Surely the only convincing synth pianos are sample-based ones? A sound as rich and expressive as that of an acoustic piano is far too complex to be rendered by subtractive synthesis... isn't it? We find out... This is the 42nd article in a 63-part series. Read all parts.
You might think that you'd have to be pretty wrinkly to remember the days when synthesizers were unable to
You could go back as far as 1954, and propose the earliest Wurlitzers, or to the mid-'60s, when the Fender Rhodes, Wurlitzer EP200, and Hohner electric pianos first appeared. But let's be honest... despite their electromechanical (as opposed to purely electronic) sound-generating mechanisms, none of these sounds like an acoustic piano. Each exudes piano-ness, and you can sometimes use them when a piano would be the preferred instrument, but try to play a Rachmaninoff piano concerto on one and you'll soon discover its limitations.
If you're sneaky, you might s
For obvious reasons, monophonic synthesizers are not admissible as piano substitutes. Neither, as you will know if you were ever forced to use one, were the host of ghastly electronic pianos of the early '70s. So let's now jump to the introduction of polyphonic synths in 1974. Hmm... still no good. The Yamaha GX1 couldn't sound like a piano, nor could the Oberheim 4- or 8-Voice. Moving forward another few years, we can also discount the Prophet 5, the OBX, the Jupiter 8, and all of the other big, analogue polysynths of the era. Well then, what of that hyper-expensive late '70s sampler, the Fairlight CMI? Sorry... its memory was too limited to hold and replay a convincing set of piano samples.
Let's move closer to the present, and enter the digital era. As we all know, the Yamaha DX7 was capable of remarkable imitations of electric pianos such as the aforementioned Fender Rhodes, Wurlitzers and Hohners, but even its phenomenal FM synthesis engine was incapable of generating acoustic piano timbres. Then, in 1984, the hyper-expensive sample players cracked it, when the Kurzweil 250 offered the best emulation yet heard the famous 'Kurzweil Piano' on which the company's reputation is still based.
Two years later, this became affordable when the Roland HP5600, its stage counterpart the RD1000 (the 'Elton Jo
Even as recently as 1987, no programmable synthesizer had produced a convincing piano sound. Then the Roland D50 introduced what we now know as S&S, or Sample and synthesis, which, for the past 15 years, has been the standard synthesis method across most of the industry. Next came the Korg M1, and some players liked its piano (though I hated it). But the real breakthrough was the Roland U20. Launched in 1989, its RS-PCM engine was an ancestor of Roland's JV sound engine, and its piano patch was almost as good as those produced by the most powerful samplers of the era. This was remarkable, because the U20 was a cheap, basic sample-replay keyboard with hardly a parameter to its name. But the samples were good, the looping was excellent, and the rudimentary envelopes did the job required of them.
By the dawn of the 1990s, S&S sound generators were de rigeur, and piano sounds began to pour forth from every £199 home keyboard. Nowadays, almost every synth offers a piano patch (or 20) and our ears have become so accustomed to them that many people have become unable to distinguish between a real piano and a synthesized imitation. Hang on... that's not true. I should
We've encountered this situation before. In August 2001's instalment of Synth Secrets (see www.soundonsound.com/sos/Aug01/articles/synthsecrets28.asp), I pointed out that it's not possible to create authentic-sounding acoustic guitar patches using subtractive synthesis. And therein lies a hint as to the nature of the problem. Sure, a piano hammers its strings rather than plucks them, but the two instruments exhibit some significant similarities. For one thing, piano strings interact with each other in different ways, depending upon their pitches and the number free to vibrate at any
It's not a very encouraging scenario, I'll admit. Nonetheless, this month's task is to develop an understanding of the piano in order to synthesize it as best we can, so we'll start by taking a look at the piano mechanism itself...
There are many types of piano, from Granny's unplayable Victorian upright, to the works of art that are the nine-foot grand pianos found in the more expensive concert venues. Most have 88 keys (which is why the largest synths and workstations use this number) although a few have more. This means that a typical piano has a fundamental range of over seven octaves, which is far greater than any other instrument (except for large pipe organs and the extended pianos, which, with their extra keys, reach to eight octaves!) Given that a young, healthy human can hear a range from approximately 20Hz to 20kHz which is pretty much equivalent to 10 octaves this means that a large piano covers as much as 80 percent of the range of human hearing!
An 88-note grand produces its soun
As you can see in Figure 1 (above), the strings are suspended above a soundboard. However, despite being strengthened using struts, the soundboard is not a structural part of the instrument. This is because the pressure exerted by the strings can be as high as 20 tons, which would snap the board in an instant. Consequently, a heavy iron frame is used. Apocryphal stories exist of concert grands falling from a great enough height to cause the frame to collapse. The energy thus released is considerable: a 20-ton explosion is just as destructive whether unleashed by a piano or a briefcase of C4 plastic explosive.
Let's now look at the striking mechanism (see Figure 2 above). When you press a key, a system of levers (which I have shown here in greatly simplified form) causes a hammer to strike the appropriate string(s). If you look at the positions of the pivots and consider the movement of each part of the mechanism, you can see that a small amount of travel on the playing surface of the key translates into a very rapid movement of the hammer head. When this strikes the strin
If you refer back to that August 2001 instalment of Synth Secrets, the one on how guitars produce their sound, you'll recall that, after you pick a guitar string, it vibrates at its fundamental frequency and overtones. I also mentioned that because the plucking position cannot be a node of zero displacement certain harmonics will be emphasised or eliminated depending upon the plucking position. Figure 3 (below) shows how a pluck in the centre of the string precludes the even-numbered harmonics from the initial spectrum.
Now, consider the piano string, which is not plucked, but hammered. Whereas the position at which a guitar string is plucked determines its maximum displacement, the piano hammer remains in contact with the string long enough to ensure that the position at which the string is struck is a node of zero displacement. If the hammer position were to be halfway along the string, you would, for an instant, have two sections whose lowest pitches lie one octave above the fundamental of the whole string. This means that the funda
The situation becomes even more complex if the hammer position is not halfway along the string. For example, if you hammer a piano string a third of the way along, you will divide it into two parts, one having a fundamental an octave above the other. But even this is simple compared to the situation where the hammer position is, say, 17.549 percent of the way along the string. As you can appreciate, the two pitches thus produced are unrelated to one another, and both are unrelated to the pitch of the whole string. I have shown the fundamentals of two such sections in Figure 5 (see above).
However, this situation lasts for just a fraction of a second. Soon after the hammer has completed its action, it bounces off the string. The vibrational energy is then free to run along the whole length of the string, and, by a convoluted mechanism of energy transfer, the string begins to vibrate at its fundamental and harmonic frequencies. However, the spectrum of the sound will still depend upon the striking point.
Given this, you would think that, to obtain a consistent tone, piano builders would position the hammers consistently from one end of the keyboard to the other. But this is not the case; you will find them anywhere from one seventh of the way a
Got a headache yet? Then get this... Most notes are generated by three strings, and it's all but impossible to tune these to the same pitch. You can get very close, to the point where any beating between them is almost undetectable, but the strings will soon become out of phase with one another, such that one string is moving 'up' while another is moving 'down', and so on. This leads to interference, with the strings swapping energy, reinforcing and at other times cancelling each others' modes.
Hmm... it's becoming fairly obvious that we can't fully analyse the vibration(s) in the string(s), but at least we can state how the energy from these vibrations is transmitted through the bridge to the soundboard. Except that we can't. Using different bridges can change the sound of a piano by a remarkable degree, and given that pianos generally have two of them one for the treble strings, and one for the bass and that they are coupled through the soundboard, we find that even this is too complex for us. What's more, piano soundboards have an irregular shape and are chamfered, so our previous discussions of vibrations in flat plates are, at best, approximations to the way that a s
So where in terms of subtractive synthesis do we go from here? Sure, we can use three detuned oscillators to imitate the strings in a tricord, and add a couple more to create the atonal impact (see Figure 6 on the next page). We can even add contour generators and VCAs to crossfade between the two. But we will never be able to synthesize the complex interactions that give the piano its unique character. We could complicate Figure 6 by adding some sort of feedback to modify individual oscillator's waveforms and amplitudes, and this would no doubt generate interesting, organic sounds. But it would not be the same as a piano, and it would not fool you. We don't even know what starting waveform to use for the oscillators!
Many synths allow you to affect the loudness of a note using velocity sensitivity. And, although a piano's spectral response to changes in velocity can be very complex, its amplitude response is fairly straightforward.
Firstly, we know the general shape of the amplitude envelope for each note. There's an initial impact followed by a slow decay. We also know that if we don't release the note, the tail can linger for tens of seconds, which tells us that the rate of the decay diminishes as the note progresses. This is because, as the pairs and tricords interact, the rate at which energy is transferred to the soundboard (and is thence dissipated into the air) diminishes. I have shown the resulting envelope in Figure 7.
Of course, the piano has a large dynamic range, so we must make the amplitude contour velocity sensitive, as shown in Figure 8. What's more, the amplitude curves of low notes decay more slowly than those of high ones, so we should also make the
We can synthesize this using the architecture in Figure 10 (on the next page), which uses velocity sensitivity and keyboard tracking to affect both the maximum gain of a VCA and the decay rate of the contour that shapes it (in truth, there should be a handful of additional mixers and amplifiers, but I have omitted these for clarity).
Having created a simple model to synthesize the amplitude response, we must now consider the spectra of different piano notes, and how these change in time.
For any given note, we can separate the sound into three distinct stages: the initial hammer blow, the transition period during which the strings begin to oscillate harmonically, and the tail, which is dominated by the fundamental, and whose higher harmonics decay most rapidly.
I have accounted for the first of these sta
The second stage is much harder to emulate, because it is here that the nature of the waveforms is changing most rapidly. I suppose it's possible that we could invent a synth architecture to imitate this, but I know of nobody who has succeeded, and (even if possible) the block diagram would take up more pages than are left in this month's copy of Sound On Sound. We'll simply have to return to this stage later. So let's move to the third stage, which is the simplest to reproduce, requiring (to a first approximation) little more than a contour generator and a low-pass filter.
Experience tells us that piano notes are brighter when hit harder (see Figure 11) so we will need to scale the filter appropriately. Furthermore, piano notes are brighter at high pitches than they are at the low ones. But remember that the high-fre
This means that the filter cutoff frequency must respond to note number (or pitch CV), key velocity, and some form of contour, with the decay rate of the contour responding to the note number (see Figure 13).
If I wanted to complicate matters, I could point out that, for the lowest notes on a grand piano, the fundamental pitch has very low amplitude, and the note that you think you hear is to some extent implied by the harmonics. This suggests that we require a high-pass filter for the lowest notes in our synthesized sound. But I think we should ignore this. There's only so far we can go before we reach the point of diminishing returns, adding complexity for little extra benefit.
Next, we must turn to the subject of tuning. I mentioned in that instalment on the physics of the acoustic guitar that a string's harmonics are stretched as the pitch increases and/or the excitation increases in amplitude. This is because the string requires a finite length in which to bend over the bridge and nut, thus shortening the effective length. Not particularly important at the fundamental frequency, this becomes more significant at higher harmonic numbers, and stretches the harmonic series from 1:2:3:4:5:6... to something that may look more like 1:2:3:4.01:5.02:6.04... and so on (don't take these numbers too seriously; I just made them up to illustrate the point).
This stretching of the harmonic series has far greater consequences on a piano than a guitar because, on the piano, we are able to play chords reaching across seven o
Putting It All Together
If I now combine all the elements discussed above into a single patch (see Figure 15, below), you can see that it's a biggie which exceeds the capabilities of most synths even without a complex oscillator section to recreate the authentic piano tone! And, even when carefully programmed on a large modular synth, it sounds like a Wurlitzer or Pianet. It does not sound like a Bösendorfer.
This is hardly surprising, and it would still be the case even if we modelled the hammers and strings perfectly. This is because we have totally overlooked the resonances of the soundboard and the glorious reverberant effects of the piano body itself.
What's more, we haven't even touched upon complicating factors such as the action of the pedals. The most important of these is the right-hand 'sustain' pedal, which lifts the
So... is it impossible to create an acoustic piano patch on an analogue synth? The strict answer is 'yes', but as someone who performed for a couple of years using a 76-note analogue polysynth as a stage piano, I have to admit that the situation is not as gloomy as it seems. Sure, the patch I used would never fool you into thinking that you were listening to a real piano, but, like the Fender Rhodes, Wurlitzers and Hohners mentioned at the start of this article, it was piano-like, and useable for rock and roll. The polysynth in question was the Roland Super JX10, and next month, I'll show you how it managed it.