Amit Weiner – Ph.D
The Jerusalem Academy of Music and Dance
The Time Component in Arvo Pärt’s “New Simplicity”
or What is the Meaning of a Rest Whose Length Is of Zero Half-notes?
“Music turns time into audible sound” (Suzanne Langer)
“But one moment, Suzanne, how is it possible to hear a rest of zero half-notes?” (Amit Weiner)
Introduction: Absurdities, Illusions and Unanswered Questions
Zero half-notes, you ask yourselves? Could there be some mistake in the title of the article? Is there any logic here in a rest having the length of zero half-notes? And how would it be indicated in the musical notation system that is familiar to us? And, say it is zero half-notes, why not have a rest of zero quarter-notes or zero whole-notes? And is it equal in value to a note whose length is of two half-notes? Is there any logic in all of this?
Indeed, there is logic! Pure, unadulterated logic, as we will discover by the end of the article. These absurd questions are the result of the conspicuous processes the world of music has undergone (as, also, has the world itself) over the course of the 20th century: mathematization and the will to control. The subject of discussion is the act of one process: mathematization and technology cause the illusion of control. But it is merely an illusion as we will see in due course. As the catastrophes befalling the world in the 20th century increased and strengthened, music became more and more mathematical and the illusion of control over musical material increased. The First World War brought about Dodecaphony (five years after the war, in 1923) and World War II introduced “Total Serialism” (seven years after the war, in 1952); Schönberg “is dead” and, with him, so is Dodecaphony. Each war had brought about the desire for more accuracy in the composing down of music and more control over its parameters. Following each catastrophe, composers made the decision to no longer surrender themselves to feeling: this feeling was not to be allowed to return. Feelings had caused disillusion and had led to frightful results. “This time we will work with the mind”, composers said to themselves, hoping that, with that, they had found the solution to their distress. Was this a mere intellectual illusion and no more?
Indeed, in due course, we will understand that the aspiration for order and absolute organization always leads to chaos (and not only in music. For example, take Nazism and its results.)This is the paradox outlined here: with absolute order, just like the lack of absolute order, both, actually, lead to chaos.
The mathematization of music is characteristic of twentieth century styles that are different from each other in the most extreme ways: there is no other period in the history of music in which such different styles can be found, styles such as the “Total Serialism” of Pierre Boulez and the “New Simplicity” of Arvo Pärt, the latter shown in Example no.1 as follows.
Example no.1 “Aliinal – For Alina” for piano, bars 1-5, Arvo Pärt (1976)
Look at Example no.1, compare it with works by Boulez, and see if this convinces you: is there any period in the history of music wherein one can find two such opposing styles at the same time? Is it possible that the discipline of mathematics, in fact, unifies these two different worlds? And how does all this connect to the rest of zero half-notes in the title of the article?
In order to answer these questions, which touch on the component of time in Arvo Pärt’s “New simplicity”, we need to begin by observing this component as it appears as an expression of “Total Serialism”.
The Component of Time in “Total Serialism”:
“This was the post-Hiroshima period…Something needed to be built on the ashes of the victims of the war of Fascism and Nazism. And we did it” (Luciano Berio)
Background: “The post-Hiroshima period”…”something needed to be built”…these finely distinctive expressions of Berio do not leave room for doubt: Europe, being destroyed (musically and physically) after World War II was looking for a new messiah. The previous messiah had been a disappointment. He had been too emotional, too romantic. He had been too Jewish (Schönberg) or he had been too anti-Semitic (Hitler). He was still working with the older forms of the nineteenth century (such as sonata form; such as genocide). Long live the new messiah (Boulez, the big brother always watching you) who is devoid of feelings. Long live cold intellect! Rows of 12 components in every parameter – finally now there was complete control over the material! Away with Romanticism!
“Total Serialism” was, in effect, the world of music’s first reaction to the trauma that had caused World War II. It is no wonder that “Total Serialism” had grown out of an industrial German town with a significant Nazi past - Darmstadt. From Nuremburg it would have been too much. Berlin was also still being reconstructed from ruins. But Darmstadt? The perfect choice. No one would notice it. The Germans were, allegedly, trying to forget the past (but only allegedly). Complete emotional alienation and total mathematization had led them to the extreme antithesis, to the excessive emotionality of Hitler’s speeches of the 1920’s and 1930’s, to emotionality that had enraptured millions. The war had left European composers in a deep emotional crisis and in the state of searching for a way to express through the medium of music what had befallen them and the world. Theodor Adorno’s well-known aphorism “To write poetry after Auschwitz is barbaric” was still echoing in the ears of the first serialist composers. And the writing of poetry, that is, lyrical and emotional writing, had now become considered as anarchism and a focus of ridicule in the eyes of the cold, anti-Romantic intellectuals, declared by the latter in the 1950’s. The mathematization of every musical parameter – this was the serial message as expressed in an article of Pierre Boulez, whose title is loaded with gun powder “Schönberg is Dead” (resemblance to Nietzsche’s “God is dead” is not coincidental), and was designated to shake up conservative composers, to arouse young people into a kind of rebellion of the kind of “the king is dead; long live the new king” Oh, those Germans! They thought we would not be paying attention. They thought the world would not notice that, seven years after the previous king’s suicide, they had brought to the world a new, totalitarian message in the guise of the escape from the former totalitarianism. “Totalitarian Serialism” – a sobriquet even Boulez himself had blurted out in an unforgettable Freudian slip. And who would be the new leader? Who, if not the French composer himself, the new leader of the rebels. A Frenchman! How convenient! Nobody would notice the watchful eye of the new big brother….
Approach to the Time Component: One of the most complex aspects of “Total Serialism”, perhaps more than in any other 20th century style, is the use of the time component which had given serial composers complete control, mathematically speaking. The tendency of Serialism towards mathematical principles finds its strongest expression here in a musical parameter that is basically mathematical – rhythm. This parameter allows for the discipline of mathematics to work in perfectly, resulting in Rows of 12 durations leading up to the most complex of rhythmic manipulations, more so than the world had seen till then.
One of the first works to present this practice is a work by Olivier Messiaen’s “Mode of Durations and Intensities” for piano, whose tone row is shown in the example below:
Example no.2: the row forming the basis of the work -
Olivier Messiaen, “Mode de valeurs et d’intensités”. (1949)
In the example, it can be seen that each note of the row is a 32th note longer than its previous note, achieving, in this way, 12 durations which Messiaen called “chromatic durations”. In addition, each note in the row is furnished with its own specific dynamic marking, with a total of six dynamic markings (and not twelve, as would be typical of “Total Serialism”). An interesting point to mention is that this tone row also formed the basis for Pierre Boulez’ work “Structures 1” and both these works constituted prototypes for the whole serial style.
From time to time, as has been mentioned, the discipline of mathematics led serial composers to absolute absurdity. Take a look at the following example from Karlheinz Stockhausen’s “Klavierstücke 1”
Example no.3: K.Stockhausen “Klavierstücke 1” (1952) bars 5-6
This example points to complicated rhythmic complexity that is taken to a point of absurdity so achieved through the serial method: as it were, the most complicated calculations are needed in order to understand how 7:8 + 11:12 actually equals 5:4. Mindboggling, indeed! But can one assume that the intention here is that performance should be mathematically accurate? Go off and find a pianist who is capable of making such a complex calculation and accurately! It is absolutely clear who the performer will be: the computer. However, Stockhausen’s intention here is not a precise performance, but, all told, an acceleration written in notes, with the complicated rhythm intended to point out this acceleration without, indeed, supplying us with information as to the precise length of each note. But, lo and behold, the discipline of mathematics controls this acceleration perfectly: when the numbers are organized in order in this table: we get a simple arithmetic series: 4,5,7,8,11,12…and there is absolutely no coincidence in this. Now here we have the next question: what is the next pair of numbers in the series? The answer is at the foot of the page.
Facing an impossible rhythmic complication such as this, we can understand the extreme rhythmic undermining as the basis of Arvo Pärt’s work “For Alina”, shown in Example no.1 above, where there consist merely two rhythmic values throughout, in the form of short as opposed to long – a black circle versus a white circle. Only a composer like Pärt, who had begun his compositional journey as a serialist, walking the rocky road of rhythmic complications such as 7:8 + 11:12 = 5:4, could arrive at the extreme and pure rhythmic simplicity existent in the work “For Alina”.
However, Pärt’s other works from his post-serial period contain a surprising secret. Supposedly, so it seems, there exists in them pure, rhythmic simplicity, almost simplistic in nature. This is the origin of the name attached to this style -“New Simplicity”. However, we will very soon discover that visual appearances and what our ears hear are deceptive here. The “New Simplicity” is, indeed, that which brought the absurdity of the zero half-note rest to the world. In what manner?
The Time Component in the “New Simplicity”
“I am not convinced that there can be progress in the world of art. The progress of advancement is characteristic of science. Art represents a much more complex situation…” (Arvo Pärt)
“There is no progress in art”…. “Progress and advancement are characteristic of science”… In the year 1976, following a crisis in creative activity lasting eight years, during which he was almost not involved in composing, a sharp change of direction took place in the style of the Estonian composer, Arvo Pärt. In that year, the composer, who, till then had been identified with “Total Serialism”, wrote his composition for piano “For Alina”; see Example 1 above. It will be no exaggeration to say that this work was as an atom bomb falling on the world of modern music, which did not know how to comprehend this music, music that aesthetically seemed to be returning back hundreds of years to the Middle Ages. This work issued in Pärt’s later style, the “Tintinnabuli” as he called it, a style belonging to the “New Simplicity” style. The “Tintinnabuli” publicized Pärt’s name widely, he, who till then, had been an almost anonymous composer outside of Estonia, and this is the style still associated with him till today.
In analyzing Pärt’s compositions written in the “Tintinnabuli” style, we have happened upon a sensational discovery, something that is, at first glance, difficult to believe of it: there exists a close and inseparable connection between the “Tintinnabuli” music – which is modal, diatonic, minimal in rhythmic values, mystical, meditational, and sparse in information – and the music of “Total Serialism”, the latter appearing to be the absolute opposite of it – chromatic music, devoid of any tonal center, using the most complex rhythms, placing emphasis on intellectual control, consisting of broken melodic lines to the degree of absolute pointillism and neuroticism laden with information. We are, in fact, talking about two sides of the same issue, that which appears at the beginning of this article – the mathematization of music.
Approach to the Time Component:
Let us observe a work that publicized Pärt in the world of music, winning him great popularity – “Tabula Rasa”- a concerto for two violins, string orchestra and prepared piano (1977). The translation of its Latin title is “blank slate”, referring to the fact that a person is born with no prior knowledge and that he/she is likened to a blank slate onto which he/she will record knowledge. Pärt, himself, presumably felt like a blank slate in his new style, as he endeavored to flee from all he had learned as a serialist, trying to create a new musical language for himself
In the following, we will focus on the time component and on Pärt’s approach to rhythm only, according to how it is revealed in the first movement of the work. The title of the first movement “Ludos” (Game) is an indication of Pärt’s intention: before us we have a mathematical game of algorithms and in musical patterns. The movement is constructed as a theme and variations, its form being A1,A2,A3…and so on to A8 (In due course we will understand why there are, in fact, eight variations.) Each A section is constructed of a number of elements which undergo gradual mathematical changes in each of the ensuing variations according to plans, all of which have been laid down in advance. We will now focus on the opening element, which, in itself, is especially interesting: A bar of rest (bar 2 of the work): the whole of section A opens with a bar of general pause (G.P.) constituting, in fact, a motif of the work. It should be noted that Pärt, in his works, relates to rests as musical material in the full sense of the word. As proof to this: the whole work ends with four bars of general pause, an occurrence devoid of all meaning from the point of view of the musical outcome. (How can these four bars be heard? Is there any difference between four bars of rests at the end of the work and one bar of rest with a fermata?) However, for Pärt the rests and their exact length are of constructional- and mathematical importance and the rests constitute a part of the schematic process based on his writing. And what is this process? The reduction or expansion of each pattern in the work in a totally mathematical manner. An example of the reduction: Pärt reduces the bar of rest throughout the movement by the duration of a half-note each time it appears, as can be seen in the following example:
Example no.4. Arvo Pärt “Tabula Rasa” (1977), analysis of the bars of rest throughout the first movement.
In the example, it can be seen that bar no.2 is a bar of rests, its duration being eight half-notes; bar 11, which opens part A2, has the duration of seven half-notes and, in this manner, bar 25 is a bar of rests of six half-notes, and so on and so forth, till, in the eighth section – A8 – the rest disappears. Is this really so?
In fact, mathematically speaking, we have here a bar worth zero half-notes. The embodiment of the absurd – a bar the length of zero half-notes! However, the discipline of mathematics dictates this unequivocally. We now understand the reason why the work consists of eight variations on the A subject: if there had been more that eight variations, we would reach a bar of rests of minus one half-note (see example)…Is the rest of minus one half-note more absurd than a rest of zero half-notes? Difficult to know. …and the concluding question: what is the calculation that leads to the fact that the bar whose length is zero half-notes is supposed to be bar 202, as can be seen in Example no.4, and the bar whose length is minus a half-note should be bar 247? Once again, our heads indeed reel from such strange deliberations. The answer is at the foot of the page.
An additional aspect constructed totally mathematically, this time based on mathematical expansion, is the first violin’s line in this movement: the melody, on which we will now focus. In the course of the whole movement, this line is constructed according to basic rules that can be formulated as exact mathematical algorithms and one can have the computer draw out from them the “output”, which is the work itself. Following are these basic rules, formulated as algorithms of a computer program:
• The time signature is four quarters and all the notes of the first violin part are quarter notes in value.
• Each phrase will begin with two repeats of the note “A” and will end with three repeats of “A”.
• The phrase is constructed exclusively of steps of seconds in the “A” Aolian mode.
• In each phrase there exists a symmetrical opening equal in its movement in opposite directions from “A” and this opening will increase by one step in each direction in each phrase.
The next example shows the second phrase of the eight, demonstrating these basic rules:
Example no.5 A. Pärt, “Tabula Rasa”, second phrase, bars 12-13, the upper first violin part.
It can be seen that the four basic rules formulated above exist in this example.
Bar 3 of the work, which constitutes the first phrase of eight, is given to being comprehended, in retrospect, as also functioning according to the same four algorithmic basic rules as formulated above. See next example:
Example no.6 Arvo Pärt “Tabula Rasa” first phrase, bar 3, upper first violin
In keeping with the four basic rules of the algorithm, one is led to believe that the four notes existing in Example no.6 actually comprise of two congruent patterns, starting with two “A” pitches and ending with three “A”s, whereby between them there is a symmetrical opening of seconds at an interval of zero second intervals. Zero seconds! This explanation is liable to sound totally absurd (what is an interval of zero seconds?) but in Pärt’s “Tintinnabuli” (as in also in “Total Serialism”, as we have seen above) the total mathematicization of the patterns leads to these kinds of absurdities from time to time. Bars having the duration of zero half-notes…a symmetrical opening of zero second intervals…The questions with which we began the article are very slowly beginning to clarify themselves.
One can extract the continuation of the phrases of the first violin part for the duration of the movement automatically from the principles formulated above. The third phrase will, as expected, have a length of three bars:
Example no.7 A.Pärt “Tabula Rasa” third phrase, bars 24 to 26, first upper violin part.
It can be seen that the number of bars of each phrase will be according to the size of the interval between the basic note to the end of the phrase: for the interval of a second – the phrase will be two bars long (Example no.5 above), for the interval of a third - a phrase the length of three bars (Example no.7 above), and so on. The fourth phrase will lead to the interval of a fourth moving in each direction from the central note, and its length will be, as expected, four bars:
Example no.8 A.Pärt “Tabula Rasa” fourth phrase bars 44-47, first upper violin part.
And so the process continues right through to the eighth (and last) phrase, which will open with the interval of an octave in each direction, and its length will be eight bars:
Example no.9 A.Pärt “Tabula Rasa” eighth phrase, bars 162-169, first upper violin part.
Before us, in which case, we have what is suitably called “Automatic Writing”. This writing derives from “Total Serialism” and, in it, the composer determines only the principles on which it is based, with the music emerging automatically from these principles, as it were, “untouched by human hands” over the course of the process of the work. Like those same stickers on mineral water bottles, “not touched by human hands”, this term became the hallmark of quality of products in the 20th century. In fact, if we were to program into the computer the principles of the basis of the role of the first violin, as formulated above, the computer would produce a score part identical to that of Pärt.
Is this a saving? Or perhaps an advantage? These questions, despite the great interest they are likely to arouse, touch on aesthetic and almost political views, but this is not the place to discuss them (and, perhaps, these questions are outdated, questions that had been discussed time and time again during the 1950’s and 1960’s.)
We have only touched on the tip of the iceberg of an issue that is extremely broad: the time component in both styles, for the sake of appearances, and to what the ear hears, looks different in the extreme, i.e. “Total Serialism” and “New Simplicity”. We have discovered a number of surprising truths regarding the existing connection between the two styles, and, in the process of doing so, we have met with a number of especially strange mathematical-musical mutations: rests of the duration of zero half-notes; rests of minus one half-note; four bars of general pause (G.P.) at the end of a work; complicated rhythmic equations such as: 7:8 + 11:12 = 5:4…. oh my gosh! Is this “music” – the art of the Muses” as referred to in Greek mythology and as the most exalted expression of the human spirit and the direct expression of the “will” according to Schopenhauer?
We have managed to discover that there exists, surprisingly, in Pärt’s “Tintinnabuli” a serial thought process on all levels of the musical language: in the parameter of duration, in the choice of pitches, in the length of phrases, in the development of phrases in the course of the movement, in the use of motifs and also in the formal construction of the movement as a whole – all of these are based on strict, predetermined principles which do not allow for any deviation and which are completely based on “Automatic Writing”. The application of serial principles on all levels of the writing, including the formal construction of the work, actually provided the environment for Pärt’s total emotional separation from the compositional process. In fact, it also led to total alienation from the musical experience as a whole. The discipline of mathematics is that which determines the rules here and not personal aesthetics or the strength of imagination of the artist. We have seen that the work actually evolves from within itself, from beginning to end, after the composer has determined the basic rules, that is, the basic mathematical algorithm. (On the other hand, this algorithm is indeed based on absolutely personal aesthetic choices, and, from here, we observe a huge difference between Pärt and Boulez in the resulting music.)
Why then does Pärt adhere to the principles of Serialism in his later style, a style which is so different from serial music? Could it be that it was a kind of therapy for the composer, who had spent so many years composing in the serial style, a style foreign to him and that did not serve his emotional and aesthetic objectives? Or is it that Pärt perhaps did not manage to sever his ties from the strong – and sometimes destructive – influence which “Total Serialism” and the charismatic figures which led it in those same years had planted (with that same French big brother who was always watching you)?
And what about the questions that were presented at the beginning of this article: what is the meaning of a rest whose duration is zero half-notes? Well, at the end of the day, Boulez and Stockhausen’s serial music, just as Arvo Pärt’s “New Simplicity”, does not sound like mathematical music. Indeed, let us stop for a moment to ask ourselves this question: what does mathematical music sound like? Is it really possible to hear mathematical principles in the music itself? Surely, as was stated at the beginning of this article, these composers had achieved only an illusion of control over the parameters. For music is a cunning art, escaping from the hands of the composer from the moment when he/she completes it; even if it appears to the composer that he/she has succeeded in organizing the elements in perfect, mathematical fashion, it is liable, in the long run, to sound like expressionistic chaos in the hands of Boulez or like meditative music of the Middle Ages in the hands of Pärt. Surprising, is it not?
If so, we now know that both in the very complex use of the parameter of time, as we have met in the music of Stockhausen, and in simple practice bordering on simplicity, as we have met in the music of Pärt (as in the complete movement comprising exclusively of quarter notes) the same mathematical complexity hides behind both, and that both styles are based on formulas and algorithms anchored in “Automatic Writing”….like bottles of mineral water, works written, so to speak, “untouched by human hands”. Technology, mathematics, the will to control…have we already mentioned those?
And still, a number of questions remain unanswered:
How does that same mathematical-musical “baby boom” that erupted after World War II – Total(itarian) Serialism – continue to exert an influence on the world of music of today?
How come Arvo Pärt was the one to succeed in penetrating the barrier of the general public and in bringing his works to large audiences, much more so than Stockhausen and Boulez?
And how, for goodness sake, can one solve the illogical equation, nevertheless stemming from unadulterated and pure logic:
7:8 + 11:12 = 5: 4 ???
 This appears in Naphtali Wagner’s book “Music Then and Now” Tel Aviv, Mappah Publishing, 2004) page 83.
 From the title of an article by Boulez, who lit the fire of Serialism in the World, winning himself the name of the “serial manifesto”. Boulez, Pierre” Schoenberg is Dead” from “Stocktakings from an Apprenticeship”, New York, Oxford University Press, 1991.
 Arvo Pärt (1935- )
 Arvo Pärt “Für Aline” © Copyright 1990 by Universal Edition A.G., Wien/UE 19823
 From an interview with Berio that appears in the book: Ron, Hanoch Schönberg is Dead – The Vanguard of Music, Rise and Fall, His Rise and Fall, Tel Aviv, 2009
 Adorno, Theodor, An Essay on Cultural Criticism and Society page 34 in “Prisms”, translation S. & S. Weber, MIT Press, Boston, 1967
 See on this article and on the rebellion of young people led by Boulez: Hanoch Ron ibid. pages 7-16. On the other hand, a cynical criticism by Maurizio Kagel can also be found in Boulez’ article. “Although Boulez shouted ‘Schönberg is dead’ twenty years ago, he was conducting works by Schönberg twice a week. His utterance was, indeed, of empty words”. Ibid. page 104
 Shaked, Yuval Developing Music, Tel Aviv, Dvir 1992
 Griffiths, Paul Modern Music and After, page 29-30, New York, Oxford University Press, 1995
 For a comparison between the two works and an analysis see: Whittall, Arnold The Cambridge Introduction to Serialism , New York, Oxford University Press, 2008
 Karlheinz Stockhausen (1928-2007)
 Karlheinz Stockhausen Klavierstücke 1-4 für Klavier Nr.2©Copyright 1954 by Universal Edition London (Ltd) London/UE 12251
 This example appears as an instance of the rhythmic complexity to which serial music reached, also in the book: Grant, Morag Josephine, Serial Music, Serial Aesthetics. Cambridge, Cambridge University Press 2001 page 210
 Answer: 16,17. Why? Between each pair of consecutive numbers there is a skip increasing by one (1) each time. 4,5 – skip 2 to 7,8, then skip 3 to 11,12 – and then skip 4 to 16,17.
 Hillier, Paul “Arvo Pärt”, Oxford University Press, New York 1997, page 65
 In contradiction to this simplicity, an opposing movement emerged: the “New Complexity”, of which two of its prominent composers are Michael Finnissy (1946- ) and Brian Fernyhough. (1943- ).
 The expression was implied in Aristotle’s writings and even mentioned in the Ethics of the Fathers: “To what is a child who learns to be compared? To ink written on a fresh sheet; and to what is an old man who learns to be compared? To ink written on an erased sheet.” Ethics of the Fathers, 4,20. But it is most likely that the basis of the expression to which Pärt was referring in this work was taken from the philosopher John Locke.
 Is it so that there is an influence of John Cage here? Does, indeed, the work ‘4.33 use the rest as musical material or, in fact, does the background noise, created as the work is being performed, function as the fundamental musical material?
 All the examples from “Tabula Rasa” are protected by copyright of: Tabula Rasa Doppelkonzert für 2 Violinen, Streichorchester und präpariertes Klavier© Copyright 1980, 2001 by Universal Edition A.G., Wien/UE 31937
 The distance between the bars of rests increases each time by 5 and 4 alternately. For example: between the first two in Example no.4, bars 2 and 11 have a difference of 9. Between the next pair, bars 11 and 25, there is a difference of 14. Between the next bars, bars 25 and 43, there is a difference of 18, and so on. That is to say, the arithmetic series of the differences between each pair of bars is:…9,14,18,23,27,32,36, meaning that each time5 or 4 are added alternately. In this way, one can arrive at the numbers of the imaginary bars, the absurd bars of zero half-notes and minus a half-note: bars 202 and 247.
 This expression is my own and appears in more detail in the thesis on which this article is based: Amit Weiner (2011) “Serial Components in Arvo Pärt’s “New Simplicity”, a thesis accompanying my PhD in Composition, Bar Ilan University.