The Technique of Beauty [9]

— Clock Time

The Hague, March 1, 2015

Dear Mr. Haas,

Thank you for your extensive text on kairos and chronos. Here are my thoughts and comments. Let me begin by saying that I am neither a linguist, philosopher, nor scientist —I am a composer. More of a “Roman” than a “Greek,” an agrarian who knows how to count and organize.

My initial plan for responding to your text was to use an essay by the Russian musician and writer Henry Orlov as a point of departure. I will indeed refer to his essay, but only after addressing three topics based on previous writings of mine. You may have read these somewhere already, but that doesn’t matter — I’ll be reworking them here in any case. The three topics are: memory and recollection, repetition and sequence, and inventio and replica. As you’ll understand, these topics are interconnected, and they also relate to our differing experiences of time. Afterward, I will speak not only of kairos and chronos but also of clock time — a kind of time that seems linked to chronos, yet is fundamentally different on another level. My thoughts and comments may be rather speculative, but then, who cares?

Kind regards,

-CB

Memory and Recollection

Let us define memory as a collection of information that has actually been stored in our brain over time. Whether this information has been stored accurately, is complete, or fragmented — perhaps because it was not entirely understood — is not relevant for now. We are simply establishing that something has been recorded in some way or another. Next, let us define recollection as the evocation or activation of that memory. During this retrieval of data from memory, various errors can occur. I am not an expert in this field, but using what we call “common sense”, three logical conclusions follow.

First, information could be lost during storage. Second, the memory itself might show signs of deterioration; the stored information might gradually or suddenly change in content (or form, leading to a similar effect), possibly due to a shock or disruption. Third, the stored information could be altered in content (or form) during the process of retrieval. In short, there are multiple stages at which the composition of information in memory might shift — during the initial recording, throughout its conservation, and upon its recall. The recalled information is what we refer to as recollection.

Whether this framework is scientifically or philosophically accurate does not concern me at the moment; for now, it should suffice, and we can work with it.

The resulting structure resembles the practice of Western European music: memory is like the score, a coded form created at a particular moment, while recollection is the performance, the interpretation of that score. Similar questions arise here as with memory and recollection, which is precisely what musicologists and musicians continually investigate.

For instance, the first movement of Beethoven’s Große Sonate für das Hammerklavier is marked at a metronome setting of 138 for the half-note, meaning it should be played at a rate of 69 measures per minute. The first movement, including the prescribed repeat of the opening section, has 524 measures. This tempo would yield a duration of a little over seven and a half minutes. But that would obviously be very unmusical, since the tempo must be slowed at numerous points due to phrasing and expression; there are fermatas, ritardandos, and countless a tempo markings indicating that it should not rush ahead like a runaway train. Let’s say, for these reasons, we extend the duration by one to one and a half minutes. Even then, the great pianists — of whom I own recordings — such as Wilhelm Kempff, Sviatoslav Richter, and Alfred Brendel, take significantly longer. Richter, the fastest, takes almost eleven minutes; Kempff skips the repeat and finishes in just under nine minutes; and Brendel — the youngest of the trio — takes over eleven and a half minutes. Both Brendel and Kempff take just over two and a half minutes for the repeated section, meaning that if Kempff had included it, he would also reach around eleven and a half minutes, like Brendel. Clearly, Beethoven’s tempo marking poses a challenge. The score (memory) says one thing, but practice (recollection) transforms it into something else, either to make musical sense (interpretation) or because of physical limitations.
These recordings reveal a deliberate interpretation — the pianists are certainly not pushing to their technical limits in terms of speed but are instead making a musical choice.

Another example: in 18th- and early 19th-century music, the sequence of a quarter-note triplet and an eighth-note triplet was notated as a dotted eighth note followed by a sixteenth note. Every performer understood the intended rhythmic notation. However, because we began to write out this triplet rhythm precisely in later times, that shared understanding has faded; it has vanished from our collective musical memory, occasionally leading to dillema’s. Consider the opening of the sixth song, Wasserflut, from Schubert’s Winterreise. We briefly discussed it in our email exchange — the piano part has an eighth-note triplet in the right hand, while the left hand displays the dotted eighth-sixteenth pattern I described earlier. How should this be performed? Should the left hand follow the triplet movement of the right hand, or adhere to the notated note values? In the latter case, a subtle jolt is heard at the end of each beat. The same problem appears in the fourth song, Erstarrung, but here it is unmistakable that the triplet feel should prevail, as the triplet rhythm is consistent throughout. In the fifth song, Der Lindenbaum, the issue arises as well in the second verse; here, it’s more challenging to decide how to execute the dotted rhythm, as this rhythm also appears independently in the piano introduction — in the second measure and just before the vocal entrance. This gives the dotted rhythm its own musical role, and a literal rhythmic interpretation can therefore be justified.

These are just two examples, each presenting a clear, concrete technical issue. However, bringing a score to life involves an ongoing questioning of what the notated code means musically, how it should be interpreted, and what the musician intends to express through it — it is not merely a matter of technicalities. We can see how, with increasingly precise notation from the 19th century onward, we’ve drifted further from our musical intuition, from a natural and fluid approach to music-making. It’s as if the concept of recollection — due to the rising dominance of the concept of memory — has been pushed completely into the background. Since the 19th century up until the 1960s, the score progressively tightened its grip on musical practice. A similar observation applies to the concept of memory, which has completely overshadowed that of recollection. Thankfully, a shift occurred in musical practice from the 1960s onward, mainly through musicians focusing on earlier periods, such as the Baroque and Renaissance. Older scores contain far less information than modern scores, so the score had to take a step back. This change proved a blessing for music-making overall. In terms of memory and recollection, digital advancements have had a significant impact. A computer has flawless memory, so we have increasingly delegated that activity to machines. This shift could at least allow the aspect of recollection to regain importance; however, we are far from reaching that point, as our awareness of the differences between these activities remains underdeveloped. We are outsourcing memory because we are awed by the machines’ capabilities; in a sense, we are giving up our memory.

Repetition and Sequence

In music theory, the repetition of a melody fragment — where the rhythm is repeated but the melody is played at a different pitch (usually a second higher or lower) — is called a sequence. A well-known example is the refrain from the English Christmas carol Angels We Have Heard on High (of French origin, by the way), which features a threefold sequence on the word ‘Gloria’. The text of the refrain is Gloria in Excelsis Deo, and the first syllable of ‘Gloria’ is extended through the triple sequence. Western classical music is full of sequences. The opening of Beethoven’s Fifth Symphony — who doesn’t know it?

This opening of the symphony, where the foundational rhythm that will define the entire work is introduced, consists of a double sequence. The first theme, which begins immediately afterward, is also structured as a series of sequences. The rhythmic structure of the melody of this theme is as follows:

We observe a three-layered and three-part structure, where the first two elements of each structure have the same form and length, while the third differs slightly and is somewhat longer. Such a three-part structure is called bar form in classical theory, likely a reference to the structure of medieval troubadour songs — the songs of bards. The structure of a bar form can be represented as A-A-B. At level I—the level of phrase construction — we see the large bar form (in German, you refer to this as a Satz). On the lower level II — the level of motif construction — we find three bar forms [a-a-b]. Level III is the level of the specific rhythm.

Here we encounter an interesting issue: there are various levels of repetition. On the lowest level — that of concrete rhythms — we hear whether melody notes are repeated or not; on the level of motifs, we hear motif repetitions; and on the level of phrase structure, we hear the repetition of phrases. But we also hear repetitions on the larger structural level: the exposition in the first movement is repeated and later reappears (in a varied form) in the recapitulation [reprise]. Listening to the piece on another occasion would also constitute a repetition. Additionally, a stylistic quotation or reference to another, similarly related composition is a form of repetition as well. But how do these repetitions relate to each other? Does the term become so all-encompassing that it loses its meaning?

This reflection at least clarifies that sequence and repetition are not synonymous concepts, which seems to have a specific purpose. A sequence is indeed a form of repetition, but repetition is not necessarily a sequence, much like a cow is an animal, but an animal is not necessarily a cow. In classical music theory, a sequence occurs within a phrase; it’s a technique for shaping a phrase. Let me illustrate this with a paraphrased text example as a thought experiment.

De Bondt is a composer, De Bondt is a teacher, but De Bondt is also a Dutch man.
Haas is a musicologist, Haas is a writer, but Haas is also a German man.
De Bondt receives letters from Haas, De Bondt writes letters to Haas, and De Bondt and Haas have never met.

In the first sentence, the sequence of “composer,” “teacher,” and “Dutch man” can be viewed as sequences in a bar form, A-A-B: “composer” and “teacher” serve as comparable categories [A], namely professions, while “Dutch man” provides information about origin and gender [B]. The second sentence has an identical structure; however, it is not a sequence of the first but a repetition. The third sentence deviates from this pattern; although the structure is the same as that of the first two sentences, the content differs because it addresses the relationship between the two individuals mentioned in the first two sentences.

The distinction between the different layers in the structure is of great importance in music theory. Repetition is essential because it shapes form. Just as in a building, the beams, building blocks, windows, and roof tiles serve as the “repetitions” that give structure to the building, and in a painting, the figures, colors, and strokes do the same, in music, time is used as building material, and repetitions provide structure. We can only form an image of large concepts like time and space through division; for this, we work with small units. A 6/4 time signature is too large to understand musically; we must break the six down into two groups of three or three groups of two. Ultimately, we can conclude that music always revolves around units of two or three. Every time signature can be reduced to a combination of these two values. Five can be three plus two or two plus three, but seldom is it simply five. The number one, on the other hand, is too small and insignificant. A 1/4 time signature is nonsense. A time signature is fundamentally about differences in tension; there must be at least one strong and one weak beat. The one, of course, is the unit with which the two and the three (and the more complex combinations derived from them) are counted.

Returning to the difference between sequence and repetition — or rather, to the subdivision of the phenomenon of repetition into meaningful categories. As mentioned, a sequence occurs within a phrase; well, the tension that occurs within a phrase, and the tension that occurs between different phrases — what does this difference mean, and what does it point to? There is, to my knowledge, an unwritten law that prescribes using no more than double sequences, because otherwise — and this is my interpretation — the music steps outside the kairos moment. What does this latter statement mean? If kairos is the experience of a moment, how can a sequence give shape to this moment? With the common sense I referenced at the beginning of this letter, I believe I can assert that a single sentence can express a kairos moment.

A sentence is a singular statement that, although it may consist of various components, ultimately conveys a singular message. “The king is dead.” “The king has tragically passed away.” “The king has tragically passed away due to an accident.” “The king has tragically passed away while riding; the animal panicked and ran away.” One way or another — the king is dead. “The sudden death of the king was a heavy blow for the queen.” These are actually two statements, thus two phrases: “The king is (suddenly) dead.” “The queen mourns.” We can discuss this at length, but those two statements are the case. As long as expansions or elaborations occur within any of these statements, such as through sequences, the message remains within that one phrase. I refer to this as a kairos moment. This may be scientifically nonsensical, but it is indeed a clear, verifiable statement. We can work with that.

Let me rephrase this last point: when we can work with this, we have a valid (and manageable) tool at our disposal to distinguish between different types of repetition; namely, the repetition that occurs within the kairos experience and the repetition that occurs outside of it, in flowing time. Just as an important chord, which the composer allows to resonate, creates the illusion of an ‘extended’ moment, of frozen time. For instance, consider the two chords with which Mozart’s Don Giovanni begins. These are two chords, so we can also imagine that a phrase takes place within such a conception of time. The sequence emphasizes the ‘delay’ of time rather than its progression. Thus, this form of repetition occurring at the phrase level has a different function than that at a higher level—at least, at first glance.

Inventio and Replica

By inventio, I mean a newly and originally created concept. Inventios serve as the counterpart to imitations or replicas. I will once again try to clarify this with musical examples. A fugue theme is an inventio; its accompanying countersubject is also one. In the divertimenti (the sections where the theme is absent) of the fugue, which are usually based on a part of the theme (or the countersubject), we see a special case of the sequence. (The whole story is, of course, much more complex than I can describe in brief.) The sequence in the divertimento is used for a different purpose than the theme. A theme — just like a phrase — is a shape [or figure]; it belongs to the domain of kairos. As argued earlier, the sequence typically falls under the category of frozen time, but in the divertimento, it is meant to facilitate progression, to modulate, or to showcase the musician’s virtuosity. I call this form of sequence a replica. Using “borrowed time,” a bridge is made to another moment. The later repetitions of the theme in the piece — after the exposition — are not replicas; they are simply repetitions. A replica is thus a special form of repetition; it is essentially a form of mass production.

Another example may clarify this further. The first four measures of the first theme of Mozart’s Sonata Facile (KV 545) constitute an inventio, while the following eight measures — mainly scalar figures — consist of forms of replicas. The same applies to the second theme, except that the last eight measures here do not consist of scales but of broken chords, which — this is a harmonic replica — traverse the circle of fifths. What is interesting about this sonata is that the inventios of both themes do not appear in the development of the piece; only the replica sections are used — the typically pianistic passagework.

One might consider a replica a form of theft, or, more kindly put, imitation. However, this does not imply that a replica is morally inferior to an inventio; it depends on the context. Inventios without replicas seem, at the very least — let me express myself carefully — problematic; I cannot think of a piece that consists solely of inventios. In any case, all cadenzas are replicas. Perhaps we should view them as artifacts. To regard a replica as of lower order than an inventio means considering fluid time as inferior to frozen or suspended time. I wouldn’t be surprised if you are among those who hold this opinion.

Finally, a brief note about the Mozart sonata I just referred to. I spoke of the “typically pianistic passagework” that made up the development section, typical because one would expect a development of the thematic material (the two inventios), yet nothing of the sort occurs; only the scales from the first theme and the circle of fifths from the second. At the end of the development, there is a modulation to F major, and we then hear the first theme, but in the ‘wrong’ key. That’s the joke; we initially think we are finally starting the development because the first theme now sounds right (in a different key as a development would entail), but then we gradually realize that this is indeed a very literal repetition of the theme, not a varied one. Only when variation occurs — during the repetition of the scalar sequence, but with inversion of both voices — does modulation return to C major, and then suddenly we are in the transition measure leading to the second theme. There was no development; we were already engaged in the reprise, just in the ‘wrong’ key. This realization — understanding in a single moment that we have been misled — that a section we thought was the development turns out to be the reprise, that is kairos. Thus, a higher level, the level of form, can also produce a kairos experience. That’s why I wrote “at first glance” at the end of the previous paragraph. Repetitions generally do not evoke a kairos experience, but it is indeed possible.

Actually, we already knew all of this, as it was the subject of Beethoven is Doof.^*) I find myself repeating. The inevitable practice of a composer.

*) De Techniek van de Schoonheid [2] – JCdV.

Time and Music Experience

The essay by Henry F. Orlov, The Temporal Dimensions of Musical Experience, was published in 1979. I received it from a brilliant former student of mine, the composer and pianist Leo Svirsky. Svirsky wrote to me that Orlov was the fourth husband of his former piano teacher. A personal connection always adds something extra, don’t you think? Even when sensory taste is satisfied by a work of high artistic quality, it enhances the joy of the experience — truth be told, right?

That was a bit of a silly remark, but there is some truth to it. A personal touch ultimately forms part of the experience of a text or artwork. Orlov actually writes about this in his essay. I don’t know if you are familiar with the text, so I will first discuss it in general terms — perhaps unnecessarily.

The essay explores the experience of time when listening to music. This can be very different for each individual listener. This is not only true for music; traveling can also bring very varied experiences of time.

Many recognize the following experience: the long drive to southern France, the sign on the highway just over the border from Belgium — coming from Mons — that says: Paris 222 km. And you are still in Paris. The sign after Paris towards Bordeaux reads: Bordeaux 565 km; that’s an unbearable distance if you have to cover it in your little Dafje Daffodil, a tough stretch to cover in your DAF Daffodil, ‘clever little lever’ [‘pientere pookje’ in Dutch – JCdV] and all. Driving in your car, windows open because of the heat, while the rush of wind continuously whirls through your head — and if you decide to temporarily brave the heat to give your ears a rest and roll up the window, you find that window still doesn’t close properly; the rushing sound has only decreased a bit in volume. Meanwhile, the endless fields of grain, corn, and sunflowers with enormous sprinklers flash before you like a continuously repeated pause film; and while your thoughts drift off, they never show a coherent structure — at best, a discomforting bulge in your pants as you think about how the woman sitting next to you is going to pamper you that night in the hotel, the tent, or the cottage (which ultimately doesn’t happen due to excessive fatigue and too much alcohol consumed); you learn the route while driving. The next times you drive the route, you recognize the distance signs, the dreary place names that suggest the worst, like Cambray, Douai, St. Quentin (wasn’t that a prison?), Compiègne, Créteil, Dourdan, Meung (cow!), Étampes — thankfully, they are interspersed with Laon, Orléans, Issoudun, Romorantin-Lanthenay, and Chalon — then it seems that the journey is shorter, as if time is going faster. In fact, this seems to already be the case on the return trip. A repeated route is a faster route.

Another trompe-l’œil in time experience is the rapid change of environment, language, and culture after a (relatively) quick journey over a longer distance. It’s as if body and mind have bridged the distance, but the soul is still on the way, on foot. It’s also interesting to note the sensation after returning from a stay of several weeks, on one hand feeling as though you’ve been gone for “an eternity,” but on the other hand, feeling like it “was over before it even began.”

Orlov begins his essay with a reference to an experiment from the early 1920s conducted by a Russian psychologist named Belyaeva-Examplyarskaya. When I read that name, I had to pause for a moment. Examply-etc.? That name couldn’t be real! However, Svirsky later told me that it was not uncommon for scientists working under such peculiar pseudonyms in the Soviet Union at that time.

In any case, this Examplyarskaya published her research under the title On the Psychology of Musical Perception [Moscow, 1924]. In the study, a group of individuals listened to three preludes by Scriabin, each played three times over three sessions. The participants had to indicate how long they thought the preludes lasted. The three preludes have a duration of around two minutes. The number of participants varied between 13 and 23. The errors in their time estimations were significant, with overestimations reaching half an hour and underestimations down to five seconds. The average estimates were too high for all three preludes.

Of course, we must realize that clock time had a different meaning a century ago than it does today. In our media and computer age, we are accustomed to thinking in seconds; just think of sports like running, cycling, and speed skating, where times are measured to the thousandth of a second. The first time a stopwatch was used in the Olympics was in 1916, the so-called “Micrograph” by Heuer, which could measure down to one-hundredth of a second. In the everyday life of the 1920s, this accuracy was of no significance. Nevertheless, we also recognize the misleading game of time experience that occurs when we listen to music, which transcends all eras.

We need to pause a bit longer on the phenomenon of “clock time.” The distinction between chronos and kairos needs further elaboration. The mechanical clock has increasingly influenced our experience of time. Historically, we know the sundial, the hourglass, and the water clock, but sometime in the fourteenth century, the mechanical clock emerged, ultimately leading to the modern chronometer and stopwatch. In music, we have the metronome; Beethoven received an early model from its inventor, Maelzel. This has been discussed previously, particularly in the context of Viderunt Omnes. Clock time could be seen as a variant of chronos, as it also involves succession. In that case, one could distinguish two variants within chronos: clock time and biological time, such as heartbeat, breathing, and walking. This distinction is important because Orlov refers to it; he does not use this term himself but speaks of “objective duration” and “biological clock” in relation to “right time.”

After briefly addressing historical theories on the experience of time, Orlov cites William James (from a text dated 1890), who establishes a connection between the variation and impact of successive events and the duration of experienced time compared to remembered time: interesting and varied experiences lead to a shorter estimation of experienced time, but a longer estimation of remembered time. This raises an intriguing question for Orlov: How can two contradictory concepts of time coexist in our memory?

For, recollecting an empty time as very short, we also remember how long it seemed; and recollecting a time rich in experience as very long, we nonetheless remember how quickly it passed.

To unravel this aporia, Orlov distinguishes between two types of time experience: projective time and reflective time. Projective time is an impression of duration, while reflective time is one of (musical) content — simplistically put: one is form, the other content.

Projective time is a personal impression, dependent on the listener’s cultural background. Someone hearing a piece for the first time has much to discover. Furthermore, the more the listener knows about the cultural context of the work, the more there is to uncover. With repeated listening, new elements will be discovered during the initial experiences, leading to refinements and new connections. However, over time, the information — and thus the interest — will diminish, and the experienced time will be felt as longer. Additionally, emotional state plays a role; someone who is madly in love while listening will experience the work differently than someone suffering from excruciating toothache.

Reflective time, on the other hand, reflects the value and significance of the listening experience. The following factors, derived from information theory, come into play: interesting versus boring, compact versus empty, active versus passive, and finally, the degree of repetition. Furthermore, while listening, we make distinctions between the musical content, the sequence of moments, the structure and architecture of the piece, and the density of the time experience. This ultimately leads to a valuation of time.

Contemplative time is obviously the measure of content, while projective time is the reflection of its formally organized duration as apprehended by the listener. The more he is involved in the two-sided process of following and understanding the music, the longer his contemplative time seems, and the shorter his projective experience appears to be. There is then a greater discrepancy between the two eventual readings. Which of the two experiences listener would consider essential and worth reporting on whether his perception is focused on content or form.

There are evidently two types of musical experiences: one that unfolds in time — chronos — and another that experiences the whole as a single extended moment — kairos. For example, when I write to you about the first movement of Beethoven’s Fifth Symphony, you can grasp a (musical) image of this movement all at once. You don’t need to listen to it in its entirety first. This is an experience we all share. Does this happen because we remember a certain characteristic element, such as the opening motto? Or is there more to it, like the overall structure, the harmonic development, the sound of the work as a whole? I lean more toward the latter. Orlov concludes his essay with two references to composers that confirm this notion. One is by Mozart, who writes in a letter to his father that he could hear a complete composition as a whole, rather than as a sequence of sounds. The other is a quote from Beethoven: “…the underlying idea never forsakes me. It arises, it grows; I hear and see an image before me from every angle, as if it were cast like a sculpture.”

(I cannot find the source of Mozart’s letter, nor that of Beethoven’s quote; Orlov does not mention them. Perhaps you can do this better than I can, after all, it is your métier.)^*)

*) In chapter [10] Haas responds on this matter [JCdV]:

I checked out the Mozart letter and the Beethoven quote you asked about.
– The letter of Mozart is a hoax, he never wrote it, so it’s apocryphal.
– The quote is not written down by Beethoven himself, but by Louis Schlösser who met him in 1822 or 1823 (the precise year is unclear to me) and wrote about it in his ‘Persönliche Erinnerungen an Beethoven’. The ‘quote’ is the answer Beethoven supposedly gave to a question my Schlösser about how he composes.

[This chapter concludes with an analysis of the first thirty-three measures of Ravel’s Adagio assai from the Piano Concerto in G, which is published separately on this site. — JCdV.]