In the previous article “Explaining Brass Instruments - 1. The Basics” I wrote:

The player activates the body of air inside the tubing so that it vibrates in resonance with the tubing length…The player activates the body of air inside the tubing so that it vibrates in resonance with the tubing length. 

The frequencies that the tubing will resonate at are determined by the Harmonic Series. The lowest one (the Fundamental or 1st Harmonic) is the note whose wavelength is double the length of the instrument’s tubing. (The explanation for this is outside the scope of this article, but can be found in such publications as “Fundamentals of Musical Acoustics” by Arthur H Benade.)

This illustration shows the modes of resonance up to the seventh harmonic.

Here are the notes (based on a fundamental of C)  that these modes represent.These notes are the only notes available to the Bugle and other non-valved “Natural” brass instruments.

The 1st harmonic is not usable on Trumpet. The first note for a beginner will normally be either the 2nd or 3rd harmonic. Recreational players will be satisfied with playing up to the 8th harmonic C. Skilled players will play up to the 12th harmonic G. Maynard Ferguson often played to the 16th harmonic C. The French Horn regularly plays up to its 16th harmonic.