Psychomusicology—Perceptual/Cognitive Research with Implications for the Composer and Performer
Stimulation of interest in the study of music as a sensory experience has generally been attributed to Helmholtz. But the scientific and technological advances of the past two decades, coupled with concentrated research efforts by music researchers, have resulted in a small but expanding body of studies characterized by measurement of human responses to musical stimuli which have been structured in tightly controlled experimental designs. In contrast to the related science of psychoacoustics—which is concerned with responses to variations of isolated tonal events—the music designs deal with response to contextual music; that is intervals, rhythms, brief melodies, chords, and so forth. These studies frequently borrow both their experimental and analytical designs from psychoacoustics and other related areas in psychology; but as this new field of research grows, it is obvious that unique ways of dealing with musical stimuli and consequential responses will be invented. Needless to say, the study of the perceptual/cognitive relationship of music and man is a young branch of psychology that shows promise as an independent science. Laske provides strong rationale for this new science (see chapters 1-3). He calls it "Psychomusicology," relating it to the established field of psycholinguistics (pp. 24-27).
One of psychomusicology's major goals is to contribute, through analyses of how people react to music, to a better understanding of the "mental processes underlying the acquisition and the use of music" (Laske, p. 25). The results of the studies conducted to date, although not numerous or conclusive, are beginning to respond to that goal. It might be appropriate to examine some of the findings in regard to their application in practical music. This article undertakes that task, with an emphasis on the processes of composition and performance. It seems reasonable to pair composers and performers, since they collaborate in bringing the musical message to the listener. But first it is appropriate to examine music as a meaningful message, followed by descriptions of how composers and performers create and recreate that message.
Single pitches are the raw materials from which musical logic is made but individually they have little musical meaning. It is not till two pitches are joined in sequence or simultaneously (melodic and harmonic intervals) that a musical event occurs. Real music unfolds as these events are sequenced in time, stimulating the listener's thought patterns. These patterns are interpreted by the brain as concrete or abstract images with emotional content; it is likely that the listener cannot adequately describe the images with words. Nevertheless the messages conveyed by music are logical and reliable, judging from the fact that entire compositions (or parts of them) can consistently evoke the same images, either for individual listeners or for groups of listeners.
Creation and recreation are constructive processes involving a series of tasks; Figure 1 illustrates a probable sequence of the basic tasks necessary to compose music.
The composer begins with a scheme, an overall plan for writing the music. Within this framework he proceeds to build a logical sequence beginning with intervals (melodic or harmonic) as the basic units, and progresses to the end of a section of music or of an entire composition. Figure 1 shows melodic and harmonic intervals developing through two parallel sequences; undoubtedly the composer travels between the sequences many times as he writes his music. Notice that tonal or atonal structure, tempo, dynamics, instrumentation, etc., are fed into the process at strategic stages.
Figure 1 shows that the interval and its relative durations (rhythm) are the composer's basic tools, and that when used interactively, they provide him with a means for creating music. Tonality (or atonality) is another tool; it begins to take place later in the process. After the section or composition is complete, the composer may reexamine his music with the intention of adding tempo or dynamics—or he may orchestrate it. There is the possibility that he has done these things from the beginning, as indicated in Figure 1 by the dotted lines ascending from the "tempo, dynamics, instrumentation" box to the "interval" boxes.
Figure 1 represents a straightforward case for how the composer writes music. A basic assumption is that composing is a sequential process with the interval (and its rhythm) as the building block. By no means does it illustrate the psychological dimensions of creating music, that is, the many complex mental strategies which the skillful composer brings together in order to decide what intervals to write and in what order to arrange them. Obviously his decisions are guided by the musical image he holds in his brain and the concepts of how that image can best be expressed via the musical message. The psychological dimensions (and their interactions) of composing are largely unknown; it is not the purpose of this article to attempt to list them in detail.
While the psychological dimensions of performing music—either from notation or from memory—probably are not as complicated as composing music, they are not well known, either. Figure 2 represents the process of performing music while reading from the score.
The performer starts with a visual scan of the music: meter, key signature, tempo, dynamics, etc. He begins the performance by first observing (in sequential order) either a single note or a group of notes, then matches that observation with his equivalent mental representative. Once the mental representative is established, the performer can search his memory for the set of responses which he has learned to associate with it. These responses include the appropriate physiological manifestations such as breath control, fingerings, vocal mechanism control for singers, bowings, and so forth. Of course all these stages occur so quickly in sequence that there appears to be no delay from the initial act of observing the note or group of notes to the actual performance. But to keep the performance flowing from note to note and from phrase to phrase it is necessary to include a buffering system, one that supplies notes at a constant rate. This is provided for by the arrow (Fig. 2) returning from the "search" box to the "observe" box. It simply means that when a match is made and a particular search is under way for a set of responses, the performer is already observing another note or group of notes, thus buffering any gap that might otherwise occur between performances that result from single observations.
The preceding definition of music and descriptions of the acts of composing and performing (Figs. 1 and 2) provide maps for the psychomusicologist. Not only are the parts of those general processes identified separately in these maps, they are presented in such a way that it is possible to see how one part leads to another. Thus the psychomusicologist can select an area in which he wishes to conduct experiments, hoping that the results of research in all areas will eventually lead to theories that detail the interrelationships between the musical constructs and the psychological dimensions required in the composing and performing of music.
The majority of experimental studies performed by psychomusicologists deals with the structures of melody and how they are perceived by musicians and nonmusicians. Understanding how melody is perceived is of primary importance to the psychomusicologist and could be of special interest to the composer and performer; therefore the remainder of this article is devoted to summaries of experimental studies in the perception of melody. The experiments were undertaken with the purpose of isolating the ways people respond to the various components of melody (contours, intervals, transpositions, etc.). The musical stimuli were typically presented to one or more groups of subjects of varying ages and musical experiences (but mainly musicians and nonmusicians of college age); the number of subjects in each of the groups ranged from about three to over 200. Most of the experimental designs required subjects to listen to brief musical excerpts (melodies, phrases, intervals) that were altered in various ways, asking them either to recall certain aspects of the music, or to recognize certain features by comparing an excerpt against one previously heard. Subjects responded with music notation, by singing, or by verbal or written responses, such as "yes, it is the same," or "no, it is different." Responses were then subjected to statistical analyses, allowing the researcher to make objective conclusions regarding results.
Table 1 lists the variables most commonly studied in the aural perception of isolated pitches and melodies.
Not considered are music experiments in the sensory modes of vision, touch, proprioception (muscle movement), or literature dealing with long term memory and with physiological and neurological measures of responses to musical stimuli. Since it was claimed earlier that isolated pitches had little musical meaning, the 11 variables listed in the left column of Table 1 will not be considered. A review of experiments with isolated tones may be found in Ward (1963, 1970), Plomp (1976), and Roederer (1973). However, the melody column (Table 1, column 2) lists the structural features of melody that influence the ways we perceive the melodic message when they are varied.
The perception of melodic tempo is beginning to receive some experimental attention. In a study made by Kuhn in 1977, college musicians were required to play brief, simple tunes at both loud and soft dynamic levels. The subjects tended to increase the tempo as they continued playing; but the tempo was not affected by performance at loud and soft dynamic levels. Kuhn claimed that this experiment supported the results of his two previous tempo studies (Kuhn, 1974; Kuhn and Gates, 1975). However, he required his subjects to distinguish between their soft and loud performances on the basis that "a difference between the soft and loud sections must be perceivable" (1977, p. 223). Perhaps precise specification and measurement of dynamic levels would have affected tempo or other aspects of the music. Perception of dynamics and its various levels awaits further study. In a related tempo study, Madsen (1979) had 200 college musicians and nonmusicians judge two sets of 25 series of beats that either increased or decreased in tempo or remained the same. Both groups of subjects were more accurate with the decreasing tempo series, and the musicians showed greater improvement than the nonmusicians only on the second set of 25 series (although the nonmusicians did improve their performance significantly). Madsen states that "throughout the study all subjects had a propensity to 'hear' toward the slow side when they were wrong" (p. 63). This inability to deal perceptually with increasing tempos could account for the performance of Kuhn's subjects: they were unable to detect their own gradual increase in tempo. Why they increased the tempo is a question yet to be answered fully. One might speculate that if performers are better at hearing decreasing tempos, it may be possible that this sensitivity leads them to detect even the slightest decrease in tempo (as they perform), thereby causing them to overcompensate by playing at a faster rate. Or another theory might be that, for whatever reason, the performer increases his tempo, but fails to correct the increase since perceiving faster tempos is difficult.
There has been considerable speculation regarding the preferred tunings used by performing musicians; that is, which is the preferred tuning: equal temperament, just intonation, or the Pythagorean scale? After a review of research analyzing the performances of small ensembles and soloists, Ward concludes that taken as a whole, performers play in the equal tempered tuning. However, they consistently play all pitches on the slightly sharp side (relative to the tonic). This conclusion is supported by a series of studies (Geringer, 1976, 1978; Madsen, 1966, 1974; Madsen and Geringer, 1976; Siegel and Siegel, 1977) which also illustrate the musician's preference for sharper performances accompanied by greater acuity in detecting flatness in melodies and other contextual music. Thus it seems that although musicians prefer sharpness, they cannot discriminate it nearly as well as flatness. Perhaps the overcompensation speculation made earlier in regard to tempo applies as well to intonation.
Our understanding of rhythmic perception is incomplete, even though considerable research has been undertaken in this area (see Winick, 1974 for a rather complete, annotated listing). Rhythm is a basic musical element, but isolating it in laboratory situations is complicated, as it interacts so strongly with pitch, intensity, and the underlying pulse (beat) and meter of the melody. Many of the older studies attempted to relate rhythm to the "natural kinesthetic movement" of individuals, especially children. Generally those studies concluded that rhythm can be expressed through bodily movements, but that it is not always "natural." Children and untrained adults can imitate simply rhythms, but they cannot always deal with the more complex rhythmic concepts. Furthermore there appear not to be uniform kinesthetic responses to rhythms across groups of people. Reacting to rhythmic figures results in individual kinesthetic responses (with individual degrees of accuracy).
The more recent rhythm experiments have been less concerned with kinesthetic movement and its accuracy than with cognitive responses to the specific structural features of rhythm in melodic contour. Pick asked young children to identify rhythmic patterns in melodies. She discovered greater accuracy for those patterns that fell within structural boundaries rather than across boundaries (e.g., across ends of phrases). Her results confirmed conclusions made by Dowling ("Rhythmic groups") in an earlier study. This phenomenon may be related to problems in understanding the meters of melodies (and thereby using meter as an organizational force) since Jones found that his subjects had considerable trouble in identifying the simple meters (two and three beats to a measure, using a variety of rhythms), of the melodies he played for them. His subjects ranged in age from 5 to 12 years. The best performances were obtained by children in the 9 1/2 to 12 year age group, and their average score was only 33 percent correct.
Aside from variances in judgment of meter (and its pulse), other complications in rhythm arise from interaction of pitches in melodies with perceptions of durations and intensities (accents). For example Divenyi discovered that estimates by his musicians of the durations of brief, silent intervals between two pitches were affected by the frequency ratios of the pitches. Two classic studies by Woodrow (1909, 1911) provide strong evidence for the importance of both duration and intensity in short melodic patterns. Essentially he found that intense and/or long tones stand out perceptually; furthermore the intense pitch tends to appear as the beginning of a pattern whereas the long tone appears as the end of a pattern. Obviously, definitive conclusions about the perception of rhythm cannot be made at this time.
The recognition of transposed melodies has sometimes been accepted as a rather simple perceptual task. It is a simple task, provided the transposed melody is a familiar tune. Both musicians and nonmusicians listen for the distance, or exact intervals, between the pitches (Attneave and Olson). Complications arise when musicians and nonmusicians attempt to identify new melodies. According to Frances, his musicians performed better than nonmusicians on all melodies, transposed tonal melodies were easier to identify than transposed atonal melodies, and transposed tonal melodies with rhythmic structure were easier to identify than arhythmic, tonal melodies. He also reports that all subjects performed better when the transcriptions were played at the octave (but this was true mainly for the tonal melodies); and that transpositions close to the original melody are more difficult to perceive than distant transpositions. There is strong support in the literature for the octave as a rather special perceptual phenomenon (Deutsch, 1972; Dowling and Hollombe, House). A discrete perceptual space or "band width" seems to be contained within the spatial dimension of an octave.
The shape or contour of a melody is an important perceptual element, but even more crucial is the interval, the building block of contour. In a series of studies Dowling (1971, 1972, 1973 "The Perception", 1978) and Dowling and Fugitani made the following conclusions regarding identification of brief melodies: (1) both musicians and nonmusicians use exact interval sizes in identification of familiar melodies, (2) both use the melody's contour to identify unfamiliar melodies (i.e., subjects heard an unfamiliar melody once, then they had to decide if a melody that followed was the same as or different from the first melody), and (3) musicians were more accurate in identification of unfamiliar melodies because they were also capable of comparing the two melodies for relative interval sizes (e.g., a minor third and major third are relative). Taylor, in a concentrated study of exact intervals ("Perception of Melodic Intervals"), found that almost all intervals (12 ascending, 12 descending) were perceived differently by his college musicians when those intervals were imbedded in melodies as compared to the intervals heard in isolation. Correct identification of all intervals was influenced significantly by the type of melodic context (i.e., the types of intervals surrounding the particular interval to be identified). Furthermore most of the intervals were perceived more accurately in shorter melodies and when they were placed at the end of the melody. Thus intervals are not stabile phenomena when sequenced to make melodies. They are in fact subject to perceptual change as a function of their temporal placement in a melody, and also as a function of the type of intervals that precede and follow them. One should not assume that a melody consists merely of a sequence of intervals; those intervals are uniquely transformed by our perceptual systems as the result of that sequence.
The concept of tonality and its function in melodies has been explored by Frances, Long, and Taylor ("Perception of Tonality"). Frances used three groups of subjects: musicians, semiskilled musicians, and nonmusicians. They had to identify a changed tone by its melodic rank in the second playing of both tonal and atonal melodies. Musicians were able to do this more accurately than the other groups; but all subjects were significantly less accurate when they had to identify pitches in atonal melodies. Frances concludes that twelve-tone music does not provide perceptual unity as is claimed by some twelve-tone composers. Frances believes the strong perceptual unity of tonal melodies is acculturated, and he evaluated statistically many scores for evidence of the source of tonality. He concluded that tonality is acculturated from the underlying progression of chords, not from the progression of melody; Long's experiment was similar to that of Frances, although she required her subjects to decide if a single tone presented after brief melodies (Taylor's melodies, see below) was or was not present in the melody. Her results confirmed Frances' findings: skilled and semiskilled musicians outperformed the nonmusicians, and identification of tones was much easier in tonal melodies than in atonal melodies. Taylor ("Perception of Tonality") designed an experiment not only to determine if his 12 melodies (constructed a priori to be atonal and tonal) could be heard as tonal or atonal, but also how strongly the tonality or atonality appeared to his musicians, semiskilled musicians, and nonmusicians. Subjects vocalized a single pitch (after hearing the 7, 11, or 15 pitch melodies) which represented their estimate of the tonal center. Results indicated that the musicians and semiskilled musicians did distinguish melodies as tonal and atonal, and that a tonal strength scale existed for them. However, the nonmusicians could not deal perceptually with the concept of tonality. The contour and length of the melodies did not affect the subjects' estimates of tonality or tonal strength.
Melodic tonality and atonality are strong perceptual factors and the former may even serve as a sort of perceptual organizer. But it seems clear that tonality does not "acculturate" naturally; that is in order to use it perceptually, one must learn tonality, either intentionally or perhaps by acculturation to tonal music. Interestingly, there is little evidence thus far that atonal melody has acted, or will be able to act as the same kind of perceptual organizer as tonal melody.
Although it is reasonably well established that the variables discussed above (items 1-9 in the right column of Table 1) are vitally important to perceptual theory, the manipulation of single pitches in melodic context is useful in studying short term memory (STM, is generally regarded as lasting up to 20 seconds) for melody or parts of melody. Deutsch asked subjects to remember a tone as either identical to or different from an earlier tone. Presented between the two tones was either a series of six pitches or six spoken numbers. Deutsch found that the numbers created little interference in memory for the tone, but the intervening pitches caused severe interference. She also found that memory for the first tone could be enhanced by duplicating it with one of the intervening tones (she duplicated the second intervening tone). Long's study provided evidence for tonal interference, since her subjects more often remembered the correct tone when the melodies were briefer, that is when fewer intervening tones occurred between the first and second tones. Williams' investigation of STM required college music majors to sing a pitch previously heard as part of a 3, 5, or 7 pitch melody. The position (in the melody) of the pitch to be sung was identified for the subjects. Williams' results confirm Taylor's findings that the last parts of a melody are more easily remembered. He also included response delays in his study, and discovered that both longer delays and longer melodies resulted in greater loss of memory for the pitch. However, there was more loss of memory due to melody length than to response delays, thus supporting the theory that intervening pitches can create strong interference in short term memory.
It is too early to describe with theoretical models how results from psychomusicological research can account for the perceptual/cognitive activities required for the creative and recreative acts of composition and performance. But when that time arrives, the melody factors discussed in this article must be incorporated into the models.
Finally, it seems clear that trained musicians have the advantage over untrained musicians in terms of hearing accurately melodic structures as they unfold across time. This accuracy stems from an ability to hear more in the music; that is to be able to make better use of the information it conveys. Although musical training refines one's perception, all the melody variables discussed above are real factors that temper perception, even for musicians. This being true, it is a mistake to believe that music notation is a faithful representation of how that music is heard. Additional psychomusicological research may improve our understanding of this dichotomy.
Attneave, F., and R.K. Olson. "Pitch as a Medium: A New Approach to Psychological Scaling," American Journal of Psychology, 1971, Vol. 84, pp.147-166.
Deutsch, D. "Music and Memory," Psychology Today, December 1972, pp. 87-89, 119.
__________. "Octave Generalization and Tune Recognition," Perception and Psychophysics, 1972, Vol. 11, pp. 411-12.
Divenyi, P.L. "The Rhythmic Perception of Micro-melodies: Detectability by Human Observers of a Time Increment Sinusoidal Pulses of Two Different Successive Frequencies," Research in the Psychology of Music, 1971, Vol. 7, pp. 41-130.
Dowling, W.J. "The Perception of Interleaved Melodies," Cognitive Psychology, 1973, Vol. 3, pp. 322-337.
__________. "Recognition of Inversions of Melodies and Melodic Contours," Perception and Psychophysics, 1971, Vol. 9, pp. 348-349.
__________ . "Recognition of Melodic Transformations: Inversions, Retrograde, and Retrograde Inversion," Perception and Psychophysics, 1972, Vol. 12, No. 5, pp. 417-421.
__________. "Rhythmic Groups and Subjective Chunks in Memory for Melodies," Perception and Psychophysics, 1973, Vol. 14, No. 1, pp. 37-40.
__________. "Scale, and Contour: Two Components of a Theory of Memory for Melodies," Psychological Review, 1978, Vol. 85, pp. 341-354.
__________ and D.S. Fugitani. "Contour, Interval, and Pitch Recognition in Memory for Melodies," The Journal of the Acoustical Society of America, 1971, Vol. 49, No. 2, Part 2, pp. 524-531.
__________ and A.W. Hollombe. "The Perception of Melodies Distorted by Splitting Into Several Octaves: Effects of Increasing Proximity and Melodic Contour," Perception and Psychophysics, 1977, Vol. 21, pp. 60-64.
Frances, R. La perception de la musique (Paris: Librairie Philosophique J. Vrin, 1958).
Geringer, J.M. "Intonational Performance and Perception of Ascending Scales," Journal of Research in Music Education, 1978, Vol. 26, No. 1, pp. 32-40.
__________. "Tuning Preferences in Recorded Orchestral Music," Journal of Research in Music Education, 1976, Vol. 24, No. 4, pp. 169-176.
Helmholtz, H.L.F. von. Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (Braunschweig: F. Vieweg & Sohn, 1863).
House, W.J. "Addenda: Octave Generalization and the Identification of Distorted Melodies," Perception and Psychophysics, 1977, Vol. 21, p. 601.
__________. "Octave Generalization and the Identification of Distorted Melodies," Perception and Psychophysics, 1977, Vol. 21, pp. 586-589.
Jones, R.L. "The Development of the Child's Conception of Meter in Music," Journal of Research in Music Education, 1976, Vol. 24, No. 3, pp. 142-154.
Kuhn, T.L. "Discrimination of Modulated Beat Tempo by Professional Musicians," Journal of Research in Music Education, 1974, Vol. 22, No. 4, pp. 270-277.
__________. "Effects of Dynamics, Halves of Exercises, and Trial Sequences on Tempo Accuracy," Journal of Research in Music Education, 1977, Vol. 25, No. 3, pp. 222-227.
__________ and E. Gates. "The Effect of Notational Values, Age and Example Length on Tempo Performance Accuracy," Journal of Research in Music Education, 1975, Vol. 23, No. 3, pp. 203-210.
Laske, O. Music, Memory, and Thought: Explorations in Cognitive Musicology (Ann Arbor: University Microfilms, 1977).
Long, P.A. "Relationships Between Pitch Memory in Short Melodies and Selected Factors," Journal of Research in Music Education, 1977, Vol. 25, No. 4, pp. 272-282.
Madsen, C.K. "The Effect of Scale Direction on Pitch Acuity in Solo Vocal Performance," Journal of Research in Music Education, 1966, Vol. 14, No. 4, pp. 266-275.
__________. "Modulated Beat Discrimination Among Musicians and Nonmusicians," Journal of Research in Music Education, 1979, Vol. 27, No. 2, pp.57-67.
__________. "Sharpness and Flatness in Scalar Vocal Performance," Science de l'art—Scientific Aesthetics, 1974, Vol. 9, Nos. 1 and 2, pp. 91-97.
__________ and J.M. Geringer. "Preference for Trumpet Tone Quality versus Intonation," Council of Research in Music Education Bulletin, 1976, Vol. 46, pp. 13-22.
Patterson, B. "Musical Dynamics," Scientific American, 1974, Vol. 231, No. 5, pp. 79-95.
Pick, A.D. "Listening to Melodies: Perceiving Events," in Perception and Its Development: A Tribute to Eleanor J. Gibson, A.D. Pick, ed. (New York: John Wiley and Sons, 1979).
Plomp, R. Aspects of Tone Sensation (New York: Academic Press, 1976).
Roederer, J.G. Introduction to the Physics and Psychophysics of Music (New York: Springer-Verlag, 1973).
Siegel, J.A. and W. Siegel, "Categorical Perception of Tonal Intervals: Musicians Can't Tell Sharp from Flat," Perception and Psychophysics, 1977, Vol. 21, pp. 399-407.
Taylor, J.A. Perception of Melodic Intervals Within Melodic Context (dissertation, University of Washington, 1971 [Dissertation Abstracts, 1972, Vol. 32, 6481A-6482A]).
__________. "Perception of Tonality in Short Melodies," Journal of Research in Music Education, 1976, Vol. 24, No. 4, pp. 197-208.
Ward, W.D. "Absolute Pitch, Part 1 and Part 2," Sound, 1963, Vol. 2, Nos. 3 and 4, pp. 14-21, 33-41.
__________. "Musical Perception," in Foundations of Modern Auditory Theory, J.V. Tobias, ed., Vol. 1 (New York: Academic Press, 1970).
Williams, D.B. "Short-term Memory Retention of Pitch Sequence," Journal of Research in Music Education, 1975, Vol. 23, No. 1, pp. 53-66.
Winick, S.S. Rhythm: An Annotated Bibliography (Metuchen: Scarecrow Press, 1974).
Woodrow, H.A. "A Quantitative Study of Rhythm," Archives of Psychology, 1909, Vol. 14, pp. 1-66.
__________. "The Role of Pitch in Rhythm," Psychological Review, 1911, Vol. 18, pp. 54-77.
Jack A. Taylor, Professor Emeritus, retired from the College of Music, Florida State University in 2001 and subsequently served three years as Visiting Professor at the University of North Carolina, Greensboro. Taylor earned an MA in composition and a PHD in Systematic Musicology from the University of Washington. At FSU he was Professor of Music and Director of the Center for Music Research. He taught courses in perception and cognition, research, and computers. Taylor has published a number of publications in those areas, and has been active in CMS, MENC and ATMI since the beginning of his college career in 1970. In his retirement he enjoys traveling, writing, and photography.
Dan M. Urquhart received a doctorate in music theory from the Eastman School of Music in 1968, then accepted a faculty position in the theory/composition department of the College of Music at Florida State University. He taught undergraduate and graduate theory couses until his retirement in 1996. Urquhart also is known for his compositions: Psalm 149 (chorus and tape), Mooscapes (concert band), and Sonatine for Clarinet and Piano, and others. Dr. Urquhart currently lives in Sioux Falls, South Dakota and devotes most of his time to composition.