As I explained last month, virtual synthesis consists, in principle, of recreating what happens inside a 'real world' instrument in the ethereal domain of Digital Signal Processing. The technology involved can be viewed as an extrapolation of effects processing (with which we're all reasonably familiar) back to the point where the sound is first generated. It applies to real mechanical musical instruments as much as to electric or electronic ones where the sound is generated and modified by discrete analogue components.
When modelling analogue synthesis, software engineers replace each element of the synthesis process (oscillators, filters, envelopes, and so on) with software routines which interact in exactly the same way as their analogue counterparts. The process of modelling earlier musical instruments is actually simpler, in theory, as it separates the process into just two sections, however, the implementation of each of these sections may well be much more complex than the modelling of the individual elements of analogue synthesis). The technical terms for these two sections are 'driver' and 'modifier'.
In the simplest terms, you could think of the driver as what actually produces the sound in the first place -- or, to be slightly more scientific, how the energy is initially put into the system. In the case of a guitar, the driver would be the finger or plectrum hitting the string; in a wind instrument, it would be the breath passing through the mouthpiece; in a violin, it would be the bow scraping across the string. These are all actions which produce the initial vibration, and as such they 'drive' the systems.
The modifier is fairly easy to comprehend: it is the part of the musical instrument which takes the initial vibration and changes it into what we recognise as the sound of that instrument. This would be the bridge and sound box on a guitar or violin, the tubing on a wind instrument, and so on.
|"Technics took an alternative route to giving modelling technology a reasonable amount of polyphony at an affordable price."|
Although the conventional acoustic piano is such a complex system that an authentic model would cost a fortune in DSP hardware, the somewhat simpler system developed for electric pianos is much more feasible to physically model, and as a result there have been some quite successful models of electric pianos, by Technics on the WSA1 (see the 'Higher Polyphony The Technics Way' box), and Korg on the Z1 (many of which have been bought by traditional keyboard players because of the authenticity of their Rhodes and Wurlitzer patches). The driver in the electric piano system is, of course, the hammer hitting the tine; a physical action. The modifier is the pickup placed over the tine to capture and amplify its sound, and this part of the process is electrical. It may be worth recalling at this point that in instruments referred to as electric (electric guitar or electric piano), the source of the sound is a physical event and the mechanism for amplifying it electrical. In instruments referred to as electronic (such as the organ or synth), the entire sound-generation process is electrical.
Having decided what our driver is, in the case of the electric piano, we have to create a model of what happens when the hammer hits the tine. Clearly, there is a degree of timbral change in the initial sound, based on how hard the key is struck, so not only do we need to vary the volume of the sound but also to create a different harmonic series based on the velocity of the key-strike. The increase in the proportional level of higher harmonics on harder key-strikes is a fairly well documented phenomenon which conforms to the natural increase in brightness which many musical systems exhibit when more energy is put in. This is because higher harmonics require more energy to generate at a given volume (because there are more cycles per second), so when there's less energy present in the system, the amount converted into higher frequencies is reduced disproportionately. This not only explains why a low-velocity key-strike produces a duller sound, but also why the initial strike produces the brightest point in the sound, after which the sound quickly becomes duller. An electric piano sound very quickly approximates to a sine wave at the fundamental frequency of the note. This is fairly standard stuff and will not cause too many problems for any software DSP engineer worth his salt.
Figure 1 shows the parameters for the Electric Piano Model in the Korg Z1. The settings were programmed by producer Martyn Phillips for a Wurlitzer sound. If you look at the Hammer parameters, you'll see that the Wurlitzer is fairly velocity sensitive (76, where 0 equates to no velocity and 99 is incredibly velocity sensitive), but generates very little attack noise. Rhodes patches created with this model tend to have at least a setting of 35 for click, unless they're emulating the DynoMyRhodes electronics, in which case a setting of 75 is more appropriate.
The most interesting part of the electric piano model is the modifier. This is to be expected, as the driver part of the electric piano, the struck tine, is a very small, uninteresting sound (which is why it was easily covered by a sample in the Technics WSA1). The most successful electric pianos used a fair amount of electronic processing to turn this sound into something more interesting to the ear. Clearly, an in-depth analysis of how the sound is modified by such electronics is more the domain of the software engineer creating the model than the musician using the model to recreate his electric piano timbres. Indeed, many of the terms used for the parameters are drawn from electronic circuit design. However, each separate physical model tends to have one key parameter which leaves you in no doubt about the authenticity of the model (as you'll see next instalment, when I talk about Rosin Amount for bowed string and Embouchure for brass/reed instruments). In the case of Electric Piano models, this key parameter is clearly Pickup Position, which appears in both the Technics WSA1 and Korg Z1 electric piano models.
Anyone who owned a Rhodes or Wurlitzer piano in the '70s should remember the fashion for opening them up and individually adjusting the position of the pickup over the tine. It was a very time-consuming process, but was perhaps the best way of customising your sound, as it really did bring about major changes in the timbre of the instrument. At one extreme it was possible to achieve a very bright, thin sound which would cut through anything, while moving the pickup to the other end of its travel yielded a plummy, mellow sound (a bit like the difference between the bridge and neck pickups on an electric guitar).
The joy of physically-modelled electric pianos is not only that this Pickup Position parameter allows you to change the apparent pickup position without all that tedious mucking about inside the instrument with a screwdriver: you can also do it in real time, while you're playing. On the Technics WSA1, pickup position is available on the unsprung mod wheel, while most electric piano patches on the Korg Z1 have the pickup position mapped to the Y component of the X-Y pad. This means that in both cases you can fiddle with pickup position until you get the sound you like and then leave it there (using the X-Y Hold switch on the Z1).
Many people are familiar with the fact that the electronic organ works as a sort of primitive additive synthesizer. Drawbars control the level of a series of tone wheels, each of which (in theory, at least) should produce a sine wave representing one of the harmonics in the natural series. These form the driver component of the system, with the rotation of the tone wheels being the original source of the sonic energy in the system. This, of course, dates back to how pipe organs (perhaps the first additive synthesizers) changed the timbre of the sound by adding together pipes of related pitches to create a fuller sound. Electronic organs had as many as 10 drawbars, which gave the ability to mix together the lower pitches in the harmonic series to create different registrations (the latter is originally pipe organ terminology, referring to a series of stops for each of the sets of pipes which were either in or out -- ie. on or off). Nowadays, we would probably refer to them as presets, as they essentially change the timbre of the instrument.
This is rather a simplification of what happens inside the most enduring versions of the electronic organ -- and we must not, of course, forget the major 'external processor' involved: the Leslie speaker, which modulated the organ sound, making it sonically more 'interesting'. As so often happened with early analogue applications of technology, the actual product departed from what it should have been according to its 'on paper' design, but was none the worse for that. Indeed, the organs which came closest to producing pure sine waves were the ones often referred to as 'cheesy' these days. The distortion produced in the classic Hammond sound, often a product of ageing tone wheels and abused circuitry, added greater harmonic complexity than simple harmonic addition ever could, often in a similar way to the complex but aurally pleasant distortion produced by guitar amps and distortion pedals. Clearly, a physical model of electronic organs which could only recreate the theoretically pure organ sound would only be of interest to those recreating kitsch '60s lounge music. So organ models need to recreate the more complex phenomena which resulted in the more enduring organ timbres.
The first instrument to use modelling technology to recreate electronic organ sounds was the Technics WSA1. This instrument does not use physical modelling in the purest sense of the term, as the basic source of most driver sounds is samples (see the 'Higher Polyphony The Technics Way' box for a more complete description of Technics 'acoustic modelling' technology). However, for electronic organ sounds, single-cycle waveforms could be added together to model how the basic organ timbre is built up using tone wheels at related frequencies.
In Organ mode, the WSA1's backlit LCD display changes to give a representation of drawbars, which can then be modified with the sliders next to them. This means that harmonic content can be changed in real time, just like in all those Keith Emerson solos (although I have yet to see the modulation parameter for routing virtual knives into the cabinet...).
On the Korg Z1, although the assignable knobs below the display can be set to control the level of up to five drawbars (or groups thereof), the way in which organs are modelled is slightly different. Each oscillator can have a different model loaded into it, but the Organ model only has three drawbars (although there are three different variations on a sine wave or triangle wave for each drawbar to control the level of). The best way to make a complex organ sound is therefore to switch both oscillators to the Organ model and then use each one to produce three different drawbar harmonics. The Sub Osc can also be used to produce the fundamental, so that the six drawbars can be set to higher harmonics. The Jazz Organ patch in Figure 2 demonstrates this very clearly: the Sub Osc is set to the fundamental (16' in classical pipe organ terms), Osc 1 is set to the second, sixth and twelfth harmonics (8', 22?3' ' and 11?3') and Osc 2 has two drawbars set to the eighth harmonic (2') and detuned slightly; the third drawbar is doubling up the fundamental.
The other section of the Z1 you can see in Figure 2 is brought into play all the time for electric organ sounds: it's the rotary speaker effect algorithm. This gives the Leslie effect, which, as I mentioned earlier, is synonymous with enduring organ timbres. (If you're interested in how the Leslie cabinet works, or the history of Hammond organs, take a look at our 'Vital Organ' feature in the October 1997 issue of SOS). Indeed, where such organ sounds are concerned, the Leslie effect is the major part of the modifier, in that (apart from some distortion caused by knackered circuitry, key-clicks caused by worn contacts, and so on) it is the rotary effect which gives the sound its character and charm. This is where the line between physical modelling and DSP effects blurs to the point where one can be seen as part of the other. In fact, a physical modelling instrument which could not apply a rotary speaker effect could hardly be said to properly cover organ modelling. Fortunately, both the Z1 and WSA1 (the only two synths which claim to cover organ modelling) both have effects algorithms for rotary speaker simulation.
As you can see from Figure 2, the proper modelling of a Leslie speaker includes parameters for the rate and acceleration of both the rotor and the horn, as well as for the distance and spread of the virtual microphone which is picking up the sound. Mod switch 2, just next to the X-Y pad on the Z1, is normally used to swap between the slow and fast rotation rates.
The Organ models on both the WSA1 and Z1 are not just restricted to the modelling of electronic instruments. Both are extremely adept at pipe organs of the ecclesiastical variety, although in both cases the rotary speaker is best eschewed in favour of the largest hall reverb available on the machine. Figure 3 shows a typical Classical Pipe Organ patch. You will notice that all modulations have been switched off and that the click component, so common in electronic organs, is also defeated. Then it simply remains to select the required footages (remembering, again, that the Sub Osc can be used to add in an extra footage at the bottom end) and give the hall reverb its largest possible setting.
This move from the electronic to the acoustic world (albeit still within the digital domain) leads rather nicely into the remaining chapter on physical modelling, coming your way next month. I'll be looking at plucked string algorithms (which produce both acoustic and electric guitars, harpsichords, and other plucked string instruments, such as dulcimers and spinets), and at the three most widespread uses of physical modelling in the acoustic world -- brass, reeds and bowed strings.
Although the balance of this piece has been based around Korg's MOSS system (with a small contribution from Technics' acoustic modelling), next time I'll be broadening the palette to include the Yamaha VL system in its many incarnations, including the cheapest physical modelling unit to date, the VL70M. Until then, see if you can lay your hands on a WSA1 or Z1 to try out some of the electric piano and organ sounds we've been looking at. If not, a Korg Prophecy will be good preparation for next month, as it also covers plucked strings, brass and reeds.