Talk:Riemannian theory

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The accompanying illustration of Riemannian dualism is misleading about Riemann's thinking. Although the diagram does show dualism, it shows it in the context of scaler Roman numeral theory, which Riemann never used. Seeing as one of Riemann's biggest projects was to build a functional system of harmony, it would be better use a diagram built around that idea, or better yet, make a very simple diagram which does not contain anything further than dualism itself. — Preceding unsigned comment added by Baumgaertner (talk • contribs) 19:08, 23 March 2014 (UTC)

Is that Riemannian theory?
The remark above, from 2014 (!), that the illustration shows dualism "in the context of scalar Roman numeral theory" is only partly right. It is true that the illustration shows Roman numerals, but these are not really needed. The real problem is that the caption to the illustration says that it presents "minor as upside down major", but that is not true: the descending scale is not minor, it is Phrygian! The reason why this descending scale is G Phrygian instead of C Phrygian is unclear – or, better said, it is that the author (Hyacinth) wanted it to show both the C major and the C minor chords as originators of the scale.

This raises two points:
 * 1) That Riemannian theory does not reduce to dualism;
 * 2) That Riemann's dualism is based on the ideas of undertones.

About the first of these points, it seems obvious that the most important aspect of Riemannian theory is his theory of functions. This is already detailed in the Function (music) article, more precisely in its section about German functional theory. However, what is discussed there is the modern functional theory: as this article says, "German theorists have abandoned the most complex aspect of Riemann's theory, the dualist conception of major and minor". A link to that article may therefore not be sufficient and the present article should present the theory as Riemann himself described it.

About the second point, Riemann's dualism arises from the idea that much as the upper harmonics justify the fifth and the major third above the fundamental (say, G and E above C), the under harmonics produce a fifth and a major third below the fundamental (say, F and A♭ below C). Functions are judged accordingly: the dominant above C is G, the subdominant F; the dominant below C is F, the subdominant G. Etc. This is a theory about which even Riemann eventually began to doubt, I think, but this all should be mentioned.

Much of what the present article discusses comes from Klumpenhouwer (1994) and actually concerns the relation between Riemann's theories and Neo-Riemannian theory (and more generally modern transformational theories). This is but a marginal aspect of the matter, especially from the point of view of Riemann himself. I won't further discuss whether Neo-Riemannian theory is properly so named, but to say that I have my doubts about it.

In any case, an article about Riemannian theory should include a lot that is not even alluded to in its present version. There is a lot of work to be done about that and I am afraid I don't know enough about Riemann to do it myself, but I urge other Wikipedians to think about it.

— Hucbald.SaintAmand (talk) 19:05, 27 June 2020 (UTC)


 * "Riemann's "dualist" system for relating triads was adapted from earlier 19th-century harmonic theorists. (The term "dualism" refers to the emphasis on the inversional relationship between major and minor, with minor triads being considered "upside down" versions of major triads; this "harmonic dualism" is what produces the change-in-direction described above. See also: Utonality)"


 * At least the text above has a citation. If he's not dualist why are there 'Schritts' and 'Wechsels'? Hyacinth (talk) 07:55, 8 July 2020 (UTC)


 * Of course, Riemann was dualist! There is no doubt about that. As Klumpenhouwer makes clear, however, he was not the first. What I denounce is that his theory is sort of reduced to dualism, in this article. Tonal functions, which must be considered the main aspect of Riemann's theory, are mentioned only in passing while they should form the core of the article. Even about his dualism, his belief in undertones is not mentioned. I repeat that this article is hardly about Riemann's own theory. It mentions Schritt and Wechsel but, as the article itself mentions, this aspect belongs to the 1880's, more specifically to Riemann's Skizze einer Neuen Methode der Harmonielehre of 1880. Riemann continued to develop his theories for 38 years after that, but the article does not say a word about these. — Hucbald.SaintAmand (talk) 09:59, 8 July 2020 (UTC)

Melodic minor as upside down major
modified the caption of the first musical example to indicate that it is the descending melodic minor that is upside down major. But the example is far from clear, because of a problem inherent in this theory of the inversion of the scale. What the example shows is a G phrygian descending scale – indeed an inversion of the ascending major. The figuring indicates "Cm" (C minor, but this cannot refer to the G scale), and the figures appear to follow the descending scale more or less at the lower fifth: i VII VI v iv III ii° i apparently denote triads on C B♭ A♭ G F E♭ D C. This implicit scale indeed is descending melodic minor, but it is not an inversion of the ascending major scale. I defy most WP readers to make much sense of all this.

I don't really know what to do. I should browse through Riemann himself to see whether he ever mentioned the inversion of the scale (I won't have the time just now) – I doubt he did, I think that this results from a modern extrapolation about dualism. As it is, the example seems to me more confusing than explaining. Whuddyathink? — Hucbald.SaintAmand (talk) 07:41, 12 July 2021 (UTC)