Talk:Negative harmony

Thanks for creating this article, @Yuriklee! I've just translated the article to Chinese Wikipedia.

There is one sentence that I don't fully understand (and could benefit for people's explanations), namely:

"Second, the "negative" form is transposed by a fifth relative to the original, rather than remaining within the same key area."

This sentence appears at the end of the section on Function, discussing the differences between melodic inversion and negative harmony.

I wonder how the interval of a fifth is calculated here. I understand that if you invert the C major triad [c Oberklang] to F minor triad [c Unterklang] over the axis of C, then from a monistic perspective, the root (C) is transposed down by a fifth; and if you are in the key of C, and you invert C major triad [c Oberklang] to C minor triad [g Unterklang] over the axis of E-quarter-flat (which is the midpoint between the tonic C and the dominant G in the key of C), then from a dualistic perspective, the Haupttone [dualistic fundamental] is transposed up from C to G by a fifth (which I think Riemann would call a Quintwechsel [i.e., Quint = up a fifth, wechsel = invert over the dualistic fundamental]). However, if you take something like a dominant major triad in the key of C major (which would be the G major triad), and invert it over the E-quarter-flat axis, then you would get the F minor triad (the subdominant minor triad). It's very difficult to argue a fifth relationship between G major triad and F minor triad. So I wonder if I'm misinterpreting @Yuriklee's original wordings here.

Secondly, what does "key area" mean here? Or could you just change it to "key"? I always find the term "key area" to be somewhat ambiguous. From a modal mixture perspective, one could argue that the key of C major and the key of C minor are both in the key area of C. So if you are inverting everything in the key of C mixture about the axis E-quarter-flat, then you are still in the key of C mixture.

If anyone could help me understand this a bit better, that'd be great! Or otherwise, perhaps we could make this sentence a bit easier to unpack in the article. ​ ​ ​ ​ ​ ​ ​

Many thanks!

——星球统领 (talk) 19:49, 20 March 2026 (UTC) [reply ]

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