I love the idea of an F# (or E even) string, but I have to wonder about how many people would never hear it because their speakers weren't up to the task.
the harmonics would be good enough. . . . .
Nahh. Its a whole 'nother world down in the area below 30 Hz. The fundamental becomes something you begin to feel, not so much hear; an almost visceral experience. Not many people have really experienced strong fundamental down there. Pipe organs are about the only musical instrument that can produce notes of adequate strength near that area (and you need to hear it live, not from a recording). If you're going to be satisfied with just the harmonics, why bother?
The remark by andrewd is very germaine to the problem of properly producing an F#0 (23.12 Hz) fundamental. In the seventies, Cerwin Vega created the Sensurround system for Paramount (I think) for the movies "Earthquake" and "Midway". I think there was a third, but I never saw it nor recall the title. The horns they desiged used 2-18" "Earthquake" (the fore-runner of the "stroker") drivers that were capable of over 1.5" excursion in the folded-horn to produce max SPLs of over 130 dB for a bandwidth of 16 to 63 Hz. In comparison, direct-radiator bass cabs can be designed to produce strong fundamental in that area, but not at very high SPL and to do so would be a cabinet I would not be interested in moving.
The other side of the coin is that below 30 Hz I'm not sure I would really call content musical. Most of the real-world info in that area would be impulse, non-musical events - explosions, earthquakes and the like.
In the mid-seventies, I designed and built a set of speakers for home stereo use that measured -3 dB output at 18 Hz. I used some the highest quality 15" woofers that existed then, but believe me, they weren't capable of very high output at that frequency. Direct-radiating drivers just can't move the volume of air, even an 18" considering excursion/power limitations, necessary for even moderate SPLs. Direct-cut records that contained pipe organ were about the only source material that had adequate amplitude that wasn't eq'd down as they were on regular commercial records. But even a properly designed bass horn with a cutoff at F#0 with smooth response would be of almost unmangeable proportions for general gig use. I decided that building such a system just didn't represent a useful tool for musical sound. I'd say the same for a bass with an F#0 string. Its hard enough to find basses that can do justice to a B0 note at 30.87 Hz, let alone a practical cab that can produce the note. Very few commercial cabs, bass or PA, have cutoffs below 50 Hz.
Enter the subject of psychoacoustics - very interesting stuff. check out this link if interested and want to wet your whistle (Pun intended, but I still like real fundamental. Once experienced, harmonics just don't cut it for me.):
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and
http://en.wikipedia.org/wiki/Psychoacoustic_model
Enjoy,
Lloyd Howard