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I. INTRODUCTION

Composers of contemporary music make use of awide variety of techniques in their music. Regardlessof the harmonic vocabulary or medium used, one thingthat great compositions of all styles and genres have incommon is an effective and interesting use of thetemporal elements of music. This is particularly evidentin acoustic and electronic compositions whichfrequently use of a mixture of metered and free, non-metered elements. Although many articles, books andpapers have presented methods of defining, discussingand understanding pitch materials, a proportionatelyinsignificant number have dealt with the fundamental,temporal aspects of contemporary music, and virtuallynone deal with non-pitched based music. Since thetemporal aspects of a composition are of fundamentalimportance, a method of defining, understanding anddiscussing the full gamut of the rhythmic and temporalrelationships for pitched and non-pitched based musicis essential.

Most existing rhythmic theories and analyticalsystems apply only to metered music, as do those ofMaury Yeston, who at the end of The Stratification ofMusical Rhythm adds the disclaimer that his theoriesare “... limited to a kind of tonal music in which themiddleground rhythmic levels exhibit some regularityof motion.” (Yeston, 1976: 148) Others, like JonathanKramer’s The Time of Music (Kramer, 1988),thoroughly cover the philosophical unfolding of timewithin a work and the effects of tonality and pitchmaterial on the perception of time in a work. LikeYeston, however, Kramer remains almost exclusivelywithin the realm of metered music, providing only apassing mention of non-metered works (1988: 77).

The analytical concepts put forth in by Larry Austinand Thomas Clark (1989: 131-143) are more generaland applicable to a much wider variety of types ofmusic. Although these ideas are helpful in determiningthe rhythmic density and alignment at a detailed level,they require a great deal of time and computation. Forthis reason, these tools are most useful only afterspecific areas and strata of musical material have beenisolated and identified. Moreover, the results of suchanalysis are in the form of raw data, and are not

indicative of the relationships and transformations thatmay be taking place in the music.

So, how would one begin understand or discuss thetemporal characteristics of a work which moves freelyfrom metered to non-metered sections? Yeston states:

“Extreme caution should be exercised inevaluating the universality of a theory. If it istoo specific to a small domain of musicalphenomena, a theory may mistake the uniqueaspects of very few compositions for generalprinciples. On the other hand, if the theory istoo general, the degree to which it mayilluminate specific problems may be marginalwhen compared with the effort expended inarriving at general principles and solutions.”(1976: 148)

This paper presents a cognitive-based system ofidentifying and labeling basic temporal elements. It isdesigned to be a first-level tool for theorists, composers,and teachers and is applicable to music regardless ofthe presence or absence of pitched-based materials,meter, or notation. Although general in nature, theapplication of this system is very easy and simple. Mostimportantly, in the case of sample-based computermusic and many 20th Century acoustic works, temporalanalysis can reveal underlying structures that might notbe otherwise evident.

II. FACTORS WHICH DEFINETEMPORAL ELEMENTS

When listening to music, regardless of pitch content,media, or style, the mind analyzes and organizes thesound it hears in order to comprehend it. Acoustically,when two or more sounds of differing amplitudes and/or timbres are sounded together, an effect calledmasking (Backus, 1969: 90) may cause the strongersound to dominate, resulting in the perceiveddisappearance of the weaker sound. Similarly, whenthe listener is presented with a variety of sonic elements,the mind relegates some as being predominant, orforeground material, and some as less dominant, or

Temporal Elements: A Cognitive System of Analysis for Electro-Acoustic MusicROBERT J. FRANKrobfrank@smu.edu

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background material. The mind focuses on the primaryelements while background material is mentally“masked” and perceived in a subordinate role or, insome cases, not consciously perceived at all. Studieshave shown that the human mind reacts to theoccurrence of a sonic event and then projects forwardin time an expectation of what is to come (Dowling,1986: 214-215). As long as an event continuesaccording to what the mind expects, there is little mentalattention required. When something unexpectedoccurs, such as a change in the pattern, there is abiological reaction within the brain signaling thatsomething has unexpected has occurred. New eventswill also elicit this signal. Both reactions will bringabout psychological conditions which shift the mind’sattention to the new or different event, while continuingevents will elicit less and less of a reaction (Dowling,1986: 214-215).

Consistent, unchanging elements are perceived asbeing more stable and can be more easily assigned abackground role in favor of new material whichdemands more attention. Hence, material that isinitially perceived as foreground material may later beperceived as background material when: a) it is repeatedso many times that the mind is thoroughly familiar withit and no longer requires the same amount of attentionor energy to process the information, or b) some newmaterial upsets the order of priority in the mind of thelistener. This interplay of consistency verses changeresults in the perception of, and transformationsbetween, foreground and background material and iscrucial to understanding the pacing and temporalunfolding of events in a composition. By defining thetemporal elements used and their relationships, we notonly create a tool for discussing specific aspects of acomposition but also increase our awareness of theserelationships, resulting in a greater understanding ofthe music.

SustenanceThe most stable, unchanging element is one that is

said to sustain, or continue consistently withoutinterruption after its initial attack. How long must apitch/silence continue to be considered sustaining? InMusic Cognition, W. Jay Dowling uses the term“psychological present” to refer to that temporal spanof attention which we consider “now,” and duringwhich the mind processes information as a whole(1986: 79) The term psychological present does notrefer to the actual present which is occurring as youread this. Rather, it refers to a short interval of time,like a buffer, during which the mind determines if

events are to be perceived as a single unit or as separateevents. Related materials are grouped together andprocessed as a single unit. This is the function thatallows us to perceive speech as “words” rather thanstrings of phonemes. If the material continues beyondthis time-span, the mind must find a new way to dealwith it, since the “buffer is full” so to speak. Beyondthis limit, the mind must categorize an event as eithera continuation of the primary event or segment thematerial and perceive it as one or more new, separateevents, thus effecting our basic perception. Researchhas set the psychological present at a normal maximumof about 2-4 seconds with some rare cases of up to 9 or10 seconds (Dowling, 1986: 180). Events occurringentirely within this brief period are mentally groupedinto, and perceived as, single units. Sounds or silencewhich exceed this limit in a consistent manner willgenerally be cataloged by the mind as a continuationof a previous event or, in this case, as sustaining.

RepetitionSimilarly, shorter events which occur within the

psychological present and then continue to consistentlyrepeat beyond that time span will be psychologicallygrouped into a unit perceived as a continuation of thepattern. Pitch and timbre can play a determining rolein the perception of repetition (Yeston, 1976: 50-51).However, a high degree of similarity may be sufficientcause for a pattern to be perceived as repeating, but toa lesser extent than an exact repetition. Therefore, inthis paper repeating elements will be defined aspatterns which repeat identically. Similar events whichrepeat will be considered a weaker sub-category of thiselement. Another weaker form of this type of elementoccurs when the length of the repeating elementexceeds the psychological present. When this occurs,it may not be at first perceived as a repeating elementbut after a longer period of time, i.e. several repetitions,may perceived as such. In this paper, these type ofelements will be referred to as long-repeating elements.

A common application of this principle is found inthe use of the “Alberti Bass” accompaniment, ostinatofigures, tape loops, and other repeating patterns. Withthese figures, composers can sustain rhythmic interestand direction without distracting from the foregroundmaterial. Another application of this is in minimalism,where subtle changes introduced after the material hasbeen shifted to a background-type perception elicit astronger response that they normally would have ifintroduced within a changing, non-consistentenvironment.

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Alignment to a Common PulseAnother factor to be considered is alignment to a

common pulse. When an event or a combination ofevents conform to a common, recurring interval of time,a pulse emerges. Extended to a higher level, regularlyaccented patterns of pulses form related groups,commonly referred to as meter. As there are a multitudeof works on this subject, there is no need for a detaileddiscussion of this topic. However, we must note thatalignment to a pulse has a great impact on ourperception of music. In this paper, aligned events willrefer to events that are coordinated to a common,recurring interval of time. Although metered eventsare a narrower interpretation of this factor, they willnot be a requirement of the definition.

Fusion and Auditory StreamingAs summarized by Dodge and Jerse (1997: 44-45),

when approximately 10-12 or more events occur persecond, our mind does not react to each as a separateevent, but groups them together into a single elementthrough a process called fusion. Thus, a granulatedsound is not perceived as a rapid series of repeatedevents, but rather as a single, sustained stream of sound.When a series of events that have the same timbre, orsome other unifying aspect, occur in sequence, we alsoperceive them as a single auditory stream (Dodge andJerse, 1997: 59). This is why a series of events of thesame timbre, even if they do not repeat, are perceivedas a single stream. Hence, a series of non-repeatingevents with the same timbre, register, or other unifyingaspect, such as a phrase of spoken text, may beidentified as a single, non-repeating element. Similarly,a group of elements that exhibit a high degree ofconsistency (such as an orchestral unison passage) mayalso be grouped into a single element for easier analysis.

III. DEFINITION OF THE FIVE BASICTEMPORAL ELEMENTS

When a single sound, silence, or series of soundsoccurs within the period of the psychological present,it will be referred to in this paper as an event. In thefollowing discussion, let us define an element as anevent or series of events continuing beyond thepsychological present.

Sustaining elements by their very nature provideno opportunity for repetition or alignment beyond theinitial attack and, as such, are unique. Within non-sustaining elements, however, the factors of repetitionand alignment to a common pulse each have an effecton the perception of the resulting material. This means

that different combinations of these two factors willresult in perceptually different elements. Hence, wemay derive five basic temporal elements: sustaining,aligned/repeating, aligned/non-repeating, non-aligned/repeating and non-aligned/non-repeating.

SUSTAINED

Aligned/Repeating

Non-Aligned/Repeating

Aligned/Non-Repeating

Non-Aligned/Non-Repeating

(S)

(A/R) (NA/R)

(A/NR) (NA/NR)less stable

more stable

Figure 1: Basic Temporal Elements

1. SustainingA simple example of a sustaining element is a long

fermata. The technique of “pedal point” is anotherexample of this type of element.

2. Aligned /RepeatingIn this type of element, events repeat to a

coordinated regular pulse. It is often used in manytypes of music as an accompanimental figure.

3. Aligned /Non-RepeatingUnison passages, homogenous chorales, and

metered music with distinctly independent lines withmetrically congruent subdivisions of the beat are allexamples of aligned/non-repeating elements. Althoughthis type of element may contain recurring motifs andpatterns, it does not contain consecutive repetitions likealigned/repeating elements.

4. Non-Aligned/RepeatingIn this genre there is no coordinating temporal pulse.

In polyphonic textures, each sub-element proceedsindependently of the others but contains within itselfrepeating events.

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5. Non-Aligned/Non-RepeatingThis genre has no coordinating pulse, no

continuously repeating figures, and individuality ofsub-elements. Non-aligned/non-repeating elements areused in common practice cadenzas and many twentieth-century solo works.

The preceding categorization of basic temporalelements is intended to be general, not absolute or all-inclusive. There are an infinite number of “gray areas”between each genre and it is often these “gray areas”that are of the greatest interest in a work. Just as tonaltheory can be used to help understand modulatorypassages or passages of tonal ambiguity, these basictemporal elements may also be used to shed light oninteresting musical passages of temporal ambiguity.

IV. COMBINATION OF TEMPORALELEMENTS

Temporal elements can, of course, exist singularlyor simultaneously with other elements. In a singularrelationship, different temporal elements are juxtaposedone after the other for temporal contrast. Composersfrequently employ this technique to help define formalsections in a work.

When two or more elements begin in a simultaneousrelationship, there may be a few moments ofdisorientation during which the mind is attempting todetermine upon which element or elements to focus.As elements unfold past the psychological present, theymay begin to be recognized as repeating or sustainingelements and be relegated to a background role, or asnon-repeating elements or single events, and perceivedas foreground material.

Another means of combination is achieved by thegradual layering of elements. Layered elements donot have to be of contrasting type in order to beeffective. General observations seem to indicate thatthe normal active focus time for sustained elements isapproximately three times the psychological presentfor sustained elements (once to perceive the event, onceto recognize the continuity, and a third time to confirmthe continuity), or approximately 6-9 seconds. Thesame principle applies to repeated elements, with anormal active focus time of approximately three repeatsof the event. When new elements are brought in beforethis active focus time is complete, the passage may beperceived as building or possibly “rushed”, since thenewly entering elements are drawing focus away froma active (foreground) element rather than a stable(background) element. Similarly, when new elements

enter beyond the normal focus time, the passage maybe perceived as stabilizing, or possibly “lagging”, sincethere is time during which the mind has alreadyprocessed the existing information, but no new eventsenter to retain the active focus.

In a phased relationship, two or more elements existin related tempos or consistent subdivisions that resultin points of coordination at a recurring interval of time.When this coordination point arrives within the activefocus time, the relationship between the two phasedelements may be perceived more strongly. When itoccurs within the psychological present, the twoelements may even be perceived as a single, fusedelement. This type of relationship is stronger in alignedelements, where it forms the basis for our perceptionof meter.

V. TRANSFORMATIONS BETWEENTEMPORAL ELEMENTS

Just as transitional passages often provide the mostinteresting analysis in tonal theory, gradualtransformations between different genres of temporalelements result in equally interesting material. Thesetransformations fall into two basic categories: hybridelements, and gradual transformations.

By combining traits of two different types oftemporal elements, a hybrid element is formed. Thismay be used to form a transition from one type ofelement to another. One example of this is a trill, whichis a aligned/repeating element whose repeating notesare joined through fusion to form an element similarto a sustaining element. Another example of a hybridelement is a sustained FM tone with an oscillator onthe Modulation Index or amplitude. Although there isno new attack, a pulsing timbre can give the impressionof a aligned/repeating element. Weaker sub-categoriesof elements may also be used as hybrid elements. Along non-aligned/repeating element may be perceivedas repeating to some, but to others with a shorterpsychological present, may be perceived as non-repeating for several repetitions.

Gradual transformations also provide interestingtransitions between elements. For example, when anon-repeating element contains similar phrases thatbecome more and more consistent, it may transforminto a repeating element. Tempo and rate of unfoldingof events can also create transitional phrases. Intraditional music, a rallentando into a fermata is afamiliar example of a transformation from a less stablenon-sustaining element into a stable, sustainingelement, hence it’s effectiveness as a closing gesture.

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the sound, thus adding additional stability to thebeginning of the work. Following this stable sound, heselects a contrasting NA/NR element, as a transitioninto the main portion of the work.

Figure 3: Exposition

The Exposition (Figure 3) presents the two basicideas Schaeffer uses in this work: artificial, locked-loop recordings that create strong sense of meter, andnaturally occurring, NA/NR sounds that invite thelistener to attempt to find a pulse in the course ofeveryday life. The locked-loop sounds occur from :22- :53. An A/NR whistle sound serves as a transition tothe following NA/NR sample, which contains little ifany naturally occurring repeating sounds. At 1:11, heinserts a 5 second A/R loop, and then a weaker (lessstrong metric subdivisions) 4 second loop that leadsback into NA/NR material until 1:33, when thedevelopment begins.

Schaeffer develops his material by presenting lessclearly defined elements, shifting between naturallysimilar (yet not identical) weak NA/NR elements versesweak A/R loops that never present more than tworepetitions of an event. By shortening the length of

VI. APPLICATIONS AND CONCLUSIONS

AnalysisThe Electro-Acoustic literature is rich in interesting

forms and structures. Unfortunately, most theorists arereluctant to discuss these works, as well as the worksof many contemporary acoustic composers, becausewithout the security of a time signature most analysesare reduced to generalized discussions of pitch sets.Once the factor of pitch is removed, traditional analysiscomes to a virtual halt. However, within all theseworks, there exist temporal structures and relationshipsthat significantly shape the form of the work.Recognizing, identifying and labeling temporalelements and their transformations provides a specificlanguage for discussing and revealing interesting,underlying structures within these works.

With notated music, there is a fixed score in whichvarious temporal elements and their use may beidentified. In Electro-Acoustic works without a score,this may be more difficult in some ways. However,software that displays waveforms and time, such asSoundEdit16, is helpful in providing specific referencepoints in time and providing a visual graph of the work.Since this is a perceptual system, this may also be anadvantage, since the aural characteristics are moreimportant than a possibly deceptive notation. Also,since this is a cognitive-based system time is the unitof measure, not measure numbers, making this systemideally suited to electro-acoustic music.

Étude aux Chemin des Fer by Pierre Schaeffer is aclassic and well known example of musique concrète.However, as such, it is rarely the subject of analysis. Atemporal analysis of this pioneering work revealsseveral interesting structures and techniques:

The work consists of four sections: an introduction;a two-part, A-B style exposition, the first presentingA/R loops, the second presenting primarily NA/NRmaterials; a development using primarily hybridelements that blur the difference between natural andartificial loops; and a coda that mirrors the introduction.

The introduction (Figure 2) opens with an A/NRelement consisting of three whistle sounds. The closestto traditional, metered music, this element is used threetimes throughout the work, and in each case this signalsthe beginning of a new section. After this initial sound-set, he introduces a naturally occurring A/R hybridelement (the regular, accelerating clickty-clack of atrain starting). This sound is an ideal choice, since itnot only foreshadows the artificial A/R elements thathe will create with his locked-loop recordings, but italso has a sustaining high-pitched whine as a part of

Figure 2: Introduction

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each element and using closely related hybrid elements,the listener is constantly challenged to ascertain if asound is repeating naturally or artificially, with lessand less time to make this decision. Finally, he closesthis section with three repetitions of a whistle tone. Itis interesting to note that the third of these tones isallowed to sustain for several seconds, transformingthis gesture into a stable, sustaining element.

Figure 5: Coda

The coda mirrors the opening, with a naturallyoccurring A/R hybrid element (regular whistle pulseswith Doppler shift) followed by an whistle sound A/NR element. A sustained tone with even pitched pulses,this sound combines traits of sustaining and A/Relements, yet does not make use of literal, artificialloops. The closing gesture, same type of element asthe opening, rounds out the form.

TeachingIn theory and composition courses, different

methods of handling pitch materials are presented, butthere are rarely equally structured presentations of themany various methods of handling temporal aspects

of a composition. When various temporal systems arepresented, they are often presented individually asseparate “styles” such as “aleatoric”, “minimalism”,and “computer music.” This may be, in part, due to alack of a common language and method of discussingthese aspects. When these concepts are presented, itmust be stressed that there are different methods ofnotating these various elements, and that sometimesthe notation may be deceptive. By presenting all ofthe basic temporal elements together in one unifiedsystem, students may more easily approach new musicwith an open, unbiased perspective. Manycontemporary techniques aren’t seen as totally foreignconcepts but as extensions and developments of basictemporal and perceptual principles. As an additionalbenefit, understanding the underlying temporalprinciples behind the contemporary notation used inmany works allows for the easier and fasteridentification of the pitch materials employed.

In teaching composition lessons, this systemprovides specific terms which allow for the directdiscussion of the properties of a work. By identifyingspecific problems it also may suggest specific possiblesolutions. (i.e. - “You have only A/R elementscontinuing for 25 seconds in this section, but neverelsewhere in the work. This creates an inconsistentlystatic interval during which the listener’s attention willwander. Try layering a different type of element overit.”) It may also function as a compositional tool,allowing for the design of formal structures and newtransformations.

ConclusionsWhile labeling temporal elements and identifying

transformations between them may not provide thedetailed, numeric data that would result from otherforms of analysis, these processes do provide anoverview of the structures and techniques used intemporally flexible works or passages. Used as a first-level analytical tool, this method may help isolate areasof particular temporal interest and aid in determiningwhich other analytical tools might be appropriate forfurther in-depth study. It is hoped that this methodmight encourage and assist composers, theorists,students, and teachers in recognizing and appreciatingthe large-scale counterpoint of elements inherent inmusic of all styles and periods, including the oftenneglected and misunderstood music of our own time.

Figure 4: Development

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BIBLIOGRAPHY

Austin, Larry and Thomas Clark 1989. Learning toCompose. Dubuque, Iowa: Wm. C. Brown Publishers.

Backus, John 1969. The Acoustical Foundations ofMusic. New York: W.W. Norton & Company, Inc.

Dodge, Charles and Thomas A. Jerse 1997. ComputerMusic. Second Edition. New York: Schirmer Books.

Dowling, W. Jay 1986. Music Cognition. Orlando:Academic Press.

Jaynes, Julian 1976. The Origin of Consciousness inthe Breakdown of the Bicameral Mind. Boston:Houghton Mifflin Company.

Kramer, Jonathan D. 1988. The Time of Music. NewYork: Schirmer Books.

Yeston, Maury 1976. The Stratification of MusicalRhythm. New Haven: Yale University Press.

This paper was presented at the 2000 International Computer Music Conference (ICMC - Berlin) and the 2000Society for Electro-Acoustic Music in the United States (SEAMUS) National Conference. It was downloadedfrom www.robertfrankmusic.com [Temporal Elements].

for citation:

Temporal Elements: A Cognitive System of Analysis for Electro-Acoustic Music. Journal SEAMUS, Society forElectro-Acoustic Music in the United States, Austin, TX, Vol. XV, Number 2, Fall/Winter 2001.

Temporal Elements: A Cognitive System of Analysis for Electro-Acoustic Music. Proceedings of the 2000 Inter-national Computer Music Conference, Berlin, Germany.