Posted by Frederick J. Young on July 17, 2001 at 07:19:35:
In Reply to: New Article on my Web Page posted by Rick Denney on July 09, 2001 at 20:40:43:
I made a similar analysis in 1958 comparing two mouthpieces which was published in the School Musician magazine entitled "A New Sound for the Tuba." However, I was careful to make sure the notes compared were played at the same sound level. I used a General Radio Sound Level meter that measures sound level in decibels. I found that it takes practice to play a specified sound level with a completely steady tone. Keeping the sound levels the same for tones to be compared is essential because increasing the sound level usually increases the amplitude of the higher harmonics. Perhaps your software provides a provision for keeping the sound level constant. The waveforms you got for the York tuba look similar to the ones Arnold Jacobs used to get on his oscilloscope in his basement on South Normal Street. However, his were a bit more smooth. I used to help him with various problems he had with his tuba and instrumentation.
With regard to the ear and brain making you hear a fundamental, it is true that is does. However, the reason for it lies in the nonlinear response of the ear. The sound perceived by the brain is not proportional to the vibrational ampliture of the ear drums. Instead it is related in a nonlinear fashion such that the brain adds and subtracts the frequencies of the harmonics to imagine sum and difference tone. Hence a pair of 150 and a 100 Hertz harmonics sound are interpreted by the brain as a fundamental of 50 Hertz and harmonics of 100, 150 and 250 Hertz. I am not sure what the nonlinear mathematical function used by the brain is, but if one knows it he can make calculations based on your measurements. These would indicate what the brain perceives.
Your new web page is very good and should aid in the understanding of the tuba!