Why is the Mirror on a midpoint, rather than the root note, in Negative Harmony theory?

Question

I'm curious about why Negative Harmony music theory relies on finding the midpoint between the Tonic and Dominant Degrees in a scale, and flipping the scale around that point, instead of simply playing the scale's intervalic pattern inverted from the tonic.

For instance, when mirroring C Major at the midpoint between the Tonic and Dominant, you get:

C - G D - F E - E♭ F - D G - C A - B♭ B - A♭ (I pulled this little diagram off Reddit.)

Apparently, the mirror point lands between the Major, and Minor third. (E, Eb, respectively.)

But why is Negative Harmony done this way, and not by flipping right at the Tonic?

Up Down - C - C w - D - Bb w - E - Ab h - F - G w - G - F w - A - Eb w - B - Db h - C - C

If someone could explain to me why this isn't done, or alternatively, what to call this, if this isn't called mirror or Negative Harmony, I'd be really appreciative!

Thanks so much!

P.S: I used a scale finder tool to see the many names of scales that show up with this particular set of Notes:

https://www.scales-chords.com/fscale_res_en.php?rn1=C&rn2=A%23%2FBb&rn3=G%23%2FAb&rn4=G&rn5=F&rn6=D%23%2FEb&rn7=C%23%2FDb&rn8=C&rn9=&normal=1&greek=1&greekalt=1&other=1&etnic=1&c1=&t1=&c2=&t2=&c3=&t3=

Obviously, lots of names for the scale, and, it is possible one of them exactly matches the Inverse intervalic pattern, I didn't check them all, but none of them match exactly what I've written down above.

Answer 1

The notion of negative harmony really comes from Ernst Levy, who discussed it in his A Theory of Harmony (1985). Recently it's become a bit of a trend thanks to Jacob Collier.

But the basis of negative harmony (or "mirror harmony") is really a rehashing of a 19th-century Austro-German theory called dualism. This system was actually about mirror inversions around a chord root. Take, for example, C major: C E G. The harmonic dual of this chord measures the intervals from C, but in the opposite direction. C to E is an ascending major third, and C to G is an ascending perfect fifth. As such, the harmonic dual has a descending major third (C to A♭) and a descending perfect fifth (C to F).

You'll notice that this creates an F-minor triad. (But back then, they actually called this "C dual minor," since it was generated starting on C.)

In contrast, negative harmony sought a way to change the mode of the key without changing the tonic. As such, it inverts around the midpoint between tonic and dominant. This way, the negative harmony of C E G is C E♭ G, and major just switches to minor. (But note that chords built on other scale degrees will typically change their root.)

In other words, harmonic dualism does exactly what you're asking about: it inverts around the tonic pitch. But negative harmony just changed the rules a bit by inverting around tonic and dominant.

---

PSA: Due to the recent influx of questions on negative harmony and the number of views these questions receive, I've taken the liberty of creating the negative-harmony tag. Feel free to consult the other questions marked with that tag!