Time Metaphor and Prime Numbers in Anatol Vieru's Symphony No. 5

Abstract

Time Metaphor and Prime Numbers in Anatol Vieru's Symphony No. 5 Livia Teodorescu-Ciocănea (bio) and Joel Crotty (bio) Introduction We argue that Eminescu's poetry has the potential to generate a distinctive musical aesthetics. Anatol Vieru captured this aspect in his Fifth Symphony and directed it towards an original musical poetics rooted in a series of "key words" from Eminescu's poems, such as: moon, horn, longing, death, ever, comfortless, far away. A unique approach to Eminescu's imagery is the association between the idea of the passing of time and the increase of the distance to the mathematical origin of the prime numbers and their multiples. We also suggest that the metaphor of the deepening in time is also mirrored by the generally augmenting gap between two consecutive prime numbers towards infinity.1 Vieru metaphorically expresses this parallel especially in the first part of his Fifth Symphony, based on the poem "Peste vârfuri"2 (… Mai departe, mai departe, Mai încet, tot mai încet, … [Far away and ever [End Page 43] farther, Softer still, its fading breath …]3). In Vieru's The Book of Modes4 the composer provides the analyst with a few ways into understanding the processes behind his Fifth Symphony, with some emphasis on the first part. Brief commentaries on the other parts of the symphony will complete the presentation: folkloric essence (Part II Colinde, colinde5); symbolistic alliterations (Part III Dintre sute de catarge6) and philosophical statement (Part IV Glossa7). This paper focuses mainly on the first part of the Symphony, based on Eminescu's poem Peste vârfuri, which is rich in philosophical ideas about time, space and loneliness. Our study presents synthetically and in an original graphical manner the mathematical underlying network of the first 97 bars of the first part of the Vieru's Symphony No. 5, revealing the superimposed and interconnected layers of events that metaphorically refer to Eminescu's philosophy of time. The analysis takes into account the use of prime numbers in the organization of chords unfolding and further provides brief observations about rhythmic values and macrostructure, which are also in connection with primes. Over the last one hundred years or so, many composers including Bartók, Schoenberg, Messiaen, Stockhausen, Xenakis, Ligeti, Niculescu, Grisey, and Gubaidulina have developed musical organizational methods that have derived from extra-musical realms, like special applications (formal or metaphorical) of mathematical principles8 such as: the use of symmetry, golden ratio, Fibonacci series, calculus of probability and statistics, magic square, set theory, group theory, fractal theory, etc. Common descriptions of their music may include loose references to physics: centricity9 paralleled with gravity (posttonal or modal and spectral music) or non-centricity (atonal), crowded textures or nonthematical surfaces (see Ligeti's micropolyphony in Requiem) associated with mass, energy, tension. Another inspirational source for composers' musical imagination came from acoustics (waves, spectrum, harmonic/inharmonic spectrum, polyspectrum, etc.), resulting in various forms of spectralism10 (Murail, Grisey, Radulescu) or from psychoacoustics (spectral listening, sensory consonance or dissonance).11 Terms derived from quantum mechanics (fusion or fission) are to be found in musicology, like spectral fusion or spectral fission (Sethares, 2005). A number of procedures used in electronics have inspired composers like Reich, Riley, Adams, Penderecki, Ligeti, Saariaho (loops, synchronization/non synchronization, sound/noise continuum, ring modulation, condensation/rarefaction, etc.). [End Page 44] In his Fifth Symphony (written between 1984–85 and premiered in 1986), Anatol Vieru reveals a method of organizing the occurrence of major and minor triads upon algorithms based on the unfolding of prime numbers and their multiples reduced to primes, according to the principle of the Sieve of Eratosthenes (that is a mathematical method of extracting prime numbers from composite numbers and thus eliminating nonprimes).12 In previous of his works such as Clepsidra I (1968–69), Clepsidra II (1970), Sita lui Eratostene (1969), or Symphony No. 2 (1973), he used the Sieve of Eratosthenes principle to control the appearance of certain musical events.13 "Time passing" and its poetical perception is the core of interest for Anatol Vieru in the Fifth Symphony. "Eternity is the ephemeral raised to continuum power"14 wrote Vieru in his...