I have a formula that I use to figure out which transposition to
use with which horn I’m playing on which part. I include it here because so many
people have asked about it.

From and To

The first step is to recognize transposition as a
“to” and “from” question. Or more accurately, it is a
“from” and “to” question. You consider the
relationship “from” the instrument you’re playing “to”
the instrument the music was written for. The difference between these two
gives us an interval and a direction for transposition. For example, if
I’m playing B flat trumpet and reading D trumpet parts, I ask myself
“What is the interval FROM Bb TO D?”. The answer
is “Up a Major Third”. 

The main thing here is to get the “from” part
right. You begin with the horn in your hands and go TO the
instrument on the page. From you to the page…..not the other way. This
is very important because getting it backwards will cause you to transpose
in the wrong direction. FROM Bb TO D  is UP a major
third, not down.

Transpose the Key Signature

The next step, after you figure out the interval, is to
transpose the key signature. Say that name of the key in your mind and
transpose that name by the same interval determined by the FROM and TO
question. Using the same example as above, but playing a piece of music
with a key signature of Eb, you would transpose the key signature up a
major third to G. The key of Eb is three flats and your are going to
change that key, in your mind, to the key of one sharp. 

I know this can get confusing. Maybe you’re wondering
what the difference is between the key of the trumpet and the key of the
music. They are not the same thing. The key of the trumpet is determined
by the length of the tubing. With the smaller instruments, the notes come
out higher. We label the differences between those instruments with note
names. But this is not to be confused with the key of the music. Any
instrument can read music written in any key signature. So don’t let that
confuse you. When we say trumpet in D, we are talking about a small
trumpet that plays higher than the Bb trumpet. How much higher? Look at
the FROM and TO again. The D trumpet plays a major third higher than the
Bb trumpet.  

Now, as I said, if a piece of music is written in the
key of A flat, it is no longer A flat when you transpose it. And it’s
important to recognize the new key signature so the actual transposition
of the music doesn’t become a note by note effort. When you transpose the
key signature first, you can play a lot of things by scale degrees instead
of trying to figure each note out individually. Once you’ve changed
the key signature, scale passages and sequences become very easy. You just
play the next note up (or down) in the key. This frees your mind to look
ahead for traps, like accidentals and large intervals. 

Transpose Groups of Notes

But I’m getting ahead of myself here. Let’s look at the
third step in this formula. In this step you determine what the transposed
notes are. This comes from the “From” and “To”
question again. The interval you divined from that question tells you what
the transposed note becomes. Looking at our original example, transposing FROM
B flat TO D, we see that all of the notes should be transposed UP a
major third. If you have a written F#, then you play an A#. 

Like I said earlier, figuring out what the new key is
first really helps make the whole transposition thing a lot easier. If we
had to transpose every note individually, we wouldn’t be able to play the
music in tempo. So changing the key first allows us to transpose groups of
notes at one time. If you have a written E flat major scale and need to
transpose it up a major third, you simply play the G major scale. 

And really, that’s what makes this formula work is that
it helps us tap into technique we already posses on our instruments. It
normalizes transposition. After all, we all know G major scale, right? 

And the cool thing about transposition is that a second
scale degree remains a second scale degree in both keys. A tonic triad in
the written key is still a tonic triad in the transposed key. A flatted
third in the written key is still a flatted third in the transposed key.
So transposing this way really makes good use of the skills you should
already have as a player. 

Here’s a summary of the formula:

First

Determine the interval by asking yourself, what is the
interval FROM the key of the instrument I’m holding in my hands TO
the key of the instrument the music was written for. 

Second

Transpose the key signature according to that interval. 

Third

Transpose groups of notes based on their position within
the key.

Fourth 

Keep an eye out for traps such as large intervals and
accidentals.