A transposition is to change the melody and harmony to another diatonic scale with a different root but same mode.
A modulation is to change the mode within the same diatonic scale (e.g. from Ionian to Aeolian, from Ionian to Dorian etc)
A transposition or modulation is called harmonic if the two roots differ by an interval of 5th or 4th
A transposition or modulation is called melodic if the two roots differ by an interval of 3rd
A transposition or modulation is called chromatic if the two roots differ by an interval of 2nd.
We discuss in the next the advantage and disadvantages of an harmonic transposition versus an harmonic modulation.
