[CAUT] The fundamental - where is it?

[Greg Graham]

Regarding the bass end and our perception of fundamental, I was tuning in some modular-style practice rooms last week and heard what I thought was an electric bass practicing in the next room.  I looked in and it was a student playing a Yamaha U3.  The walls filtered out all the high frequencies.  Seemed like lots of fundamental going on in there, normally hidden by all the upper partials.

A0 fundamental of 27 Hz or so is really low.  It would be hard to hear even if it was the only thing moving air.  

I was playing some clarinet duets with a student today and experimented with interference tones (Tartini tones).  If one player holds A5 while the other acscends slowly from F5 to G#5, you hear the "beats" as a clear tones in your head.  

A5 (880 Hz) minus F5 (698.5 Hz) equals 181.5 Hz, 
which is a little flat of F#3 (185 Hz)

A5 vs F#5 beats 140 Hz, close to C3
A5 vs G5 beats 96 Hz, close to G2
A5 vs G#5 beats 50 Hz, close to G1

The interference tones were very easy to hear at C3 and G2, but I was suprised how the character started to change from a tone to more of a buzz at G1, and also at how low that tone seemed.  I really had to concetrate to realize it was there.  

My point here is that a 50 Hz tone, even with an edgy waveform, doesn't jump out at you.  Go an octave below that and, well, we shouldn't expect to hear lots of fundamental.  

This University of New South Wales (Sydney, Australia) website has some useful music-related acoustic science (but not specifically about pianos):

http://www.phys.unsw.edu.au/music/

If you want to hear some 30 Hz sine waves (between A#0 and B0), try their hearing test page:

http://www.phys.unsw.edu.au/jw/hearing.html

Of course, you need speakers or headphones capable of actually producing 30 Hz.  Uh, and ears capable of hearing 30 Hz.  This isn't much good as an actual hearing test, but it is a handy tone generator.

Greg Graham