Is there a quick rule-of-thumb for finding negative harmonies?

Usually they are explained by drawing a circle of pitches and pairing them by lining up the 'positive' and 'negative' pitches. But this needs a diagram. How does one quickly decide the negative of, say, the supertonic chord without having to draw a diagram?

I suspect this may turn out to be a very naive question.

EDIT: I presume the downvote is for not explaining negative harmony. I felt it unecessary to do so (since only someone who knows it can answer and youtube is awash with vids), and impractical, (since I barely understand it.)

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    I don’t think negative harmony is a common term, where does it come from? Jul 7, 2019 at 12:17
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    I'm not sure if the question is naive or not, but it sure is difficult to answer. It's a bit as if you were asking "How does one quickly find out a relative minor key without drawing a circle of fifths/fourths?" I guess, the only quick way to go about it is to have an eidetic memory and knowing one's chords by heart. Other than that, you could program a tool that would do it for you. That's what I would personally do (as I do not have eidetic memory).
    – Pyromonk
    Jul 7, 2019 at 13:20
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    Beflummoxed by the terms 'negative' and 'positive' harmony.
    – Tim
    Jul 7, 2019 at 13:47
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    @PatMuchmore Negative harmony is all the rage on YouTube at the moment. Jul 7, 2019 at 13:57
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    Are you looking for a quicker method than the ones shown in the "Related" questions on the right side of the page? Unfortunately it's hard for me to imagine a quicker way.
    – Richard
    Jul 7, 2019 at 14:54

2 Answers 2


There is a relatively simple algorithm, depending on what you think is relatively simple. We'll just need to assign some numbers to the chromatic scale, with the major third in the key being 1 and the minor third being -1. You can extend this as far as you need to, so:

enter image description here

Now just change the sign. I in this key (CEG) is -4 1 4. Changing signs yields 4 -1 -4, or G Eb C, just as expected. V7 (4 8 -2 2) becomes -4 -8 2 -2, or C G# F D: the inversion of iiø, as expected. It doesn't matter if you use 8 for B or -5.

This might seem a little clunky at first, but it's not that much different from on the fly transposition, which is fairly simple to learn how to do. You could also think about it in scale degrees, instead of trying to get absolute names, and then you would only have to work it once, as long as you're comfortable working with relative degree.

enter image description here

In this chart, you'll see the note transformation, but I've also put the new scale degree in, and you'll notice that the root becomes the 5th, the 2nd becomes the 4th, &c in inverse proportion to the scale degree, so in practice, you can count down from the 5th as your original note goes up. In this case let's take V7, so scale degrees 5 7 2 4. That means count down a 5th from G (if in C), a 7th from the G, 2nd from the G and 4th from G, giving us C, Ab, F, and D, the expected iiø.

This also means, if you are familiar with interval inversion, that you can calculate the negative counterpart from the inversion. Perform the interval inversion (root = root, 2 = b7, 3 = b6, 4 = 5, etc) and then go down a fourth from that, and that will be the negative degree.

enter image description here

So to put this to practice, if your chord contains the root, the 3rd and the 5th, then the inversions are root, b6 and 4. Go down a fourth from those and you have 5, b3 and root, or G, Eb & C, as expected. Any one of these methods should work, will not require pre-charting, and should be able to be performed on the fly once you are used to it.


No, there isn't. You just have to draw the diagram. Well, you could, beforehand, draw a giant table of all possible diagrams: every axis, every triad, say. But looking it up in the table might not be any faster. Also, see Richard's answer.

  • Thanks. I feared as much. But counting the intervals down from the root seems to be a way to do it.
    – PeterJ
    Jul 8, 2019 at 10:34
  • @PeterJ, that's basically it: create the negative by listing the ascending intervals above the bass/root as descending from the bass/root. Jul 8, 2019 at 15:30

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