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• # Harmonic Shift Oscillator

\$355The 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. You can separately control the tuning, the level of the harmonics, and the harmonic stride—the spacing between consecutive harmonics. When the harmonic stride is integer valued, you can get tones that sound similar to the traditional sine, triangle, square, and sawtooth, although the waveform will be different. If harmonic stride is non-integer valued, you'll get a complex inharmonic waveform.

The Harmonic Shift Oscillator has CV control over all parameters, with carefully chosen ranges. It responds well to self-modulation. With frequency, harmonic stride, and harmonic level modulation available, even a single HSO can produce extremely complex, evolving soundscapes with no other input. See the drone video, below, for a demonstration.

The HSO produces two outputs with all frequency components one quarter turn out of phase, making different wave shapes for the same harmonic content. However, because they reach their peaks differently, they'll distort differently. At higher harmonic levels, the HSO itself will produce warm and gentle distortion. While you have to be a little careful of phase issues, these two outputs are a great starting point for stereoizing a signal.

# Specs

Size 12HP 25mm +12V 80mA−12V 75mA 7Hz–50kHz ~7 octaves ~+9dBu–~+12dBu,−8V–+8V peak 20kΩ (FM and HS),100kΩ (others) 150Ω 2kΩ (min), 20kΩ+ (ideal)

# Detailed Description

The Harmonic Shift Oscillator produces a waveform according to the following equations:

$\sum_{n=0}^{\infty} L^n \sin((1+nS)\omega t)$

(left output)

$\sum_{n=0}^{\infty} L^n \cos((1+nS)\omega t)$

(right output)

Where $$\omega$$ is the fundamental frequency (FM and V/OCT), $$L$$ is harmonic level (HL), and $$S$$ is harmonic stride (HS). $$\omega$$ ranges from around 2Hz to 20kHz, with 300Hz near the center. $$L$$ ranges from 0 to just over 1, with a linear range. $$S$$ Ranges from 0 to just over 4, with 1 near the center.

Both FM and V/OCT inputs are exponential, but HS and HL are linear. Note that this means a true zero is available for $$L$$ and $$S$$, either of which will result in a pure sine wave output.