Post tonal theory pdf

Includes bibliographical references and index. Music—20th century—Analysis, appreciation. K8 print DDC The reasons for this are not hard to imagine. One problem, however, has been the lack of appropriate instructional materials. Materials and Techniques of Post-Tonal Music is organized primarily by compositional technique and only partly chronologically. Most chapters deal with some aspect of music rhythm, for instance throughout the period, but there is a quasi-chronological method in the ordering of the chapters.

No attempt is made in the text to teach music history per se or to explore in detail the style of individual composers. Instead, the emphasis is on musical materials and compositional techniques. Each chapter includes an introduction, several subheaded sections, and a summary.

The discussions are illustrated by a large number of musical examples drawn from music literature since With few exceptions, the examples are currently available in audio format, and as many of them as possible should be listened to.

The last part of each chapter consists of exercise material that in most cases is divided into four subsections: Fundamentals, Analysis, Composition, and Further Reading. See the Bibliography for complete bibliographical references for notes and Further Reading assignments. Materials and Techniques of Post-Tonal Music is appropriate for a unit as short as several weeks or as long as a year.

In the former case, we suggest omitting some of the chapters that are less vital for a short overview—perhaps Chapters 1, 7, 8, 11, 13, and 15, for example, depending on the interests of the instructor and students. Few teaching situations would allow the thorough study of every chapter and the completion of all of the exercises.

Some of the Further Reading exercises, in particular, are appropriate only for the more advanced and highly motivated student. Another point to keep in mind is that some chapters 9 and 10, for instance require more time than the average to complete successfully, while others such as 8 and 15 require less. To a certain extent, the chapters in this book are freestanding because they do not follow a chronological sequence, but there are exceptions. Chapters 9, 10, and 13 should be taken up in that order, although other chapters may be interspersed between them.

Also, some instructors assign Chapter 9 very early in the sequence so that students can have longer to practice with the concepts that it presents.

Finally, Chapters 2 through 6 form the core foundation for many of the chapters to follow, so it would not be advisable to omit any of them. Various new concepts and topics have been introduced: parsimonious voice-leading, scalar transformations, the New Complexity, and set theory in less chromatic contexts.

The discussions of spectralism and of electronic music have both been expanded. The most dramatic change has been the addition of a supporting website www. David Rains was generous in sharing his expertise in the area of electronic music, while Mary Blackman applied her considerable organizational skills to the task of obtaining permissions. Many of the changes found in the second edition were suggested by Kent Kennan, whose close reading of the text was most valuable.

The revision of Chapter 12 was done with a great deal of assistance from Charles Menoche, also of the University of Texas at Austin and a true authority on music technology. A number of people made helpful suggestions that were incorporated into the third edition, and I am grateful to them all but especially to Robert Fleisher of Northern Illinois University, Timothy McKinney of Baylor University, and Kip Wile of the Peabody Conservatory.

The revision of Chapter 12 was largely done by Keith Kothman of Ball State University, whose expertise was most appreciated. The planning for the fourth edition was aided enormously by the input of various colleagues across the country, including L. Finally, we would like to express our gratitude to our wives, Mary Robertson and Lisa Garner Santa, for their encouragement and for their inspiring love of music.

Tonal music and the principles that govern it did not develop overnight, of course, nor did they decline overnight. Nevertheless, it is safe to say that by around the tonal system had become so strained by chromaticism and by the desire for originality that further development of the system seemed impossible. We will use the term post-tonal in this book to refer to music that does not follow the traditional conventions of tonal harmony.

This does not necessarily mean, however, that the music being referred to is without a tonal center. The whole issue of tonality in post-tonal music will be discussed more thoroughly in Chapter 5. But in diatonic tonal music the difference between diatonic and altered tones is always clear, and seldom do we lose our tonal bearings, our sense of key and scale, and our immediate understanding of the function of the altered tones.

Diatonic relationships also prevail at the background levels of a diatonic tonal composition. Think of the keys that Bach is apt to reach in the course of a fugue, or the traditional key schemes for sonata forms and rondos.

All represent diatonic relationships because in all cases the secondary tonalities are closely related to the primary tonality of the movement. Much of the harmony of chromatic tonal music can be analyzed by using the same vocabulary for altered chords, modulations, chromatic nonchord tones, and so forth, that we use in the analysis of diatonic music.

It is partly a matter of emphasis. Two triads or keys are in a chromatic mediant relationship if they are of the same quality major or minor and their roots are a major 3rd or minor 3rd apart. These relationships are illustrated in Example lowercase indicates minor. We will often number the 12 pitch classes from 0 to 11, with 0 usually representing the pitch class to which C belongs. Third- related triads of opposite quality major and minor sharing no pitch classes at all are said to be in a doubly chromatic mediant relationship, as in Example Chord roots, inversions, and qualities are indicated below the example.

The progression contains two circle-of-5ths progressions D—G and C—f and three chromatic mediants. Except for the last chord, the excerpt illustrates a real sequence, a sequence in which the pattern is transposed exactly, as opposed to a diatonic sequence, in which only the notes of a single diatonic scale are used, thus reproducing the pattern only approximately. A real sequence has the effect of quickly throwing the music out of one key and into another, even if only for the duration of a few chords.

Real sequences contribute a good deal to the brief tonicizations that are typical of much chromatic harmony. The root movements involve two chromatic mediant relationships and one tritone. Notice that in each case the dominant 7th chords share exactly two pitch classes. This is true only of dominant 7th chords whose roots are separated by a minor 3rd or a tritone. Example illustrates two more characteristics of chromatic harmony—suspended tonality and nonfunctional chord successions.

Play through the example and see what you think. Nonfunctional chord successions are often the result of what is commonly called parsimonious voice leading, which simply means voice leading that is as smooth as possible.

While parsimonious voice leading such as augmented-6th chord resolutions and the so-called omnibus progression3 also may be found on occasion in traditional harmony, they are the exceptions that prove the rule.

The resulting verticalities are usually tertian triads and 7th chords , but the chords form nonfunctional successions or brief tonicizations.

For instance, play through Example The essential elements are a chromatic descent from B4 to E4 in the top voice and B2 to E2 in the bass to make a convincing cadence.

On a higher level, the progression in this excerpt is simply tonic—dominant—tonic, beginning with the incomplete tonic triad at the opening of the phrase. The music preceding the cadence makes use of parsimonious voice leading and creates a nonfunctional chord succession. The chords in Example were created primarily by parallel or similar motion. Three independent gestures combine to produce the chords in Example The second element is an augmented triad in the inner voices beginning in the third measure of the excerpt , which moves, more slowly than the soprano, chromatically downward through a minor 3rd.

The nonfunctional voice-leading chords created by the combination of these three gestures are sometimes tertian and sometimes not; some of them are highly dissonant mm. Copyright renewed. In many cases they come about through the juxtaposition of apparently independent musical ideas melodies, sequences, and so on with no attempt being made to put those dissonances into any traditional context, and they often contribute to a feeling of suspended tonality. Augmented triads and diminished 7th chords are both examples of equal division of the octave.

Real sequences frequently divide the octave into equal parts, usually by transposing the pattern by a minor 3rd or a major 3rd. This is closely related to the concept of the interval cycle, which is the transposition of a pitch class two or more times by the exact same interval.

We mentioned earlier that pitch classes are sometimes represented by the numbers 0 through 11, with 0 usually representing C. An augmented triad results from a C4 cycle, as in 0 4 8 or 1 5 9 and so forth, and a diminished 7th chord results from a C3 cycle, as in 0 3 6 9 or 1 4 7 10, etc. All of these divide the octave into equal parts. We will learn about other interval cycles in the next chapter. This term is appropriate only when used in the context of a tonal composition.

A more thorough study of atonality will have to be postponed until later chapters, although the term will come up from time to time throughout this text. SUMMARY The decline of the tonal system as the primary organizing force in music coincided with and was largely due to the ascendancy of chromaticism. Diatonic tonal music is essentially diatonic on all levels, whereas chromatic tonal music is based to a much greater extent on the chromatic scale.

Some of the characteristics of chromatic tonal harmony are listed here in the order in which they are introduced in the chapter: Chromatic and double chromatic mediant relationship Tritone relationships Real sequences Brief tonicizations Suspended tonality Nonfunctional chord successions Parsimonious voice leading Unresolved dissonances Equal division of the octave interval cycles Atonality is not a characteristic of music of the nineteenth century.

NOTES 1. See the Bibliography at the end of the book for complete citations. Some prefer to use T and E or t and e for 10 and There are various well-founded objections to this term.

For each triad below, list the four triads that are in a chromatic mediant relationship to it. Name several traditional chord progressions in tonal harmony that make use of chromatic mediant relationships. Use Roman numerals. Which of the following progressions involves dominant 7th chords that share two pitch classes? For each dominant 7th chord below, list the three dominant 7th chords that share two pitch classes with it.

Berlioz: Requiem , mm. What is it, and what is the relationship between that key and G minor? Chords 12 and 14? Chords 15 and 16? Explain in your own words what is really going on in this passage. Wagner: Siegfried, Act I, Scene 1, mm.

Explain this passage as best you can in your own words, following the approaches used in the previous exercises and in the chapter text.

Continue this example, using chromatic mediants above the asterisks and employ- ing conventional voice leading. Wagner: Siegfried, Act I, Scene 2.

Using only augmented triads in a four-voice texture, see if you can combine a chromatically ascending soprano line with a circle-of-5th sequence in the bass. Continue for several chords. Compose a passage similar to Example , using a chromatically descending melody with chromatically ascending half-diminished-7th chords as an accom- paniment. The accompaniment chords should be in second inversion and should ascend faster than the melody descends.

Let the dissonances fall where they may. Compose an example in four-part texture using a conventional harmonic progres- sion and employing mostly stepwise motion in all of the voices. Then elaborate with a generous application of stepwise nonchord tones, especially chromatic passing tones, neighbors, and suspensions. The added tones, in most cases, should not create sharp dissonances minor 2nds, major 7ths with the chords tones or with each other. Be sure to do this work at a piano!

The excerpt below can serve as an example. Maximally smooth voice leading is the most extreme form of parsimonious voice leading, in which only one part moves by half step while the other parts hold common tones. Write a series of quarter-note chords for three upper voices that is maximally smooth. It should begin and end with the same chord, and the top voice should move exclusively by descending half step or by common tone.

All chords in the series should be one of the four triad types major, minor, diminished, or augmented , but inversion may be used freely. Label all chords using chord symbols C, Cm, Co, etc. Then add a bass line that moves exclusively by common tone or by leap, and is composed solely of notes from the chords above.

Hint: Compose the upper parts at the same time while playing them with your right hand on the piano. The approach and terminology used in the texts will probably differ from each other as well as from this text. Complete bibliographical information is provided in the Bibliography at the end of this book.

Aldwell, Edward, and Carl Schachter. Harmony and Voice Leading. Benward, Bruce, and Marilyn Saker. Music in Theory and Practice, Vol.

See Chapter 12, Chromatic Mediants. Kostka, Stefan, and Dorothy Payne. Samson, Jim. Music in Transition. Music of the Twentieth Century. See Chapter 1, Tonality in Transition. Steinke, Greg A. Bridge to 20th-Century Music. Though these scales have not been discarded altogether, composers since the early twentieth century have also made use of a large number of other scale formations.

Not all of these scale formations are new—in fact, some of them had been used long before the tonal era and had since fallen out of fashion. In counting the number of notes, we do not include the octave, so the major scale, for instance, is a seven-note scale. Notice that the intervals between adjacent notes of the scale are all major 2nds and minor 3rds. Because this version of the scale contains no half steps, it is sometimes called the anhemitonic pentatonic scale. One could think of it as a diatonic scale with the notes that form its dissonant tritone scale-degrees 4 and 7 in major removed.

Pitch-class arithmetic may be easier for you to understand if you visualize it on a clock diagram, substituting 0 for 12, as in Example The only tertian chords that could be constructed from Example are triads on C and A and a minor 7th chord on A. The accompaniment here uses no particular scale, although the tonality is certainly C. A few measures later, the same melody is harmonized again with major triads, but this time each melody note is the 5th of its triad.

Reprinted by permission. Other versions of the pentatonic scale are possible—versions employing minor 2nds and major 3rds—but they occur less often in Western music. It is constructed entirely from major 2nds although one of them has to be notated as a diminished 3rd.

Enharmonic spelling of the scales is common. The whole-tone scale is often associated with Impressionism, and especially with Debussy, but it is also found in the music of many other composers. Interestingly, it is even more limited than the pentatonic scale, both melodically and harmonically. No triads other than augmented ones are possible, and the only complete 7th chords available are the major-minor 7th chord with the 5th lowered the traditional French augmented-6th sonority or raised.

Example begins with three measures using WT—0 followed by two measures using WT—1. The tonality or tonalities of the passage would be open to some inter- pretation. The accompaniment will be discussed in more detail later in this chapter. Notice that the pitch-class content of the two scales is the same: 0—1—4—5—8—9. Rotations of the major scale produce the seven diatonic modes. But modality was enthusiastically rediscovered by a number of early twentieth-century composers.

Though the modal theory of the Renaissance recognized both authentic and plagal modes, the distinction is not important in modern usage. One way to present the modes is to notate them using the pitches of the C major scale Example Minor Modal Patterns Aeolian: same as natural minor.

Phrygian: same as natural minor with lowered 2. You will not always be able to identify the scale being used just by determining the tonal center and looking at the key signature because not all composers use modal key signatures. Instead, a composer might use the conventional major or minor key signature and add the accidentals necessary to produce the modal scale desired. This is the case in Example , where we see a G minor key signature used for a G Phrygian theme.

The accompaniment to this Lydian tune consists only of A major triads in second inversion. In Example the music drifts easily from D Aeolian mm. Note that this is not a modulation, because the tonal center is unchanged. Fourteen modes can be derived from the scales shown in Example 2— All of them use major and minor 2nds exclusively, yet none of them is identical to any of the diatonic modes. These two scale systems, along with our familiar diatonic modal system, exhaust the possibilities for seven-note scales using only major and minor 2nds.

A familiar example is the harmonic minor scale. Example would seem to be constructed from a G Aeolian scale with a raised fourth scale degree. This scale, illustrated in Example , consists of alternating whole and half steps or half and whole steps , so another name for this scale is the whole- step-half-step scale. Yet another name for it is the diminished scale because it can be partitioned into two diminished-7th chords.

In terms of pitch-class content, there are only three transpositions of the octatonic scale—the three shown in Example — but they can begin with either a half step or a whole step, and they may be spelled enharmonically. For instance, if the scale contains the pitch classes 0 and 1, no matter where they occur in the scale, we label it as OCT 0,1.

The octatonic scale is a rich source of melodic and harmonic material. It contains all of the intervals, from minor 2nd up to major 7th. An excerpt from a twentieth-century Russian work appears as Example In this passage Scriabin uses OCT 0,1. The octatonic scale has also found a home in contemporary jazz, where it is especially useful in improv- isation over diminished 7th chords and altered dominants.

In some cases it is only the harmony or only the melody that is chromatic, while in other cases both are. In Example Hindemith omits only the pitch class D in the course of an note melody.

Turn back to Example and consider the accompaniment. Assigned to B. Nevertheless, microtones, like the diatonic modes, were rediscovered in the twen- tieth century by composers who used them in new and varied ways. A number of methods have been derived for specifying microtones in musical notation. Other methods have typically involved variants of the traditional system of accidentals.

The resulting intervals are no larger than quarter-tones and may be smaller, the precise size being determined partly by context and partly by the choice of the performer. Traditional accidentals are used for half-step intervals. A method used by Witold Lutoslawski is seen in Example The midpoint, of course, would be the quarter-tone between these two pitches. Harry Partch advocated microtones of various sizes, especially a tone scale using unequal intervals, and he designed instru- ments to play them.

Stringed instruments would seem to be the most suited of all traditional instruments for playing microtones, pianos and organs the least. Nevertheless, microtonal works for specially tuned pianos have been composed. The most natural environment of all for microtones is the electronic medium, where the entire pitch spectrum can be precisely partitioned into intervals of any size or combination of sizes; however, a discussion of electronic music will have to be postponed until a later chapter.

There are always other possibilities. Another possibility is the simultaneous use of more than one scale type. We have already seen this in connection with Example , where a whole-tone vocal duet was provided with a chromatic accompaniment. In Example an E Phrygian melody is set over an E major ostinato. The scales most often encountered in post-tonal music are included in this chapter, but you should not be surprised to encounter still others, some of which may not even have names.

Vincent Persichetti illustrates and names several on p. Joseph Yasser, in A Theory of Evolving Tonality, attempted to show that a tone scale would be the logical historical successor to the chromatic scale. Harry Partch, Genesis of a Music. Of the scales listed in the Summary section: a Which one s consist of two augmented triads?

Puccini: Turandot , Act I, Rehearsal 42, mm. Name the scale. Ricordi and Company London Ltd. Debussy: Six Antique Epigraphs , I, mm. If it is, the melody combined with its accompaniment uses what G scale?

In that case, the melody combined with its accompaniment uses what C scale? Anton Webern: Symphony, Op. What scale is being used? This excerpt suggests several scales, all with D as a tonal center. Be sure to con- sider the accompaniment when answering the following questions: a What scale is used in mm.

Do they form a diminished scale? Joan Tower: Island Prelude , m. Given that information, what scale is used here? Music by Joan Tower. All Rights Reserved. Ravel: Valses nobles et sentimentales , II, mm. What scale is it? What is it? Name it. Compose short melodies illustrating the pentatonic, whole-tone, octatonic, and chromatic scales. In each melody, try to emphasize the tonic note as well as those notes that are especially characteristic of that scale.

Continue this example, using the G Mixolydian mode. Continue this example, using the F Dorian mode. Compose an example that makes use of several different scales, using the Casella excerpt as a model Example 2-B-4, that is, the excerpt from Chapter 2 exercises, Part B, Exercise 4; please make note of this format because it will be used throughout the book.

Label each scale you use, and use scalar transformation to move between them. Compose an example of two-voice counterpoint using the octatonic scale. Start with a slow, rather simple tune, unaccompanied, and bring in the second voice after a measure or two. Continue to a cadence on an octave. Compose for instru- ments in your class, or be able to play it at the piano.

Techniques of Twentieth Century Composition. Pentatonicism from the Eighteenth Century to Debussy. Persichetti, Vincent. Twentieth-Century Harmony. See Chapter 2, Scale Materials. Piston, Walter.

Slonimsky, Nicolas. Thesaurus of Scales and Melodic Patterns. Vincent, John. The Diatonic Modes in Modern Music. Much music since is also basically tertian, but there is in addition a good deal of music using chords built from 2nds, from 4ths, and from combinations of various intervals.

Even the tertian music frequently uses new kinds of tertian sonorities, as we shall see. Also, chords sometimes seem to result more or less accidentally from the combination of harmonically independent lines. The present chapter surveys in an organized way the chords found in music since The contexts in which these chords are used is a subject that involves both voice leading and harmonic progression.

These topics will be taken up in Chapters 4 and 5. Certain composers make more use of these sounds than do others. Still other composers rarely make use of these more traditional sounds. Fourth Edition Joseph N. Pitch-Class Sets Chapter 3. Some Additional Properties and Relationships Chapter 4.

New chapter openers highlight learning objectives and new in-brief boxes present key concepts. Selected pages Table of Contents. Pat Muchmore rated it it was amazing Nov 22, User Review — Flag as inappropriate This is unquestionably the best book on the subject. Now published by Norton, Introduction to Post-Tonal Theory has been thoroughly updated to reflect the latest developments in the field, with additional coverage of posttonal theory and voice staus.

The Fourth Edition helps students identify key theoretical points and guides them through the process of analysis, while also offering new recently composed musical examples—all at an exceptional value. To see how a matrix looks and functions, please try the Matrix Generator applet. To see a complete list of rows used in the works of Schoenberg, Webern, and Berg, see jlondon carleton.

Next, some of the more advanced concepts with relation to serial music will be briefly summarized. The twelve-tone technique quickly gave rise to several further developments of the system that help to promote consistency in atonal music.

The first of these advanced techniques of twelve-tone composition, hexachordal combinatoriality, was first used by Schoenberg, although the specific terminology and the full extent of its possible uses were only adopted later by serial composer Milton Babbitt. The Set Analyzer , when the first six notes of P0 and I5 are entered, will analyze them as literal complements. This is accomplished by using intervallic similarity within the row with the intention of making two or more of the row forms identical.

To see this in action, try entering the chromatic scale 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, T, E into the Matrix Generator , and see how this reduces the number of unique row forms. An ancillary side-effect of this technique is that invariant rows are also combinatorial. Many who tried twelve-tone composition also experimented with applying the technique to sets of fewer than twelve tones.

When Russian composer Igor Stravinsky began to compose using the twelve-tone technique in the early s, some of his pieces successfully displayed serialism with fewer than twelve pitch-classes. This technique allows all 12 transpositions of the row forms to be seen, even if analytically extraneous pitch classes appear in the matrix.

Many other more recent composers have experimented with serial technique within an extended not always harmonically functional tonal language. Serialism, as defined as a musical trend encompassing more organizing principles than the twelve-tone system alone, came into full force around in association with the Darmstadt International Summer Course for New Music in Germany. The process of serializing musical elements other than pitch involves the selection of twelve or however many elements are in the series used in the piece rhythmic values, dynamic levels, types of attacks, etc.

The row orderings are then followed in adding all of these parameters to the music. The complexity and algorithmic precision of such composition techniques led composers to try allowing computers to carry out the compositional process once the series has been selected. Post-tonal music that eschews tonal functionality certainly demands more of its audience because of the relative difficulty in perceiving harmonic relations without tonal function.

Often listeners are forced at least before intensively studying a work to attend to more primitive meaning-creating structures that exist in music, based on perameters independent of harmony, diatonicism, intervallic size, and tonal content.

These features of the music, including rhythm, motive, shape, and gesture, are often associated with the relative height of pitches regardless of pitch class or intervallic content. The techniques of contour analysis are designed to offer insights into the non-pitch-specific aspects of all music, both tonal and post-functional.

Contour analysis thus ignores the exact notes and intervals of the musical material, instead attending to which notes are higher and lower. A contour segment CSEG , is a numeric representation of the relative heights the notes in any melody or melodic fragment. It is an ordered collection, with as many elements as there are notes n , each numbered from lowest to highest beginning with 0 according to the height of the note within the segment.

This shows the motivic unity between these two melodic fragments, while ignoring their differences. The two pc sets and have different but similar interval vectors.

Like twelve-tone rows, these ordered collections can be inverted, retrograded, and retrograde-inverted and still retain their motivic identity. However, it also abstracts the general shape of longer melodic segments before determining the prime form.

The process by which longer melodies can be reduced to simpler contours was introduced by Robert Morris.

The first and last c-pitches are never reduced out, and the process is recursive, repruning the CSEG until it can be reduced no further all c-pitches are maxima or minima. Uploaded by. Joseph N. First published in Now published by Norton, Introduction to Post-Tonal Theory has been thoroughly updated to reflect the latest developments in the field, with. Jospeh Additional Properties and Relationships Chapter 4. Similarly, Straus is sufficiently expert in the entire corpus of musical theory to make cross-references sometimes outside contemporary music and underline common grounds as needed… the operations covered in detail earlier to which a tone row can be subjected, for example.

The music of the twentieth and twenty-first centuries in its cultural, social, and intellectual contexts. Basic Concepts of Pitch and Interval Chapter 2. Permits students to make effective use of concepts for free atonal music in the analysis of twelve-tone music. Despite its length, each is dealt with thoroughly and without omitting anything that needs to be known in order to understand the way musicians have composed in the many idioms developed since the Second Viennese School. Every chapter offers guided analysis and theory exercises that give students the opportunity to apply the concepts discussed in the text, and an appendix provides answers to selected exercises, giving students instant feedback on their work.

There is a comprehensive and useful index.