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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!

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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 4 '14 at 18:16
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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 4 '14 at 19:01
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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 4 '14 at 20:29
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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 5 '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 6 '14 at 3:35
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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.

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