middle c.

A continued study of imperfection and perfection ....

So admittedly I have been researching piano sample sets online. Perhaps out of some morbid fascination I am not sure. Or an innate desire to always have a better sound than I have at my current disposal (the library of samples that came packaged with Logic and my half-tuned in-need-of-restoration Bechstein). Regardless of reason, however, I know full-well that a sampled piano will not be able to physically replicate the sound of a true acoustic piano (and not even taking into account the difference in touch with even the highest end, hammer-weighted actions found on high-end controller keyboards – they simply will not compare to a Renner or Erard action found on a grand piano). The reason, perhaps oddly this time, is actually perfection.

Take for example this scenario: an über-high-end piano sample (meaning made with, say, twelve velocities per note, from pppp to ffff with sustain on and off) can be comprised of more than two thousand samples (88 x 12 x 2 = 2112), at least 80GB of data and require at minimum 4GB of RAM even when using various morphing technologies that allow offloading of processing power based on samples actually used – not entirely unlike MPEG compression albeit slightly different in theory) but – and this is key – it falls apart reproducing what an acoustic piano does naturally – overtones. The necessary processing power to replicate even the simplest set of overtones is at least to-date challenging (and yes, I realize a new Mac Pro for instance can be stuffed with 16GB of RAM – but I want to say there is actually a degradation in performance when using too much RAM? – but the aforementioned 4GB of RAM is simply to reproduce the given samples on their own, not taking into account the overtones of multiple sampled notes, which is why I chose the word "challenging").

But just pluck a string (of fixed length) and you get overtones. No RAM required. Perfection. Mathematical anyway, as they are integer multiples of the fundamental frequency.

Take Middle C (actually, we'll use the C an octave below as our fundamental – known as C3 on the piano – thus placing Middle C as the second harmonic of the fundamental which is always an octave above or 2x the fundamental frequency). This string, when the piano is tuned to concert pitch, vibrates at 131 cycles per second (actually, 130.81Hz but I will round up for simplicity). The second fundamental – as stated – is 2x that frequency, or 262Hz (Middle C/C4). The third harmonic is 3x the fundamental, or 393Hz (the G above Middle C, or a 5th above C4 – same thing). The fourth harmonic is 524Hz, or C5 – two octaves above the fundamental or a fourth above the third harmonic). The fifth is 655Hz, or E5 (a third above C5). The sixth – 786Hz, or a 5th above C5 (notice how the 4th, 5th and 6th harmonics form a C major chord two octaves above the fundamental C?). The seventh overtone is tricky – it produces an unwanted note due to physics and harmony. But in our unfound wisdom we have devised a cunning scheme to avoid it on the piano by placing the hammers near the 7th node of the speaking length of the strings (a node is a point along a string where it does not vibrate – so by dividing the length of the strings by 7 and placing the hammers at a distance of 1/7th the length of the string – approximately – this overtone is avoided – mostly, and since it is an overtone and reduced by this placement it is basically not heard). Brilliant. And I'll avoid the elaboration of why this is to be avoided, but basically it is a very flat minor seventh (hence, the division by 7 of the string length) of the fundamental and does not sound harmonious.

OK, I realize I could continue that ad infinitum but in any regards – the overtones are mathematical and thus perfect. However, they create dissonance (in other words, an imperfection). The key is that there is good dissonance (a diminished chord, for example) and there is bad dissonance (a flat minor-seventh), so-to-speak. In the case of harmonics, dissonance is absolutely necessary. For it is in this very dissonance that what is known as timbre is created (subtle, but yet another example where imperfection is necessary). And timbre is loosely-defined as "the quality of a musical note or sound that distinguishes it from another." It is what allows us to tell the difference between a guitar and a harp. Or a trombone and a tuba. Or a Bechstein and a Bösendorfer. And as hard as engineers have tried, the dissonance and thus imperfection resulting from the near-perfect mathematical equations going on with a struck string, let alone ten or twelve or twenty all vibrating at once, is not possible with digital samples.

At least not yet. Perhaps someday, but that really is beside the point. I still am refusing to drag myself into an analog vs. digital debate. To each their own. But as I listen to high-end sample after high-end sample of some of the finest pianos in the world meticulously recorded in elaborate studios and then go back to hammering away on my Bechstein, the coloration of the sound (hence, the timbre of all the overtones) is much more intense than what can currently be achieved with sampled instruments.

And with that I digress ....