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I think I understand the basic concept of negative harmony, rotating around an axis.

I get basic functional chord negatives like these...

       inversion table

            Eb E
         D        F
      C              G
   B                    Ab
A                          Bb
normal chord | negative chord

    V7  GBDF | CAbFD iiø4/2
    ii6 FAD  | DBbF  bVII6/4
    IV  FAC  | DBbG  v6/4 (minor triad)
    I   CEG  | GEbC  i6/4

I think I'm generating the negative chord correct, but how do they get used?

Should I treat those negative chords as having some kind of negative functions or qualities similar to the normal chords?

  • does iiø4/2 "function" like a dominant to a tonic i6/4?
  • is the sense of chord stability inverted: in negative harmony are 6/4 chords stable?
  • should the negative chord be treated strictly as the specific inversion? Meaning is i6/4 the negative of I and i in root position is not the negative of I because it is the wrong inversion?

If there aren't any typical, practical applications, and it's a unique, personal approach for each composer, I get that.

I only want to know if there are typical approaches, because when I hear 'negative harmony' I think 'harmony as the art of chord progressions' - whether functional or non-functional - not just a method for inverting isolated chords.

3

Flipping pitches about an axis, as you demonstrate, is normally called "inversion" and normally applied to a melody, such as a fugue subject or tone row. There it is effective in making a new melody with a complementary contour.

"Negative harmony" is the more controversial practice of applying the same operation to chords and chord progressions. It /can/ reveal kinships between chords in some cases. To take your first example, if V7 can substitute for V in V-i, negative harmony suggests putting iiø6/5 for iv in iv-I, and this indeed works. It does NOT suggest what bass notes to use.

This is a felicitous example, however. Most functional progressions (e.g. 7th chords by downward 5th) lose their functional character after negation, which is one reason why negative harmony has remained somewhat suspect among analysts and mainly unknown among composers.

  • How did you get iiø6/5 from V7? V7 inverted is iiø4/2. – Michael Curtis Jul 24 at 20:03
  • As I said, negative harmony does not suggest bass notes. iiø4/2 - i6/4 is an absurd cadence. It's more sensible to say: if we add a 7th in the authentic cadence, then we add a 6th in the plagal one, keeping the bass notes. – Mirlan Jul 26 at 0:24
  • So after the negation/inversion it just becomes an unordered set of pitches? Where does that idea come from? Is there a particular book or theorist? – Michael Curtis Jul 26 at 0:28

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