Bob Kolada wrote:Think of a bugle call- the open pedal is the 1st partial, whatever pitch your tuba is in the open note right below the bass clef is the 2nd,.... The "false partial" is one that some tubas have anywhere from a 4th to a 6th below the 2nd.
Well....that's where it gets sticky. "Partials" are frequencies that actually occur (look at the Fourier Transform and see a peak). "Harmonics" are theoretical beasts - for brass instruments they are a design goal - not a given, by any means.
It's entirely possible that a given instrument will have a "first partial" that is NOT part of the harmonic series. Be careful about trusting your ears. That "false tone" just might be the actual "first partial" (which just might sound a bit strange because the overtone structure doesn't quite match your expectations). That "fundamental" just might be a complex sound that includes all of the harmonics EXCEPT the first one - which will sound to your ear just like a complex sound that includes all of the harmonics.
When you play a "note", do you want:
a) a pure tone of the right frequency f, or
b) a complex sound with all frequency peaks at f, 2f, 3f, 4f, ..., or
c) a complex sound with frequency peaks at f, g, h, i, j, k,..., [question: what does this "sound like"?], or
d) a complex sound with frequency peaks at 2f, 3f, 4f, ...[question: what does *this* "sound like"?]
???
a) is for electronic music freaks
b) is for Yamaha freaks
c) is for Alexander freaks, or "false tone" afficianados
d) is for those who like to play off the bottom of the piano
The theory that looks so nice for ideal strings is very useful - it makes musical sense, and those who believe in the Fairy Tale can make good use of it as a model that gives them correct answers to many interesting questions. The only problem with it is that it's simply not true for brass instruments with bells and mouthpieces. A major goal of a tuba designer is to make the tuba behave AS IF the theory actually applied. It turns out that this is very difficult and very complicated.
If the model works for you - by all means use it. Just don't try to push too hard on the extremes (e.g., the "first partial"). Don't be shocked when a particular partial doesn't quite match up with the "harmonics".
If you want to be completely confused by the REAL world, I have found that Figure 8.19 in Fletcher & Rossing is an excellent starting point. [and notice that this is *before* we add the mouthpiece]