Spurlock comments on The Best Textbooks on Every Subject - Less Wrong

167 Post author: lukeprog 16 January 2011 08:30AM

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Comment author: komponisto 17 January 2011 06:22:42PM 18 points [-]

Music theory: An Introduction to Tonal Theory by Peter Westergaard.

Comparing this book to others is almost unfair, because in a sense, this is the only book on its subject matter that has ever been written. Other books purporting to be on the same topic are really on another, wrong(er) topic that is properly regarded as superseded by this one.

However, it's definitely worth a few words about what the difference is. The approach of "traditional" texts such as Piston's Harmony is to come up with a historically-based taxonomy (and a rather awkward one, it must be said) of common musical tropes for the student to memorize. There is hardly so much as an attempt at non-fake explanation, and certainly no understanding of concepts like reductionism or explanatory parsimony. The best analogy I know would be trying to learn a language from a phrasebook instead of a grammar; it's a GLUT approach to musical structure.

(Why is this approach so popular? Because it doesn't require much abstract thought, and is easy to give students tests on.)

Not all books that follow this traditional line are quite as bad as Piston, but some are even worse. An example of not-quite-so-bad would be Aldwell and Schachter's Harmony and Voice Leading; an example of even-worse would be Kotska and Payne's Tonal Harmony, or pretty much anything you can find in a non-university bookstore (that isn't a reprint of some centuries-old classic like Fux).

Comment author: Spurlock 20 January 2011 01:56:47PM 3 points [-]

I've always found traditional music theory to be useless if not actively damaging (seems to train people in bad thought habits for writing/appreciating music). Can you summarize Westergaard's approach? I know why the typical methods are bad, but I'm interested in what exactly his alternative is.

Comment author: komponisto 20 January 2011 09:21:06PM *  8 points [-]

Can you summarize Westergaard's approach? I know why the typical methods are bad, but I'm interested in what exactly his alternative is.

In ITT itself, Westergaard offers the following summary (p.375):

  1. we can generate all the notes of any tonal piece from the pitches of its tonic triad by successive application of a small set of operations, and moreover

  2. the successive stages in the generation process show how we understand the notes of that piece in terms of one another

(This, of course, is very similar to the methodology of theoretical linguistics.)

Westergaard basically considers tonal music to be a complex version of species counterpoint --- layers upon layers of it. He inherits from Schenker the idea of systematically reversing the process of "elaboration" to reveal the basic structures underlying a piece (or passage) of music, but goes even further than Schenker in completely explaining away "harmony" as a component of musical structure.

Notes are considered to be elements of lines, not "chords". They operations by which they are generated within lines are highly intuitive. They essentially reduce to two: step motion, and borrowing from other lines.

A key innovation of Westergaard is to unify pitch-operations and rhythmic operations. Every operation on pitch occurs in the context of an operation on rhythm: segmentation, delay, or anticipation of a timespan. This is arguably implicit in Schenker (and even in species counterpoint itself) but Westergaard makes it explicit and systematic. Hence he arrives at his "theory of tonal rhythm" which is the core of the book (chapters 7-9).

The table of contents, at the level of chapters, should give you an idea of how different Westergaard's book is from other texts:

Part I. Problems and Assumptions

  1. What are we talking about?
  2. Notes
  3. Lines

Part II. A First Approximation: Species Counterpoint

4. Species counterpoint
5. Simple species
6. Combined species

Part III A little closer to the real thing -- a theory of tonal rhythm

7. Notes, beats and measures
8. Phrases, sections, and movements
9. Performance

Appendix: Constructing a pitch system for tonal music

EDIT: 1,2,3 under Part II and Part III should be 4,5,6 and 7,8,9 respectively, which is what I typed. I mostly like the comment formatting system here, but that is one hell of a bug.

EDIT2:: fixed.

Comment author: arundelo 21 January 2011 01:55:56AM *  1 point [-]

Thanks for the summary. I may get this book.

You can defeat automatic list formatting if your source code looks like this:

4\. Species counterpoint##
5\. Simple species##
6\. Combined species

except with spaces instead of "#" (to prevent the list items from being wrapped into one paragraph). Edit: If the list items have blank lines between them, the trailing spaces are not necessary.

(The creator of the Markdown format says "At some point in the future, Markdown may support starting ordered lists at an arbitrary number.")

Comment author: komponisto 21 January 2011 07:14:20PM 0 points [-]

Thanks, fixed.

Comment author: Spurlock 21 January 2011 03:18:08PM 0 points [-]

Interesting, thanks. I don't know if that sounds right or even useful, but it definitely sounds interesting, I'll be putting it on my "books to check out" list. I get the impression that it's very reductionist approach, which is a promising sign.

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