Posted by Paul R. Ogushwitz on December 05, 1998 at 07:29:24:
In Reply to: Re: Re: Re: Re: false tones posted by Aaron Eichelberger on December 04, 1998 at 19:28:58:
Aaron, thanks for a clearly stated explanation. Caution in your second paragraph: the fundamental you describe is for a BBb tuba -- it changes correspondingly for tubas pitched differently. (Judging by your excellent third paragraph, you are aware of this. I think it deserves clarification for the non-physicists who read this thread.)
Your guess that the horn stops behaving as a single-open tube and starts behaving as a double-open tube at low frequencies may have some merit. Near the fundamental frequencies, the wavelength of sound approaches the length of the horn; also edge effects at the bell are most pronounced. However, I submit that the principal cause of the false tones is interference between the 2nd and 3rd harmonics produced at the player's lips. For example, if you are playing an BBb tuba and buzzing Eb five spaces below the staff (which is about 38 Hz), the second harmonic of the buzzing lips is Eb (76 Hz) and the third is Bb (114 Hz). The difference frequency is 114 - 76 = 38 Hz, so the 38 Hz buzzing is actually enhancing itself by interference between its own overtones. The same holds true for D (108 - 72 = 36), Db (102 - 68 = 34), and so on.
The perceived limitation on one's ability to produce these tones may be due to volume or flow rate of air required to maintain the sound.