Texture in Post-World War II Music

Texture in Post-World War II Music

Robert Strizich

In my opinion, our traditional concepts, definitions and terms are inadequate for the discussion and analysis of new textures in post‑World War II music. Indeed, much music written since 1945 is quite beyond the grasp of standard analytical terminology, chiefly because so many of these works make exclusive use of textures and textural procedures that depart significantly from conventional practices. Current literature on contemporary music is not too helpful in this regard either. In fact, the topic of texture has generally been treated superficially (if at all) in recent articles, essays and books on new music.

Therefore, there is a need for an investigation of this topic that would consider several issues: 1) a definition of texture that would be expansive enough to cover recent textural phenomena; 2) a detailed analysis of basic types of new textures; 3) the development of an adequate terminology for them; 4) a consideration of how new textures have been employed in the overall compositional context. Such an investigation not only would enhance our ability to discuss and analyze recent music, but also would increase our general understanding and appreciation of this repertoire. This paper represents an initial attempt at such an undertaking, and it is my hope that it will encourage further discussion.

Let us begin with the problem of defining texture. Traditionally, textures have been divided into three types ‑ monophony, homophony and polyphony. The usual definition compares musical texture to the disposition of threads or strands in a woven fabric, a metaphor that is actually most pertinent to conventional polyphonic structures._[1]Other definitions have seen texture as the relationship between voices in a composition, the quality of the sound produced by a given combination of instruments, or the way in which sounds are connected in time. _[2]Most of these standard definitions, while useful to some extent, are still too limited to apply meaningfully to music written after 1945.

I propose that a definition of texture must take into account the perception of musical events both "outside of" and "in" time. Texture must be viewed as the interrelationship of sounds in a musical structure evaluated from both the vertical and horizontal perspectives, whereby the analytic concern is not only with the number of sounds heard simultaneously from instant to instant, but also with their horizontal connections. In this context, the term "vertical" refers to the density (that is, the relative "opacity" or "transparency") of the structure measured at any given instant, as if the music were suddenly stopped and a vertical "cross section" taken. The term "horizontal," on the other hand, refers to linear interrelationships and coherence produced by successive sound events over spans of "in time" perception.

With this more all‑inclusive definition in mind, we can now examine some basic types of recent textures. Perhaps the earliest non‑traditional texture to achieve currency after 1945 was that created by the interweaving of disjunct polyphonic lines in the manner of middle‑period Webern. This represents a considerable departure from conventional polyphonic models due to at least three factors: the use of disjunct melodic shapes, the frequently amorphous rhythmic structures, and the continual overlapping of the lines. I will refer to such textures as "disjunct polyphony."

Early 20th‑century prototypes of disjunct polyphony occur in works by Webern such as his Drei Lieder, op. 18 for soprano, clarinet and guitar (1925). The contrapuntal relationship between soprano and clarinet in this piece is relatively easy to follow due to the difference in timbre. However, due to the dramatic shifts in register and the resultant overlapping of the lines, the soprano and clarinet share the same registral space much of the time. This produces an intricate, web‑like textural condition quite new in Western music up to that time.

Early 20th‑century prototypes of disjunct polyphony occur in works in Webern such as his Drei Lieder, op. 18 for soprano, clarinet and guitar (1925). The contrapuntal relationship between soprano and clarinet in this piece is relatively easy to follow due to the difference in timbre. However, because of the dramatic shifts in register and the resultant overlapping of the lines, the soprano and clarinet share the same registral space much of the time. This produces an intricate, web‑like textural condition quite new in Western music up to that time.

Many European serial works of the 1950's ‑ written during the heydey of the Webern "cult" ‑ provide numerous more recent examples of disjunct polyphony. Typical are passages from Boulez' Piano Sonata No.1 (1951), his seminal Le Marteau Sans Maître (1953‑55), and Stockhausen's Kontra‑Punkte (1953) and Zeitmasse (1957).

Le Marteau and Kontra‑Punkte are texturally quite similar to the Webern example just mentioned. The contrapuntal textures are more‑or‑less discernable due to the timbral differences between lines. However, the ever‑changing rhythmic shapes and the continual overlapping of the disjunct melodic contours all produce a more intricate, timbrally complex web of counterpoint than one finds in traditional music.

On the other hand, in Zeitmasse and the Boulez Piano Sonata No.1, the lines are of the same or very similar timbres. Thus, their disjunct nature and continual interweaving tend to weaken the contrapuntal integrity of the structure. Rather than perceiving a clear contrapuntal relationship between lines, the listener may hear a sort of quasi‑random 12‑tone activity loosely filling up a certain registral space (Example 1).

Example 1: Boulez, First Sonata, second movement, mm.65-67.

Another type of novel texture employed in some recent works consists of a polyphony of contrasting "layers." A layer may comprise either a single line or a group of voices. Some factors that contribute to the individuality of distinct layers are: character, style, timbre, harmonic condition, rate of activity, rhythmic or metric structure, and even spatial placement. Such textures might appropriately be referred to as "multi‑layered polyphony."

Again, there are precedents for multi‑layering dating from the early part of this century. Ives, for instance, frequently wrote collage‑like superimpositions of contrasting structures which resulted in multi‑layered counterpoint. While many of his efforts in this direction involve the effect of massing (and will therefore be considered below), some works of Ives are transparent enough for the listener to perceive a clear counterpoint of contrasting musical streams. Works such as his Unanswered Question (1908) come to mind in this regard; here, the different streams are characterized by contrasting styles, meters and tonalities, and the overall effect is of a superimposition ‑ even collision ‑ of disparate musics.

Multi‑layering is evident in more recent works by composers of many different persuasions. One of these is Elliot Carter, whose works have been influences in no small way by those of Ives. In Carter's Double Concerto for piano and harpsichord (1959‑61), layers are unified by a common purpose and style; however, they are distinguished from one another by intervallic content, rate of activity, timbre and spatial placement. From another composer of quite different inclinations - Iannis Xenakis - one may choose a surprisingly similar example: in a passage from Xenakis' Atrées for chamber ensemble (1957‑62), layers are characterized both by different timbres and radically contrasting types of activity, yet bound together in one unified whole, like layered strata in a veined rock (Example 2).

Example 2: Xenakis, Atrées, Part II, mm.23-28.

Special instances of layered polyphony also occur in certain "minimalist" works of the 1960's and 70's. I am thinking especially of so‑called "phase" or "process" music, in which layers are melodically and harmonically identical. A complex, kaleidoscopic series of ever‑changing relationships between lines arises when the material is phased against itself due to a shifting of metrical placement and/or tempo.

Many phased textures tend to result in aural "fusion," and will therefore be treated later. Some, however, are clear enough for components to be heard as constituent parts in a contrapuntal relationship. This is the case, for example, at the beginning of Steve Reich's well‑known Violin Phase (1967), where the basic material is in duplicate, but with each line out of phase with the other to varying degrees.

A furthur type of untraditional texture ‑‑ and one that is more‑or‑less unique to the mid‑20th century ‑‑ consists of a quasi‑entropic scatter of isolated sounds or sound‑events over the time and register fields. Such structures are sparse enough in vertical and horizontal density for individual events to be perceived seperately. Borrowing a term already used to designate such situations, I will refer to this condition as a "pointillist texture."

The actual progenitor of pointillism is the so‑called klangfarbenmelodie of Webern. Particularly in his arrangements of J. S. Bach, Webern establishes two principles: the breaking up of a melodic line into short fragments, and the performance of adjacent fragments by instruments of contrasting timbre. Webern's own early works make use of klangfarbenmelodie. A good example is the extremely short fourth movement of his Fűnf Sűcke fűr Orchester, op. 10 (1913), where four successive melodic fragments (played by mandolin, trumpet, trombone and violin) comprise an entire musical statement.

As Webern's melodic style becomes more abstract and disjunct, the former timbral isolation of melodic fragments leads to a timbral isolation of individual notes. Take, for example, the beginning of the first movement of his Symphonie, op. 21 (1928). Here the lines of the double canon are highly disjunct, most of the notes are preceded and followed by rests, and no more than three notes are phrased together at one time. The lines are furthur fragmented timbrally in Klangfarbenmelodie style, so that adjacent notes in a line are often played by instruments of contrasting timbre.

Of course, the basic motivation in this case is similar to that in a disjunct polyphonic structure ‑‑ the interweaving of disjunct, overlapping contrapuntal lines. However, the actual aural effect is quite different due to the continually ‑ changing timbres and the isolation of individual notes by rests. Because these disjunct, disjointed and timbrally ‑ fragmented lines tend to share the same registral space much of the time, it becomes increasingly difficult for the listener to perceive the polyphonic organization, and easier to hear the music as a pointillist structure. Notes begin to be heard as isolated sound‑points scattered across the time and registral fields, like stars sparkling against a dark night sky. In stretching traditional melodic and contrapuntal organization to its limits, Webern has prepared the way for an altogether new textural concept.

Post‑World War II European composers picked up Webern's challenge immediately, and carried the Austrian master's ideas to greater extremes. The second movement of Boulez' Piano Sonata No.1, for example, begins with a very disjunct structure in which notes are presented, for the most part, one at a time (Example 3). While this passage does have melodic and gestural qualities, it certainly strays far from the conventional concept of "line." As a series of short fragments ‑ each highly disjunct and isolated by rests ‑ it is akin to, but more extreme than, Webern's op. 10, no. 4.

More radical from a textural standpoint is Boulez' well‑known Structures Ia for two pianos (1955). The "linear" organization of this work ‑ involving the superimposition of layers of row‑forms whose rhythmic, dynamic and articulative profiles are serially predetermined ‑ has been well established from the analyses of Ligeti and others._[3] In sections where there is an obvious differentiation in dynamics or articulation between strands, it is possible to maintain some sense of counterpoint. But in passages where there is dynamic and articulative similarity between strands, it is difficult to perceive linear structures. In such cases, the highly disjunct contours, the constant overlapping and the irregular, serially‑determined rhythms all encourage the perception of a quasi‑entropic scatter of sound‑points (Example 4).

Example 3: Boulez, First Sonata, beginning second movement, mm.1-4.

Example 4: Boulez, Structures 1a, mm.42-44

Boulez Structures (c) 1955 by Universal Editions Vienna (c) renewed. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition Wien.

Subsequent works by other composers have gone much further in this direction, the result being true pointillist textures in which no linear motivation is apparent. Sound‑events become points scattered over the time and register fields rather than constituent elements in a line. Thus, emphasis is placed on the individuality of each separate sound‑event. Registral correspondences, timbral relationships and density‑fluctuations are of primary interest, and the listener's attention is also directed to harmonic formations, depth effects and global shape.

The opening of the middle section of Penderečki's Threnody to the Victims of Hiroshima (1960) is a good example of this sort of pointillist texture (Example 5). Here, a heterogeneous collection of long and short sounds (including some noise‑oriented events) is scattered in a quasi‑random manner over both the register and time fields. Rather than focussing on lines, or even necessarily on individual sounds, the listener perceives the overall global shape of the texture, and the condensations and rarefactions in density that it undergoes.

As Pousseur has pointed out, yet another sort of pointillism occurs in John Cage's infamous Aria (1958)._[4] Here, isolated sound objects ‑ each of a different vocal and theatrical character ‑ are scattered sparsely over the time field. While the sounds in Penderečki's pointillist textures occur within the framework of an overall syntax or process, the sound objects in Cage's Aria are embedded in neither syntax nor process; each event is an occurrence in and of itself, unbound and unmotivated by what came before and what is to follow.

My criterion for a pointillist texture has been that while contributing to a global shape, sounds must still be perceivable as discrete events. Likewise, in disjunct polyphony the structure must be transparent enough for the listener to hear lines of counterpoint separately. However, if one increases either the horizontal density of a pointillist texture of the vertical density of a disjunct polyphonic structure, a state is soon reached in which individual events or lines can no longer be followed; perceptual fusion then occurs, resulting in a "massing" effect. In other words, when the point is reached at which either horizontal of vertical density becomes great enough, sound‑events lose their individual identity in a global percept. Borrowing a term already introduced by Xenakis, I will refer to such conditions as "cloud textures."

Example 5: Penkerecki, Threnody to the Victims of Hiroshima, mm.26-31.

Cloud textures may either be homogeneous or heterogeneous with regard to their constituent elements. Homogeneous mass effects can be created by the exclusive use of short detached sounds, as in a pizzicato passage from the first part of Penderečki's String Quartet No. 1. They can also be created by concentration on sustained sounds, as is the case with the arresting glissando clouds from Xenakis' Pithoprakta for string orchestra (1955‑56) (Example 6). Each of these examples gives the effect of a quasi‑random scatter of sound events over the time and register fields, the Penderečki consisting of short points of sound of similar timbre, and the Xenakis comprising a shower of fragmentary, short glissandos.

Heterogeneous textures are also subject to massing, of course. In these cases, however, the fusion threshold is probably somewhat higher, since a combination of dissimilar materials is likely to resist the massing effect more easily than a uniform collection of sounds. Some examples of heterogeneous clouds are the central part of the middle section of Penderečki's Threnody, which contains both staccato and sustained sounds, and a page from Earl Brown's Available Forms (1961) that also comprises similar material (Example 7). Both the Penderečki and Brown convey the effect of a quasi‑random scatter of points of sound and sustained tones; they differ, of course, in that the Penderečki uses exclusively string timbres, while the Brown excerpt ‑ written for chamber orchestra ‑ employs a wide variety of timbres.

Cloud textures are not the only ones in which massing takes place. In some works, one also encounters dense contrapuntal structures with a large number of strands, each of which is characterized by more‑or‑less conjunct motion and quasi‑traditional linear shapes. Frequent overlapping, similarity of character between lines, and moderately high vertical density create a situation in which individual lines are not perceived, but instead contribute to a global effect. Such textures could be referred to as "dense polyphony."

Examples of dense polyphony are especially frequent in the works of Penderečki. In a section of his St. Luke Passion (1965), predominately conjunct melodic patterns in the strings are superimposed to create a dense texture in which individual lines are not clearly distinguishable (Example 9). In a similar passage from his Devils of Loudon (1969), a large chorus vocalizes 16 sinewy, gradually ‑ ascending lines simultaneously; again, no individual lines will be heard distinctly (Example 9). In both cases, the similar character of the lines, the frequent overlapping and uniform timbre all assist in creating perceptual fusion. Vertical "cross sections" from these two passages reveal a fairly dense concentration of pitches.

Example 6: Xenakis, Pithoprakta, mm.243-246.

Example 7: Earle Brown, Available Forms.

Example 8: Penderečki, St.Luke Passion, Passio et mors domini nostri Jesu Christi

secundum Lucam, Part I, (pp. 33-34 of score).

(c) by Moeck Verlag, Celle/FRG, for all countries with the exception of: Copyright 1967 by Polskie Wydawnictwo Muzyczne, Krakow/Poland, for Poland, Albania, Czechoslovakia, Hungary, Rumania, Union of Soviet Socialist Republics, Chinese People's Republic, Cuba, North Korea, North Vietnam. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Moeck Verlag, Celle/FRG.

Example 9: Penderečki, Devils of Loudon, Act II, rehearsal #45, (p.130 of score).

One often encounters even more "opaque" polyphony in which the superimposition of strands is so dense that a given vertical musical space is almost solidly "filled up." Lines are again conjunct and similar in character, their individuality completely submerged in the global mass. The vertical density is so high that cross‑sections will show a quite consistent 1/2‑step separation between voices. In such cases, the polyphony is heard almost as a linear "activation" of a solidly‑filled musical space. The term "micro-polyphony" has been invented for this sort of texture by Ligeti, many of whose works from the 1960's make considerable use of this technique.

The chief early 20th‑century prototypes of micro-polyphony are doubtless to be found in certain works of Bartók. At the beginning of his String Quartet No. 4 (1928), for example, a series of tight half‑ and whole‑step clusters are articulated by very conjunct lines which also progress mainly by small intervals. Such linear articulation of cluster‑like structures is a direct precedent for the more intricate types of micro-polyphony used by Bartók's fellow Hungarian Ligeti.

Ligeti's Atmosphères for orchestra (1961) contains a most remarkable passage employing such micro-polyphonic structures. With the strings deployed divisi, 56 polyphonic strands are superimposed upon one another. The overall global shape of the passage is simple: a very wide cluster gradually narrows down to an activated cluster with the ambitus of only a minor third. In detail, however, the passage is actually a complex web of many micro-polyphonic lines that are related to one another canonically. Vertical cross‑sections taken at any point reveal consistent, massive clustering. Needless to say, individual lines are not heard as such, but instead contribute anonymously to the global effect (Examples 10a and b).

In some works, of course, a given musical space is filled solidly in a static, "steady‑state" manner with sustained sounds. In such cases, the musical space is often packed with sustained pitches separated by only 1/2 or even 1/4 steps, and the result is essentially a prolonged cluster. I will refer to such situations as "pitch‑band textures."

There are also some early 20th‑century precedents for banding in which the technique is employed in much the same way that it has been used recently ‑ to define a musical space in quasi‑visual terms. An unusual page from Ive's Psalm 90 for chorus, for example, expands out from, and contracts back to, middle C, with the musical space filled in at all times by whole or half steps. The opening of the third movement of Bartók String Quartet No. 4 presents a static, cluster-like chord in the uper three strings which gradully expands as the movement progresses.

Two basi types of banding are encoutered in post-1945 music: pitch bands with a static ambitus, and those that are contoured. A the very end of his Threnody, Penderečki superimposed several layers of static pitch bands; here the individual bands are so tightly packed that there isonly a 1/4 tone separation between constituent notes, causing the band to have a thick, dense and more "noise-like" sound (Example 11). Lutoslawski also superimposes slightly sctivated pitch bands of constant ambitus in hi Trois Poèmes d'Henri Michaux for chorus, where 1/2 step separations are employed; here the 1/2 step separations give the banding of looser, more traditional cluster-like sound, akin to the "classic" uses of cluster by Bartók and Cowell.

Example 10: Ligeti, Atmosphères, mm.44-49 with registral reduction

Ligeti Atmosphères (c) 1963 by Universal Editions Milano (c) renewed. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition A.G.

Example 11: Penderečki, Threnody, mm.67-70.

One also finds a variety of contoured pitch bands in recent literature. The score of Penderečki's Threnody contains entire pages with pitch bands of changing contour, and passages from Ligeti's Volumina for organ (1960, see Example 12) and Xenakis' Nuit for chorus (1967‑68) also employ contoured banding. The massive pitch band at the beginning of Ligeti's Atmosphères is contoured timbrally in a manner reminiscent of procedures used in electronic music: over a cluster of very wide ambitus in the strings, the winds then superimpose a narrower cluster which is the "filtered," as first flutes, then bassoons, and finally clarinets and horns drop out successively.

The last type of texture in which massing occurs is the multi‑layered texture. Such a texture may approach mass proportions when it becomes so dense ‑ by virtue of the number of layers ‑ that it is difficult for the listener to distinguish individual layers from the global mass. As in multi‑layered counterpoint, layers may comprise either lines or entire musical structures characterized by their own timbre, style, metrical structure, rate of activity, or other factors. Due to the multiplicity of layers in multi‑layered fusion, the listener is overwhelmed by the activity and proliferation of sounds and is only imperfectly able to sort out the shapes and interrelationships of the various layers.

Ives' concern with the superimposition of contrasting musical streams resulted in many such textures. Typical is a passage from his Central Park (1906), in which seven layers ‑ contrasted by means of rhythm, timbre and style ‑ are superimposed. A similar situation obtains in the "snow storm" music from the opening of Berg's Altenberglieder, where six separate rhythmic structures are superimposed. The complexity and high density of such passages insure a global perception.

Similar effects resulting from multi‑layering occur in recent large‑scale pieces such as Berio's Passaggio (Example 13), and even in small‑scale works like some of Conlon Nancarrow's more complex studies for player piano.

Multi‑layered fusion is also common in many so‑called "minimalist" works. For example, in the original recording of Terry Riley's In C, the superimposition of numerous layers of different repetitive motives creates some intricate massing effects. Fused perception also takes place in the denser sections of a process piece such as Reich's Violin Phase, due both to the high density and to the timbral uniformity of the layers. A similar result occurs between the two streams in Ligeti's Continuum for solo harpsichord (1968). Indeed, Ligeti intends that perceptual fusion should take place, for he instructs the performer to play fast enough so that "individual tones can hardly be perceived, but rather merge into a continuum." In such a case, fusion is the result not only of the high rate of activity, but also of timbral uniformity.

So far, I have considered new textures only as isolated phenomena, extracted from their overall compositional context. In closing, therefore, I would like to consider briefly some of the ways in which textures occur in real musical situations. Of course, new textures do often appear in their "pure" forms, as already described. But more frequently, they are compositionally manipulated to contribute to an overall process or expressive gesture. Textures tend to be manipulated in four basic ways: by superimposition, overlapping, juxtaposition, or transformation.

Superimposition is one of the most common ways in which new textures are presented. For example, a passage from Ligeti's Aventures for voices and chamber ensemble (1962) superimposes a cloud of unpitched vocal sounds over a low sustained pitch band played by horn, violoncello and contrabass. In a passage from Jan Bark's orchestral work Pyknos (1968), clouds in the winds and brass are superimposed over an activated pitch band in the strings. In both of these examples, the effect is of a composite texture comprising two different strata, each stratum distinguished by its own texture and timbral makeup.

A frequent sort of superimposition involves the combination of a melody with one of the textural types, resulting in a sort of "melody with accompaniment." This procedure occurs in Nono's Il canto sospeso (1956), where an instrumental pointillist texture serves as an accompaniment to a solo tenor melody. In Penderečki's St. Luke Passion, instrumental pitch bands often accompany melodies sung by the soloists.

Example 12: Ligeti, Volumina, rehearsal #13.

Example 13: Berio Passagio, Stazione IV, (pg.37 of score).

Berio Passagio (c) 1963 by Universal Editions Milano (c) renewed. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition A.G. Wien.

Juxtaposition frequently conveys an effect of surprise and drama. For example, at one point in Stockhausen's Kontra‑Punkte, a quiet pointillist texture suddenly erupts into a loud, extremely dense cloud texture, and then just as suddenly reverts to a sparse condition with varied dynamic levels (example 14).

Overlapping is often used to achieve continuity, forward motion, or an increase or decrease in musical tension. Overlapping structures of pitch bands, for instance, are very common in the works of Penderečki. A well‑known passage is the end of his Threnody, where continously overlapping bands build up tension in preparation for the electrifying tutti cluster with which the work closes (example 10).

Finally, transformation enables a composer to change gradually from one textural condition to another, thus effecting a sense of transition, evolution, or (again) an increase or decrease in tension. Transformation is achieved by the purposeful and directional alteration of any basic aspect of a texture. Timbre, density, rhythm, dynamics, types of material or articulation are just some of the parameters that can be modified.

Examples of textural transformation abound, but two should suffice to give a brief idea of this procedure. In David Bedford's Music for Albion Moonlight for soprano and chamber ensemble (1966), a sparse, heterogeneous pointillist texture is transformed into a more homogeneous cloud by means of both an increase in density and a shift in dynamic balance (example 15). In Penderečki's Devils of Loudon, a basically traditional contrapuntal texture gradually changes into dense polyphony by means of an increase of vertical density and rate of activity (example 16). Both of these passages achieve an effect of gradual intensification, due to the calculated increase of activity, dynamic level, and vertical or horizontal density. Other examples of textural transformation will, of course, behave very differently, depending on the musical, expressive and dramatic requirements of the individual situation.

Example 14: Stockhausen, Kontrapunkte, m.79-91.

Stockhausen KONTRA-PUNKTE (c) 1953 by Universal Editions (London) Ltd. London. (c) renewed. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition (London) Ltd., London.

Example 15: David Bedford Music for Albion Moonlight, page 13 of score.

Bedford Music for Albion Moonlight (c) 1966 by Universal Editions (London) Ltd. London. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition (London) Ltd., London.

Example 16: Penderečki Devils of Loudon (rehearsal #11).

Penderečki The Devils of Loudon (c) B. Schotts' Sohne, Mainz, 1969. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for B. Schott's Sohne Mainz.

In closing, it might be useful to review the textural typology that I have discussed by referring to the accompanying conceptual diagrams. Here, the salient characteristics of the basic types of texture are illustrated graphically, providing a visual adjunct to the score excerpts and my verbal descriptions. Please note that in these diagrams, the textures are grouped into three large overall categories ‑ complex polyphony, pointillist textures, and mass textures ‑ for greater ease of organization. A final sheet groups the textures according to both their vertical density (relative opacity or transparency) and their constituent make‑up (homogeneity or heterogeneity). This provides two additional methods according to which one can conceptualize the different textures in relationship to each other.

Mass

cloud

dense polyphony

micro-polyphony

pitch band

Bibliography

Boulez, Pierre. First Sonata. (Paris: Amphion, 1951).

Boulez, Pierre. Structures. (Vienna: Universal, 1955).

Berio, Luciano. Passagio. (Milan: Universal, 1963).

Bedford, David. Music for Albion Moonlight. (London: Universal 1966).

Brown, Earle, Available Forms II. (New York: Associated Music Publishers 1965).

Goldstein, Malcolm. "Texture," in Dictionary of Twentieth‑Century Music, edited by John Vinton (London, 1974), pp. 747‑753.

Lansky, Paul. "Texture," in Dictionary of Twentieth‑Century Music, edited by Vinton (London, 1974), pp. 741‑7.

Ligeti,György. Atmosphиres. (Universal: Vienna, 1963).

Ligeti, György. "Pierre Boulez," in Die Reihe, Vol. 4 (1958), pp. 36‑62.

Ligeti, György. Volumina. (Universal: Vienna, 1967).

Penderečki, Krystof. The Devils of Loudon. (Mainz: Schotts Sohne, 1969).

Penderečki, Krystof. St.Luke Passion, Passio et mors domini nostri Jesu Christi secundum Lucam. (Krakow: Polskie Wydawnikstwo Muzyczne, 1965).

Penderečki, Krystof. Threnody to the Victims of Hiroshima (Krakow: Polskie Wydawnikstwo Muzyczne, 1961).

Pousseur, Henri. "Music, Form and Practice," Die Reihe, Vol. 6, pp. 77‑93.

Stockhausen, Karlheinz. Kontrapunkte. (Vienna: Universal, 1953).

Xenakis, Iannis. Atree. (Paris: Editions Salabert, 1968).

Xenakis, Iannis. Pithoprakta. (London: Boosey and Hawkes, 1967).

[1] Goldstein, Malcolm. "Texture," in Dictionary of Twentieth-Century Music, edited by John Vinton (London: E.P. Dutton, 1974.), p.747.

[2] Lansky, Paul. "Texture," in Dictionary of Twentieth-Century Music, edited by John Vinton (London: E.P. Dutton, 1974), p.741

[3] Ligeti, Gyцrgy. "Pierre Boulez," in Die Reihe, Vol.4 (1958), pp.36-62.

[4] Pousseur, Henri. "Music, Form and Practice," Die Reihe, Vol. 6, p.87.