Posted by Rick Denney on May 06, 2001 at 16:20:58:
In Reply to: Contra-Octave in band playing posted by Austin H. on May 03, 2001 at 17:31:29:
A technical comment:
The note, when played down an octave, contains more information than just the fundamental. I played with my new minidisc setup this weekend, and did a computer spectral analysis of a few notes, which will be the subject of a future posting (and an article on my web page). But I realized something exceedingly simple that had previously escaped me.
Any tuba sound comprises fundamental and a series of harmonic overtones. As Fred Young has pointed out many times, the harmonics might create higher levels then the fundamental, because of the way they add up. But the note an octave down has a large number of harmonics in the sound that are not present in the note an octave up.
Consider the case: A low Bb (below the staff) has a fundamental frequency of about 58 Hz. In the sound, you will find the following frequencies present in significant amounts:
Harmonic, Frequency
1, 58
2, 116
3, 174
4, 232
5, 290
6, 348
7, 406
8, 464
9, 522
10, 580
11, 638
12, 696
13, 754
14, 812
15, 870
16, 928
All of these harmonics were audibly present in my low Bb, and several of them were at higher levels than the fundamental, though the actual waveform showed the fundamental with the greatest amplitude.
Now, here's the same series from the Bb on the staff, an octave above:
Harmonic, Frequency
1, 116
2, 232
3, 348
4, 464
5, 580
6, 696
7, 812
8, 928
Notice something? The lower note has a much richer collection of overtones, and more information at higher frequencies than the higher note. And it also has overtones that do not resonate with the note an octave up. In fact, my lower Bb had measurable harmonic frequencies that were higher than the upper Bb. I suspect that the pedal Bb would be much more the case.
Guess what? That's why the lower note can, if used inappropriately, create a muddy texture. The higher note provides a leaner, cleaner sound.
This is why so many digital imitations of the tuba are so bad. Not all notes develop the same harmonic series. The best tubas--the ones with good scale--probably have a smooth transition of tone shape as you go up and down the instrument. But I'm getting ahead of myself.
Rick "the fun of the Fast Fourier Transform not overcoming the horror of hearing his own recorded 'playing'" Denney