Synth School, Part 10: Modelling Electric Instruments

Tips & Techniques

Published in SOS August 1998
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PART 10: MODELLING ELECTRIC INSTRUMENTS

Last month, PAUL WIFFEN looked at how virtual synthesis can emulate analogue synths whilst going beyond their hardware-based limitations. Now he looks at its applications for imitating and exceeding older instruments such as electric piano and organ. This is the 10th article in a 12-part series. Read Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, Part 11 and Part 12.

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.

DRIVER & MODIFIER

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."
But before we look at the modelling of traditional western classical orchestral instruments, which are somewhat complex sound-production systems, let's look at how the theory of driver and modifier is applied to some rather simpler electronic instruments which pre-date analogue synthesis.

NEW MODEL PIANO

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).

ORGAN TRANSPLANT

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.

HIGHER POLYPHONY THE TECHNICS WAY

The main obstacle to the development of affordable physical modelling synths over the last five years has been the expense of the DSP hardware. The flood of polyphonic DSP-based machines which hit the market last year (Yamaha AN1x, Roland JP8000, Korg Z1, Nord Lead 2) was very much due to recent decreases in cost and increases in power of DSP chips. Before this price/performance breakthrough, companies working on the development of physical modelling, such as Yamaha and Korg, were forced to limit the polyphony of their early instruments (the VL1 and the Prophecy) to a single voice. This wasn't too much of a problem, as these instruments were principally designed to recreate the voicing of monophonic instruments such as brass and woodwind or lead and bass synths, and it allowed all the power available to be concentrated into a single powerful voice.

However, Technics took an alternative route to giving modelling technology a reasonable amount of polyphony at an affordable price. They realised that the greatest amount of DSP power was taken up by producing the driver, the original sound before the resonator modifies the harmonic content. By replacing a modelled (and therefore processor-intensive) driver with a PCM sample, they could save an enormous amount of processing power -- power which could be ploughed back into increasing polyphony. As a result, when other modelling synths on the market were duophonic at best, the WSA1 had 32 voices of polyphony, a figure still not achieved by the most powerful current modelling synths. (With the optional 6-voice expansion, the Korg Z1 still only clocks in at 18 voices, for about the same retail price that the WSA1 had on its release in 1995.)

To make PCM samples work as drivers for a modelling synth (rather than as the more 'finished' sound you'd normally expect from the PCM sound sources in an S+S synth), Technics had to record the samples in as primitive a way as possible, removing as much of the resonator component as they could from the samples. So strings were miked as close to the string and as far away from the sound hole of violin or guitar as possible, while woodwind reeds were sampled without the resonating column component. This makes the raw samples in the WSA1 rather less polished and exciting than those in the average PCM-based synth.
A perfect example is the source samples for the electric pianos, which have much of the toy musical box about them when heard unmodified.

Fortunately, no-one is expected to listen to these raw samples as they were recorded. When the sampled driver is passed through the DSP resonator section, the acoustic modelling process recreates the same timbral and enveloping changes which take place inside the instrument once the initial sound has been triggered. So what's the advantage in this? Why not just use a sample which has the final sound of the instrument?

The answer to this lies in the increased expressivity which can be achieved by modifying the resonating component with real-time controls. The amount that can be done with 'finished' samples is fairly limited, especially with fairly crude 'analogue'-style filters and envelopes, which can make the sound brighter or duller, and end sooner or later, but can't make it fundamentally different. The harmonic variation which modelled modifiers can introduce is much more akin to the kind of filtering offered by Emu's Z-plane synthesis, as represented by Morpheus and UltraProteus, for example. Modifications are at the same sort of level as multi-band graphic EQs with serious amounts of cut and boost available, or even the more complicated parametrics which can precisely tailor frequency components.

The much more complex and subtle variations which can be produced by modelling the modifier component of an instrument system get to the heart and soul of an instrument's expressivity, without the problems that cross-switching or cross-fading samples brings. In the case of the electric pianos on the WSA1, you can control parameters such as pickup position and pickup sensitivity, as well as the timbral effects of the electronic circuitry itself. Using DSP for the modifier side of the process meant that much of the subtlety and precision of physical modelling could be introduced without the cost of the drivers being produced entirely by DSP.

Sadly, the WSA1 (and its module counterpart, the WSA1M) were not major hits in the S&S-dominated market. They were launched at a time when the demand for subtlety of expression for players and authenticity of real sounds was an all-time low, and the market requirement was for sounds suited to techno and related dance styles. Having discovered some potential for the type of real-time modulation favoured by the dance producers in Technics' acoustic modelling process, this author participated in the production of an expansion board full of drum loops and analogue oscillator timbres, in an attempt to save this developing technology from becoming obsolete before it matured. Unfortunately this Dance board was released too late to save the instrument from the ignominy of the discounted blow-out, and the last WSAs were sold off at a quarter of the original RRP, complete with the Dance board. However, anyone who picked one up at this final price (or buys second-hand at a similar price) secured an amazing deal, as the value for money of the original RRP has still to be equalled in terms of polyphony, if not fidelity, by the modelling synths of the present day.

Technics chose not to continue the technology of acoustic modelling in the form of follow-up WSA products, but one component at least lives on: the way in which the WSA's electronic organ sounds was programmed has been used in Technics' KN5000, and it's from this instrument that we've sourced the LCD screen illustrating the modelling of organs via virtual drawbars.

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.

LESLIE FILLIP

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.

ORCHESTRAL MANOEUVRES

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.

This is the 10th article in a 12-part series. Read Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, Part 11 and Part 12.

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