Negative Harmony, Gulp

or I’m talking to the man in the mirror

I suppose it had to happen… Thank you TH (aka “confused of Bristol”) for asking about the en vogue topic of negative harmony. I completely understand your confusion.

Ah, I do love these opportunities to give my opinion and get myself digitally shouted at…

A disclaimer – I have used this concept from time to time, but not often and I’m not an expert. Certainly it’s interesting, but often in real life the wrong kind of “interesting”, at least to me. And I’m extremely broad-minded (so broad-minded it’s occasionally cost me gigs…)

Every now and then jazz – in its constant search for new things or even a theory of everything – gets a new craze. So let’s talk about this season’s hat.

There are different ways of thinking about this stuff, but I’m just going to stick to the basics and give an easy shortcut for use in jazz. First we should give some thought to the foundation of the idea – the proposition that there is an inverted version of the overtone series called, not surprisingly, the undertone series. Time for a bit of philosophy…


The problem for me (and many others) is that while overtones exist in nature, undertones just don’t. The concept is artificial, theoretical – you can imagine reversed time, but you can’t undrink a cup of coffee that gets hotter as you do it. Exploring non-real entities is interesting and can certainly produce useful results. For instance you can’t have £15 + £7.30i in your pocket – yet i (the square root of -1) sings out everywhere in maths.

And in physics (as far as I understand it) the overriding concept is one of symmetry, rather than negativity as such. So I think the problem is in the naming. “Negative harmony” sounds really cool but in my view, what we’re really talking about here is “mirror harmony”. Does that get a little bell ringing in your head? Inverting musical lines is centuries-old…

Some Undertones. We approached them for comment but they were too busy having teenage kicks, which is fine by me…

There’s a slim argument that doing this with single lines may convey a certain discernible “negativity”, but no contrapuntalists are on record as regarding the result as “negative” lines (not even Bach, and he was a rare musician whose mathematical understanding went past four). As to harmony, I think the case disappears entirely – we simply don’t hear chords upside down.

“.forwards experienced it’s but backwards working be may You”
“?evitagen siht sI”
“?hrtf hR”

The notion of mirror harmony has been explored in great variety in modern classical music (see books like Persichetti). In that respect, it’s intended to be an arbitrary system of organisation to generate interesting compositional ideas, rather than some deep truth about music.

ABC – EASY AS 321…

It’s crashingly simple – you can mirror any group of notes across any chosen reflection point. In this case, the surface of the mirror is a note that doesn’t exist. Since the I is the most resolved and the V is the most tense, why don’t we imagine a midpoint betweem them? Might as well. Halfway between the I and V in eg the key of C is the space between Eb and E. To mirror a note count the semitones up and replace it with a note the same number of semitones down. E <-> Eb, F <-> D, F# <-> Db, etc.

So Dm triad becomes Bb triad, G triad becomes Fm triad and C triad becomes Cm triad.

(The fact that the tonic flips polarity leads some to conclude that negative harmony is where minor comes from. Personally, I don’t agree. I reckon medieval wandering musicians just found that changing the third got them more amorous attention…)

You can do this with any chord type or voicing. Unless you have an Andromedan brain, you can’t do the mirroring work on the fly, so here’s a jazz shortcut…

We spend half our lives playing turnarounds, right? We also get bored and often convert every chord to a dominant. So…

E7 A7 D7 G7 (C)
maps to
Abm6 Ebm6 Bbm6 Fm6 (Cm)

Some things to note:
1. We’re approaching the key centre by a string of minor plagal (IVm-I) cadences rather than authentic (V-I) cadences. There isn’t really anything “negative” about plagal cadences, but it gives some kind of natural flow.
2. We’re losing flats rather than sharps as we approach. Some would argue that means we’re getting brighter rather than darker during the progression.
3. If you complete the process for every scale tone, a Mixolydian scale inverts to a Dorian one. Modally, that’s the point when major becomes minor – rather neat (but full modal mirroring gets rather knackered beyond this case…)
4. I hope you can already see that if you want to use this as a substitution under a “positive” melody it’ll produce some pretty hairy bitonality. Expect to get clouted if you try it with a singer…
5. Have fun looking for patterns and things – there are some to be found.

There’s a lot more that can be explored on a rainy day. I’d say this is a good first step into using this stuff (it might even be all you need). But I’d also say it’s a tool, not a rule.


1. Approach the key centre from the “wrong” direction – by 4ths rather than 5ths.
2. Make every chord a minor 6th.
3. Be prepared to alter either the harmony or melody to avoid clashes. Often.
4. Be careful about unleashing this stuff on an unprepared band. Chances are they won’t think you’re being “artfully anti”, they’ll think you’re drunk…

Incidentally, the concept originated from a guy called Levy who wrote a book called A Theory of Harmony. Not THE Theory of Harmony. As theoretical treatises go, it’s an unusually slender read. It also strikes me as an admirably determined attempt to smash square pegs into round holes.

Okay. I’d love to discuss the subject in the comments, but please leave the internet blowtorches at the door. Especially if you’re a congregant of the Negative Harmonic Church and intent on burning me for heresy.

Tagged with: ,
Posted in a) Soloing Scales & Modes, e) Rants & Ramblings
3 comments on “Negative Harmony, Gulp
  1. Thanks for addressing this in a practical and straightforward manner. I have been waiting a couple years for someone to make this post. My favorite is number 4 – [Be careful about unleashing this stuff on an unprepared band. Chances are they won’t think you’re being “artfully anti”, they’ll think you’re drunk…] 😂 Here is my take on the subject:

    • Jason says:

      Nice piece Eddie. I agree with your criticism that negative harmony isn’t consistent. The sum of the squares of a right triangle don’t SOMETIMES equal the square on the hypotenuse. E doesn’t MOSTLY equal mc squared. Pi is NOT 22/7.
      The irony is that people who really hold to negative harmony tend to invoke logical argument, yet the premise is demonstrably flawed when you test it against more than the most convenient cases. As a theory it gets easily disproven by contradiction. There are just too many “ah yes but”s…
      I’d be happy enough if they just said “this an interesting thing and it can produce cool results”. It is and it can. But so many people seem determined to wish it into being some kind of eternal truth…
      Also – to be candid – often it just sounds like crap (at least to my “positive ears”). Just because something is interesting doesn’t make it useful.
      (Great surname btw – bet there are some cool band names to be made out of that.)

  2. Thanks for covering this. I always wanted to know more about it, but I was too tired. Now I can at least answer a student’s question about it.

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