CRUDE NOTES - NOT READY TO PUBLISH
If there were no valves on the euphonium, the partials of Bb1 would be the only notes we could play. To get the rest of the notes, we need to add tubing to the length of the bore. That’s what the valves do. Each valve adds a certain length of tubing to the path the air takes from the mouthpiece to the bell.
So to play a Bb, we leave the valves open. To play an A, we close the 2nd valve. For an Ab, we close the 1st valve. To play a G, we can use the 3rd valve or a combination of 1st and 2nd (minor second plus major second equals minor third). To play an F# (or any of its partials), we combine the 2nd and 3rd valves (minor second plus minor third equals major third). To play an F (or any of its partials), we combine the 1st and 3rd valves (major second plus minor third equals perfect fourth). To play an E (or any of its partials) we combine all three valves (major second plus minor second plus minor third equals tritone, or augmented fourth).
So far, so good, but there’s a problem. To lower the pitch of Bb to A, we need to add a certain length of tubing. The amount of tubing we need to add is proportional to the wavelength of the partial we’re playing - about 6% - but the length of each tube on the instrument is fixed, not proportional. Six percent of the wavelength of Bb2 is longer than 6% of the wavelength of Bb4.
Instrument makers deal with this by making the tubing a little too short for perfect intonation in the low register, and a little too long for perfect intonation in the upper register. Intonation is okay in the middle register.
We can usually deal with intonation problems in the upper register either by lipping the pitch up a little or by using alternate fingerings. For example, on a Besson euphonium, I usually find A4 to be better in tune when I use valves 1 and 2 (9th partial over G), while on a Yamaha I find it to be better with valve 2 alone (8th partial over A).
The low notes are noticeably sharp. That’s because we use multiple valves, each of which is already a little sharp on its own.
There is no way to fix the intonation perfectly, but there are a couple of things instrument makers do to reduce the problem. One is to add valves that lengthen the overall length by additional intervals beyond those handled by the first three valves. The other is to add short lengths of tubing that only come into play when multiple valves are closed at the same time (this is called the compensating system).
So we have three-valve, four-valve, five-valve, and compensating four-valve euphoniums. On the latter three types, the first three valves are even more out of tune than on a three-valve instrument, because the expectation is you will use the fourth (and possibly fifth) valves to compensate for intonation problems in the low register.
Dave Werden has a nice explanation on his site: The Three- and Four-Valve Compensating System.
Something I’ve noticed about adult amateurs and young students is that they (or their parents) invest in an expensive euphonium with the compensating system or with five valves and then never use the fourth or fifth valves. They are even more out of tune than they would be if they played a three-valve instrument. Just purchasing a high-end euphonium doesn’t automatically make anything happen (other than reducing your bank balance). You have to use the equipment.
Non-compensating euphonium:
Compensating euphonium:
Valves 123 are sharper than on a 3-valve instrument.
compensating tubing is not engaged
compensating tubing is engaged