Why the obsession with the lowest octave

On 1/21 Dan_Ed wrote:

To ignore the range from 20 to 40 Hz is to deny the FACT that there are harmonics down in that range that do affect realistic music reproduction.

and on 1/22 Arj wrote:

adding on to Dan_ed's post, from what i could figure out the fundamental at 40 Hz has a subharmonic at 20 Hz as well as overtones at 80 /160

If I understand these statements correctly, then a harmonic overtone series is produced both upwards and downwards in frequency from the fundamental frequency. That's just not my understanding of harmonic overtones. With very rare exceptions acoustic instruments produce only higher frequency overtones. Am I wrong? Can someone please explain the math.

Dan_Ed, good point about cymbal and bass content. Large cymbals are basically enharmonic and their frequency spectrum can go from 30Hz to 60+kHz. The bass content shouldn't be that surprising since the cymbals in question are 11" diameter and greater. They are the size of large woofers.

Onhwy61... Two signals, one at 30 Hz and the other at 20 Hz will yield a "beat" at 10 Hz.

Yeah, and a snare drum whack is maybe an even better example of the very complex sounds we listen to.

I think what sometimes happens is we read the definition where is says that the harmonics are "integer multiples" but we forget that there is a negative integer series that fills in below the fundamental and we get that bell curve shape around the fundamental. This is in the frequency domain.

Dan_ed... I don't believe that you can call modulation below the fundamental a "harmonic".

Consider a violin string. It is fixed at each end. and sounds a fundamental tone. But, by soft placement of a finger in the middle of the string you can immobilize that point of the string so that each section (end-to-middle and middle-to-other-end vibrate at a higher frequency because the length of sting is shorter. I don't see any way to make the string vibrate at a lower frequency (other than by loosening it up).

Mixing two different tones is another story but the lowest frequency is called root and the rest are overtones that are higher. When you play instrument with complex harmonic structure (typical for percussion instruments) like piano - each key produces tone and overtones. There is no sub-overtones. The same is with guitar and many other instruments. Some things like bells produce subharmonics but for the rest of the instruments it is not common. You can obtain subharmonics with violins using special techniques (not very common) but you won't get it from the piano's individual keys.