Rating: 
Summary: sad
Review: "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.)
Rating:
Summary: Fool's Paradise
Review: 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.
Rating: 
Summary: fatuous
Review: 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.
Rating:
Summary: nonsense
Review: Argumentum ex cathedra ("this is good because we say so", "this is good because it's the 'standard text'", etc.) is a material fallacy of presumption (it's logically invalid). Nevertheless: 1) The point of writing a review at all is to "argue" for or against the worth of the thing one is reviewing, to evaluate it critically, not to parrot your teacher or the thing's back-cover blurb. 2) The book in question has been roundly dismissed by reputable musicians since its first publication, most notably by the eminent composer and theorist George Perle (see "The Martian Musicologists" chapter of his "The Listening Composer") and by the eminent music historian and theorist (and contributor to the New York Times) Richard Taruskin. 3) The standard theoretical text, to the extent there is one, about the atonal music of Schoenberg, Webern, and Berg is "Serial Composition and Atonality" by George Perle (mentioned above). The standard works about set theory were written by George Cantor (the inventor of set theory). "The Structure of Atonal Music", on the other hand, is really neither music theory nor mathematics, but numerology. 4) Really to do musical analysis requires intellectual application and imagination. "The Structure of Atonal Music" does have a certain following among teachers and students unwilling or unable to apply themselves, but this circumstance is no recommendation. 5) "Academic" is a verb, not a noun. 6) The John Rahn book is deservedly out of print.
Rating:
Summary: quackery
Review: For full-length critiques of the author's "analytical method" (not) see "Pitch-Class Set Analysis: An Evaluation" in The Journal of Musicology, volume 8, number 2, Spring 1990 and "Reply to van den Toorn" in In Theory Only x/3, October 1987. I'm going to concentrate here on a single instance of its abuse of terminology: This book talks a lot about the "cardinality" of its sets of pitches. In mathematical set theory (i.e., real set theory) an infinite set is defined as a set that can be put into a one-to-one correspondence with a proper subset of itself (a subset other than itself). Obviously, no FINITE set can be put into a one-to-one
correspondence with a proper subset of itself. We can't pair each of the notes of a C major scale, for example, with each of the notes of a C major triad. How can an infinite set? Consider the set of positive integers. If we multiply each of its elements in turn by two, we get the set of even numbers. The set of even numbers is a proper subset of the set of positive integers. Any set that can be put into a one-to-one correspondence with the set of positive integers is
"denumberable" and assigned a "cardinal number" of zero. The set of even numbers has a cardinal number of zero, and so does the set of rational numbers. The set of real numbers is not denumberable and has a cardinal number greater than zero. Yes, a finite set has a cardinal number also, but that number is merely the number of elements it contains, and this is so merely to generalize the property. Mathematical set theory is really concerned with the cardinal number of INFINITE sets, which as you can see now, I hope, is a much trickier thing than the cardinal number of finite sets. If it were only concerned with how many elements are in finite sets, it wouldn't bother to introduce the term. The book in question, on the other hand, is ONLY concerned with FINITE sets, the subsets of the equally-tempered chromatic scale, and thus for it to speak of their "cardinal number" (and worse their "cardinality") is to trivialize and distort the term. Why does it? I can only think to impress the reader, vainly.
Rating:
Summary: Music, not math
Review: 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.
Rating:
Summary: Music, not math
Review: 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.
Rating:
Summary: The standard text
Review: How can one argue with the original standard text? It was obviously written by an academic for academics, but it a great book nonetheless. If you are looking for a more gentle introduction, try John Rahn's Structures of Atonal Harmony.
Rating:
Summary: whoops!
Review: I mean "an ADJECTIVE" (of course).
Rating: 
Summary: Kids, respect the old man!
Review: 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.
| 
