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The other day I was trying to write a canon by inversion, and I wondered whether there are any general guidelines (other than trial and error) as to what kinds of melodies tend to sound "good" under transformations of melodic inversion.

By "good" I don't necessarily mean very beautiful, but rather at least somewhat plausible as a melody in a traditional tonal framework. For the sake of discussion, let's consider both exact inversion (where the major mode, for example, becomes the Phrygian mode on the mediant) and tonal inversion (where in C major, the step C-D simply becomes C-B, etc.).

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    Maybe you should write first the inversion and then listen to the original version ;) May 13 '20 at 7:41
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Almost all good melodies are not bad when inverted, at least around their first note. Melodic interval of seconds map to seconds, thirds to thirds, fourths to fifths and vice versa, sixths to sixths and sevenths to sevenths.

You could make a list of intervals then their inversions around whatever axis you like.

As an aside, sometimes inverted melodies (as well as retrograde and cancrizans) can be improved by only applying the transformation to "important" notes and modifying unaccented nonharmonic tones as needed. Accented nonharmonic tones are usually important as they do stand out in a melody.

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  1. Begin with the root tone.
  2. The first note should be a long value.
  3. The second note might be a fifth a second or a third (up or down)
  4. Pentatonic scale are good to play inverse
  5. To go sure for 100% create a melody which contains already its inversion in the second phrase.

(last proposal was just a little joke)

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Exactly as ttw's answer, in most situations, inverted melodies of an already good melody will make sense.

The trouble, however is finding the underlying chord progression that fits well with the inverted melody that does not involve the progression breaking any rules of harmonic progression or straying into an unknown domain (consecutive augmented chords for example).

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