Understanding Post-Tonal Music

Introduction: An Overview of Twentieth Century Compositional Styles

The Century of Plurality: Tonal, Post-tonal, Atonal, and Other Styles

The Stylistic Mosaic

Chapter 1. Pitch Centricity and Composition with Motivic Cells

Pitch Centricity

Diatonic Collections

Pentatonic Collections

Analysis 1.1. Debussy, "La cathedrale engloutie," from Preludes, Book I (Anthology, no. 1)

Analysis 1.2. Stravinsky, Introduction to Part I, from The Rite of Spring (Anthology, no. 4)

Chapter 2. Pitch Centricity, Equal Divisions of the Octave, and Symmetry

Interval Cycles and Equal Divisions of the Octave

Symmetrical Motivic Cells

Symmetry Around an Axis

Symmetrical Scales

Analysis 2.1. Bartok, "Song of the Harvest," from Forty-four Violin Duets (Anthology, no. 5)

Analysis 2.2. Bartok, "Whole-tone Scale," from Mikrokosmos, Vol. 5 (Anthology, no. 6)

Chapter 3. Introduction to Pitch-Class-Set Theory

Preliminary Concepts

Pitch-Class Sets: Orderings and Basic Relationships

Pitch-Class Sets: Further Properties and Relationships

Pitch-Class Set Theory: A Summary

Chapter 4. Analyzing Atonal Music

Analyzing Atonal Music

Analysis 4.1. Webern, "Five Movements for String Quartet," Op. 5, III (Anthology, no. 10)

Analysis 4.2. Schoenberg "Angst und Hoffen," No. 7 from Book of the Hanging Gardens, Op. 15 (Anthology, no. 11)

Chapter 5. Drawing on (and Reinterpreting) the Past . . .

Neoclassicism

Analysis 5.1. Stravinsky, Agnus Dei, from Mass (Anthology, no. 13)

Hindemith's Theoretical and Compositional Premises

Analysis 5.2. Hindemith, Interlude in G, from Ludus tonalis (Anthology, no. 14)

Chapter 6. . . . And Inventing the Future

Ultramodern Aesthetics

Ives and Musical Borrowing

Analysis 6.1. Ives, "The Cage" (Anthology no. 16)

Analysis 6.2. Crawford, Diaphonic Suite No. 4, III (Anthology no. 17)

Chapter 7. Twelve-Tone Music I: An Introduction

The Twelve-Tone Method

Basic Principles

Building a Row

Labeling Row Forms

Building a Twelve-Tone Matrix

Identifying Given Row Forms Without Using a Matrix

Analysis 7.1. Dallapiccola, "Contrapunctus secundus," from Quaderno musicale di Annalibera (Anthology no. 18)

Chapter 8. Twelve-Tone Music II: Invariance, Symmetry, and Combinatoriality

Invariance

Webern and Row Symmetry

Analysis 8.1. Webern, Piano Variations, Op. 27, II (Anthology no. 20)

Hexachordal Combinatoriality

Analysis 8.2. Schoenberg, Klavierstueck, Op. 33a (Anthology no. 21)

Chapter 9. Serialism: Developments After 1945

Control vs. Indeterminacy

Stravinsky and Serialism

Analysis 9.1. Stravinsky, "Lacrimosa," from Requiem Canticles (Anthology no. 22)

Analysis 9.2. Boulez, Structures Ia (Anthology no. 23)

Milton Babbitt's Serial Methods

Chapter 10. Expanding the Limits of Musical Temporality

Rhythmic and Metric Irregularities in Post-Tonal Music

Temporal Issues in the Music of Messiaen

Analysis 10.1. Messiaen, Introduction, from Turangalila Symphony (Anthology, no. 24)

Tempo as a Structural Element in the Music of Elliott Carter

Analysis 10.2. Stockhausen, Stimmung (Anthology no. 25)

Chapter 11. Aleatory Music: Sound Mass, Texture, and Timbre

John Cage's Creative Journey

Analysis 11.1. Lutoslawki, Jeux venitiens, I (Anthology no. 26)

Analysis 11.2. Penderecki, St. Luke Passion, no. 13, "Et Surgens Omnis Multitudo" (Anthology no. 27)

Analysis 11.3. Gubaidulina, String Quartet no. 2, Reh. 1-21 (Anthology, no. 28)

Chapter 12. Electronic, Computer, and Spectral Musics

The Principles of Sound Synthesis

Analysis 12.1. Stockhausen, Telemusik, Sections 1-5 (Anthology no. 29)

Composition with Computers

Analysis 12.2: Jonathan Harvey, Mortuos plango, vivos voco

Analysis 12.3. Barry Truax, Riverrun (Anthology no. 30)

Spectral Music

Chapter 13. Integrating the Past and Reimagining Harmony

Integrating the Past

Analysis 13.1. Berio, Sinfonia, III (Anthology no. 31)

Analysis 13.2. Ligeti, Ramifications, mm. 1-44 (Anthology no. 32)

Analysis 13.3. Crumb, "Primeval Sounds," from Makrokosmos, vol. 1, no. 1 (Anthology no. 33)

Chapter 14. Simplifying Means

Minimalism

Analysis 14.1. Reich, Violin Phase (Anthology no. 35)

Nonfunctional Triadic Voice Leading

Analysis 14.2. Adams, Nixon in China, Act I, "News" Aria, mm. 374-542 (Anthology no. 36)

Analysis 14.3. Paert, Cantus (Anthology no. 37)

Chapter 15. Into the Twenty-First Century

Analysis 15.1. Torke, Adjustable Wrench, mm. 1-72 (Anthology no. 38)

The Return of the Motive

Analysis 15.2. Thomas, Spring Song (Anthology no. 39)

Analysis 15.3. Ades, Asyla, II (Anthology no. 40)

Analysis 15.4. Saariaho, Ariel's Hail (Anthology no. 41)