The piano is a well-loved music composition tool for a reason. Not only do the piano's 88 keys contain virtually all the notes you'll ever need to create a solid foundation for a full orchestral composition, but the entire piano is tuned to concert pitch. Concert pitch simply means that when you hit a C on the piano, you are actually playing a C.
However, if you play a C on a transposing instrument, you get another note entirely, and this is where it can get confusing. For example, if you were playing a B-flat clarinet, and the sheet music showed a written C, you would actually be playing a B flat concert pitch. If you were to play a written C on an E-flat alto sax, you would actually be playing an E flat concert pitch.
The easy answer for why transposing instruments are the way they are has as much to do with convenience as with historical tradition. Most instruments are too small to contain the 88 notes of a piano, so most instruments have only a fraction of the piano's tones available for use. Brass and woodwind instruments are built so that by pressing and releasing sequential valves or keys, the musician either moves up or down to the next note of the scale. The key is that these valves and keys are used in a particular sequence.
All instruments in both woodwind and brass families are designed this way, and because of this, a clarinetist can theoretically pick up a saxophone for the first time and soon play a song he is familiar with on the clarinet. This same musician can pick up an oboe or a flute and make just as easy a transition — theoretically, at least. Depending on the instrument, there may be one or two extra or fewer buttons on the instrument's body, but the main notes — A, B, C, D, E, F, and G — will be there.
The usefulness of transposing instruments is most obvious when you look at the basic saxophone family. If you pick up any saxophone and play a C, you'll hold down exactly the same buttons for each instrument. However, you'll hear a different tone depending on what type of saxophone you have: soprano and tenor saxes are pitched in B flat, and alto and baritone saxes are pitched in E flat. Because saxes are transposing instruments, you can learn one set of fingerings and play all of the instruments in the saxophone family.
In the old days, back when staff paper and especially sheet music were expensive, the members of an ensemble would all read the same piece of music, and the musicians had to make the necessary transpositions in their heads. These days, however, the burden of transposition is now carried solely by the composer/arranger, who writes out individual pieces for each musician/instrument in the corresponding pitch and key.
