Transposition by clef substitution

Transposing a piece, in its best-known form, means moving every note by the same interval up or down, one at a time. It works, but it is slow. There is another way, older, that moves no note at all: it leaves each note where it is on the staff and swaps the clef in your head. Under another clef the same positions have other names, and the music comes out transposed.

Written or read, with or without a clef

Lacerda arranges transposition in two pairs (Lacerda 1966, ch. XXXIX). Written transposition is done on paper and poses no great difficulty, because whoever transposes has time to avoid and correct mistakes. Read transposition is done while reading the music, as you play or sing; it has to be instantaneous and takes a great deal of practice.

Either can be done without a change of clef, moving each note by the required interval, or with a change of clef, mentally replacing the music's clef with another one, chosen according to the interval of transposition (Lacerda 1966, ch. XXXIX).

	Without a change of clef	With a change of clef
Written	each note is rewritten the interval up or down	read in the new clef, write in the old one
Read	each note is worked out while playing	read straight in the new clef

The change of clef is the tool of read transposition. In written transposition it is only an aid: you read the note in the new clef and write the result in the original clef (Lacerda 1966, ch. XXXIX).

The note stays, the name changes

Take the note in the second space of the treble staff. It is an A. Now imagine, in place of the treble clef, the C clef on the third line. The note has not moved, but that clef's second space is B:

Hear the passage

Hear the passage

A has become B: the note has gone up a second without anyone touching it. If every note of a passage is read that way, the whole passage goes up a second.

How to find the clef

Lacerda gives a three-step procedure (Lacerda 1966, ch. XXXIX):

1. choose any note of the original passage;
2. without moving the note on the staff, mentally give it the name it must have after the transposition;
3. find the clef that gives that position that name.

It is the reasoning of the example above, run backwards. To transpose up a tone, the A in the second space has to become B, and the clef that calls the second space B is the C clef on the third line.

Seven clefs, seven transpositions

Doing the same sum for each clef of the setticlavio, starting from the treble clef, turns up something neat: each clef shifts the note names by a different interval.

Clef	The A in the 2nd space becomes	Reading it transposes
C on the 3rd line	B	up a second
F on the 4th line	C	up a third
C on the 2nd line	D	up a fourth
F on the 3rd line	E	up a fifth
C on the 1st line	F	up a sixth
C on the 4th line	G	up a seventh

Since a seventh up gives the same name as a second down, a sixth up the same as a third down, and so on, each clef also serves for the complementary interval going down. The seven clefs cover the seven note names, and so they are enough for any transposition. It is one of the reasons musicians kept studying them after most had fallen out of use.

The clef gives the note's name, not its octave. A reading in a new clef can come out an octave higher or lower than wanted, and whoever transposes fixes the octave by ear (Med 1996, ch. XXVII).

The key signature first

Before reading a single note, set the clef with the key signature of the new key (Lacerda 1966, ch. XXXIX). The clef gets the letter right; the signature gets the sharps and flats right.

Lacerda's example: a passage in G major is to be transposed to F major, a tone down. The C clef on the fourth line calls each position by the letter below, and the F major signature puts the flat on B (Lacerda 1966, ch. XXXIX). A passage in G major:

Hear the passage

The same positions, read in the C clef on the fourth line with the F major signature:

Hear the passage

And the written result, back in the treble clef:

Hear the passage

Accidentals

The key signature takes care of the notes of the scale. But if the passage has accidentals, they have to appear in the transposition too (Lacerda 1966, ch. XL).

Without a change of clef, you simply apply the same interval to them as to the other notes (Lacerda 1966, ch. XL). With a change of clef, the clef changes the letter but copies the sign, and the copied sign is not always right. Lacerda gives a rule for knowing which notes change their accidental (Lacerda 1966, ch. XL):

1. apply the required transposition to C major; the notes that will change accidental are those in the key signature of the key you arrive at;
2. those notes, when read with an accidental, go up a chromatic semitone if the signature is of sharps, and down a chromatic semitone if it is of flats. Other notes with accidentals keep their sign.

His example: from G major to A major, a tone up, with the C clef on the third line. C major a tone up gives D major, whose signature has F sharp and C sharp. So, reading the passage in the new clef, every F and every C with an accidental goes up a chromatic semitone (Lacerda 1966, ch. XL).

A passage in G major with two accidentals, a B flat and a C sharp:

Hear the passage

Transposed to A major:

Hear the passage

The B flat, read in the C clef on the third line, lands on the C position and brings its flat along. C is one of the notes of the rule, so the flat goes up a chromatic semitone and becomes a natural: C natural. The C sharp lands on the D position; D is not in the rule, and the sharp stays: D sharp. Checking by degrees, the lowered third of G major has become the lowered third of A major, and the raised fourth has become the raised fourth. That is what Med asks of every transposition: that each note keep its function (Med 1996, ch. XXVII).

For minor keys the rule is the same, still reasoning in major. From D minor to F sharp minor, a major third up: C major a major third up gives E major, and the notes of the rule are F, C, G and D (Lacerda 1966, ch. XL).

Where it is still used

Med notes that read transposition made more sense when every clef was in common use, and that written transposition is preferred today (Med 1996, ch. XXVII). With notation software, which transposes a passage in one click, writing has become easier still.

Even so, the technique lives on wherever transposing has to happen on the spot. Accompanists use it when a singer asks for a song a tone lower. And conductors use it to read the transposing instruments' parts in an orchestral score: the B flat clarinet part, which sounds a major second below what is written, read in the C clef on the fourth line, gives the real note names; the F horn part, which sounds a fifth lower, read in the C clef on the second line.

What comes next

Transposition by clef substitution brings together two things already known, the clef and the interval. The next step is to look closely at the instruments that live transposed, and why their parts are written at one pitch and sound at another.