I’m a big fan of the “horn” family but have trouble understanding how horns are able to play the same scales and modes that a piano is able to play, being that horns only have a few valves. In some cases, such as the trombone, horns don’t have any keys on them at all.
This is EXTREMELY intriguing yet confusing to me. Please explain if you’re a horn player or have knowledge of the “horn” family. I’m familiar with music and its jargon so feel free to get technical if necessary.
Put as simply as possible, horns are tubes. Blowing in special ways makes certain notes sound from those tubes. By changing one's embouchure, those notes start at a fundamental, then gradually go up in harmonics. The first notes (in key C) would be C, G, C, E, G.Those notes are the ones we hear when a bugle is played - Reveille, Last Post, etc. Bugles only play the harmonic series of notes, and can't play the ones in between. Read on.
On a trumpet, for starters, there are three valves. One drops any open note played by one semitone, another by two semitones, and the other by three semitones. So using a combination of valves, you can lower any open note by up to six semitones.
Let's take the first G note. To get F♯, press the semitone valve. To get F, press the tone valve. To get E, press two valves to drop a tone and a half. (there's one valve alone that can do this). To play E♭, press the two valves that drop two tones. To get D, press the two valves to drop two and a half tones. And to get C♯, press all three.
That's the more complicated bit, as between the open notes, there's more semitones than anywhere else further up in pitch. Notice that between G and the next C, there are only two tones.
So at this point, not so many notes are needed, so the valve pressing is more simple. Next, between that C and the E, there's even fewer, so again, not so many valve changes are needed.
Now, onto trombone. There are actually valve trombones, which work the same as trumpets, etc., but for the standard trombone, imagine those extra lengths of tube brought into play by pressing valves are now a single continuum of tubing, operated by the slide. At various places along that slide, there are all the notes found similarly to pressing valves. There's also loads of extra notes that are going to be out of tune!
You can play several different notes with the same fingering, controlling the note with your lips. On a trumpet, starting at middle C, you can get C, G, C, E, G, B♭, C. Then each fingering (or slide position) will move all these notes downward by a particular number of semitones. Note that half-way valve-presses are not used.
On a trumpet 3rd valve is the same as 1st + 2nd, so there are 7 combinations including no valves pressed. The combinations give you a chromatic range starting at F# below middle C upwards as far as your technique will take you.
Consider a bugle. It can play a limited number of notes. As you say you're 'familiar with music and its jargon' perhaps you'll understand that they can play a selection of the harmonic series for that length of tubing.
The 'buttons' switch in extra lengths of tubing. The available set of notes shifts downwards as the overall length of tube increases. On a 3-valve instrument valve 2 lowers them by a half step, valve 1 by two half steps, valve 3 by three half steps. So, in combination, we can shift the set of available notes down by one, two, three, four five or six half steps. That's enough to 'fill in the gaps' over a useful playing range.
I'll go with a physics-style answer. And there are two parts to it.
Part 1: The Valves
When you strum a guitar string, versus strumming a guitar string with a fret held down, you're raising the pitch by shortening the length of the string. The string vibrates at a faster frequency, pushing the pitch up.
Well, the valves do the exact opposite of guitar frets - they enlongate the tube, lowering the pitch. The middle valve lengthens the tube the pitch by 5.94%, lowering the pitch accordingly... which corresponds to a semitone lower note coming out of the trumpet. The first valve lowers it 12.2% (full tone), and the third lowers it 18.9% (three semitones.)
Part 2: The Harmonics
Any instrument capable of producing a pitch is doing it by resonance. With the guitar, it's a string vibrating; with the trumpet, it's a column of air. But the thing about resonance is, it can resonate at any harmonic.
An easy way to see this is to pluck a guitar string away from the middle, and then carefully place a finger at the exact midpoint of its length. If you do it right, the note will suddenly jump an octave. Why? Because you've dampened the fundamental for that string... but you didn't impede its second harmonic, an octave higher.
How does that work with a trumpet? Well, the sound isn't coming from a one-time pluck of a string. It comes from the trumpet player 'buzzing' their lips on the mouthpiece. If they buzz their lips at the same pitch as the second harmonic, it'll play the second harmonic. But if they buzz their lips at the third harmonic? Then it'll play the third harmonic. What's really going on is that the trumpet is simply amplifying the pitch the trumpet player is buzzing into the mouthpiece!
Some cool factoids that stem from this:
Anyway, here's a youtube video that might help out:
