Phase distortion synthesis
Encyclopedia
NOTE: any readers who are struggling to understand this text, here are links to the missing Figures A and B:
Figure A
Figure B
NOTE: any readers who are struggling to understand this text, here are links to the missing Figures A and B:
Figure A
Figure B
NOTE: any readers who are struggling to understand this text, here are links to the missing Figures A and B:
Figure A
Figure B
Phase distortion synthesis is a synthesis method introduced in 1984 by Casio
in its CZ range of synths
, and similar to phase modulation synthesis in the sense that both methods dynamically change the harmonic content of a carrier waveform by application of another waveform (modulator) in the time domain. Casio introduced the term 'phase distortion'. Yamaha had previously produced the first Phase Modulation synthesizers in their DX series of synths: Yamaha mistakenly promoted their machines as FM when in fact used phase modulation. Both methods produce composite waveforms whose harmonics are the sum and difference of the carrier and modulator waveforms.
Figure A shows how a sine wave gradually turns into a saw wave as the readout phase angle gets more and more distorted. Depending on whether a frequency counter x, is above or below the current distortion point d (the sharp knee in the phase angle insert) one of two equations must be solved:
if(x > d)
return sin( x * d / pi);
else
return sin((x-d) * pi / (1-d) + pi);
Figure B is similar to A, only showing the development of a square wave instead. For x values below the first knee in the phase angle insert, the y values will vary rapidly between -3.14 and 0 resulting in the initial sharp rise of the square. Values between the first knee and the center knee all equals 0.0 resulting in the squares flat ceiling in the first half wave. At this point there is again a sudden rise in the phase angle up to 3.14, resulting in the fall of the square wave down to its flat floor at -1.0 where it stays until the frequency counter wraps around and repeats the process.
Casio's implementation of PD utilised a single modulating and carrier waveform, however, as the waveforms were composite, many harmonics were created in the resultant, output waveform. This is different to Yamaha's approach where only sine waves (single harmonics) could be used as carrier or modulator (either 4 or 6), though Yamaha did change this in later machines and allowed the use of composite waveforms such as saw tooth waves.
On the Casio machines the waveforms available for use were rich in harmonics such as a square wave. Other waveforms that are supported on the CZ range are impulse, half-sine and double impulse. The CZ synths also generate synchronised and windowed sine waves in order to emulate resonant filter sweeps.
The phase transforms are all assembled from piecewise linear functions under binary logic control and shows characteristic sharp knees (and for some transforms, even sudden jumps) as they move from minimum to maximum, where the frequency counters accumulator wraps around and starts over. The sharp knees are smoothened out by the roundness of the modulated sine wave and not too noticeable in the resulting signal.
:
To summarize in other terms, the filter implementation is a form of digital hard sync, but adds a triangular descending volume envelope running within the sync period. Because the volume always ends at zero, the discontinuities that would cause aliasing in native digital hard sync are avoided. Filter sweep effects are generated in the same way that hard sync effects are generated: by modulating the frequency of the resonance waveform, the timbre changes, adding and subtracting harmonics as desired.
Casio made five different synthesizers
using this method of phase distortion synthesis.
The VZ-1's synthesis method ("Interactive phase distortion") includes Frequency modulation synthesis
as well as an improved version of phase distortion.
Figure A
Figure B
NOTE: any readers who are struggling to understand this text, here are links to the missing Figures A and B:
Figure A
Figure B
NOTE: any readers who are struggling to understand this text, here are links to the missing Figures A and B:
Figure A
Figure B
Phase distortion synthesis is a synthesis method introduced in 1984 by Casio
Casio
is a multinational electronic devices manufacturing company founded in 1946, with its headquarters in Shibuya, Tokyo, Japan. Casio is best known for its electronic products, such as calculators, audio equipment, PDAs, cameras, musical instruments, and watches...
in its CZ range of synths
Casio CZ synthesizers
The CZ series were a family of low-cost Phase distortion synthesizers produced by Casio mid-1980s. There were eight models of CZ synthesizers released: the CZ-101, CZ-230S, CZ-1000, CZ-2000S, CZ-2600S, CZ-3000, CZ-5000, and the CZ-1. Additionally the home-keyboard model CT-6500 used 48...
, and similar to phase modulation synthesis in the sense that both methods dynamically change the harmonic content of a carrier waveform by application of another waveform (modulator) in the time domain. Casio introduced the term 'phase distortion'. Yamaha had previously produced the first Phase Modulation synthesizers in their DX series of synths: Yamaha mistakenly promoted their machines as FM when in fact used phase modulation. Both methods produce composite waveforms whose harmonics are the sum and difference of the carrier and modulator waveforms.
Figure A shows how a sine wave gradually turns into a saw wave as the readout phase angle gets more and more distorted. Depending on whether a frequency counter x, is above or below the current distortion point d (the sharp knee in the phase angle insert) one of two equations must be solved:
if(x > d)
return sin( x * d / pi);
else
return sin((x-d) * pi / (1-d) + pi);
Figure B is similar to A, only showing the development of a square wave instead. For x values below the first knee in the phase angle insert, the y values will vary rapidly between -3.14 and 0 resulting in the initial sharp rise of the square. Values between the first knee and the center knee all equals 0.0 resulting in the squares flat ceiling in the first half wave. At this point there is again a sudden rise in the phase angle up to 3.14, resulting in the fall of the square wave down to its flat floor at -1.0 where it stays until the frequency counter wraps around and repeats the process.
Casio's implementation of PD utilised a single modulating and carrier waveform, however, as the waveforms were composite, many harmonics were created in the resultant, output waveform. This is different to Yamaha's approach where only sine waves (single harmonics) could be used as carrier or modulator (either 4 or 6), though Yamaha did change this in later machines and allowed the use of composite waveforms such as saw tooth waves.
On the Casio machines the waveforms available for use were rich in harmonics such as a square wave. Other waveforms that are supported on the CZ range are impulse, half-sine and double impulse. The CZ synths also generate synchronised and windowed sine waves in order to emulate resonant filter sweeps.
The phase transforms are all assembled from piecewise linear functions under binary logic control and shows characteristic sharp knees (and for some transforms, even sudden jumps) as they move from minimum to maximum, where the frequency counters accumulator wraps around and starts over. The sharp knees are smoothened out by the roundness of the modulated sine wave and not too noticeable in the resulting signal.
Simulating a resonant filter
Figure 19 from the 1985 CZ-series patent shows how to emulate the variable resonance found in analogue voltage controlled filtersVCF
VCF may refer to:*Vaginal contraceptive film, a type of spermicide birth control*Valencia CF, a Spanish football club in La Liga*Vapor cloud fire, a deflagration fire*Variant Call Format, a standard for storing gene sequence variations...
:
- (a) The base frequency counter, wrapping around every period.
- (b) The resonance frequency counter at a slightly higher frequency, being reset (or "synced"Oscillator syncOscillator sync is a feature in some synthesizers with two or more VCOs . One oscillator will restart the period of another oscillator, so that they will have the same base frequency...
) when the base counter wraps around.
- (c) The resonance frequency counter used as a sine wave readout. Note the nasty sudden jump at the reset!
- (d) The inverted base frequency counter.
- (e) Multiplying c by d. The sudden jump in c is now leveled out.
To summarize in other terms, the filter implementation is a form of digital hard sync, but adds a triangular descending volume envelope running within the sync period. Because the volume always ends at zero, the discontinuities that would cause aliasing in native digital hard sync are avoided. Filter sweep effects are generated in the same way that hard sync effects are generated: by modulating the frequency of the resonance waveform, the timbre changes, adding and subtracting harmonics as desired.
Casio made five different synthesizers
Casio CZ synthesizers
The CZ series were a family of low-cost Phase distortion synthesizers produced by Casio mid-1980s. There were eight models of CZ synthesizers released: the CZ-101, CZ-230S, CZ-1000, CZ-2000S, CZ-2600S, CZ-3000, CZ-5000, and the CZ-1. Additionally the home-keyboard model CT-6500 used 48...
using this method of phase distortion synthesis.
The VZ-1's synthesis method ("Interactive phase distortion") includes Frequency modulation synthesis
Frequency modulation synthesis
A 220 Hz carrier tone modulated by a 440 Hz modulating tone with various choices of modulation index, β. The time domain signals are illustrated above, and the corresponding spectra are shown below ....
as well as an improved version of phase distortion.