Transposing is the act of playing something in a different key from where it was originally written. You might transpose a song from its original key in order to keep its highest and lowest notes within a comfortable range on an instrument, or to accommodate the vocal range of a singer. You might want to put the song in a key where an instrument would have easier notes to play.
Most instruments are in "concert pitch", meaning that the same pitch is heard as the one that is shown on the page. Other instruments (such as clarinet, trumpet, saxophones) are not in concert pitch. They are transposing instruments. For example, the most common clarinet is "in Bb". This comes from the acoustic characteristics of the instrument, for when all the keys are closed and the clarinet is played a Bb note comes out. Notes of the Bb scale become the easiest to play, so the tradition has been to shift the notation over and notate these as the notes of the C scale since it is easier to write (there are no sharps or flats in C major).
The trumpet, soprano sax, and tenor sax are "in Bb". That means that if you write the note "C" for them, when they play it a "Bb" concert (i.e. on the piano) will come out. You must write a major second (whole step) above the note you want to hear for trumpet and soprano sax. The soprano sax is also in Bb and has the same transposition as the trumpet. The tenor sax is also in Bb, but you write the notes for it a major second and an octave higher than you want to hear them come out.
Let's transpose the following phrase from Duke Ellington's "Satin Doll":
Everything has to be written a step higher for trumpet, soprano sax, or clarinet.
The key signature is C major. A whole step above "C" is "D", so we use a key signature of two sharps.
If the player was going to improvise, they are supposed to think "Dm7" for the first two beats. A whole step up from "D" is "E", so the first chord symbol is rewritten as "Em7".
The first note that they play is supposed to sound like an "A" in order to match what the piano player, guitarist, and bass player are doing when they look at the concert pitch score above. If we want to hear the note "A" come out of the trumpet, soprano sax, or clarinet, then we have to write the note "B", since it is going to sound a whole step lower than written when they play it.
Here are the three bars transposed:
Notice that there are no accidentals in the transposed part, since there were no accidentals in the concert pitch part. This works if you use the right key signature. If you use the right key signature you can do the rest of the transposition mechanically. If you're going to transpose the score up a step, change the key signature and then just move every note head up to the next line or space. Just make sure you stay within the written range of the instrument--you don't want to ask your player to do the impossible.
If you were going to do the same piece for tenor sax you would use the same key signature and chord symbols. The first note would also be an "A", but you'd write it up an additional octave higher:
Here's another fragment from later on in the same piece:
When we transpose this for trumpet, soprano sax, or clarinet we'll again move everything up a step. This time there will be accidentals in the second measure--two of them, and in the same position as in the concert pitch version above. A whole step above "Bb" is "C natural". A whole step above "Ab" is "Bb":
The alto and baritone saxes are "in Eb", that is, when you write a "C" for them, they will play a concert "Eb". The alto sounds a major 6th lower than written, the baritone a major 6th plus an octave. You may need to review how intervals work, in this case, especially the major 6th (M6).
Our excerpt from Satin Doll written for alto saxophone looks like:
Again, using the correct key signature means that there won't be accidentals in the transposed part where there are none in concert pitch score. If you use the right key signature it's easy to move the part up a major 6th. Start counting from the line or space where the note head is in the concert pitch version and count up six lines or spaces to position the note head in the transposed version.
In the other example of the piece there were accidentals in the second bar in the concert score, so we will see them in the same place in the transposed version for alto saxophone. A major 6th up from "Bb" is "G natural", a major sixth up from "Ab" is "F natural".:
The other thing you need to be aware of when you transpose for instruments is to know what range of notes are comfortable and/or possible to play. The piano can play a very wide range of notes, from the lowest to the highest. Other instruments have a narrower range, for example the violin can not play low notes written on the bass clef.
There is no single answer for what the written and sounding ranges of most instruments are. It also depends on who is playing the instrument--a student will have limitations that a professional player will not. The following ranges are guidelines, showing what a skilled player is typically capable of. You will want to leave the lower and upper notes off for players with less experience.
Trumpet, soprano saxophone, and tenor saxophone are in Bb. You write the parts for trumpet and soprano saxophone up a whole step. You write the part for tenor saxophone up a major 9th (a whole step plus an octave).
Alto and baritone saxophones are in Eb. You write the part for alto saxophone up a major 6th. You write the part for baritone saxophone up a major 6th plus an octave.
The most common flute is in C, that is, it does not transpose. It's sounding range is:
The piccolo has about the same written range but sounds an octave higher. The alto flute is in G, the bass flute is in C, and sound a 4th and octave lower, respectively.
The clarinet family includes Bb contrabass, Eb contra alto, Bb bass, Eb alto, A, Bb, C, Eb (soprano), and Ab sopranino. The Bb is by far the most common and has a sounding range:
It is written a whole step higher than it sounds.
Trombones are non-transposing instruments. The tenor trombone is the most common and it's approximate sounding range is:
The bass trombone can go down a few notes below the tenor.
