# What is the formal definition of 'transpose'?

I've heard people use the word "transpose" to describe going from a major key to a minor one. I've heard other people say that's an incorrect usage because you can only transpose in the same tonality. The Oxford Learner's Dictionary defines it as: to write or play a piece of music or a series of notes in a different key ...without any reference to whether that different key is in the same tonality. What is the correct definition and if you can only transpose major-to-major and minor-to-minor, is there a formal term for going from major to minor?

• Worth noting that transposition is isomorphic to geometric translation: it should keep the original distance between notes the same. – moonwave99 Feb 3 at 13:58
• @moonwave99 Or like scalar multiplication: multiplying every note's frequency by a constant factor produces a dilation of sorts - yet our brains think of it in a more linear manner – user45266 Feb 3 at 19:57
• All notes of a beat/melody/composition -n notes, i.e. -4 or -7 or -12 is a transposition of the notes. – aliential Feb 3 at 20:43

To transpose a piece of music is to change the pitch of all notes by the same interval. The intervals between adjacent notes in the piece will remain the same.

Major keys can only be transposed to other major keys. Minor keys (natural, harmonic, or melodic) can only be transposed to minor keys of the same kind.

This is because the pattern of intervals in the key will not change in a transposition.

You should also change the key signature. This way, all notes without accidentals will not have accidentals in the transpose. Notes with accidentals in the original, will still have accidentals (but possibly of a different kind) in the transpose.

For example, if we transpose the C major scale: C D E F G A B C

into the key of D major (up a major second), we get: D E F♯ G A B C♯ D

(Both of the sharps will be taken care of in the new key signature of D major.)

Another example, if we transpose the C harmonic minor: C D E♭ F G A♭ B♮ C

into D harmonic minor (again, up a major second), we get: D E F G A B♭ C♯ D

(The natural accidental on the B-natural corresponds with the sharp accidental on the C-sharp. The other flats are taken care of in the key signatures)

To change a piece from a major key to a minor is not really a transposition because the pattern of intervals will have to change. This is not so easy to do and probably won't sound right.

To transform from major to a natural minor you'll have to flatten the third, sixth, and seventh. If its a harmonic minor you'll have to sharpen the seventh back up (to where it was) with an accidental.

If you are using the same tonic note, you might call this a parallel transformation. But if you are using a different tonic note its more like a transposition and a parallel transformation combined.

• Although with the modern scale, the intervals aren't exactly the same. – Acccumulation Feb 3 at 22:24
• @Acccumulation - the intervals - M3, P5 etc., are exactly the same, and I dare say the relative pitch difference is the same too. Are you thinking about 12tet? – Tim Feb 4 at 10:02
• @Tim According to this, the ratio between C and D is 9/8. If you raise that to the third power, you get 1.42. But the ratio between C and G is 4/3, or 1.33. – Acccumulation Feb 4 at 22:18
• @Acccumulation - what I meant was that C>D - in an octave (providing they're next to each other) will always be M2. Playing round with numbers won't chnage that. – Tim Feb 5 at 7:45

I have only ever heard transpose used to go from one key to a different key (major to major, minor to minor), or else from one octave to another. If you go from major to minor or from minor to major, I would use the word modulate.

• Did you mean to delete the bit in brackets? I think it'd make more sense if you did. – Old Brixtonian Feb 3 at 3:52
• No. You transpose from a major key to another major key, and also from a minor key to another minor key. – Jomiddnz Feb 3 at 4:27
• Sorry - I misread it as "maj to min, min to maj". It's late and I'm overtired! +1 – Old Brixtonian Feb 3 at 4:42
• I‘ve edited my answer: You also can transpose an octave down ... and stay in the same key. – Albrecht Hügli Feb 4 at 13:33

I always used this term transposing only from one key to another key (not parallel key, not relative key - and not diatonic transposition). Some notation software offers you the option of chromatic or diatonic transposition. So there seem to be 2 different interpretations of the use of transposing.*1)

Edit:

I forgot to mention the octave transposition - and the option up or down!

If we count the possibilities of transpositions „ from key to key“ there would be only about 12.

But there are the transpositions of the 12 different intervals up and the 12 intervals down (plus 1-4 octavas.) So actually there are so many more options!

Key and tonality are the same thing.

In modern western music, the central element of composition is the 7-tone major or minor scale. These sets of notes happen to be more than just a random group of 7 notes: they contain a rich collection of relationships between notes. For instance: have you ever noticed how strong the attraction is between B and C in C major? Play a C major scale and stop on B: feeling the pull towards the next note?

There are other relationships in these 2 scales that extends even to the chords you can build by stacking notes in series of thirds (C-E-G-B for Cmaj7, G-B-D-F for G7) and I won't go into details here but suffice to say that each note of these scales can be assigned one of 3 harmonic functions that will drive the harmonic movement and steer it to wherever the composer wants to go.

The key of a piece is only the label we put on the harmonic world within which the harmonic journey meanders.

Modulation is the technique that allows the composer to visit other harmonic worlds, to go to "another key". The first trick to achieve that is to recognize that chords can exist in different tonality, albeit having different functions. For a basic example: Cmaj (C-E-G) exists in C major (with a Tonic function) but also on F major (where it has a Subdominant function) and in G major (with a Dominant function). While writing in C major, the composer could decide to consider his Cmaj as the Dominant of Fmaj and continue writing in Fmaj for the new section, possibly going back to C major to end the piece.

Transposition is a technical trick to allow the musician more playing comfort. Example: playing a piece in F# major on the guitar is a pain, and most beginners would use a capo on the 2nd fret to allow for more open strings and easier chord positions. Or they could just decide to shift the entire song 2 semitones lower and play in E major instead. No harmonic value but a heck of a lot better on the guitar... Same with singers. Most have a range in which they're most comfortable or just sound best.

We transpose when we shift a melody up or down, to suit someone's vocal range better.

The trumpet is a transposing instrument. That means that everything is written a little funny.

When you want to change key, you modulate. There is a little transition, and then hey presto, you're in a different key (or tonality).

The word "tonality" is pretty much equivalent to "key." But when we say "tonality," that has a stronger appreciation of the role each note plays in its context. The sequence "5 - 1" (e.g. G - C) sets up a strong feeling of tonality right away. When we have established a tonality, we, and the listener, have a strong sense of where we are, and which note is tonic.