#4 The Perception and Organization of Time in Music

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UDC: 78.01
     781.1/.6
COBISS.SR-ID 258609932 

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Received: Sept 4, 2017/
Reviewed: Sept 27, 2017/
Accepted: Sept 30, 2017

The Perception and Organization of Time in Music

Maja Marijan
Belgrade Center for Music and Dance, Serbia
[email protected]

Citation:
Marijan, Maja. 2018. "The Perception and Organization of Time in Music." Accelerando Belgrade Journal of Music and Dance 3:4

Abstract

In this article the author approached to musical time as complex phenomena using terms such as absolute and relative time. Author defined time as an objective time of the musical composition and the subjective time as psychological experience. Accordingly, absolute time is organized within the composition – it is objective and defined, thus can be expressed in size by the properties, values and symbols of musical elements, notation and timing. Musical time as the psychological phenomena is relative referring to the organization of time in performer's mind, as well as how the performance is perceived and experienced by listeners. The nature of organization of elements of musical time in the performer's mind lies in the conception of the structure of the temporal organization generated by the performer's subjective expression, knowledge of the musical form, and motor/kinesthetic ability. Furthermore, the idea of the temporal structure also incorporates experience and practice, as well as intuition and aesthetic valuations. Thus, the structure of time is not independent – it interacts and relies upon other structures, building performer's conception of the whole. Author concluded that understanding the time structure in music, i.e. how to recognize its symbols, how to organize it for the performance and while performing, is very important aspect of the musical expertise. Furthermore, in music education the special emphasis has to be laid on the musical time through learning and understanding its symbols, because perception and recognition of temporal structure would deepen student's interpretation and knowledge of the form, and develop expressive and qualitative performance.
Keywords: musical time, mental structures, articulation, tempo, rhythm, meter, temporal organization

Introduction

Sound is a mechanical energy that is created by vibration of an object. These vibrations, spread through the air, oscillate forming sound waves. A sound is also considered as a pressure wave which creates sound energy (Brownell 1997). How is sound perceived? Hermann von Helmholtz and Georg von Békésy suggested that ears are ingenious device which transform sound waves or mechanical energy into the electrical signals perceived by the brain (Ibid.). However, this electric signal or its original primitive form, a mechanical wave, is not a simple kind of data. The sound wave has many properties such are pitch, timbre, loudness, and timing. Each property can be recognized separately, because it has been shown that these elicit different brain regions (Thaut et al. 2014; Samson 2003; Allen et al. 2017), although tight interactions between these properties exist (Krumhansl et al. 1992).
        Perception of sound is a complex neurological, cognitive, and psychological activity (Iakovides et al. 2004). To perceive a sound means to perceive loudness, timbre, pitch, and duration, all at the same time, but also we can follow each property separately (Jerde et al. 2011). All four aspects of sound have an impact on perception, memory, and completeness of the mental image. The completeness of an image of an auditory stimulus depends on our auditory mechanisms and how an auditory stimulus is encoded by our auditory system (McDermott et al 2008). The perception of pitch, loudness, timbre and duration is dependent on many factors: 1) the nature of the sound source and acoustic medium (Frissen et al. 2010), 2) how the sound is moving through the medium and around us, 3) our physical location relative to the sound source, 4) our auditory system, cognitive abilities, attention, and also 5) musical experience (Pantev et al. 1998; Takashi et al. 2001). In this article we will focus on one important element of the sound, the musical time, and explore its structure, organization and perception.

I
The listener's perception and organization
of musical time

In this section the author tries to answer the question: how musical time is perceived by the listeners? The author will start with the hypotheses that perception of time and representation of the temporal organization of the music depends on the representation and understanding of the structural properties of the musical form (Clarke and Krumhansl 1990). Musical form is organized as hierarchical structure of elements which listeners perceive in a time span, creating a mental image of the form (Lerdahl 1983). If the boundaries of the sections are clearly perceived, the timing structure will be also clearly represented within the mental image. On the other hand, the temporal structure will allow the listeners to evoke the sections of the form in their mind and relocate the segments (Halpern 1988a) or to imagine the melody in the accustomed tempo (Halpern 1988b). Therefore, the author presupposes that the temporal structure is built upon the intuitive knowledge and familiarity with the musical syntax (in non-musicians) and theoretical knowledge, motor structure, intuition and aesthetic analysis of the form (in musicians).
        Time is the ambiguous feature. It has two dimensions. The first dimension of the time is objective time, meaning that the time has computational property expressed by numbers and terms such as hours, minutes, years, months, etc. In music, we count measures and note durations. Second dimension of time is subjective time, which refers to the inner experience of time that cannot be measured: it belongs to subjective category, although time remains the objective feature. The subjective perception of time can be defined as a psychological time where the listener's emotions (Asutay 2014), as well as stimuli of the outer world, play a great deal in our experience of time.
        Music is expressed in time. Unlike sculpture and painting which exist in space and are approachable by sight, music, like poetry, is expressed by sound which takes place in space and time. It is suggested that the perception of music is a complex cognitive process employing ability to create temporally ordered architecture of sound sequences in rapid successions (Thaut et al. 2014). All elements of the form such as harmonic flow, melody, meter, rhythms, motives, themes, and phrases are organized in time, and while listening to the music, we do not count time, we hear time. Thus, it can be said that the music is time in sound, and also, a sound in time. While listening to music in real-time, humans are constructing musical knowledge through sensation and representation (Reybrouck 2017). Musicians build a mental map of the form due to developed auditory imaginary ability (Alleman et al. 2000). Through experience, listeners build structures of musical syntax and develop expectations and judgements.
        Familiarity with the musical syntax and type of music allows listeners to understand how the elements are connected and related to one another (Burkholder 2006). Thus, listeners can tell if the musical phrase is correct/complete or incomplete or wrong. Incompleteness will make the listeners uncertain about the form of the musical sentence. For example, if a melodic phrase is played completely, listeners will have the feeling of a closed unit. If a phrase is not properly ended or stops suddenly, the listeners will have the feeling that the phrase has not been finished yet, because the phrase does not give satisfaction of the completeness. The time span of the phrase, to which the listeners were accustomed to, would be shorten and because of this, the phrase would sound unfinished. Therefore, this example shows that it is not just the rules of harmony that govern the completeness of the phrase, but the listener's experience of the musical time is also incorporated in the mental structure of musical knowledge.
        Music can alter the listener's experience of time and space (Schäfer et al. 2013). Some slow pieces will produce the feeling that the music lasts for a very long time, although the piece of music is short. Accordingly, the music which sounds pleasant will be judged shorter than the unpleasant (Droit-Violet et al 2013). Also, the judgements over the time span of the musical segments and listener's expectancies of the musical time depend on the familiarity with the time structure of the form. The common classical phrase consists of two sentences which share similar motivic structure and the same number of bars, and the only difference between them lies in the endings of each phrase – the first one's cadenza is on the dominant (half cadenza) and the second sentence usually has the authentic cadenza (V-I):

Example 1a. W. A. Mozart, third theme from the Rondo “Alla Turca” from the Sonata A Major KV 331
Mutopia Project. Copyright: Public domain
http://www.mutopiaproject.org/ftp/MozartWA/KV331/KV331_3_RondoAllaTurca/KV331_3_RondoAllaTurca-a4.pdf

If the musical sentence above (Example 1a) is played, the ordinary music listener, accustomed to this “common” classical structure, will “feel” the overall temporal organization of the phrase, and according to this, the expectations of the temporal organization of the musical sentence will be satisfied in listener, i.e. the listener will find this music idea to be organized properly. In another words, the judgement over the formal structure will be made according to the feeling of the time, assuming that no theoretical knowledge is used. If we apply some modifications in the formal structure of the phrase, we will break the listener's expectations. This modification will produce very strange effect on the listener who expects the phrase to have the “standard” timing structure. Harmonically, nothing is changed, the modified phrase ends with the authentic cadence, but the time expectancy is changed. Let's assume that we have not changed the first sentence of the phrase, instead we made some modifications to the second sentence:

Example 1b. (modified by the author)

This modified version of the second sentence sounds very strange and unnatural due to:

1) unusual melodic flow: the jump of the fourth (marked with the arrow) breaking the flow which is supposed to move upwards;
2) the metrical deviation: ending is on the weak metrical accent;
3) the form deviation: modification of the structure of the form is sized to the non-standard three bars.
4) the impossible continuation: after this phrase, the new section is introduced with the upbeat, therefore this modified structure destroys the laws of the good temporal organization of the structure.

From this example we can learn that it is not only important to organize the harmony or melody of the phrase for the music to be judged as good, but also temporal organization is something that underlies these properties. If harmonic or melodic structure is not properly organized in time, the music would be perceived to be out of order, hard to follow, and the listener's expectancies would be confused.
        Therefore, we can assume that listeners and musicians have developed the sensation for the time of the standard musical phrase that serves as a guide mark for judgements of form completeness. However, great composers often find different paths to break the rules of the classical form, thus modeling the musical time of the form. They are playing with our sensation of the standard/learned timing by 1) applying various compositional techniques which shorten or prolong the phrases and sections, 2) introducing motive modifications and/or adding new material, or 3) creating free-form structures thus modifying our expectances of the standard phrase duration in a masterly way. These modifications we can find anywhere, but those are emphasized especially in many free-form structures such as Preludes, short Fantasies, development sections or the introductions of the Symphonies:

Example 2. L. van Beethoven, Introduction from the Symphony No.1 in C Major op. 21
Ludwig van Beethovens Werke, Serie 1: Symphonien, Nr.1
Leipzig: Breitkopf und Härtel, 1862. Plate B.1. Copyright: Public Domain
https://imslp.org/wiki/Special:ReverseLookup/440381

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These forms are like improvisations where the composers express their imagination and take on the freedom to play with the elements of the form and break the standard rules. The free-form structures musicians often describe as to be “in one breath”, because the musical time is represented as one unit, without easily noticeable endings or the boundaries between the segments. The music material is often fragmented and the phrases do not represent accomplished/complete units, but “flow” one into another. In the Example 2, the harmonic progression in the beginning of the introduction (the first four bars) has the ambiguous structure as well as the cadence, which is on the tonic of the G Major or on the dominant of the C major? Further, in the 8th bar there is a weak resolution, yet this does not establish the tonal center. The further postponement of the main key is shown again in the form of the deceptive cadence V-vi (bar 10). Finally, in the last two bars of the introduction, there is a clear preparation for the resolution (dominant is preparing the tonic of the main key, C Major, with which the Exposition begins). The resolution is also marked with the change of the tempo (Adagio molto – Allegro con brio) and with the change of the character of the music (from slow, dignified and cantabile mood, to the fast, playful/excited expression). The temporal organization of the segments in the introduction can be defined if the listeners can recognize the boundaries, i.e the endings/cadences of the parts. Although the sections inside the introduction can be determined by less stable cadences, the time span of the introduction is perceived from the beginning to the last bar of the introduction, as the close unit. This is due to the final cadence which has clear preparation and stable resolution. Therefore, the listeners will perceive the time of the introduction as “in one breath”, i.e. from the beginning to the first stable ending without being aware of the time span of the sections.
        Thus, the experience of the time of the musical form arises from the harmonic organization of the phrase and perception of boundaries between the phrases. However, the boundaries between the phrases/sections, from which the attention is relaxed and aroused again, can be expressed not only by the harmonic properties such as cadences, but also these could be longer pauses, changes of the tempo between the sections, changes of the meter, or changes of the rhythmic profiles of the sections. The more the distinction between the boundaries is delayed, the more perception of time of the segments will be experienced as prolonged.
        In the next example, J. S. Bach's Prelude in C Major, although there are harmonic markers which indicate the borders between the sections, the rhythmic monotony hinders the judgement of the borders of the sections, so that the time of the Prelude is perceived as “in one breath” (Example 3). This Prelude is like many other Preludes in the opus of J. S. Bach. They are in the improvisational manner, where the melody is constantly in the movement (perpetum mobile) and where the composer performs his artistic freedom. The perception of time of the Preludes is achieved not by sections, but as the whole. The perception of these Preludes can be compared with the perception of the bronze figures of Giovanni Bologna:

They [bronze figures (author's remark)] are made to be looked at long, and also closely, for those that are autograph are wonderfully delicate in technique, and sometimes gilt. They are meant to be turned round in the hand, and then they give an aesthetic stimulus of that involuntary kind that sometimes comes from listening of music. (Shearman 1967)

Furthermore, although the form of the Prelude is small (35 bars), the experience of time is not in the agreement with the size of the form. This experience is the same as we have with the Bologna's miniature figure, such as The Mercury, in our hands:

The raised arm, which, in the front view, soars like a rocket from the weight-bearing foot, is melodiously curved into the lowered left arm in the side view, and sprung against two other curves, from head to the right foot, and from the left elbow to the left foot; turn it a little more and the raised arm flows into the right leg and the line from the left foot runs through the body to the head. (Ibid.)

Example 3. J. S. Bach, Prelude and Fugue C Major BWV 850
Editor Franz Kroll, Bach-Gesellschaft Ausgabe, Band 14 (pp.18-21)
Leipzig: Breitkopf und Härtel, 1866. Plate B.W. XIV. Copyright Public Domain

Therefore, the perception of formal structure of the phrase has impact on our experience of the time. The listeners can organize the inner time of the composition if they can perceive clearly the boundaries of the phrases and, consequently, develop the mental image of the musical form and its elements. Accordingly, if the listeners can separate one phrase or section from the other, they can experience the timing structure of the sections as well as the global time of the piece. But, if the musical piece has rhythmic or formal monotony or there are no opposite characters/moods and defined endings, as shown in the Example 3, listeners cannot perceive the clear boundaries between the phrases, so their attention is constantly delayed, and their experience of the time is continuously prolonged. This type of music structures requires constant attention, and will produce fatigue in the listeners if the form is quite long. For this reason, these structures are often short or belong to the introductory or development sections. Therefore, the composer has to adjust all the elements of the form to the time structure of the form very thoughtfully.
        Moreover, classical composers often break standard 4+4 or eight-bar structure of the sections on the places where this structure is expected. Here deviations are made for several reasons: firstly, to break monotony of the formal structure, secondly, to introduce the complexity of the musical idea, and lastly, to break the listener's expectations of time. Modifications of the structure often underlies the developing sections, but not uncommonly there are many examples where the main themes have developing form bounded very tightly with the rest of the structure, so that the listeners can hardly perceive the boundaries and time span of the sections:

Or there are examples where the theme is expanded and elaborated through registers:

Example 4. L. van Beethoven, the first theme of the Waldstein op.53, III movement.
Ludvig van Beethoven, Piano Sonata op.53 Waldstein in C Major. Ed. Heinrich Schenker (1868-1935),
New York: Dover Publications, 1975. (pp.370-401) Copyright: Public Domain.

In the example above (Example 4), the Rondo's Theme A is continuously expanded from the bar 31, where the first boundary could be recognized, up to the bar 62, where the final cadence conclude the theme. Thus, the attention is hold for the 62 bars, from which new material of the bridge appears.
        However, composers of 20th century have found new ways to express the form, so the approach, experience and perception of time are different. In their works, time is not the simple component of the harmonic progression of the sections as in the traditional works. The elements of the temporal structure, such as rhythm, tempo, meter, are the main builders of the expression. In another words, the modern music does not express charming melodies in a classical sense, but exposes the complex temporal structure that constructs the form.
        How can the listeners orient themselves in these compositions and percept the time structure? Compositions of the modern music, like piano pieces of John Cage or Karlheinz Stockhausen, have many pauses which are treated as the musical ideas that build the composition. It seems that these pauses are the time poles on which the global time structure resides (the duration of the form). These pauses are like “the resting points” (author's term) in which listeners can feel the time structure. These “resting points” i.e. pauses, enable the listeners to feel the boundaries of the sections (Deliege 1989) and perceive the time span of the sections. Whereas the music of the minimalists (Example 5) has constant flow with the same rhythmic pattern, thus, it will hold the attention of the listeners, and expanding their perception of time:

Example 5. Philip Glass, Etude No. 6
Source: https://musescore.com/user/186390/scores/3583541

The other possible approach to define the boundaries of the segments of the modern music, thus developing possible temporal idea of the segments, comes from the listener's predictability and surprise produced by constructive elements of the music: dynamics, articulation, note groupings, texture of the chords, changing the meter (Stockhausen 1958). Clarke and Krumhansl (1990) showed that perception of boundaries of the musical segments relied on the all constructive elements: pauses/silence, dynamics, textures, rhythms, changes in pitches and registers, changes of the contour of the melody, and similarities/repetitions. They showed that listeners could determine the position of the sections according to their temporal organization, especially those at the beginnings and endings, whereas the sections positioned in the middle were harder to determine. According to the author, as she has stated before, this is due to the perception of boundaries of the segments. If the sections are perceived as closed forms, than their temporal organization is clearly perceived. On the contrary, the time span of the segments of the developing sections is perceived as long as the clear closing cadence appears.
        However, above researchers examined the perception of musical time and perception of the boundaries of the segments after the listeners had heard the composition. But what if the listeners have never heard the piece before, i.e. how listeners organize their perception for the very first time they hear the piece? If the composition is heard from the beginning to the end, the listeners will develop the image of the composition and will have the idea about the time organization/time span of the sections within the whole. On the contrary, listening to the musical piece for the first time will result in the ambiguous perception of the temporal organization of the whole. Every time after a longer pause, listeners will think that the composition is finished, although it is not. Although inner timings are precise, like rhythmic patterns, meter and tempo, overall time of the complete form remains ambiguous to the listener. How to know if the piece comes to an end? Well, only after the (last) performer bows and goes off the stage. Thus, the performer is indeed the part of the time structure of the music and serves as a final “bar” in the score of the indeterminate form. This suggests that if the form is indeterminate to the listeners, the perception of the time span of the form and its sections will be uncertain.
        Therefore, in contrast to the classic form where the time structure is perceived as a result of harmonic and melodic flow and it is predictable due to listener's exposure and experience, in compositions of the modern era, time is an active structural part that guide the listeners from motive to motive, from phrase to phrase, changing their attention from sound to silence, and make them to wonder if the sound will appear again, thus the composition will be continued, or the composition will come to an end. However, only after the composition is heard fully, the listener will create an image about the time structure of the piece and, accordingly, the structure of the form will be clearly presented in the listener's mind.

II
The organization of time of the form

In the music composition, temporal structure is organized and represented through:

• Rhythmic structure
• Metrical structure
• Temporal structure of the segments
• Organization of the tempo

Rhythmic structures, metrical structures, and time span of the segments belong to the absolute category of the temporal structure. The properties of these structures are objective, determent, and cannot be changed. They are written in the score, they have their own symbols and are set as frame for the melodies and harmonies.
        Rhythmic structure refers to the temporal organization of the sound. It can be the inner temporal organization within one sound or the temporal organization of the sound groups. The inner temporal organization of the sound refers to the time span of the rhythmic unit: whole note, half note, quarter note, eighth note, sixteenth note, etc. The time span of the rhythmic unit is experienced as pulses which occur periodically within the unit. The perception of these pulses has important role in the performer's organization of the rhythmic structure. Each pulse is evenly distributed and counted within the unit, but their number depends on the established tempo, meter and type of the unit (weather it is whole note, half or quarter note, etc). For example, if the meter is 2/4, and the tempo is fast, then each of the quarter note will have only one pulse (counted as “one” - ”two”). But at the same meter and at slower tempo, the inner pulse of the main unit (quarter note in this case) has to be divided into two pulses or even four pulses, i.e. the quarter note is now divided into smaller units. This division of the inner pulse of the rhythmic unit is important for the performer in order to keep the accuracy of execution of the rhythmical patterns (see Figure 1). This is important when dealing with the long values, such as brevis, whole note or prolonged whole note. If the performer does not feel or count the inner pulses, or divides these values onto equally positioned smaller units within the time span of the note value, the rhythm will not be precise, and, thus, performer will be lost in the temporal structure of the phrase. The disposition of inner pulses is also important when we deal with rhythmic patterns or sound groups, which consist of dotted and tide values (see Figure 1).

Figure 1. Division of the rhythmic units

While rhythmic structure gives the flow and motion to the form, metrical structure organizes the temporal elements within the form. Metrical structure is the organizational unit of the temporal structure of the composition. It establishes the main rhythmic unit, and determines how many units are per bar/measure. Furthermore, as the inner pulses are equally organized within the rhythmic unit, the beats are the properties of the meter that are organized within the bars. In another words, the properties of the metrical structure are the tempo markings and periodically placed beats within the bar. The beats are, in fact, regularly arranged rhythmic values which occur at the same positions from the first to the last measure. The beats are expressed as strong and weak pulses equally arranged in the measures. Depending on the meter, in the bar can be one or two strong beats, while the rest are weak, even beats (see Figure 2). This division on the strong/underlined and weak/relaxed beats underlies rhythmic and harmonic structures and enables the listener to perceive the structure of the inner time of the measures (Palmer and Krumhansl 1990). Any irregularity in the placement of the beats can lead to confusion in the perception of the musical meter (Bouwer et al. 2018). Also, this notion of beats as strong and weak has implication for harmonic rules - modulation, endings, voice shifting - which are placed usually on the strong rather than the weak place in the bar.

Figure 2. Organization of beats inside measures with different metric properties.
Strong beats are indicated with the red line above each strong beat.
If there are two strong beats in the bar, the first one is
considered to be stronger than the other one.

The beats are perceived as accents. In meter 2/3 the strong and weak accents will be perceived as shown in Figure 3:

Figure 3. Presentation of the beats

This “imaginative” accentuation is not emphasized in the performance and it is not suggested to underline the beats, because the music would become uniform and mechanical. Melody, articulation and harmony are placed in the way that the beats are felt as periodical pulses shown above. But the accent on the first beat is emphasized only when it is indicated in the score, as the part of the articulation, or when the upbeat is introduced:

Example 6. Robert Schumann, Faschingsschwank aus Wien, Op.26
Robert Schumanns Werke, Serie VII.
Leipzig: Breitkopf & Härtel, 1887. Plate R.S. 62. Copyright Public Domain

Temporal structure or the time span of the segments is expressed by the properties that are characteristic for each segment or section. These properties are:

• the rhythmic patterns
• the melodic idea
• motivic treatment
• harmonic progression
• established tempo

All these properties build the structural idea of the sections. Every change in tempo, in motivic treatment, voicing, texture, flow and structure of the melody, harmony, and rhythm indicates that the new segment is introduced. Every delayed harmonic cadence expands the time span of the segment. Tempo has also impact on the perception of the duration of the segments: in slow tempo sections are perceived longer than in fast tempo. Therefore, time structure of the segments depends on all these properties of the form.
        As the author has stated, the first three categories of the temporal structure of the form are absolute, which means that their properties are constant, and unchangeable. Meter, rhythms, metrical beats and the number of bars cannot be changed, and any deviation or any significant alternation of these properties written in the score is considered false, and confuses the listener's expectancies. Neither performer nor the listener can by any means perform modification to these properties of the temporal structure. However, tempo is the property of the time structure that is set in the composition, thus it is absolute, but at the same time it can be considered relative, that is, tempo alters the listener's as well as the performer's perception of the form and accordingly can be differently interpreted by the performer. There are obvious differences between the performance speed of the same composition. Every performer interprets tempo according to subjective artistic image that is built on the knowledge and intuition. In this sections, the author will present the complexity of the temporal structure that refers to the organization of the tempo.
        Absolute tempo is the composer's tempo, i.e. the one which existed in the composer's mind while composing the piece. Some authors discuss that the composer is obligated to have “correct feeling for the natural tempo of every meter, or what is called tempo giusto...” (Kirnberger 1776). The given tempo determines the note values: in fast tempo composers choose small note values, while in slow tempo chosen note values are long. Furthermore, time signature and rhythmic units determine the tempo (Beck 1954). Tempo modifies the time span of note values during performance – in fast tempo sound durations will be as short as possible often articulate with leggiero and staccatissimo, while in slow tempo note values will be sustained through the vary last pulse often articulate with legato or sostenuto/tenuto. However, baroque composers, like Bach, did not put indications for the tempo. It is suggested that the notation and the rhythmic character of the music evoke in the performer the right kind of tempo (Marshall 2008). But, through musical practice, the form and harmonic progressions have expanded and become more complex and thus the composers wanted to express their ideas more clearly. One of the many solutions for this problem was to precisely indicate tempo markings whenever it was needed. Although these markings directed performers on the right path, tempo still remains ambiguous feature of the time structure. How to distinguish terms such as Allegro from Allegro con brio, or Moderato from Adagio seems to relay upon the performer's experience, judgement, taste and interjection of the form and structure. This feeling of the tempo, author recognizes as relative tempo.
        Relative tempo refers to the performer's or listener's judgements over the tempo of the composition. In listeners, tempo builds parallel time from which listeners create their judgements (Berger 2014). The judgements over the tempo as “too slow” or “two fast”, as well as the modulations of tempo, depend on the listener's experience and the musical practice level (Sheldon and Gregory 1997). Further, listeners of different age levels have different preferences for the certain type of tempo (LeBlank et all 1988). But, what about the differences in the perception of an Adagio, Moderato or Allegro? It is suggested that the character of the music has influence on the perception of the tempo: if the music is played fast and filled with strong events, the tempo will be perceived as “too fast”, and on the contrary, if the music is slow, filled with weak events, it will be judged as “too slow” (Quinn and Watt 2006).
        The problem of tempo markings is set before the performer who would wonder and ask: “What is the exact/absolute speed of the tempo markings which the composer had in his 'inner ear', and how to interpret all the changes of the tempo within the form without breaking the inner pulse of the structure?” It seemed that Beethoven tried to facilitate this problem for the performer. Setting instructions to the performer, he set his metronome markings in his works, but he did not overestimate the value of the metronome (Marx 1895). There are articles which explore this metronome phenomena, and which suggest that metronomic tempo and metronomic playing in modern world is something that is expected, desired, and seldom criticized (Bonus 2018). The musical idea cannot be expressed in a metronomic way, because “keeping of absolutely strict time is thoroughly unmusical and deathlike” (Hoffman 1920). Therefore, Beethoven's metronome markings are questioned and cannot be taken for granted, because from the writings of his contemporaries, we learn that “he played his compositions differently every time” (Marx op.cit.). Furthermore, Beethoven, in his Ninth Symphony, hesitated over metronomic mark that he would choose, but finally he wrote “No metronome at all! Those who have a right feeling do not need it, and those who have not, will not be helped by it” (Ibid.). Phrases and melodies have their own expression and breathing, and cannot be expressed as mechanical beats especially in the cantabile and long melodic phrases. Therefore, metronome markings can be regarded as an absolute and objective backbone which will guide the performer's conception of the organization of the tempo and its modifications. Relative or interpretative tempo, that is part of the performer's conception, is a possible solution to the absolute tempo of the form.

III
The representation of the time structure in the performer's mind: the performer's approach

The temporal structure of the form is mapped in the performer's mind. The absolute values of the temporal structure transform into live, multidimensional and complex mental image. The ability to structure time elements of the form is very important for the understanding of the piece and quality of interpretation. The temporal structure does not exist per se, but corresponds with other knowledge structures and intuitive structures that live in mental space. Performer's temporal structure of the form is represented in three stages:

• Organization of the rhythmic structure
• Organization of the articulation
• Organization of the tempo of the segments and form

Organization of the rhythm. The perception and execution of the rhythmic patterns are important features in the interpretation of every musician. Without rhythmic cultivation one would be prevented to express the music. To be able to percept, memorize, recognize and execute rhythmic structures of the form, performer has to go through following processes:

• perception of the meter – at the first glance, performer recognizes the metric values, i.e. perceives what type of note value is established as the main unit and how many units there are per measure (tempo markings). This will help performer to have an overview of the temporal structure of the form, how beats are placed within the measures, and accordingly, this will help performer to organize his/her ideas and expectations on the time structure.
• perception and recognition of the rhythmic structures – this refers to the perception of the rhythmic figures and rhythmic patterns, as well as perception of the characteristic figures and patterns for each section, and how the transitions between these patterns are made.
• execution – to be able to precisely execute rhythms, performer has to master his/her kinesthetic movements and has to have control over the motor apparatus. Without developed motor ability, the execution of the rhythm will sound clumsy, out of time, and without clear pulse.

Organization of the articulation. Articulation refers to the specific touch which transforms the timbre and duration of the sound. Articulation is also considered a type of touch that allows the performer to express the timing and expressibility in music. Markings for articulation modify the “normal” duration of note values. Without articulation, the notes values would sound equal in duration, and no changes in character and expression will be made. Articulation can be defined and distributed into several categories, based on how the sound durations and timbres are manipulated:

• articulation which holds the absolute durations of note values – this articulation is marked as legato, tenuto, portato with its augmentative and diminutive forms. This type of articulation does not shorten the timing values, instead, it holds and even shortly prolong the timing property of the note value. Legato, tenuto, and portato have their own symbols which enable the performer to recognize those in the score. Also, it has to be noted that legato can be misunderstood for phrasing, because both are symbolized similarly with long sinusoid bow above or under the notation. Only through experience and musical practice, the performer will be able to distinguish these different features. The technique for execution this type of articulation includes whole arm, forearm, the finger movement and cantabile touch.
• articulation which shorten the duration of the note values – it refers to staccato, saccatissimo,and pizzicato. The durations of the note values are shorter that in “normal” mode. Performer has to have specific finger technique and light touch to be able to clearly execute this type of articulation.
• articulation which change the volume of the tone – the notes are articulated with symbols for marcato, sforzato, martelato, and accents. Different kind of touch is applied when performing these expressions. The strength of the arm and fingers are important as well as performer's experience and the sound imagination, because unexperienced musicians often produce hard and even unpleasant sounds when dealing with the articulation of this type.
• articulation which manipulate timbre of the sound – symbols for this kind of touch are referred as con sordina, apagato, and muted. The subtle technique is needed in the performer's pallet of touch.

Each type of articulation has its own symbolic representation, weather the markings are dots, arcs, different types of accents, or simply written text above or below the notation. All the above mentioned articulations require trained technique, subtle ear, and aesthetic approach to the musical form. To be able to percept, recognize, memorize and execute articulation, the performer has to have skills and knowledge such as: 1) theoretical knowledge about the type and value of each type of articulation, 2) kinesthetic knowledge about how certain type of articulation has to be played, 3) physical control and 4) auditive control. Every performer has to be able to describe how certain type of articulation is performed, where it is applied, and why he/she uses it, if no original articulation is written in the score. Further, developed motor skills allow precise physical control over execution of articulation. The subtle nuances between, for example, staccato and staccatissimo, will be clear to listener, if the finger technique of the performer is mastered. The legato markings are often written within the long, singing melodies and phrases, thus this touch requires fine cantabile tone and aesthetic feeling for the quality of sound. Performer has to listen every note value to its very end, and connect it with next one without any pause or sound gap. Performer's auditive control has to be very intense and concentrated.
        Therefore, in music education, from the early beginnings, learning signs and symbols of articulation has to be one of the primary concern of the teachers, because the quality and expressivity of the performance depends on the articulation. All the finesse and delicateness in performance spring out from the performer's sense for articulation. This is similar to poetry or acting. What a pleasure we gain when actor or orator speaks with all kinds of nuances that speech can have: he/she can shout, narrate, rustle, whisper, using all kinds of accents and sounds, changing his/her voice suddenly or gradually. Weather it is music or speech, to articulate the sound is the ground of qualitative interpretation. If educators introduce this idea to the students, the students will gradually realize how this concept is important, and thus their auditory abilities and sense for the meter, tempo, timing, would be trained. Furthermore, expression and articulation are very tightly bounded. The signs for expression and signs for articulation are often used together, so it is not rare that certain kind of expression awakes specific touch. For example, terms such as cantabile, dolce, triste, and dolore are used within long phrases and usually are associated with markings such as legato, portato, portamento and tenuto; pesnate is connected with tenuto; skerzo with staccato, staccatissimo, and pizzicato; furioso with marcato, martellato, and sforzando. Therefore, terms for expression can help performer to execute articulation in accordance with marked expressions. However, exemption of articulation signs would leave performer to find the solution of how to employ the correct articulation to the music. Only analysis of the structure will help performer to understand the meaning of these symbolic signs, because melodic/interval motion, meter, tempo, and even harmony are the elements that suggest the possible articulation of the phrase.
         Organization of the tempo of the segments and form. In the composition there is, usually, one marking for the main tempo of the whole piece or movement. However, often we can find two or more main sections, like in the Sonata form, or in the pieces where several parts are connected without pauses (like in Symphonies of the romantics). If this is the case, there are several main markings for the tempo in the form slow-fast: Adagio-Allegro or similar. But, within the piece there are many alternations and modification of the main, constant tempo: sometimes those changes are perceived as accelerations, sometimes as retardations. According to this, the performer has to deal with the complex temporal structure. This process of organization of tempo is built through two phases: organization of tempo on a local plane, and organization of global tempo on a large scale.
        Organization of tempo on a local plane refers to the perception and understanding of the markings for the tempo changing. The rules of harmony, melody and motivic development impose the course of the tempo. For example, in romantic pieces, motivic development often gradually accelerates the tempo between the culmination and the resolution. In these sections we can find tempo marking such as accelerando, poco a poco, stringendo, but, ritenuto as well, because sometimes the volume of the sound would gradually become more intensive and full, so acceleration would not be possible any more at this point. Thus, ritenuto can be written at the end of culmination, between the sections or movements, or at the end of a piece. For the last, ritardando and rallentando are more commonly used. However, performer has to carefully study the piece, because it is not always the case that in the endings retardations are used. Also, the attention has to be concentrated on an idea that these deviations of the tempo within the sections have to be studied carefully, in order to keep the absolute tempo of the whole. If the performer use too much freedom to emphasize the temporal changes in sections, the musical flow would be broken and stylistic and aesthetic properties of the music would be spoiled. In another words, every deviation from the tempo, within the sections, has to be precisely studied and computed, and in harmony with the global tempo of the whole. Therefore, before the performer approaches the accelerations and retardations of the parts, he/she must first thoroughly learn the structure of the form and create a mental picture about the main tempo/tempos of the whole, and then study the temporal changes of the parts, always comparing each deviation with the main tempo. Only this way, inner temporal changes will be adjusted to the global tempo of the form, and the musical idea would be clearly presented to the listeners.
        Organization of the global tempo refers to performer's understanding of the main tempo markings. These are often written at the beginnings of the main parts of the form, sections and movements. How the performer would interpret the tempo of the first movement, understand its flow and speed? One possible approach is to compare it with the tempo of the rest of the movements. Nevertheless, tempo of a composition can be understood in regard to the character of the music. If the music is moving, gay, imbued with short note values, the tempo, presumably Allegro, will get the attributes such as lively, joyfully or hastily, more adequate than simply “fast”. Thus, the character of the music will give the tempo marking the “colorful” meaning, embedding the purport in raw words. Furthermore, tempo can be interpreted in accordance with the style. Some musicians and critiques are against the interpretations which employ too fast executions of the pieces of baroque and classic composers, because of the imperfection of the instruments of those times on which these extravagant executions would not be possible, or simply these fast tempos do not match the style. And lastly, every musician would interpret the same tempo marking differently. This is due the expertise, experience, knowledge and intuition. Even the same musician cannot repeat the same composition at the same speed every time. Thus, psychological, physical condition of the performer, as well as external social and natural factors, can greatly influence the performance and make changes to performer's experience of tempo. However, the deviations from the absolute tempo must not be too far away from the conventional idealized speed. Performer must not sacrifice the marked tempo and its general speed for his/her poor motor abilities or misunderstanding of the musical idea. Allegro cannot become Allegretto, or, in the worse case, Andante. The performer's abilities have to be adjusted always to the composition and its ideas, but not vice versa (Neuhaus 1973).
        The most ambiguous feature of the tempo modification in the performing practice is rubato, or tempo rubato. Understanding the tempo rubato requires aesthetic approach to the form, musician's experience, intuition and musical knowledge. Rubato means “to steal” or “rob” (Latham 2011) the time. The performer's approach to rubato is the following: for how much he/she shortens the time in one place of the phrase, for the same amount has to be extended (the time) at the other place. Rubato quite often imposes before the musician the variety of problems over the tempo. It is regarded as the problem of temporal synchronization between the leading voice and accompaniment, but also as the performer's modifications of the tempo of the whole piece during performance (Hudson 1996, Hudson 1997). Rubato or tempo rubato is written within the phrase or section, and its flow is often interrupted with the marking a tempo, which means that the tempo which was established before the rubato has to be applied.
        But, what exactly is rubato? It cannot be either precisely defined through exercise, or be carried from teacher to pupil. It is not constant feature of the temporal structure. It is a modification of the tempo in the process of the live performance, in front of the audience. This modification can be regarded as the improvisation of the tempo, thus, it is very tightly connected with the aesthetic feeling and intuition, the musical taste, cleverness and intellect of the performer. To be executed with the taste, the performer has to define the global and inner tempos of the form, as well as to have an idea about the overall structure of the whole. Having this image, the performer can successfully deal with rubato. Furthermore, the structure of the music and the different aspects of the context could prompt the performer to play with rubato even if the term is not written (Timmers et al. 2000).
        Therefore, rubato can be considered as a special technique for modifying the temporal structure of the form. Flexibility and intuition with which the performer changes the tempo, or deal with tempo rubato, must not deform the musical idea, its character and flow, and have to be always within the boundaries of the global tempo of the form. Dealing with tempo rubato still remains unspecified, i.e. how the musical time would be modified at the given moment in live performance. Using rubato, the performer has to be conscious about every temporal change he/she makes. This consciousness means that the performer has to instantly make evaluations, in real-time, for every change he/she has made and to think in advance about how the modifications of the tempo have to be executed in accordance with the context of the form. This process requires great control over the thoughts and emotions while playing.
        It is worth mentioning one more element of the form that belongs to the time structure and with which performers often deal: fermata. Fermata is one of the relative properties of the temporal structure. It is a musical symbol that indicates the extension of the duration of the note value. Often, it is considered to prolong the note value up to half of the value duration or so (Kennedy 1994). Fermata is used usually at the end of a section, between the movements, or it is written at the end of a phrase which expresses the logic of the words and sentences of the text of the vocal music. How long the performer will hold note values below the fermata depends on the musical context in which the fermata is introduced, and on the artistic and aesthetic expression of the musical idea. (Neuhaus, op.cit.)

Conclusion

In this article the author made a short discourse on the temporal structure, on its properties and elements, and examined how this structure has been perceived by listeners, as well as how it has been presented in composition and how it has been structured in the performer's mental space. It is shown that the temporal structure is a complex structure of the form, as well as the important and underlying organizational unit of the composition.
        Without time and timing, the music itself could not exist, because timing is indivisible property of the sound. Generally speaking, the composition itself is, in fact, a time structure. The temporal structure corresponds with the other structures and elements of music: pitches, timbres, dynamics, harmonic rules, and melodic flow. Moreover, the temporal structure gives the motion, character, expressivity and an aesthetic idea to all these elements. To be able to perceive the temporal structure, listeners and performers have to recognize the boundaries within the form, but on the other hand, the perception of the temporal structure will allow them to comprehend the boundaries of the form. Flexibility in organization and realization of the musical time depends on the motor, auditive and cognitive skills and abilities, on experience and practice of the performer, but nevertheless, the intuition, imagination and aesthetic deliberation are the features to consider in dealing with the time structure. The performer's aesthetic approach is bounded with the conception of the temporal organization of the elements within the form. It can be said that the musical piece is the time in form, and the interpretation of music, or the concert performance is the form in time. Through analysis of the temporal structure, the performer will grasp the image of the musical idea and thus, his/her performance will be clear and expressive. This is why the author suggests that in music education teachers have to emphasize the importance of the temporal structure, because the conception, clarity, accuracy and expression will be developed in students. Through perception and understanding of the temporal structure of the form, the music would reveal herself as live, organic unit.

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