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ModMix™ ApplicationsFrequency DoublingAny continuous bipolar waveform may be multiplied by itself to give a doubled frequency, discontinuous square or pulse waves will produce a DC offset and sawtooth waves produce the same frequency with altered harmonics. A sine wave will produce another sine wave an octave higher according to the trigonometry equation for squaring a sine. sin² (A) = (1 - cos (2A))/2  Normalled connections allow this patch to be made with a single patchlead. Two Squares from one ModulatorA variation of the above squaring may be patched using the factorisation of the difference of two squares: sin² (A) - sin² (B) = (sin (A) + sin (B)).(sin (A) - sin (B))  By multiplying the sum with the difference of two signals the squares of both are produced with a single multiplication. In the case of two sine inputs this will double the frequency of both with no cross products and Modulator B is free for other use. Shape ModulationWaveforms from the same VCO may be multiplied to produce different wave shapes. A triangle multiplied by a square gives a sawtooth an octave higher. A sawtooth multiplied by a square gives a triangle.  A pulse wave may be multiplied by other waveforms from the same VCO and then width modulated. A sawtooth multiplied by a pulse gives a triangle at 50% width and changes to a positive or negative sawtooth at 0% and 100%.  Complex Shape ModulationAdding another VCO synchronised to the lower frequency generating the pulse enables a rich palette of waveforms to be created and modulated.  EMS-style Shape ModulationVoltage controlled shape by full wave rectifying a sawtooth with an offset which varies from sawtooth through triangle to inverted sawtooth.  Centre Dead ZoneVoltage controlled shape by adding positive and negative rectified halves with a common complimentary offset.  ClippingVoltage controlled limits by adding a CV offset, rectifying and then subtracting the offset to restore the DC level.  Or the reverse.  Another inverter/summer, e.g. PinMix or SwitchMix, is required to do both positive and negative clipping. LFO Modulation ProcessingLFOs with ±5V outputs require accurate reduction for control of vibrato and trills. The dual level controls provide a coarse and fine attenuation for exact pitch depths and the positive half wave rectification can be used for unipolar trills.  |
