Customer Reviews

The Structure of Atonal Music

5 star:		(7)
4 star:		(1)
3 star:		(0)
2 star:		(2)
1 star:		(7)

 

 

Forte's book is, as its title suggests, a work on
atonal music. In this role, it is regarded as an
important and seminal work. While it uses a quantitative
language, as does all music theory, and indeed music
itself, it is not a treatise on mathematics.

A few reviews below have criticized Forte for what are
claimed to be mathematical flaws. As a researcher with
a PhD in mathematics and a side interest in composition,
I'd like to counter this. As long as Forte is analysing
music, and not claiming to prove Fermat's Last Theorem,
I'm happy to let him use whatever terminology suits his
purpose. I am no more concerned about his set theory
than I am whether classical harmony is a good number
system.

Pedantry about mathematical terminology in this context
may sound impressive to non-mathematicians but is likely
based on shallow knowledge/understanding of mathematics.
More importantly, it certainly distracts from the central
focus, which is how well Forte's framework contributes to
understanding and composing a certain kind of music.

In particular, a review titled "quackery" below has been found
useful (as of this writing) to 5 of 8 readers. The
"quackery" reviewer cites the use of the term "cardinality"
as an abuse of mathematical terminology when applied to
finite sets. In fact, applying "cardinality" to finite
sets is commonplace, about as controversial as using stringed
instruments in an orchestra.

Sorry, I beg to differ with both "fatuous" and "childish and absurd". As an aspiring composer who is not a formally trained instrumentalist, and is not formally trained, but self-taught, in music theory, this book is FAR more objective than Perle's (I didn't even finish reading Perle's, the writing style was so opaque), and doesn't assume either the ability to read music or an affinity for Schoenberg, Berg and/or Webern. Plus the writing style is way more transparent. Perle's book is mostly a musicological piece, not an objective assessment of available musical materials.

I can't comment on Forte's book, since it was not *my* introduction to musical set theory. However, I would like to respond to a rather stupid reviewer from Nov. 11, 2001, who seems to believe that cardinality is a concept unique to infinite sets (in mathematical set theory). This is simply not the case. Finite sets have cardinality as well (e.g. the set {X,Y,Z} has a cardinality of 3} . In fact, the concept of cardinality for infinite sets is far more tenuous than it is for finite sets, and due to problems such as the independence of the continuum hypothesis, some philosophers and mathematicians speculate that infinite cardinality may be an untenable concept. Most do not agree, but it is certainly misinformed to criticize Forte for introducing the concept of cardinality to musical set theory with finite sets of pitches.

As to the reviewer from Nov. 27, 2001, if you don't agree with the material, why'd you pick up a book on atonal theory in the first place? You should be commenting on whether this is a good intro to atonal theory, not the merits of atonal theory itself. For that, you may feel free to argue with a sock puppet.

The Forte pitch class set table is still the most highly concentrated form of objective information on all possible structurally distinct 12TET scales that exists.

The text of the book just gives the logic behind the table.

Whether or not pitch class set theory is a viable way to analyze "dead" (already finished) compositions is irrelevant, since it's painfully obvious that the most beautiful music surely hasn't been written yet! :)

Perle's books are inscrutible examples of Schoenbergian cultist/apologist propoganda/navel-gazing.

I haven't read Pentatonic Scales for the Jazz-Rock Keyboardist yet, but judging from my previous experiences with "musicians", I'd be willing to bet that it doesn't include all 38 possible structurally distinct 5-tone scales! :)

Among the crimes committed by this book are abuse of punctuation and terminology. I was fairly far into this before I realized that by "pcs" its author didn't mean "pitch class set" (or post-coital syndrome), but "pitch classes". Had he checked any elementary grammar guide, he would have learned that the plural of this sort of abbreviation requires an apostrophe: not "pcs", but "pc's". Also: tetrachords and hexachords are contiguous segments of a scale, melodic pattern, or tone row, not arbitrary four-note and six-note "pitch collections". What the author calls "tetrachords" and "hexachords" are really tetrads and hexads. He should call them tetrads and hexads. I wouldn't make so much of these solecisms had this book any real content. Oh, well.

I too recommend PENTATONIC SCALES FOR THE JAZZ-ROCK KEYBOARDIST by Jeff Burns.

If the sole criterion for my review were the importance of a book's ideas, then this one probably deserves 5 stars. PC set theory is still the dominant framework for teaching both undergraduates and graduates how to conceptualize and analyze atonal music. However, I have to give the book 2 stars simply because the writing in which its groundbreaking ideas are expressed is so awful. Forte's prose is so dense and unwieldy that I sometimes still read the book to help myself fall asleep at night. Granted, were I to rate Kant's "Kritik der reinen Vernunft" (or anything by Hegel for that matter), I'd probably also give it 5 stars for intellectual content, and anywhere from 0 to 2 stars based on the author's ability to translate those ideas into readable prose.
Those seeking a clear, understandable introduction to the ideas contained in this book (albeit, with some slight modifications) would be advised to look at Joseph Straus's "Introduction to Post-Tonal Theory." Yes, it is ridiculously overpriced. Yes, theorists since Forte have revised PC set theory somewhat in the time since "The Structure of Atonal Music" was published. However, Straus's book has become the standard instructional textbook on this subject for a very simple reason: it's actually readable.

According to its introduction, this book intends to explain and explain sympathetically the free atonal music of Schoenberg, Webern, and Berg. According to its introduction, this is its sole intent, its reason for existing. Its introduction calls the free atonal music of Schoenberg, Webern, and Berg "refractory", difficult to understand. "The Structure of Atonal Music" (the book, in contradistinction to the structure of atonal music, the thing) is not at all difficult to understand, though, because, in fact, it teaches you nothing whatsoever about the free atonal music of Schoenberg, Berg, and Webern. It doesn't require you to be able to read music (though it purports to require you to and is stuffed with examples in musical notation that are referred to in the text and never transcribed into any other kind of notation) because it teaches you nothing whatsoever about music. If you want to kid yourself, rose-colored glasses are cheaper.

"The Structure of Atonal Music" by Allen Forte, page one:

"As an example of a pitch combination, consider the chord at the end of the first song in Schoenberg's 'George Lieder' Op. 15 (ex.1). This pitch combination, which is reducible to one form of the all-interval tetrachord [TETRAD], has a very special place in atonal music. It could occur in a tonal composition only under extraordinary conditions, and even then its meaning would be determined by harmonic-contrapuntal constraints"

The chord in question comprises an E# just below the bass clef, an A just below middle C, and a D# and G# just above middle C. In other words, it is enharmonically equivalent to a dominant raised ninth chord, voiced precisely as Gershwin (for example) voices it in his tonal compositions under very ordinary conditions, subject to the "harmonic-contrapuntal constraints" known as tonality.

Bear in mind: This is page one, example one. From here on it only gets worse.

(In case you're wondering about "Kh complexes": The author: "The letter h has no special significance, but merely serves to identify this particular subcomplex". Neither, for that matter, does the letter "K", but doesn't it sound impressive? No, I thought not.)

This book is paramount literature for the instruction and understanding of the fundamentals of atonal music. It is written in great detail with careful tempering concerning the reader. An essential must for the library of any musician studying the concepts of pitch-class and atonal music principles.

My fellow reviewers have probably read another book. This is a fundamental work for contemporary music history, a period fascinated with the notion of structure.I don't know for how long Kh complexes will be discussed... Nevertheless, it is a must for understanding the development of post-tonal theory, read it! The author has spent more than three decades correcting parallel fifths! Well, Forte is not Babbitt, Lewin, Morris or Straus (this one benefits from the others previous hard work). He, Forte, is different.I don't know if american theory has already recovered from his influence.