South Bay Philharmonic

Transposition Tutorial

Examples: A to Bb clarinet | F horn to saxophones | E horn to alto sax

Introduction

Not all instruments refer to the same pitch with the same names. For example, when a flute plays a C we really hear a C. (So we call the flute a "concert-pitch" instrument.) On the other hand, when a clarinet plays C we hear a B-flat! This means that if we want a clarinet to play a flute part, we must write pitches that are higher by just the right amount. That is, we must transpose the flute part.

We often have parts for A clarinet instead of B-flat clarinet, and for C trumpet instead of B-flat trumpet. If the player isn't used to "sight-transposing" we'll need to transpose the part. And sometimes we compensate for missing instruments by substituting others. For example, maybe a saxophone will play a French horn part. This part must be transposed as well.

A Simple Example

Suppose we have an oboe part, but no oboe player. Fortunately, a clarinet player is available. So we need to transpose our oboe part for clarinet.

Like the flute, the oboe is a concert-pitch instrument. The clarinet, however, is a B-flat instrument (see Nomenclature below). So we need to raise the pitch by a whole step. If, for example, the oboe is supposed to play a G, we must write an A for the clarinet:

Oboe

Clarinet

Unfortunately, things are usually a bit more complicated.

The Problem with Key Signatures

We transpose key signatures in the same way as notes. Imagine, for example, that our sample oboe part is in the key of G. The clarinet part should therefore be in the key of A:

Oboe

Clarinet

Unfortunately, key signatures are often omitted for the French horn! Parts for other instruments, such as the trumpet and A clarinet, are sometimes written without key signatures as well. The absence of a key signature can thus indicate either a key of C major (or A minor) or an omitted key signature. So if you see no key signature, you have to determine the correct key signature from another (non-transposing) part or from the score.

Why does this matter? Most players are used to seeing key signatures. So if we transpose horn parts for saxophone, we want to include key signatures for the saxophone player regardless of whether they were present in the original horn part.

This discussion assumes traditional notation, where key signatures are used for most instruments. Some modern scores use no key signatures for any instrument. For these scores, ignore the the instructions regarding key signatures below.

Nomenclature

"Concert pitch" (or "absolute pitch") refers to the actual pitch heard, as opposed to any name we may give to the pitch due to a transposition. In our current system of notation, a "concert A above middle C" has a fundamental frequency of 440 Hz.
This tutorial assumes you are familiar with the names of various intervals (e.g., major second, perfect fifth, etc.) and with "interval arithmetic" (e.g., an octave plus a major second is a major ninth).
When we say an instrument is "in the key of X," we mean that we hear an actual pitch of X when the instrument plays its written pitch of C.
- For example, the common clarinet is said to be "in the key of B-flat" (hence we call it a B-flat clarinet);
- so it sounds a pitch of B-flat when it plays a written C.
- That is, it sounds a whole step (two half steps) lower than its written pitch;
- so a B-flat clarinet part must be written a whole step higher than concert pitch.

Computer Software vs. Manual Calculation

If you have notation software (e.g., Finale, Sibelius, etc.), transposition is fairly simple:

Enter your existing part.
Make sure you get the key signature, any any subsequent key signature changes, correct. See above.
Invoke the software's "transpose" function.

It's important, however, to understand how to do transpositions manually, for two reasons. First, it's quite easy to instruct your software to do the wrong thing, so you need to be able to check your results to make sure you did everything right. Second, you may run into cases which your software doesn't handle. For example, your software may have no built-in transposition for the Horn in E, though you can specify it if you understand the details.

The following examples illustrate the complete manual process (though they were actually accomplished using software).

Examples

A Clarinet to B-flat Clarinet

A relatively simple transposition involves moving from Clarinet in A to Clarinet in B-flat. Here is some background info which forms the basis for the transposition procedure:

An A clarinet sounds A when it plays written C; that is, it is written a minor third (three half steps) higher than concert pitch. The B-flat clarinet is written only a whole step (two half steps) higher. Thus the B-flat clarinet part is written one half step (3 – 2 = 1) lower than a A part.

So we need to lower the written pitch by one half step to generate the B-flat clarinet part.

The following steps are used to transpose the following A clarinet part (Figure 1, top) to the corresponding B-flat clarinet part (Figure 1, bottom):

Using the score or a concert-pitch part (e.g., violin), observe that the concert-pitch key is A minor (no sharps or flats, same as C major).
Determine the expected A clarinet key signature to be C minor (3 flats, same as E-flat major).
Calculation: A (from step #1) raised by minor third = C
Note that this key signature is missing; thus we see that this A clarinet part is written with accidentals only.
Determine the correct key signature for the B-flat part to be B minor (2 sharps, same as D major).
Calculation: C (from step #2) lowered by half step = B
Lower each pitch by one half step.

Figure 1. Beethoven Symphony No. 7, Movement II, measures 91-94.

F Horn to E-flat Alto Sax and B-flat Tenor Sax

Consider the production of alto and tenor saxophone parts to substitute for French horns.

A "Horn in F" sounds F when it plays a written C; that is, it must be written a perfect fifth higher than concert pitch. The alto saxophone sounds E-flat with it plays a written C; that is, it must be written a major sixth higher than concert pitch. The tenor saxophone sounds B-flat in the next lower octave when it plays a written C; that is, it must be written a major ninth (octave plus major second) higher than concert pitch.

So we need to raise the written pitch by one whole step to generate an alto sax part.
Calculation: sixth – fifth = whole step

And we need to raise the written pitch by a fifth to generate a tenor sax part.
Calculation: ninth – fifth = fifth

Classical scores typically include four horn parts; of these, parts I and III are "high" horn parts, while II and IV are "low parts." In such cases, we usually transpose Horn III to alto sax, and Horn IV to tenor sax. Occasionally additional transpositions may be necessary depending on the availability of horn players. If there are only two horn parts, we transpose Horn I for alto sax and Horn II for tenor sax.

The following steps are used to transpose the following Horn in F part (Figure 2, top) to the corresponding alto and tenor sax parts (Figure 2, bottom):

Using the score or a concert-pitch part (e.g., violin), observe that the concert-pitch key is F major (one flat).
Determine the expected F horn key signature to be C major (no sharps or flats).
Calculation: F (from step #1) raised by fifth = C
Note that this matches the observed key signature, so we're lucky this time.
Determine the correct key signature for the alto sax part to be D major (two sharps).
Calculation: C (from step #2) raised by whole step = D
Determine the correct key signature for the tenor sax part to be G major (one sharp).
Calculation: C (from step #2) raised by fifth = G
Raise each pitch by one whole step to make an alto sax part.
Raise the pitch by a perfect fifth to make a tenor sax part.

Figure 2: Beethoven Symphony No. 6, Movement I, measures 367-370.

Horn in E to E-flat Alto Sax

Though the modern horn is usually considered a "Horn in F" (see above), horn parts of virtually all keys are encountered in classical scores. Determining the required transposition can be difficult (see this reference for detailed instructions). Please contact your conductor if you are uncertain. The following example illustrates the case of E horn.

A "Horn in E" sounds E when it plays a written C; that is, it must be written a minor sixth higher than concert pitch. The alto saxophone sounds E-flat with it plays a written C; that is, it must be written a major sixth higher than concert pitch.

So we need to raise the written pitch by one half step to generate an alto sax part.
Calculation: major sixth – minor sixth = half step

The following steps are used to transpose the following Horn in F part (Figure 3, top) to the corresponding alto sax part (Figure 3, bottom):

Using the score or a concert-pitch part (e.g., violin), observe that the concert-pitch key is A minor (no sharps or flats).
Determine the expected E horn key signature to be F minor (four flats, same as A-flat major).
Calculation: A (from step #1) raised by minor sixth = F
Note that this key signature is missing; thus we see that this A clarinet part is written with accidentals only.
Determine the correct key signature for the alto sax part to be F-sharp minor (three sharps, same as A major).
Calculation: F (from step #2) raised by half step = F-sharp
Raise each pitch by one half step to make an alto sax part.

Figure 3. Beethoven Symphony No. 7, Movement II, measures 91-94.

1. Norman Del Mar, "Anatomy of the Orchestra," University of California Press, Berkeley, 1983. See table on page 217 for a complete explanation of horn transpositions.