Advanced Music Synthesis
If you are already thinking in terms beyond unison ramp waves through a decaying cutoff LP filter with a backdrop of sweeping filtered noise, then you've probably realised that a fully variable system with comprehensive patching facilities, or at least a versatile switch-linked instrument with FM, Sync, PWM etc., is essential for original and creative synthesis, even if used in conjunction with simpler pre-patched and/or polyphonic instruments. If so, these articles will tell you about advanced techniques of synthesis to help you make your own music, however humble it is, rather than infinitely less satisfying collections of well-worn synthesiser cliches. If not, don't be put off - perhaps we can simply stimulate your imagination. And remember, if you are using equipment you've made yourself, then you have an advantage over the person who has bought something equivalent - not only do you have an insight into the way it works which can only help you in using it to the full, but you're in a position to make your own modifications and expansions when you reach its limits of capability. After all, no-one is more suited to designing the specification of a piece of equipment than its eventual user.
What makes a synthesiser different from any other electronic musical instrument, and also what makes a synthesiser player different from, in particular a keyboard player, is the extensive use of voltage control. It allows the parameters of signal generators and processors to be determined by the outputs of other generators and processors, in a way that is fundamentally independent of the method of producing the control signal or the nature of the parameter controlled. So, for example, a keyboard can control the cutoff frequency of a filter in the same way as an oscillator can control the pitch of another oscillator.
The most important difference that can exist between one piece of synthesiser equipment and another is the way the voltage controlled parameters respond to their control voltages. This is the much talked about subject of 'linear' and 'exponential' (sometimes called 'logarithmic') control voltage laws. The problems arise from the fact that it is most useful for the pitch of an oscillator to rise by one octave for each unit rise in control voltage wherever this may be in the overall range, but conventional analogue oscillators are based around integrators which give a doubling of rate of change of voltage, and therefore a doubling of frequency, for a doubling of input current. Since pitch is related to frequency in an exponential fashion, an exponential converter is required to process the control voltage (CV) in order to produce the correct response. Additional circuitry, and sometimes trimming, is needed to reduce the effects of temperature variation on the law and the tuning of each oscillator, so some systems do without precision converters, directly generating a keyboard voltage with increasing CV intervals for the same musical interval as it moves up the range. These latter are the so-called 'linear' systems, which are potentially more stable and cheaper to make. It was the insufficiently compensated exponential synthesisers of the early seventies that gave the synthesiser a reputation for perpetual bad tuning, and later on prompted one linear system manufacturer to advertise with the line "Avoid the embarrassment of an out-of-tune performance"!
Generation of a 'pre-converted' keyboard control voltage gets over one of the problems of a linear system, but since a control voltage change must be greater at higher frequencies for the same effect on the pitch, a simple effect such as vibrato requires the secondary CV to be multiplied by the keyboard voltage before it is used, and where the precision of this must be as good as that of the keyboard itself (for example when using an analogue sequencer), the multiplying operation must be very accurate. This is usually only available with the keyboard as the primary source - when two low frequency oscillator waveforms or sample and hold outputs are used to control pitch they will appear to interact to condense the higher pitches, and the provision of a cheap uncompensated linear-to-exponential converter is hardly a satisfactory answer. Glide ('portamento') is usually produced by processing the keyboard CV, and where this is so it will suffer from the same effect. Glide that has been generated by a resistor/capacitor (RC) network will have the extent of the curve increased on the way up and decreased on the way down, whereas the linear type will be equally condensed towards the higher pitch in either direction. Because linear glide features a constant slew rate for each setting of the control, it will also take proportionately longer to cover the same musical interval the higher up it is played.
A more fundamental feature of linear control is the fact that to transpose the pitch of a keyboard-controlled oscillator up or down requires the keyboard CV to be multiplied or divided - adding or subtracting a DC voltage as one would to transpose in an exponential system causes disruption of the scale intervals. Hence tuning of linear oscillators is often achieved by a 'Range' switch which changes the integrator time constant giving three or more footages, in conjunction with a 'Tune' pot which varies the gain of an input CV amplifier from around 0.6 to 1.6. Using an oscillator without a keyboard-type controller then becomes a bit awkward, since in the absence of an input CV it will not run. So an extra pot is required to provide this CV; this is called 'Sweep' or 'Free Run' and allows the whole range to be covered with a single control, though it suffers from the same old problem when a secondary CV is patched in for additional control and this time multiplication is not practical. Of course, the Free Run control must be returned completely to zero for equal temperament from the keyboard, sequencer, quantiser or whatever. Unfortunately, not doing so does not provide equal macro or micro-tones - alternative tunings of this type cannot be practically produced in a linear system, though with an exponential keyboard this is just a matter of amplifying the CV by the required scaling factor. In fact this is what happens when one exponential system is interfaced with another that employs a different pitch-to-voltage ratio.
Most exponential synthesisers use 1V/Octave as standard, but may require trimming to match the scales of physically separate units. Connecting linear synthesisers together also requires attention to the CV range, though since all oscillators must just stop with no input, and gain errors appear as transpositions, the Tune control can correct for any minor mismatches.
For those of you who like sums, all this can be represented quite simply by:
where k represents the note required and corresponds to a depressed key, and f is the frequency that will sound. In an exponential system we can vary the scale and transposition easily:
f=2(ak + b)
where a is the scaling factor and b is the interval. In a linear system, 2k is generated directly so transposition requires multiplication:
=2k x 2b
and for scaling:
f=2ak x 2b
=(2k)a x 2b
Now we see why variable scale control from a quantized CV generator such as a keyboard is impractical. It requires the value of CV to be raised to a variable power!
Figure 1 shows the relationships between linear and exponential control voltages and the pitch and frequency of a VCO.
The fact that one cannot necessarily cause an important parameter to vary in accordance with the sum of two control voltages by adding the CV's and patching the result to the parameter control input is a severe limitation of the linear control system, and makes it only really useful for small, pre-patched synthesisers, where the VCO's are always under keyboard control and simultaneous modulation of a single parameter by many signals is not required. The use of constant temperature ovens and more advanced compensation circuitry, plus the availability of internally compensated monolithic exponential VCO's means that exponential synthesiser designs have the temperature dependance of exponentiating semiconductor junctions well under control, with stability approaching that of linear instruments, and certainly good enough even for live performance.
Since voltage controlled filters are often required to track keyboard-controlled oscillators maintaining constant harmonic content for different pitches, they must exhibit the same law as the VCO's. Accuracy and temperature stability are not as important, though these will necessarily limit the usefulness of resonating filters as sine wave oscillators. It is interesting to note that the CV law of VCF's seems to impose particular design restrictions which affect the filter's audio characteristics, causing linear VCF's to sound weedy and lacking in character when compared with exponential VCF's: this is more than a matter of 2-pole verses 4-pole though discrete exponential VCF's often show steeper cutoffs than linear ones. We'll talk more about filter characteristics in future articles.
Since signal amplitude is rarely required to track another controlled parameter, voltage controlled amplifiers do not necessarily exhibit the same law as other modules in the same system. The choice is often dictated by the envelope/transient generators since the most useful envelope shapes have exponential attack and decay portions, like acoustic instruments where decays proceed with a constant percentage loss of energy from a vibrating body in each unit of time. This shape of envelope is achieved with an exponential envelope generator and linear VCA, or vice versa, and since exponential envelopes are more useful for controlling other modules, and like VCO's an exponential VCA is often just a linear VCA plus a (non-precision) exponential converter, the former alternative is the most common. This is almost always the case in small prepatched synthesisers, and often so in patchable envelope shapers, each being a combination envelope generator and VCA. The choice of linear or exponential control on a VCA is useful, especially where it is controlled by a non-keyboard initiated envelope or a periodic or complex low frequency waveform, possibly controlling the amplitude of another control signal. Where an envelope generator is of the AD or ADSR type it is usually exponential, linear slopes being reserved for multiple-stage or patch-programmable generators.
Linear control of most exponential VCO's is possible, though the input may not be provided. Where it is, a number of techniques can be used to extend the capabilities of the VCO, such as stopping the oscillator with a low input voltage (only useful where the linear control input is DC coupled), waveform shape modulation, and by far the most powerful application: audio frequency FM.
Frequency modulation is the dynamic control of the frequency of a periodic waveform, and as such includes most techniques of voltage control of oscillator frequency such as keyboard control and vibrato. However the term is usually reserved for the technique of producing new timbres by modulation of the frequency of one audio frequency tone by another, especially where it appears abbreviated to FM. This technique has the ability to produce such complex spectra using simple sine waves as the modulating ('program') and modulated ('carrier') signals that bright waveforms such as pulse and ramp are not often used, except for dense, noise-like sounds.
The effect of FM is to produce a group of frequency components above and below each harmonic of the carrier signal, each new partial being referred to as a sideband. With a sine wave as carrier, two groups of sidebands are produced, and if the program is a sine wave as well, the distribution of the sidebands is simply determined by the program frequency and the depth of modulation. This is illustrated in Figure 2, which shows spectra of a 1000Hz sine tone modulated with another sine tone at various frequencies and depths. The spacing between the resultant components is equal to the modulating frequency.
The depth of modulation is expressed as a deviation from the carrier frequency in Hz or as a percentage, and determines the spread of the sidebands with 90% of the energy contained with the range of deviation (indicated by the double headed arrows on Figure 2).
The Modulation Index is the deviation in Hz divided by the modulating frequency, and determines the relative amplitude of each sideband, so that for each value of the index there is a characteristic distribution, except where the deviation exceeds about 50% and the symmetry becomes corrupted by lower sidebands which 'reflect' through 0 Hz, adding to or interleaving with components within the deviation range. Since the number of sidebands within each half of the range of deviation is equal to the modulation index, the index tells how many significant sidebands there are in an FM spectrum. For example, in Figure 2c the modulation index is six and there are six significant components each side of the carrier.
The modulation index is an idea borrowed from the field of FM radio where the modulating frequency and the frequency deviation are small in comparison with the carrier frequency, and the relationship between the sideband spacing and the carrier frequency is unimportant. More useful to the synthesist are the deviation and the ratio of the two frequencies - if one frequency is an integral multiple of the other then the sidebands will form a harmonic series with the fundamental at the frequency of the lower, though it may be of zero amplitude. If not, a non-harmonic overtone series of the sort that is so characteristic of frequency or amplitude modulation is produced. It is interesting to note that the results of FM with simple fractional ratios such as 2/3, 3/4 are ambiguous sounds with perceived pitches dependant on acoustic or musical context.
Going back to Figure 2, it can be seen that the total spread of (b), (d) and (e), non-reflecting spectra with the same deviation, is largely independent of the carrier and modulating frequencies. Note that within the deviation the sideband pairs are of superficially irregular amplitude, and outside they decay rapidly to zero. In all illustrated spectra except (a) the carrier frequency has a lower amplitude than the strongest new component - at some values of the modulation index, the lowest of which is around 2.7, the carrier disappears altogether and the amplitudes of individual sideband pairs can also become zero at certain index values.
To make practical use of FM, we ideally need independent control of the pitch of the oscillators, the interval between the modulating and modulated oscillators, and the percentage deviation. The first two are simple enough - they are basic requirements of a system limited to simpler synthesis techniques - but the deviation is dependant on the amplitude of the modulating waveform which will normally give a constant frequency deviation in Hz, requiring multiplication to retain a constant percentage deviation with changing pitch. The resulting decrease in the number of partials and their spread as the pitch rises is a disadvantage but is usually tolerable, and sometimes quite useful, when FM is being used for simulation of natural instruments for example. The percentage deviation can be held constant over a limited range by passing the program through an exponential VCA controlled by the sum of the carrier oscillator input CV's. If you're thinking that this was the point of the exponential converter in the first place you are right, but the linear control input should be used for two reasons:
1. The exponentiation would distort a modulating sine wave, introducing extra sidebands into the result.
2. More importantly, the distortion would shift the mean level of the modulating waveform, causing the carrier frequency to rise with increasing modulation depth.
This latter effect occurs even if the program is AC coupled where it leaves the oscillator, as it must be for proper linear FM, due to the different effect exponentiation has on the upper and lower portions of the waveform. The pitch shift effect can be demonstrated quite simply on a Minimoog: with only oscillator 1 switched into the mixer, oscillator 3 is set to independent control and the oscillator modulation is turned on with the modulation mix control completely on osc. 3. Holding a note and then pushing up the modulation wheel introduces frequency modulation and the pitch rises accordingly. If this doesn't sound like too much of a disadvantage remember that a small change of oscillator frequency has a great effect on the relationship of the overtones in resultant sound. This means that retuning is needed every time the modulation depth is changed, but FM remains quite useful in a exponential system where the VCO's don't have linear CV inputs.
Linear CV systems are better suited to FM than exponential ones since the provision of a keyboard CV multiplier makes constant percentage deviation FM trivial, though not if the patchable keyboard CV modulation input is equipped with a simple linear-to-exponential converter as is often the case, when it will have to be bypassed to obtain the full benefits. These include the ability to dynamically change the deviation, which is also available with linear-input equipped exponential VCO's.
The sound of an FM tone with the modulation depth decaying after the beginning of each note is rapidly becoming something of a cliche of computer music and in particular music using modern digital synthesisers, though it would probably be described as a decaying index sound by the composers who use it, since the modulation index is still considered a useful measure of FM depth by computer synthesists. Frequency modulation is very widely used in digital synthesis systems since in addition to providing a large selection of harmonic waveforms, it saves enormous amounts of computation time over comparable methods of producing sounds with non-integrally related overtones. In fact one might almost say that FM is to digital synthesisers what resonant low-pass filtration is to simple keyboard-based analogue synthesisers.
One disadvantage with FM, which is particularly important in imitative synthesis and computer synthesis where the result of an alteration is only heard after a delay, is that to all but the most experienced synthesist finding a particular sound is a matter of trial and error, unlike subtractive synthesis where one soon learns how a filter cutoff frequency or Q must be altered to get the right timbre. This can be alleviated to some extent by using degenerate forms of technique which limit the number or values of the variables and hence the range of possible sounds, making FM easier to use.
Groups of degenerate FM spectra where the carrier and program are fixed in simple musical intervals result from the use of oscillator synchronisation and this also allows the elimination of beating effects from sounds produced by straight FM. Using Linear FM with the type of sync that unconditionally resets the second oscillator at the same point in each cycle of the first yields a whole range of waveforms which retain a harmonic overtone series whatever the settings of the VCO's. This is particularly effective where one oscillator is the source of the waveforms for both functions and the other is set at a higher footage, whereupon the second one becomes a waveform generator locked to the pitch of the first, with the timbre controlled by the FM depth and slave VCO 'pitch'. Since the latter is potentially voltage controlled, startling timbre sweep effects can be obtained, and because only true harmonic series are generated, this provides a versatile source of 'safe' sounds for melodic keyboard playing.
Figure 3 shows a patch for comprehensive evaluation of frequency modulation using sine waves with or without synchronisation. Modulation depth is under control of an envelope generator and either or both of the carrier and program can be modulated by the LFO in addition to the keyboard.
A simple single VCO synthesiser can be used for basic experimentation with FM if the filter is able to self-oscillate. The oscillator output must be re-routed to the filter CV input so the VCO generates the program and the filter becomes the modulated sine wave oscillator. An unused position on the waveform selector switch can be connected to bring in the FM if a spare pole is also available to connect the triangle output to the filter CV input, using a series capacitor to remove DC from the waveform. If the oscillator has its own output level control, taking the program from its wiper will give control of modulation depth without the need to reassign an existing filter modulation control or to add another pot. The level control should be AC coupled to the waveform switch or VCO output so that the level will not readjust itself each time the depth is altered, though if the filter is exponential a pitch shift will occur anyway.