Chuck(G) wrote:
I'm very skeptical that a human being can hear a musical tone at 14 Hz. Perhaps a pressure wave can be sensed or some harmonic content deduced, but a musical tone?
You said you couldn't hear anything from your speaker, and I told you why. It has nothing to do with music. Human hearing goes down to 3Hz if the level is high enough (with military battlefield sound simulators). The only pitch perception I have below 20Hz is intonation with notes in octaves.
Precisely--thank you for reiterating my point. Tubas are best heard from their harmonic--not their fundamental content.
My point was that even weak sounds can reach an audience if they are steady tones without much competition from other sounds. Your opinion and mine coincide for pedal tones but diverge for higher notes where I think that the fundamental has the best chance of reaching the audience and you think the upper harmonics have the best chance of reaching the audience.
Actually, full-scalle basses have been constructed (even recently). Berlioz was in love with the darned thing; the major problem being that it wasn't playable with any facility (note the levers):
I'd like to hear a tuba scaled from a piccolo trumpet, with a 3.3" bore, 32" bell, and a mouthpiece with a 2.6" cup diameter and .55" throat.
...and it's the harmonics of that bass voice that make him noticeable, not its weak fundamental.
His sounds that don't compete with other sounds make him noticeable.
While high firequencies are indeed attenuated more by porous surfaces than low, go back and take a look at the loudness curves I posted earlier. Note that they're extremely non-linear at the low end--that the low frequencies have to be boosted as the overall midrange volume gets quieter. That's why there are "loudness" controls on stereo equipment in attempt to compensate for the nonlinearity of the Fletcher-Munson curve.
Consider the implication that if the level of bass is perfect to the conductor's ears, it's going to be downright tinny at the back of the hall, where the volume is much lower.
Those curves are great for predicting hearing damage in the workplace or the difference in tone when speakers are turned way down to a low level, but nearly useless for what you're talking about. You are talking about a level reduction due to distance that would make the bass seem lacking. It just does not work that way, other factors dominate and at a distance the bass level increases compared to the rest of the music. That's why elephants and whales use low frequency tones to signal over long distances and why a jet plane rumbles at a distance and roars up close. Low frequencies carry better.
Or, as anyone listening to a marching band from the top row of the bleachers can attest--"what sousaphones?".
This is a matter of human physiology--as sounds get softer, the bass goes away.
Having multiple bass instruments out of tune and out of phase does not increase the bass output much either physically or perceptively. The harmonic output increases, but is absorbed more with distance so you end up with not much more sound than one tuba makes. I've noticed at tuba christmas that there is subjectively as much bass when a quartet is playing as when the entire ensemble of 300 is playing.
I said nothing about blowing a tuba to distortion. What I did say was that harmonic content was perhaps more important than fundamental. This can be achieved with a change in mouthpiece or construction of the instrument.
You said a player would give himself an aneurism blowing hard enough to send sound to the back of the hall, which means to me blowing really really hard on the tuba. If you put enough air pressure into a tuba to make your head swell, it is going to blat.
I beg to differ and offer a concrete example Organ builders have been building instruments with "resultant" stops for centuries, being fully aware of this effect. Many organs with stops marked as 32' really create the effect by combining a 16' voice and 10 2/3' quint. Here's an example at random:
Does anyone suppose that the tuba player honking out his pedal C is producing a fundamental tone at an audible level? Yet the ear perceives a note lower than the C an octave above. From what?
The ear is a very strange thing.
It's not strange at all. Any sum of harmonic multiples of a fundamental frequency produces a wave that repeats at that fundamental frequency even if there is no sound content at the fundamental. The ear senses pitch from the repetition rate, which you can call the fundamental frequency, but don't confuse that with energy content at the fundamental frequency which is usually called simply "fundamental". The repetition rate will stay the same as long as at least 2 harmonics are present. The ear does not conjure into existence fundamental when it isn't there, but it does detect the repetition rate.
A pedal C is a resultant tone of low C and the harmonics above it. Another name for the same phenomena is "chord", and the reason chords work is because the ear recognizes repetition rate. Major chord C E G in the staff is a wave that repeats at the frequency of pedal C. Chords start to sound muddy when the fundamental frequency from which they are built drops below about 20Hz, which not by coincidence is the lower limit of pitch recognition.
-Eric
