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[Hank Alrich]

Harvey,

I think I've read comments from you (IIRC, not a given... <g>) that lower strings of plucked string instruments rarely give us the fundamental that we'd expect from calculation according to string length, but generally speak an octave above that.

I posted about that into RMMGA, and Steve Hawkins wondered how you assessed that. I said I'd ask, and here I am asking.

Curious to know more about this. At your convenience can you fill us in on details? Please, and thank you, and no hurry. I'd be happy to copy a reply here into RMMGA if you're no longer accessing Usenet.

[Jim Williams]

When Garry Goodman uses his .250 diameter custom strings on his 12 string bass, it does do fundamentals very well. He tunes it to 15 hz and the Basson amps and cabinets reproduce it very well. No, you can't hear it well, but you can feel it. The amount of air pushing out the vents is almost like an air pump.
The high notes on this 36 fret instrument go up to the piccolo  range so it is the worlds widest range electric string instrument. Those high strings he makes are .004's to get that high up.

BTW, yes, he can really play that thing. Yes, those amps do go down to 2 hz FLAT.
www.bassonsound.com
www.garrygoodman.com

[Tomas Danko]

Hank Alrich wrote on Mon, 18 January 2010 17:27

Harvey, I think I've read comments from you (IIRC, not a given... <g>) that lower strings of plucked string instruments rarely give us the fundamental that we'd expect from calculation according to string length, but generally speak an octave above that. I posted about that into RMMGA, and Steve Hawkins wondered how you assessed that. I said I'd ask, and here I am asking. Curious to know more about this. At your convenience can you fill us in on details? Please, and thank you, and no hurry. I'd be happy to copy a reply here into RMMGA if you're no longer accessing Usenet.

Other parameters that affect the matter of reproducing the fundamental are the amount of pressure that the string applies on the saddle and nut as well as the type of hardware used to mount the strings.

For instance, a fixed stop-tail setup (i.e. Gibson Les Paul) can give you more of the fundamental as opposed to, for instance, archtops such as the Gibson L-5 or Epiphone Emperor setup.

[Edvaard]

This isn't quite the same thing that Harvey appears to be alluding to regarding hearing the sound an octave above, but something string players might be interested in anyway;

http://en.wikipedia.org/wiki/Piano_acoustics

and this one, fourth page, second graph of fig. 2, the graph of a harmonic series;

http://arxiv.org/ftp/physics/papers/0605/0605154.pdf


As explained in the Wikipedia, a low tone with necessarily shorter length is countered by increasing string thickness, but the required greater tension results in more harmonics. As the string gets thicker (and with greater tension), the total energy of the increasing harmonics starts becoming greater than the energy of the fundamental.

I have a some nice sheets showing Fourier series of low-mid-high tones on various instruments but I can't find it now. But I remember that the harmonics increased a lot relative to fundamental as the string instruments went lower.

My guess as to why we might hear it an octave above the fundamental on lower notes is that the higher amplitude harmonics combine in a sum/difference ("false bass", "subjective tone", etc.) fashion to make the octave above the fundamental more prominent.

With a larger sound board, e.g. upright bass vs.  acoustic guitar, or with tighter bridge coupling, as Thomas mentions above, the fundamental is stronger to begin with, so this octave-above phenomenon would manifest lower and not as noticeably.