The Structure of Atonal Music Reprint Edition

by Allen Forte (Author)

30 ratings

ISBN-13: 978-0300021202

ISBN-10: 0300021208

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“For some years now, a group of American composers and theorists including Babbitt, Teitelbaum, Martino, and Lewin, have been elaborating mathematically based procedures for the analysis of pitch structures in atonal music. In this book, Allen Forte expands the results of their work into a comprehensive theoretical survey illustrated with examples from a wide range of composers.”―Times Higher Education Supplement
“An attempt to ‘provide a general theoretical framework’ for the description and analysis of musical pitch-structures that resist interpretation in terms of conventional tonal or 12-note serial systems…. Not the least achievement of this book may be to establish the limits for a positive meaning for atonality…. Forte always moves forward with elegant clarity, explaining even quite conventional terms and illustrating his points with directness and care.”―The Musical Times

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Product details

Publisher : Yale University Press; Reprint edition (September 10, 1977)
Language : English
Paperback : 240 pages
ISBN-10 : 0300021208
ISBN-13 : 978-0300021202
Item Weight : 15.1 ounces
Dimensions : 10 x 7.01 x 0.7 inches

Best Sellers Rank: #810,784 in Books (See Top 100 in Books)
- #1,118 in Music Theory (Books)
- #1,320 in Music (Books)
- #14,396 in Performing Arts (Books)

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Melvin E. DuMars

Much better.

Reviewed in the United States on October 19, 2018

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This is one of several books on the topic of Twelve-tone and Pitch-Class composition that I would consider required reading. However, I am not sure that this particular subject matter is pertinent in current academia. But it does interest me since my method of Sound Composition borrows a great deal from it. But the real reason for purchasing this copy was to replace another copy that I purchased about a year ago. The older tome reeked of mold and mildew, even after I attempted to clean it. This new copy is much more pleasant to read.

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Martin Lundquist

Set theory and other numbers procedures.

Reviewed in the United States on August 10, 2020

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The game of notes as Stravinsky would say. Just methods for people that don't have the gift of melody or don't hear music in their head.

One person found this helpful

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LedFoot Coyote

Essential

Reviewed in the United States on May 8, 2013

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This is a book about set theory as it applies to the set of 12 pitch classes. As such, it will provide no subjective insight into the experience of hearing atonal music, and it looks entirely to the past to examine atonal structures. As a reading experience, it is colder and dryer than a witch's kiss, but it is essential in its organized discussion of how to apply set theory to the 12-pitched musical world, and for its identification of all possible pitch class sets. Others have expanded upon Forte's work, and some have added good positive criticism and insight but, historically, Forte expanded brilliantly on Milton Babbitt's work and so should be considered as a vital part of 12-pitch analysis.

I am deeply engaged in a study of symmetry in 12-pitch music, and Forte's book has been essential to me. The numerous one-star reviews of this book seem unnecessarily bitter and perhaps even a bit irrational.

12 people found this helpful

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lalo narbona

Four Stars

Reviewed in the United States on July 11, 2014

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Music Surgery.

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Addle

Music, not math

Reviewed in the United States on May 23, 2004

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.

89 people found this helpful

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Daniel Pi

Math Phoney

Reviewed in the United States on May 13, 2006

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.

22 people found this helpful

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MRP

Not so bad...

Reviewed in the United States on September 10, 2015

I recently began rereading it after a few years and it is better than I remember it being. I would recommend learning the basics somewhere else though. Once you've absorbed the basic concepts this book does have some useful things to offer. If nothing else i find the musical examples to be worthwhile.

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Noah I. Bassel

Interesting ideas, but...

Reviewed in the United States on August 26, 2006

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.

11 people found this helpful

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Master SASHA MILLWOOD

Essential reading if you want to understand pitch-class set theory

Reviewed in the United Kingdom on February 3, 2013

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This book, written by Allen Forte (*not* Miriam Forte as Amazon's listing erroneously states [March 2013: this has since been rectified by Amazon]), is a seminal work in the codification of quantitative analysis of pitch material in atonal music. It sets out a systematic approach to labelling groups of pitch classes, explores various relations between them, including similarity relations and set-complex theory, and is illustrated by numerous examples.

Although the book is generally well organised, the presentation can be at times confounding, for example it is almost possible to mistake figure numbers for page numbers, and the appendix mapping the similarity relations is a little challenging to read (it might require a ruler to ensure the tables are being read correctly). The explanations are fairly good, although some sections might require multiple re-readings in order to obtain a sound grasp of the topic, yet this book is (notwithstanding its rigour) more approachable than much literature on this topic, which takes knowledge of the theory as a given. Two other good guides are Rahn: /Basic Atonal Theory/ and Straus: /Introduction to Post-tonal theory/, although it should be noted that there are some small but important differences in methodology, for example in calculating the prime form of a pitch-class set and in the syntax of the set-classes as set out in the index/appendix (although all use the same reference numbers, thankfully [May 2013: although Forte's numeration is almost universally followed in the scholarly literature, I have recently read that the late Elliott Carter used his own idiosyncratic numeration, which is detailed in David Schiff's book]). Ideally, I suggest reading all three in the order: Forte, Rahn (chapters 1 to 3), Straus, Rahn (chapters 4 and 5).

Please note that this book does *not* include reference to set-class genera theory, for which you should read: Forte: "Pitch-Class Set Genera and the Origin of Modern Harmonic Species" in the /Journal of Music Theory/ Vol.32 №2 (Fall 1988), pp.187-270; followed by (for a contrasting yet arguably complementary approach) Parks: "Pitch-Class Set Genera: My Theory, Forte's Theory" in /Music Analysis/ Vol.17 №2 (July 1998), pp. 206-226.

Forte is frequently lambasted for his theory and his applications thereof, and it is true that some of the latter are of dubious pertinence, yet his theory does -- when appositely applied -- offer a clarity that expressions such as "a kind of half-diminished seventh with a flattened sixth that is spelled as a sharpened fifth" do not, and enables patterns to be discerned and explained. If you want to understand how Forte's theory works and how to apply it for yourself, or if you simply want to be able to criticise it from an informed perspective, then this book is essential reading. If you consider yourself to be a serious music analyst with an interest in atonal repertoire, then you really ought to be familiar with this methodology.

6 people found this helpful

cesar viana

Cesar Viana

Reviewed in Spain on July 27, 2015

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Un clásico. Los PC sets son el único sistema coherente, eficaz y sistemático para un análisis sério de la música atonal. 5*

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Bassegoda

El autor expone una "Teoría de clases de alturas sonoras i sus intervalos" . Bastante abstracto !

Reviewed in Spain on February 17, 2014

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Libro eminentemente teórico. Las ideas vertidas sobre la organización en conjuntos de classes de alturas sonoras i intervalos, aunque interesantes, són bastante abstractas i rozan las matemàticas más abstractas. Una buena base sobre teoría de conjuntos, clases de equivalencia i combinatoria, es muy deseable, aunque quizás no imprescindible.

Un inconveniente , a mi modo de entender, es que el autor se refiere frequentemente i por su còdigo, a conjuntos de alturas sonoras de : 3, 4 ,5 ,6, etc, sonidos, que se hallan listados i codificados en un apéndice del libro. Hubiera sido muy interesante tener este apéndice en una hoja de cartulina aparte, ya que su consulta resulta muy incómoda y como digo se necesita demasiado a menudo.

Un punto positivo del libro, según mi punto de vista, claro; és que el autor intenta establecer una teoría sobre la música atonal sin caer en el serialismo. Su punto de vista es mucho más genral. De todas formas queda pendiente la duda de cómo puede uno tener la sensación de elegir grupos de sonidos que corespondan a experiencias sonoras útilies para la composición, por ejemplo.

De todas formas creo que solamente el intento de poner orden en la compleja música atonal, ya merece la pena ; por eso mi valoración de 4 estrellas.

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