Question:

How to convert sheet music from tenor sax to alto sax and from alto sax to tenor sax?

My response:

The tenor saxophone is in the key of Bb.

The alto saxophone is in the key of Eb.

Let’s first compare those two notes.

Eb down to Bb is down a perfect fourth.

Eb up to Bb is a perfect fifth.

Personally, I can think of the perfect fifth faster than the fourth. Probably because the fifth is often a chord tone.

A perfect fourth and a perfect fifth together are a perfect octave.

Example: C up to F is a perfect fourth, and F up to C is a perfect fifth, total distance of one octave.

Therefore, up a perfect fifth is the same note name as down a perfect fourth.

And down a perfect fifth is the same note name as up a perfect fourth.

So to go from Bb tenor saxophone to Eb alto saxophone notes, you go up a perfect fifth (or down a perfect fourth).

C on tenor sax up a fifth makes it a G on alto sax. This note is a concert Bb, a concert Bb is C on tenor and G on alto.

To go from Eb alto saxophone to Bb tenor saxophone, you go up a perfect fourth (or down a perfect fifth)

C on alto sax down a fifth gets you to F on tenor sax. This note is a concert Eb, which is C on alto and F on tenor.

Another option:

If you prefer to think in terms of fourths, go for it.

Other times I’ll transpose to concert and then to the other saxophone, depending on the situation and whether it’s useful to also be able to play something on the piano, which it can be many times.