Posted by Kenneth Sloan on November 30, 2001 at 22:38:50:
In Reply to: False tones... posted by Amateur acuostician on November 30, 2001 at 10:28:55:
in short: because real instruments are neither straight pipes nor perfectly conical. They are a mixture. Designers have considerable freedom to move modes around, and try to create a useful instrument. The story you learned in "Intro to Music I" is a (useful) fairy tale.
See: _The Physics of Musical Instruments_, by Fletcher and Rossing.
On page 433, I find the statement: "Adjustment of the shape is usually carried out in the course of design to produce a mode series approximating (0.7, 2, 3, 4, ...)f0. The first resonance is very much out of alignment, produces a very weak wound, and is not used in playing. Good players can, however, use the nonlinear effects we shall discuss later in this chapter to produce a pedal note at frequency f0 by relying upon cooperation with the harmonically related higher resonances."
I note that [Young, 1960] is cited twice in the immediately preceding text.
Young,, F.J. (1960). The natural frequencies of musical horns, "Acustica 10", 91-97
I leave it to others to compute the note at 0.7*f0, where f0 is either a Bb or a C.
I suspect (but do not know...certainly not first hand!) that a good player can produce "false tones" based *either* on the 0.7*f0 mode *or* by creating a spectrum with all of the overtones *except* the target note (in the latter case, the ear analyzes the entire spectrum and "hallucinates" the missing frequency at the bottom. [there are mechanisms other than "hallucination", but I think that idea is enough to give one the idea of what's going on, even if we're not too specific about *where* it happens.
For more...read the book! (take your pick from the list below)
I suggest:
_Fundamentals of Musical Acoustics_, by Arthur H Benade (undergraduate level)
_Horns, Strings, and Harmony_, by Arthur H Benade (Scientific American/high school level)
The Fletcher & Rossing book is a graduate level text, with lots of strange mathematical symbols in it. I think traffic engineer could handle it, but DMA's might find it heavy lifting.