I am watching a trumpet player on TV and have just been struck by something that has never ocurred to me before.

Trumpets have three valves.

There are eight combinations of up-or-down for three valves. That makes eight possible notes. One octave, less than one if you count sharps and flats I suppose.

I'm pretty sure a trumpet must do better than that... what have I overlooked? 

IRF,

You get more notes on the trumpet through use of embouchure and how hard you blow.

Most instruments can play more than what valves or holes might seem to dictate. On recorder for example, by varying pressure or using the finger to slightly uncover holes you can achieve more notes and 'slide' from note to note and play jazz and rock!

John W

10/10 for Maths, but a "See Me" for Acoustics, IRF  

All brass instruments (trumpets, cornets, French horns, all of the brass-band "horn" family, euphoniums, tubas, sousasphones.. although, let's leave the trombone aside for a sec...) work the same way.  Without touching any valves, slides, rotors, etc, they will happily play the notes of what's properly called the "Harmonic Series":


Where you'll hear these most frequently on brass instruments is in bugle-calls and fanfares (bugles have no valves at all) - you move from note to note simply by "buzzing" your lips a bit faster or slower into the mouthpiece (as you get nearer the top you'll also need quite a bit of breath support from the diaphragm).  If you imagine the bugle-call "The Last Post" (since we're at that time of the year anyhow) you can quickly hear all the notes you can get *without* any valves.

The valves are only there to "fill in the gaps" for the notes which aren't "naturally" present without a bit of jiggery-pokery.  The bottom octave is pretty-much "never used" (awaits a torrent of replies mentioning obscure works and progressive jazz in which it is...) so the widest interval you ever need to "bridge" using the valves is the fifth (the first interval above the initial octave jump).  

This is why you only need three valves, because used singly in combination they offer all the chromatic notes needed to bridge a fifth.  On modern brass instruments they are set-up the same way on all instruments...

Valve 1 (nearest to the mouthpiece) - drops the sound by one tone
Valve 2 (the one in the middle) - drops the sound by a semitone
Valve 3 (farthest from the mouthpiece) - drops the sound by 1.5 tones

However, some notes of the "naturally-occuring" Harmonic Series are actually quite "out of tune" to the modern ear, and you get a better result by using valves to drop-down from a higher note that always plays in tune,  than by using the "straight" open note. This particularly applies to the "seventh" in the harmonic series, which is notoriously awry on most instruments.

There's a further nuance (which I only mention to ward-off pedantic replies)...  all of tubing-length calculations for the extra bit of tubing "toggled" by the valve are done as a %age relation to the total tubing length of the instrument.  However, once you stick all three valves down at once,  you've got a new total tubing-length and so some of the %ages are now wrong - the notes will be a bit "sharp" because there really ought to be fractionally more tubing.  This particularly applies to Valve 3, which plugs-in a socking 1.5 tones of tubing all at once...   so on Valve 3 there is usually a "correcting slider" (operated by the third finger of your left hand... otherwise only used for supporting the instrument) to make on-the-fly adjustments.   Let's imagine you have a C-trumpet (to give an easy example)...   the "bad" notes will be C# and D (and sometimes Eb),  and they will always need correcting.  Very likely Ab will also need a tweak.

Does that make any more sense now?   As you can see, the higher you go (and there are loooots more notes above the Harmonic Series in the diag - your cred with other players will be rubbish unless you can get up to "super C" these days) the closer together the "naturally-occurring" notes become.  In the baroque era they used to make trumpets much longer and lower-pitched that today (a whole sixth lower, in fact) - not to "get" those low notes, but the opposite - to put the "playable range of natural notes" more into the main range of the instrument...   because baroque trumpets had no valves at all:


Baroque-era players relied entirely on altering the "lip-buzz" for each note (plus a bit of "oomph" from the diaphragm towards the top end), and although this sounds like a very inexact science to anyone brought-up on the modern valved instrument,  there are now quite a few living players who've revived the old playing-style to a 100% accuracy standard.  The same also applies for "French" horns - Bach's fiendishly complicated horn-parts were written for entirely valveless, rotorless instruments operating on lip-power alone   To help the tuning of the notes which are "naturally" wonky,  it looks like baroque-era players sometimes made tiny finger-holes... not enough to change from note-to-note,  but just enough to bring a wayward note into the frame of acceptability  Although you can "lip" errant notes up and down to "help" them, you don't have time to do this in fast passages when you have no valves at all to help you.  The bore-circumference in baroque instruments was much smaller (around half!) than modern instruments, which hugely helps the business of shunting from note to note by "lip" alone.  The "fat" sound so greatly favoured by orchestras like the Chicago Symphony (who first pioneered the so-called "bionic brass" sound) may or may not appeal to individual tastes... but it's not at all the sound composers prior to WW2 would ever have expected, and you might (if you didn't mind being controversial) call it hugely inauthentic for anything except music written after the mid-1950s.

That's what I thought too, when I took up the bloody instrument   Although I got through to the "youth orchestra" stage (and also played in both brass bands and wind bands... "brass-banders" being very dismissive about the latter usually) I gave up on doctor's orders...  I kept hyperventilating in the upper range.

Otherwise I might have grown up to a proper brass player, wi' a motor-bike, a moustache, a leather jacket and a beer-gut

Q: HOW MANY TRUMPETERS DOES IT TAKE TO CHANGE A LIGHTBULB?
A: Ten.  One to do it, and nine others to say how they could've done it waaaay better than that, and a bloody octave higher'n'all...

The trills in Brandenburg 2 are all in a region where the harmonics are close together. For example, the one near the very beginning is between the 12th and 13th harmonics of an F trumpet (C and D). So it's all done with the lip. Damned clever, I reckon.

Just to say I've enjoyed reading this thread, especially your answers Reiner. I knew a bit about the harmonic series and the embouchure but I've learned more.

Not sure if this animation actually makes any sense. The caption is:
The illustration below demonstrates just how this works. The blue parts of the trumpet are the parts that air is flowing through. As each valve is depressed, the air is rerouted. The sequence shown is the chromatic series of the trumpet.

More here:
http://library.thinkquest.org/10693/valves.html

BTW I could see your diagram of the harmonic series.

IRF - how did you think they played the Last Post on a bugle?

I'm a bit surprised that it took so long for the valved trumpet to be invented - is the technology that advanced? Perhaps people were happy with trumpets the way they were, but anyone interested in this topic might like to hear a keyed trumpet - the instrument Haydn wrote his concerto for. It's easy to see why it didn't catch on, although the principle of keys for a brass instrument (similar to the way woodwind instruments have them) seemed to work well enough for the ophicleide.

There is some controversy as to what instrument was intended for Brandenburg 2 - after all Bach never wrote anything else comparable for F trumpet either, whereas for F horn he wrote a few other things which pose roughly similar challenges.

For good measure there's a body of opinion holding that the D horn obbligato in the B minor mass should be for trumpet, or at least in the trumpet octave.