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My understanding of melodic inversion (strict and diatonic) is taking a melody/motif, beginning on the same note and moving in the opposite direction. However, in the IB Music Revision Guide's analysis of Rachmaninoff's Rhapsody On A Theme Of Paganini, the first 4 note motif CBAB below is said to be an inversion of the 2nd 4 note motif ACBA. Can anyone tell me what we call this particular type of melodic inversion (that does not begin on the same first note) and what logic (if any) is used to create this particular type of melodic inversion, especially what note do we start on?

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  • Huh, it's not even a retrograde inversion. With that being said, the ACBA motif is dirt common in the original Paganini work (his Caprice No. 24 in A Minor), so the IB Music Revision Guide is probably onto something of some sort (even if it's slightly wrong).
    – Dekkadeci
    Jan 30, 2020 at 11:59
  • You could BAB => ABA is horizontal mirrored and C ha changed the place ;)
    – Albrecht Hügli
    Jan 30, 2020 at 14:17

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As others have said, this is neither inversion nor retrograde; and it's not even a type of retrograde inversion!

But if you're looking for a very famous example of inversion of the original A–C–B–A motive, check out the opening four notes (at the end of the second measure) of Variation 18.

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Not differentiating specific interval quality, the example includes the following melodic intervals: descending step, ascending step, ascending third.

The only thing inverted is the single step. Descending in green, it's ascending inversion in red...

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If the second figure was an inversion of the first it would look more like...

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Fig 1

Descending step, descending step, ascending step

Fig 2 (just reverse the directions...)

Ascending step, ascending step, descending step

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  • Thanks Michael, your figure makes sense in terms of direction, but should an inversion not begin on the same note?
    – John MC
    Feb 7, 2020 at 7:36
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    Not necessarily. Look at the two examples here: en.wikipedia.org/wiki/Inversion_(music)#Melodies. You may want to distinguish inversion as a procedure versus a description. Those are two sides of the same coin, but with a bit of difference. Procedurally you can invert on a starting note, or some central axis. As a descriptor you can simply describe, point out a melody features inversion. Ex. Bach's first two-part invention. Inversion is an important feature of the work. Procedurally inversion is handled very freely with transposition to many tonal regions.
    – Michael Curtis
    Feb 7, 2020 at 14:56
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There's an obvious similarity - the same four notes in a different order - but 'inversion' is the wrong label. If this is treble clef and we're in A minor perhaps the second 4 notes might be an 'answering phrase' to the first 4.

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