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I'm reading the following paper,

Lerdahl, F. (1988). Tonal pitch space. Music Perception, 315-349.

I'm interested in comparing what is written here with other equivalent theories. Some of these mentioned in the paper I've read so far are Longuet-Higgins, Schoenberg and Schenker. I'm sure there are several others which I may not even be aware of and I'd like to know about these too.

What are the significant schools of contemporary (20th century) music theory?

Thanks!

Meaningful Username
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user1953384
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    Was this put on hold because the question was asking for a list? This is so unjust and frustrating! Completely takes the fun out of this SE site. – Roland Bouman Jun 04 '14 at 18:16
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    (Part of) the motivation behind the close votes is that an answer that is just a list of references is not "good content" (as useful as it might be). By having the question structured so that a responsive answer includes _content_ about the relevant schools makes the resulting question+answers page more useful as an entity to itself. – Dave Jun 04 '14 at 18:53
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    @Dave, still not convinced. Many of the rules around SE seem incredibly arbitrary to me. Never seen any arguments why. Not fun :( – Roland Bouman Jun 04 '14 at 19:01
  • @roland Unfortunately, list questions on SE end up a mess because of the way answers are structured. I'm a regular on an SE that allows certain kinds of lists, and those questions are widely despised because so many of the answers end up being a rambling, poorly-source mess. They're also generally "fun" questions that attract newbies, which exacerbates the problem. – Bradd Szonye Jun 04 '14 at 19:10
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    @RolandBouman: I think the rules come from real problems, but on Stack Overflow. That they are strictly applied here doesn't make too much sense to me either. Especially if the scare away new users... – Meaningful Username Jun 04 '14 at 20:29
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    @BraddSzonye "..because of the way answers are structured." doesn't make sense to me. There's a question, there's answers. In what way are they "structured"? Puzzles. "...those questions are widely despised because so many of the answers end up being a rambling, poorly-source mess." What I see is a lot of people that widely despise this because the rules say we have to despise these. It seems to me you're running in circles. "They're also generally 'fun' questions that attract newbies, which exacerbates the problem" Well this conduct certainly took care of that on music SE. Not amused. – Roland Bouman Jun 05 '14 at 10:25
  • @BraddSzonye Why do you think lists "need structure to be useful"? Isn't the judgement whether the answers are useful something that should be left to the one that is reading or asking the question? So far you've mentioned problems that allude to worst case scenarios. What is the average number of answers to a question? I bet it's less then five. Not too much to browse if you're really interested in the question. – Roland Bouman Jun 05 '14 at 18:35
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    @BraddSzonye, many lists do not have to be complete to form a perfectly satisfactory answer. And many lists are closed and fairly small. Both these properties apply to this question. – Roland Bouman Jun 05 '14 at 19:07
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    Agreed with Roland here - questions such as "What are all the possible chords?" are ridiculously open ended (and we've seen that question before, actually) and are not helpful. However, a simple list containing the major schools of theoretical thought is fairly easy to put together a comprehensive, satisfactory answer. – jjmusicnotes Jun 06 '14 at 03:35

1 Answers1

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The major contemporary competition for Schenkerian reduction theories of pitch space is what is known as "Neo-Riemannian" theory, or NRT for short. NRT begins from the notion that chords -- and by extension key areas -- can be understood as moves on a kind of chessboard of tonal relations, where each move is a tonal interval (most usually the fifth or fourth on one axis, and the third on the other). The effective "distance" between chords is mapped in two directions on a lattice-like "net" of such moves (in German: Tonnetz).

The power of NRT is encapsulated in the idea that the most common chess moves along this lattice will involve what is called "maximally smooth voiceleading," where common tones are preserved and stepwise motion of voices is preferred. The most frequently occuring transformations are labeled according to the system of 19th-ct theorist Hugo Riemann did, thus the name of the theory:

P = Parallel = C major - C minor = CEG - CEbG

R = Relative = C major - A minor = CEG - CEA

L = Leading tone exchange = C major - E minor = CEG - BEG

One can model quite complicated chromatic chord progressions by chaining these smooth transitions:

C major - Ab major = PL

C major - Ab minor = PLP

C major - Fb major = PLPR

etc.

If you are interested in learning more, you can check out the work of Richard Cohn, who is a Professor of Music Theory at Yale.

Robert Fink
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    For a moment I was getting really excited, thinking this theory had something to do with [Riemannian manifolds](http://en.wikipedia.org/wiki/Riemannian_manifold). Pity, it's another Riemann guy. – leftaroundabout Jun 08 '14 at 12:25
  • Thanks! I just wanted to share this link to an introductory article on Neo-Riemannian Theory which I found in the JSTOR archives - http://www.jstor.org/stable/843871?__redirected – user1953384 Jun 09 '14 at 09:51