@audiokinesis
I’m saying that the lowest fundamentals (and sometimes the corresponding first overtones) of the lowest notes of a non-Bosendorfer grand piano contain so little energy that they do not merit being reproduced in a live music setting.
I want to try to nip this idea off, here and now!
Just try this little experiment. Find yourself a mechanical (not electronic) piano and play the lowest key. You will hear the fundamental note, plus overtones. To discover what the first overtone sounds like, move up one octave and play that key. If the two notes sound as if they are the same frequency, then you cannot hear the lowest fundamental. But my experience on a Kawai upright piano is exactly the opposite, the lowest note is clearly an octave lower and is clearly audible. Just in case somebody suggests that the fundamental one octave up is also inaudible, hop another octave up and repeat. They cannot all be inaudible!
Why an octave? An octave is just double the frequency and in Western music there are eight white piano keys spanning an octave (which is why the Latin for eight features in its name). There are seven white keys and five black keys before each octave pattern repeats - 12 notes in all. When Pete Townshend said he chose his double bass for the session, he doubled his pay by doubling this on an electric bass guitar 12 notes higher. Had me a bit confused but he was just playing one octave up, something very common in orchestral pieces where cellos double the basses, the picolo doubles the flute and so on.
The physics of the fundamental vibration of a string are well known. The vibration frequency depends on the length of the string, the mass of the string and the tension in it. The fundamental frequency is where the entire string between its fixed ends moves in the same direction. But there is another mode, where the middle of the string remains stationary, and the two halves move in opposite directions. This is the first harmonic, and it is an octave up from the fundamental.
And there are even more vibration modes, where there are four, five, six and so on stationary points in the string. By and large these modes do not sound pleasing.
One more thing. A string can also vibrate along its length, and that vibration can be picked up. Usually the sound is horrible, like a violinist’s finger sliding on the string. When bowing, it is important that the bow remains at right angles to the string to avoid longitudinal resonances. It is said that violinists take about five years to learn how to use the left hand to get the right notes. The next five years is learning how to bow properly.
So can piano be a useful guide to loudspeaker bass reproduction? Absolutely. I will take four speakers I am familiar with as examples. The first is the market-leading bookshelf speaker from KEF – the LS50. Its bass output has a 3-db roll-off at 79-Hz, which is well over an octave above the 31.5-Hz fundamental of a standard piano’s lowest note. You won’t get much of its first harmonic either!
Staying with KEF but spending maybe eight times as much, we get the slightly bigger bookshelf KEF Reference 1. Its 3-db bass rolloff is at 45-Hz so you will not get much of the fundamental but the first harmonic should be all there.
My third speaker is a full-range electrostatic from Quad – the ESL-2905. I cannot find its 3db rolloff but it is flat to 45-Hz and 6db down at 31-Hz. No real need for a subwoofer here.
Finally to a subwoofer – the 18” servo controlled Velodyne DD-18. This has a 3db rolloff at 14.1-Hz, more than an octave below that fundamental. Good for a Bosendorfer or Stuart concert grand.
The Velodyne fleshes out the Reference 1 beautifully, and takes a bit of the bass load off the Quad, which otherwise has little need of a sub.