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If a piano could play all the notes within audible range, how big would it be?

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The standard 88 keys is a very good range for a piano. It's difficult to get a clean, audible and musical tone above the top note (C8), and some pianos struggle to produce a nice sound on the top 3 or 4 notes, anyway. Stewart in Australia makes a very large and expensive grand piano with notes higher than the standard C8, and they've managed to pull it off nicely with clean tones you can hear. The Bosendorfer 295 has extra bass notes below the standard A0. I've never found those extra notes to be very useful or particularly musical - and trying to tune them is a bit of a challenge. They're so low that the lower notes are more of a rumble than a recognizable musical note, but it's still very cool, especially if playing octaves with a higher note, and you can do interesting things with it.

What's more important to mention is that on the lower bass notes, even on a standard piano, the fundamental frequency (which I believe is around 27Hz on the lowest A0) is barely audible. You could record a piano with a microphone with a lower range of 40Hz and barely notice a difference. Or you could use a filter that cuts out bass frequencies below 40Hz - and it would still sound like a piano. When you play a note on the piano, you aren't just hearing the fundamental tone, but a whole partial series of higher frequencies produced by the vibrating string: the fundamental, one octave above the fundamental, a fifth above that, a fourth above that, and a series of smaller intervals that get smaller as you progress higher. The amplitudes of the higher partials tend to diminish as you go up, but some may stick out more than others.

The tension and hardness/softness of the hammer felt changes the way the hammer excites the strings. Overly bright or hard hammers will excite the higher partials too much, producing a harsh, glassy tone. A properly voiced hammer will have more "give" as it strikes the strings - think of a tennis ball compressing as it hits a wall. There is a lot going on, as you would see with a high speed camera, but to simplify the explanation, a softer hammer with more "give" will be in contact with the strings for a longer duration, which somewhat mutes those higher partials before the hammer bounces back off the strings. When voiced correctly, this "give" produces the more pleasant, musical tone that we try to achieve when voicing hammers, because the amplitudes of the various partials are in a good balance.

Getting back to the original question, you could keep going lower and lower with longer and heavier strings in the bass, even below that of the Bosendorfer 295, and you would still hear plenty of sound - but only because of the higher partials making up the complete tone of the vibrating string. You would not hear the fundamental frequencies of those notes at all. But you really don't hear them on the lowest notes, anyway. As I indicated before, you could filter out the fundamental frequencies of the entire low octave and most people wouldn't hear the difference. But as with the 295, those extra low notes produce more of a noisy rumble or growl than a clear musical tone. So going any lower than that would just produce more noisy rumbles and growls, and it would probably not be very useful to the pianist or composer, unless you're just trying to make cool sounds for effect.

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Republished from https://www.quora.com/If-a-piano-could-play-all-the-notes-within-audible-range-how-big-would-it-be