Patterns in Harmonics

[David A.]

Is there any explaination to the patterns of the harmonics? I'll use Bb to explain my point. The first mode of Bb1 is Bb2, an octave. The second mode is F2, which is a fifth about Bb2. Then, the interval increases to a 4th when the third mode is Bb3. Basically, what I'm asking is why do the intervals of overtones decrease? Is there any explaination as the why the harmonics follow the pattern that they do?

Harmonics are integer multiples of the fundamental---as in:

Root= Fundamental Frequency times one= same frequency
2nd Harmonic=Fundamental Frequency times two=one 8v up
3rd Harmonic=Fundamental Frequency times three=one 8v+a 5th up
4th Harmonic=Fundamental Frequency times four=two 8vs up
...and so on!

In frequencies & notes:

440=A
880=A 8v up
1320=e 8v up
1760=A 2x8v up
etc;

The drawbars on a Hammond Organ emulate this natural Harmonic Scheme! Baroque trumpet (before valves) used this function to play melodies up where the harmonics are closer together!