Meet Goom - New Open Source Desktop Synthesizer

"Goom is a digital music synthesiser based on an ultra-low-cost microcontroller. It broadly emulates the architecture of traditional analogue synthesisers, offers 16-voice polyphony and is fully multitimbral, and is controlled over a MIDI interface. The total cost of the basic components to make a fully-working synthesiser is just a couple of pounds; the (optional) ‘knobs and switches’ analogue front panel interface increases the total component cost by an order of magnitude or so, mostly accounted for by the potentiometers themselves.

Features

Sixteen-voice polyphonic
Fully multitimbral (different patch on each MIDI channel)
Analogue front panel patch set-up for MIDI channel 1
Patch set-up using MIDI control change messages for channels 2 to 16
Two oscillators per voice: sine, sawtooth, square, pulse and intermediate waveforms
Oscillators can be mixed or combined using frequency modulation or frequency modulation plus feedback
Three envelope generators per voice (one ADSR and one AD for amplitude, one ADSR for filter)
Low-pass filter for each voice with resonance control
Velocity scaling on amplitude and filter cutoff
Stereo output with pan and volume control for each patch
24-bit digital-to-analogue converter
Voice architecture

The tone generation structure for each voice is shown in the diagram below. It broadly follows the conventional layout of an analogue synthesiser, but adds frequency modulation modes to increase the range of tone colours available.

One point of interest is that each oscillator waveform is controlled by a pair of continuous parameters rather than, for example, a multi-position switch. The waveform is divided into four parts: a rising slope, a flat period, a falling slope, and a final flat period. Each slope takes the shape of half a cosine wave: the first from cos –π to cos 0 and the second from cos 0 to cos π.

The first control determines the ‘duty cycle’, the ratio between the time taken for the first slope plus the first flat period to that taken for the second slope plus second flat period. The second control determines the proportion of the total cycle occupied by the flat periods.

Together these two controls allow the generation of sine, square and pulse waveforms, and an approximation to a sawtooth waveform. Furthermore, a wide range of intermediate waveforms is also available. Very roughly speaking, the first control determines the presence of even harmonics (varying on a line from string to flute, if you will), while the second control determines the overall harmonic richness.

An upper limit is enforced on the slope of the waveform such that as the frequency increases the waveform approaches a sine wave. Since the waveform and its first derivative are continuous the result is in a worthwhile reduction in aliasing without having to resort to more computationally intensive techniques such as those that involve summing individual band-limited waveform fragments. A particular advantage is that much precomputation can be done at the control update rate to reduce the work that needs to be done at the output sample rate."

Full details at http://www.quinapalus.com/goom.html