Talk:Transformational theory

Missing definition

This article doesn't really explain what transformational theory is; such as, for example, how the diagram in the article corresponds to the music, and what it is meant to demonstrate. E.g. are the pitches in the diagram notes, or keys? And what do the arrows and tree structure denote? I assume the fractions represent ratios between frequencies, i.e. a fancy way to show intervals, but what point are they making? Ben Finn 20:02, 2 April 2007 (UTC)

I would agree to the point that this article is stubby. It is very advanced music theory, graduate level, since it goes beyond set transform (retrograde inversion, etc.). Transformational theory is essentially very simple concepts- this is the type of analysis done on the fly by any intermediate keyboard student studying J.S. Bach's WTC I Prelude 1 in C, where special focus is given to the changes the happen between each measure.

The diagram in this article is a series of changes, read diagonally from the upper left. I would also like to see a wiki article describing interpretation nets, such as Klumpenhouwer Network. Benitoite (talk) 16:41, 12 March 2008 (UTC)

False claims in the article

I'm a bit worried about the statement that "the idea of a musical transformation revolves around Lewin's observation that the mathematical groups defined by musical set theory (as developed by Milton Babbitt, Allen Forte, et al.) have identity elements that are arbitrarily defined." This doesn't seem right at all -- for instance, the identity element of the group of transpositions (T0) is not at all arbitrary. What I think is meant is that the application of numerical labels to musical objects involves an arbitrary choice of reference for the term "0." But that's different.

I'd prefer to see the article made a little more accessible. Right now, it doesn't offer much help to outsiders. Njarl (talk) 05:10, 3 September 2009 (UTC)

This is not a false claim. A GIS is a torsor, but Lewin AFAIK did not know about torsors. This statement can certainly be revised, since it seems to indicate that the operation T0 is arbitrarily defined as the identity. But please don't simply remove this important definition of a GIS. I'd very much like a compromise revision, if you could suggest one. 205.153.63.30 (talk) 17:46, 7 September 2009 (UTC)

The falsity does not lie in the claim that "Lewinnian GISes are torsors." That is true. The falsity lies, first, in the claim the realization about the arbitrariness of the label "0" motivates or is central to Lewin's definition of a GIS. (Having been around him at the time, I do not think this was true; I think the motivation lies in his general attempt to put Babbitt's pitch/time isomorphism on sound theoretical footing.) Second, in the claim that the identity element of the *group* is arbitrarily defined; this is wrong. And third, in the failure to recognize that transformational theory generalizes the notion of a GIS in various ways. Transformations, as described in the second half of GMIT, need not involve GISes or torsors at all. In fact, according to Klumpenhouwer, transformational theory is supposed to replace the GIS-theory of the first half of the book; see his MTS article on the subject.

If you want to write about torsors, you might add a separate section about GISes. I would use the term "principal homogeneous space," which I think is a bit more common, at least among older mathematicians. Furthermore, Tudor Vuza's review of GMIT uses that term, so Lewin certainly was aware of it.Njarl (talk) 21:50, 9 September 2009 (UTC)

Please discuss before reverting

Recently an unnamed editor undid my changes to the article without discussing them. I am restoring my changes. Hopefully, we can work out the issues here, as per Wikipedia protocol. Njarl (talk) 16:21, 4 September 2009 (UTC)

Another questionable statement

The article currently contains this sentence passage:

"The greater abstraction that is achieved by removing definitive labels from musical objects and only defining the operations that generate one from another is transformational theory's greatest asset. One transformational network can describe the relationships among musical events in more than one musical excerpt thus offering an elegant way of relating them. For example, figure 7.9 in Lewin's GMIT seen in the illustration given here can describe the first phrases of both the first and third movements of Beethoven's Symphony No. 1 in C Major, Op. 21. Further, a transformational network that gives the intervals between pitch classes in an excerpt may also describe the differences in the relative durations (measured in eighth notes, for example) of another excerpt in a piece, thus succinctly relating two different domains of music analysis."

This is confusing to me. Traditional theory often achieves a very similar level of abstraction by using generalized labels for objects. For instance, the terms "I, IV, and V" can refer to any number of particular chords. Thus a traditional description such as "a I-IV-V progression" can refer to many different pieces. The article makes it seem as if Lewin's system is inherently more general than traditional theory because one and the same description can apply to multiple passages. Could someone try to explain this more clearly? Otherwise, I think it should be removed. Njarl (talk) 16:50, 4 September 2009 (UTC)

OK, I've now added significant new material. We need references for the articles by Hook (Integral), Tymoczko (Spectrum), and Hall (JAMS), as well as Gollin's dissertation. Njarl (talk) 14:03, 5 September 2009 (UTC)

"I, IV, and V" can refer to many different pieces, but simply describing the root motion (up a fourth, up a step) instead of the particular elements of the set of diatonic triads provides greater abstraction and greater applicability to numerous situations in music. This is precisely the benefit of transformation theory. Did you actually read GMIT? 205.153.63.30 (talk) 17:50, 7 September 2009 (UTC)

Yes, I did read GMIT. Discussed it with David many times as a matter of fact, and have discussed the formalism in print on more than one occasion. Can we have a civil discussion now?

In the actual Beethoven examples, a conventional Roman numeral description would indeed describe both passages. You say that a description of the root motion (up a fourth, up a step) would be more general and this is true -- by eliminating information, you get greater generality. However, the distinction between generality and specificity is orthogonal to the distinction between traditional object-based theory and Lewinnian transformational theory. This is because: (1) Lewinnian transformations are often more specific than the one you mention -- for instance, the "relative" transformation does not simply move the root by third; it also transforms major to minor in specific ways. (In particular, the actual figure in the article distinguishes major chords from minor using upper and lower case.) (2) Traditional theory can be more or less specific - for instance, Schenkerians use only capital roman numerals, eliminating the distinction between major and minor; these essentially describe root motion (up a fourth, up a step) without specifying triad quality.

The point is, the greater generality you describe isn't intrinsic to the transformational method itself - it's an artifact of comparing very general transformations to more specific traditional notation. This is an apples and oranges comparison. It's actually hard to explain the advantages of "transformational theory" in general way. If we can come up with a way of doing so, that would be very helpful to the article's readers. But it won't be helpful if we make misleading claims about the theory's advantages. Njarl (talk) 21:44, 9 September 2009 (UTC)

Missing image?

"For example, figure 7.9 in Lewin's GMIT—shown in the illustration on this page" - This image was removed from Wikipedia on 19 March 2011. NeoAdamite (talk) 19:11, 6 February 2015 (UTC)

"Musical object" listed at Redirects for discussion

An editor has asked for a discussion to address the redirect Musical object. Please participate in the redirect discussion if you wish to do so. –Deacon Vorbis (carbon • videos) 17:37, 14 December 2019 (UTC)