Those who were paying attention last time will remember that although the critical thing about physical modelling is that the parameters involved change depending on the instrument being modelled, the underlying theory breaks the process of modelling down into two main constituents; the driver and the modifier. The driver is the point where the energy is put into the system -- the bow or plectrum hitting the string, or air being blown through reed or mouthpiece. The modifier is the part of the system where the quality of the sound is changed by resonance and amplification. For strings, this would be the bridge transmitting the vibration of the string to the wooden case, or the column of vibrating air being modified by the size and shape of the tubing in the case of wind instruments.
The main reason for making this distinction between driver and modifier is that, broadly speaking, the driver tends to be the thing which is being constantly changed to modulate the pitch and introduce expression, whereas the modifier tends to be the more constant factor which gives the instrument its recognisable character. The problem with sampling is that it cannot separate these two elements from the final sound. As a result, the speeding up or slowing down of the sample which is needed to change the pitch produces unfortunate effects like changing the apparent size of the resonating case or column. This doesn't grate too much on the ear when the pitch change is small (a few semitones), but once you exceed half an octave the sampled instrument changes radically. This is why multisampling was developed, to change the source sample often enough across the keyboard to minimise the change in playback frequencies required to cover all the required pitches.
Sharp ears will have noticed, however, that some instruments respond much better to multisampling than others and that as a result some instruments have to be sampled much more frequently across their range than others. This is usually because of the complexity of their resonant component (ie that part which doesn't change when the pitch is changing). The more complex this part of the system, the more the vibration of the driver is changed from the original input energies. As a result, the re-pitched sample loses its authenticity very quickly, maybe within a minor third. Less complex resonant systems may allow sampled versions to be transposed as much as an octave before the altered resonance gives the game away. The most complex system, and the one which is much the most resistant to multisampling is the human voice. This is because its most important component by far is the non-pitch related changes in the resonant characteristics (as we will see later, modelling systems can make a fair stab at human vowel shapes because the resonant characteristics can be separate from pitching control).
So far, there are really only two manufacturers using modelling technology for the emulation of wind and string instruments: Yamaha and Korg (although Roland do use modelling components in their Virtual Guitar system, they are applying DSP modifier techniques to the actual sound of a real string, which replaces the virtual driver component). Yamaha were first on the scene with the somewhat pricey VL1 -- a duophonic 4-octave keyboard -- four years ago. Although the price has come down dramatically, they have not really expanded the polyphony of their implementation at all. The latest versions of what they call Virtual Acoustic synthesis are the monophonic £499 VL70m module and a single VL voice in the EX5 workstation and EX5R rack (see box on Combining Modelling with PCM Synthesis). This emphasises the strength of physical modelling for solo acoustic instruments and the fact that the DSP power required to produce polyphonic modelling is still very expensive.
So much so, in fact, that Korg's much written-about OASYS modelling system has never actually been made commercially available (despite several appearances at international trade shows like Frankfurt and NAMM), but has instead metamorphosed into a development platform, from which the technology is trickled down in more affordable packages. This represents a marked change in manufacturer philosophy; 10 or even 20 years ago, they might have tried to sell a limited number at a high price for keyboard stars like Keith Emerson or Stevie Wonder to buy (remember the Yamaha GX1 or the Crumar GDS). These days, however, even the stars prefer to keep their cash in a high-interest account until the more commercially viable versions appear.
The first trickled-down version of this technology (which Korg refer to as MOSS -- Multi Oscillator Synthesis System) was the Prophecy Solo keyboard, released three years ago. Like the VL1, it featured a shorter-than-normal keyboard, clearly showing its solo synth status (most solo acoustic instruments only offer a range of around three octaves) and was monophonic. However, it did considerably broaden the range of physical modelling, adding plucked string, brass and reeds to the various different analogue configurations we looked at in the first part about physical modelling, all for (just) under a grand on its release.
In the UK the Prophecy was a massive success, mainly due to the rediscovery of analogue synthesis as an important factor in the emerging Dance music scene (and perhaps the fact that all the old pomp rockers live here, although the biggest market for their music is still in the US). In other territories, it was a disaster as Korg distributors, scratching their heads for potential markets, attempted to sell it as a lead instrument to put on top of home organs. As a result, huge stockpiles of Prophecies built up throughout the world and these have recently been cleared through the UK for as little as £499. If you search the dealer ads in this issue, you may still find a few for sale.
Polyphonic physical modelling of strings, brass and woodwind finally hit the market last year in the form of the Korg Z1, as DSP chips came down in price to the point where 12-voice polyphony (and 6-part multitimbrality) could be provided for £1699. The models provided were expanded from those in the Prophecy up to 13 by the addition of electric pianos and organs (which we looked at last time) and bowed strings (Prophecy had only featured a plucked string algorithm).
|"...the future probably lies in hybrid instruments combining the
real-time control of modelling with the authenticity of PCM."
In fact, the complexity of real instrument modelling is definitely something which benefits from computer software control, not just for the programming of sounds, but also for simply comprehending what is going on. Thankfully, then, both Yamaha and Korg have released programming software for slightly more widely available computer platforms to aid in sound programming. This has the extra advantage that I can use screen dumps from the different sound models to illustrate my descriptions!
Yamaha produce three different editors, Visual, Analogue and Expert, in versions for the different implementations on the VL1, VL1M, VL7 and VL70m (the fundamental difference being that the VL70m has only one element available per voice, whilst the more expensive units have two).
The Visual Editor is an ideal introduction to the concepts of physical modelling. By allowing you to mix and match drivers and modifiers, it really underlines the fact that Yamaha's modelling system will let you take the output of, say, a reed and modify it through the resonant characteristics of a non-wind instrument body, like that of a cello. By pointing and clicking at the energy input device (bow, reed, finger, mouthpiece) and the resonator (horn, f-hole body, etc), you can design your own hybrid instruments and then make them more bizarre still by processing the sound through something even more (conventionally) inappropriate like a humbucking pickup. Alternatively, you could be boringly conventional and put a bowed string through a violin body or a trumpet mouthpiece through a horn.
Once you have set up the basic configuration of your revolutionary instrument and decided whether you want an alto or tenor voice version (that's high or low to you), there are nice simple editing parameters which allow you to 'tweak' the brightness, thickness, distance, breath feel and reverberation characteristics of the sound. In fact these simple controls are hooked in software to multiple parameters in the VL system, but they provide a 'no fear' editing system. Clearly, the simplification of the parameters means that you cannot get the full capability of the VL system by using this editor, but it can provide an introduction to physical modelling which is free of technical jargon.
|"Don't make the mistake of trying to do everything with one type of synthesis: give yourself as big a palette of sonic generation as possible!"|
The Expert Editor is just the opposite, and within seconds of loading it you have access to the most alarmingly-named parameters -- Slit Saturation Feedback Balance and Graham Function Argument had an old bluffer like me in a flat panic (a little research in the Penguin Dictionary of Physics tells me that the latter refers to Graham's law of diffusion). This editor is definitely not for the faint-hearted, because it really throws you in at the deep end, allowing access to every single parameter in the VL system via four or five tall windows (this software was clearly written on an A4 DTP monitor). However, as with most editing software the best way to learn about it (or any type of synthesis, in my view) is through grabbing the parameter bar, waggling it about, and seeing the effect it has on the sound.
I was a little confused at first to find that the string model had parameters for Conical Horn Insertion and other clearly brass-related terminology, but this turned out to be because the parameters for string and brass modelling on the VL are identical. This is apparently because the characteristics of a vibrating string are very similar to those of a vibrating column of air (see the box on Karplus-Strong synthesis). However, Yamaha's programmers have realised that this might be a barrier to thinking clearly about how you want to change your model to be more like a particular instrument, so there is a menu which lets you change the displayed parameter names between string and wind terminology. Thus the Slit Saturation Feedback Balance legend in a Wind model becomes Friction Function Feedback if you switch to String Terminology (whether or not this does help you to get your head round what you are trying to achieve is a debatable point!).
I have to say that this program really does deserve its 'expert' denomination, if only for the terminology -- but don't let the jargon confuse you, it is fairly easy to use to get the results you want. The one problem I found was that the Expert editor does not allow you to keep several different windows open at the same time. This means that making simultaneous changes to the driver and the modifier is not possible, though separating the driver from the modifier by a different window at least leaves you in no doubt about the effects of each on the final sound.
The third piece of software from Yamaha, the Analogue Editor, really falls outside the scope of this piece, but briefly speaking allows you to turn the VL into a fairly simple analogue synthesizer, with all the standard components you would expect.
Korg's Z1 editor for the Macintosh is very different from the various different VL editors which Yamaha offer, being a much more integrated program. Analogue and acoustic instrument modelling are both covered in the same piece of software and, at another level, parameters for both driver and modifiers are all covered in one window. The plus side of this is that you can see all the parameters for the Reed model at once. The minus side is that if you are unaware of the driver/modifier theory side of physical modelling, this software will not make you aware of it -- indeed, no knowledge of physical modelling theory is required at all to use this software.
For the most part the parameters (of which there are substantially more than in the Yamaha Visual Editor) are named much as a player of the instrument in question, rather than a physicist, would refer to them (see Bell Resonance and Lip Character in the Brass Model screenshot on page 190, for example), and even when more technical terms like Bow Differential or String Dispersion have to be used, you need only try switching it on and off to see what it does. The fact that everything within the individual model is available in one window also means that the mix and match approach of the Yamaha Visual Editor is not possible (no putting a cello bow across a flute tube in this implementation!). This is presumably because Korg's models are actually very different from each other, whereas Yamaha's VL is based around a single model which covers the territory between string and wind modelling.
The Plucked String model made its first public appearance on the Korg Prophecy, but as that was a monophonic instrument its use was limited to things like bass and lead guitars. On the Z1, the polyphony allows its use to be broadened to include strummed guitar chords and violin pizzicato as well as other instruments which you don't immediately think of as having plucked strings, like harpsichord and clavinet. Most of the parameters are fairly obvious (see screenshot opposite), with such factors as the position of the string pluck and harmonic stopping (as well as electric pickup if used), the force of the strike, the amount of damping and the dispersion within the string all not only accessible, but able to be modulated by keyboard tracking and/or all the real-time controllers.
The new string model in the Z1 is the Bowed String model, which of course means mainly members of the violin family. The real blessing of this is that finally strings which are both really responsive and authentic are available polyphonically (Yamaha's VL series have an excellent solo violin which can be duophonic on the VL1). Sample technology gave really authentic strings in one bowing style (Marcato, Legato, Sforzando, etc) but by using the real-time controllers to change the Bow Speed and Pressure, you can now make smooth changes between these different playing styles without worrying about the artifacts which come from crossfading between different samples.
Both the Reed and Brass Models on the Z1 actually have a number of instrument sub-models (to take account of the individual differences between instruments). The parameters used do not change between different sub-models; the sound, however, changes fairly significantly as you switch from one to the next with exactly the same parameter settings. This is because the Korg models do not have parameters to describe the exact shape and length of the tube. Instead these are preset for each conventional instrument within the sub-model. This, again, fits in with the Korg implementation of physical modelling which aims for accuracy in the modelling of real instruments, rather than the ability to 'morph' between different instrument configurations as you can on the Yamaha. Here are the Reed sub-models available on the Z1:
* Double Reed1
* Double Reed2
* Pan Flute
* Reed Synth
Because the size and shape of the instrument is fixed in the sub-model, the parameters which can be adjusted are principally things which may change due to the playing style, such as breath pressure. This means the expression available can be tailored very precisely to a player's technique or the style of music the instrument will be used for. Clearly, the way a clarinet sounds in classical music will differ greatly from its sound in jazz, yet the same physical instrument is used for both. It follows therefore, that it is the playing style which must differ. The parameters you see in the Reed model are what allow this difference to be made.
As with the Reed Model, the Brass model copes with different sizes
and shapes of instrument by having sub-models which you switch
between. The user-alterable parameters are once again designed
to elicit expression and feel from the model, by routing modulations
to real-time controllers like the
X-Y pad and the soft knobs below the display. The Z1 Brass Sub-Models are:
* Reed Brass
Here there are fewer sub-models than in the Reed Model, presumably because there are fewer differences between the different brass instruments than there are variations on the reed theme.
The Z1 probably represents the pinnacle of modelling achievement to date, not just because of its 18-note polyphony or multitimbrality (although these are where the bulk of the DSP horsepower is expended), but because of its versatility. It covers the same analogue territory as Yamaha's AN1x, Roland's JP8000 and Clavia's Nord Leads, but allows more flexible imitations because it can have two models at once (as we saw in the first part of physical modelling), it does electric pianos and organs as well as the Technics WSA1 we covered last time, and now we find it a more specialised modeller for acoustic instruments in a similar vein to the Yamaha VL series. If you want to get a feel for the breadth of sounds and expression that physical modelling can cope with right now, the Z1 defines the current boundaries. If you want to really explore physical modelling for authentic sounds, then beg steal or borrow a Z1 and a Mac to run the editor on. Those of you who want to experiment with the grey areas between specific models and get into the more experimental side of modelling should look at some member of Yamaha's VL family, either a second-hand VL1/7 or the current VL70M module with one or more of the software editors (Visual if you want fast results or Expert if you really like a challenge).
I get the feeling that the Z1 will look as relevant as the DX7 does now in 10 years time -- an instrument that represented a quantum leap forward at the time of its introduction, especially in terms of allowing a player's individuality and expression to come through. Given another 10 years of DSP development, we can expect to find instruments that have the power and speed to tackle the really tricky timbres like the acoustic piano, modelling the interactions between the struck strings and the undamped ones authentically in real time.
Until then the future probably lies in hybrid instruments like the Yamaha EX5 for monophonic instruments and the Korg V3 for polyphonic ones (see box, left), combining the expression and real-time control of modelling with the authenticity of PCM for big ensemble sounds for which modelling still can't create the sonic complexity.
As we near the end of this year-long round up of the different synthesis styles which have been made available commercially over the years, there is a thought I would like to share with you. My recent experiments in combining modelling technology with PCM synthesis (see box) served to underline a lesson I learnt years ago when first combining samples with analogue and digital synthesis, a technique which manufacturers eventually refined into the PCM-based synths of today. No one type of sound generation will give you all the different timbres and expressiveness you want. Don't make the mistake of trying to do everything with one type of synthesis: give yourself as big a palette of sonic generation as possible! Mix and match synthesis types to play to their strengths and cover their weaknesses. Mistrust those ads which tell you any one product will give you all the sounds you need, but encourage manufacturers who combine technologies within individual machines like the Yamaha SY99 or EX5, the Technics WSA1 or the Korg V3, as well as those who persevere with the more esoteric forms of synthesis like Kawai and Waldorf. It will be a very dull world, sonically speaking, if we all end up using PCM-based synthesis for everything (something which looked a very real danger a few years back, but which has now receded somewhat thanks to physical modelling and the re-emergence of analogue synths in dance music and the like).
Next time, we will finish off by taking a look at some more esoteric types of synthesis like granular and re-synthesis which are emerging from the less commercially driven areas of computer shareware and the Internet, further expanding the palette of sonic creativity. In the meantime, get your hands on physical modelling in some shape or form if you possibly can (remember you can now get a VL70m or a Prophecy for under £500), and don't forget to try combining it with the other synthesis types to which you have access, either in sequences or individual program combinations. Your music will be the more expressive for it.
Long before anyone succeeded in properly modelling plucked strings (see main text), there came the Karplus-Strong synthesis algorithm (after Messrs Kevin Karplus and Alex Strong, who developed it at Stanford University in California). A description of this algorithm was first published by its developers in the Computer Music Journal Vol 7 Part 2 in 1983. It is now often identified as one of the first physical modelling algorithms, as this technique anticipates modelling by defining the required stages using terms coined by physicists analysing components of a vibrating string. Essentially the way it works is to introduce a noise burst into a delay line whose time determines the resonant frequency of the string, pass this through a low-pass filter to simulate the energy loss caused by the reflection of the wave in the string and then feed back the result into the delay line.
The original version of the Karplus-Strong algorithm would produce two or three 'moderately realistic plucked string sounds' (to quote the humble Kevin Karplus) simultaneously in real time on an 8080A processor (imagine what it could do on a modern processor) and gained several US patents. It was licensed by several companies who have yet to produce a stand-alone product from it (although Kevin Karplus reports that a few companies have tried to market the technique without paying royalties).
Apparently, if the decay element from the filter is taken out then it performs a reasonable impression of a vibrating column of air in a tube open at both ends. This perhaps goes someway to explaining the similarity of Yamaha's string and wind models, in which some parameters do the exactly the same things but are given different names relating to the physical attributes of the instruments being emulated.
Most people who are familiar with Karplus-Strong synthesis will know it from its inclusion in Digidesign's seminal sample editing program from the '80s, Sound Designer (before it transmogrified into the proto-hard disk editor, Sound Designer II). Unfortunately, this implementation of Karplus-Strong, whilst producing some quite nice timbres, suffers from not being real-time. Once the computation has been done off-line, it is rendered as a sample so that it can be transferred across to whichever sampler your version of Sound Designer was supporting. This means that it suffers from the same problems in playback as all samples, ie. it gets longer the lower you play it and shorter the higher up the keyboard you go. It does, however, give you quite a nice flavour of the potential of the algorithm as a historical step on the road to current physical modelling techniques, so those of you who can track down the original version of Sound Designer (it was produced in customised applications on the Mac for the Emulator II, Prophet 2000, Akai S900 and E-max among others) can have some fun generating mutant guitars and mandolins.