Understanding Transposition Between Different Musical Instruments
Why must we transpose?
If you're an aspiring composer or musician, you need to understand your transposition. Whether you're writing for clarinet, trumpet, saxophone, or others, knowing what "concert pitch" means to these transposing instruments is vital. Heads up: this article assumes you know how to read standard musical notation.
First, you may wonder why there are "transposing instruments," instead of all instruments calling the same note 'C.' Here's the reason most apparent to me as a clarinetist: sometimes instruments are made in different sizes (such as Bb soprano clarinet, bass clarinet, and even clarinet in A), and musicians are expected to be able to play these instruments. The modern Bb clarinet typically has 7 keys, and is played with 9 out of 10 fingers. (The right thumb serves to support the instrument's weight.) With all the finger work involved in playing a clarinet, it is much easier for most people to call the same fingering 'C,' no matter the size or key of the instrument. That way, when a clarinetist reads sheet music, he or she does not need to have lightning-fast transposition skills, but instead only needs to match a note on the page with a particular fingering.
Complicated "finger work" isn't the only reason transposing instruments exist, but I think it's certainly a good enough one.
Now that we have an excuse for their existence, let's learn to work with these instruments.
Which instruments transpose?
When we say "transposing instrument," we mean an instrument that is not keyed in concert pitch. In other words, if I play a C on a clarinet and a C on a piano (which is a concert-pitch instrument), then the two C's do not sound the same pitch, even though they have the same name!
The most commonly-used concert-pitch instruments today include (these are not transposing instruments) the piano, organ, pitched percussion (like a xylophone or the timpani), flute, oboe, trombone, baritone (in bass clef), euphonium, tuba, violin, viola, cello, string bass, and guitar. Of course, others exist as well. Note that some keyboard instruments (such as the celeste and glockenspiel), as well as a C piccolo, transpose octaves. Also please note that tubas, while often pitched in different keys, are not transposing instruments. In this case, it is the tubist's job to change the fingerings he plays to get the right notes.
The most commonly-used transposing instruments are basically all modern clarinets, Bb trumpet, French horn, the whole saxophone family, and English horn.
Okay, I'm ready to transpose. Where do we start?
Sometimes, with the instrument name! I'll give you a clue: Bb clarinet, Bb trumpet/cornet, Eb alto saxophone, etc. With others, you just have to know it. For example, you must remember that the English horn is in F. French horn will sometimes tell you it's "Horn in F." In orchestras, there's often also "Clarinet in A."
Okay, we know what key the instrument's in...what does that mean, anyway? Well, here's an easy saying that will help immensely: "Sound a C, name the key." (I learned this from Dr. Don Peterson at BYU.) This means that if I play a C on my clarinet, you can walk over to a piano and play a note that sounds the same pitch. The piano's name for that pitch is the "key" my instrument is in: Bb!
So, since the piano's note names are one whole step lower than the clarinet's note names, to transfer concert-pitch notes to the clarinet, we need to go up one whole step. What about writing for a Bb trumpet? Same thing! In reverse, if you tell a clarinet and a piano to play together, and tell them the same note name, will the clarinet sound higher or lower? It will sound lower, just like the Bb (the clarinet's C!) sounds lower than the piano's C.
Don't forget: Transpositions do not ignore the black keys. If you're transposing music up a perfect fifth for a French horn to read, transpose it exactly. make sure you go up 6 half steps (not including the note you start on), or 7 half steps if you do include the note you started on as #1. For example, C -> G, B -> F# (not F-natural!). If you're transposing up a major second for a clarinet to read, make sure it's a major second, not a minor or augmented second!
As long as you do the same thing to every note, it will come out sounding the same.
...And that's basically it.
But what about memorization? Fortunately, you don't have to memorize which instruments are keyed where and in what octave. There are plenty of charts that you can use as quick references. Some are full of info, and may take a little bit of time to understand. (Entire page of source. Link near the bottom.) This one groups the instruments fairly clearly. Some of them are humorous, but still serve the purpose if you can tell the jokes from fact.
Such charts will help you in your efforts. The best charts will clearly tell you which direction and how far an instrument is transposed.
Pro tip: If you're using music notation software, it can probably handle the transpositions for you automatically. Just make sure you understand what it's doing. I like to use MuseScore because it's free, and I'm a fan of open-source projects. Using it as an example, if you copy and paste notes from one instrument line to another, it takes care of the transposition automatically so all the notes sound the same pitch. (It also notifies me with red note heads if notes are outside the regular range of the instrument. If you see this, consider bumping things up or down an octave by highlighting the line and hitting (in Windows and Linux) CTRL-up or CTRL-down.)
Quick info: The saxophones and clarinets are large families of instruments. Because they may be confusing if you're not very familiar with the different ones, I've created a small chart to show how the more commonly-used ones relate to each other. (I've omitted sopranino-voiced instruments, as well as the obsolete C clarinet. While other varieties not mentioned exist, they are far rarer.)