
Creating classic waveforms
The HSO can approximate classic analog waveforms like sawtooth and square waves by setting the Harmonic Stride (S) to 1 or 2. However, the HSO’s unique harmonic structure gives these waveforms a distinct character, making them both familiar and new.
Combining with filters
The HSO’s outputs can be further shaped using filters and other subtractive techniques, blending the best of both worlds to create rich, complex sounds.
Harmonic Shift Oscillator
(HSO) produces harmonic and inharmonic spectra through all-analog electronics. It provides similar capabilities to FM synthesis, but with a more direct relationship between the parameters and the resulting spectrum.
The official page with links to the manual and a video overview can be found at New Systems Instruments - Harmonic Shift Oscillator.
