The euphonium is really just a series of tubes that you can use to play different pitches. This page shows you all the pitches you are able to play with any given valve combination. You'll notice there's a pattern in the notes; the intervals between them are all the same. This is called the overtone series. All brass instruments work based on that pattern.
One valve combination that isn't featured on the page above is the fourth valve. The fourth valve was added to help correct for intonation problems that arise naturally in the overtone series.
What kind of euphonium do I have?
Just like cars, or shoes, or anything else you can buy, there are lots of different brands and models of euphoniums. (You might hear these instruments called baritones sometimes- there is technically a difference between a baritone and a euphonium, but we won't get into that here. You are probably playing a euphonium no matter what you call it.) The main difference we are concerned with here is whether or not you have a fourth valve. Check out the examples below (courtesy of woodwindbrasswind.com) and see which one looks most like your instrument (regardless of color).
Three-valve euphonium
Four-valve euphonium
Four-valve euphonium (fourth valve on side)
When do I use the fourth valve?
Use the fourth valve instead of 1-3. Instead of being very sharp, the resulting pitch will be much more in tune. Using 2-4 together instead of 1-2-3 will help solve intonation problems with that combination too; the fourth valve also helps extend the low register of your instrument. If your euphonium doesn't have four valves, there are some intonation problems you'll have to solve yourself; some players use embouchure or air to adjust those notes, and some players use tuning slides if they can move quickly. Some instruments even have that option built in! Talk to your band director to figure out an option that will work for you. For more intonation fixes, see theeuphonium intonation page.
Want a standard fingering chart?
These two fingering charts are written chromatically and include the fourth valve as an option.
We asked the incomparable Dr. Craig what she would say to a young euphonium student, and this is what she told us to remember:
3 "R's" of beautiful tone quality - Rich, Round, Resonant
3 "SP's" of terrific technique - Slow Practice, Slow Practice, Slow Practice
Something to practice slowly:
When you run out of scales to play... David Vining's book, Daily Routines for Euphonium, comes recommended by Steven Mead, a phenomenal euphonium soloist. Let's get those fingers working! (This book is available in treble or bass clef.) We also recommend checking out Method for the Baritone (Euphonium) by Walter Beeler. (That one is only in bass clef.)