ALGORITHMIC COMPOSITION:
For many centuries music composers, mathematicians and philosophers were fascinated by finding mathematical formulas as a method to explain and create music. Algorithmic compositions aroused from our natural need to enhance, facilitate, develop and further understand the process of music creation. It is a vessel that can transfer this process to a different domain, detached from our human physical constrains and limits. To be more precise, algorithmic composition is the application of an algorithm in the process of composing music. The interference of the composer-programmer in the algorithmic model usually stops when he or she determines the characteristics of these instructions and sets the algorithm into action. An algorithm is a group of instruction for solving or testing a specific problem in a finite number of steps. Very often, the development of a musical idea is also a problem looking for a solution. However, algorithmic composition does not provide a complete solution to the composer’s creative problems neither offers him instant creativity. It is rather a set of tools that allows a composer either to work with music starting on a higher level, thus leave ‘less’ important aesthetic decision to be taken by the algorithm (facilitate), or to explore new musical paths and ideas which otherwise would have been inconceivable.
From Pythagoras to Hiller
Probably the first association of music with numbers has been made by Pythagoras, the Greek mathematician. Around the 5th Century BC, he established mathematically the rational of the musical consonance by using the numbers [1.2.3.4] and their ratios. Pythagoras and his followers also believed in a direct relation between the laws of nature and the harmony of sounds as expressed in music. However, Greek music at the time can not be considered as a result of algorithmic composition as it was almost completely improvised [4].
In the period 1300-1450 and with the beginning of Ars Nova in France, composers like Guillaume de Machaut used the isorhythmic technique to compose music - a term refers to the periodic repetition of rhythmic music patterns in 14th- and early 15th-century motets [1].
Number ratios like the Golden Average (1:1.618) were also found in music composition as early as the 14Th century. Guillaume Dufay's (ca. 1400-1474) motet "Nuper rosarum flores”, derived its tempo information from the mathematical proportions of the cathedral in Florence, by applying the Golden mean ratio.
The birth of ‘canonic’ composition in the 15th Century was also an attempt by composers to automatically determine some extra layers of music information in their composition. In canonic composition a composer might write just one voice part and then give specific instructions to the singers to extract the additional voices from it. The word canonic derives from the Ancient Greek word of canon, which means a rule. A rule as such to a singer might be something like, start with this melody an octave lower than the original after 32 beats from the beginning of the music piece [4].
Probably the most famous example of algorithmic composition prior the 20th century was
Mozart’s Musikalisches Würfelspiel (1787). The idea is based on a random selection of pre-written measures of music. Mozart wrote the note measures and the instructions for a dice game. The result of a dice roll is compared with a table of rules in order for a specific measure to be selected. The sequence of measures finally creates a Minuet (A French origin dance) [6]. The following picture is taken from the February’s 1787 Journal des Luxus und der Moden article and describes the rules of the musical dice game. A translation of this article in English can be found in the following Internet address:
http://www.worldvillage.com/jchuang/Music/musdice/musdice
/Rules/journal.html
The 20Th century brought many innovations into algorithmic composition, most of them due to the rapid development of technology and more specifically computers. Amongst the numerous composers that have used Algorithmic composition as a creative tool are Lejaren Hiller and Iannis Xenakis. Lejaren Hiller was the first to use a computer, the Illiac, for algorithmic composition. In collaboration with Leonard Isaacson, he wrote the first computer algorithmic music composition, The Illiac Suite for String Quartet (1956) [9]. The result of the algorithm was transposed into a traditional musical notation to be performed by a string quartet later. The algorithm Hiller used was based on the process of generate-modify-select. The algorithm first generates some raw material; then applies some adjustments based on various functions; and finally selects the best results accordingly to some predetermined rules [8].
L. Hiller in the Experimental Music Studio, Illinois, 1960s
One year earlier, Iannis Xenakis accomplished Metastasis for orchestra (A Greek word describing a replication of a cell/event between one state to another higher state), using stochastic formulas worked out by hand. He later used similar techniques in compositions like Atrees (1962) and Morsima-Amorsima (1962). Many other composers later used algorithmic composition programs or methods to facilitate their music such as Gottfried Michael Koenig and his Project 1 program, Barry Truax and his POD program and Clarence Barlow with the MIDIDESK [9].
METHODS
There are many different methods that can be applied in an Algorithmic composition. We can generalize these methods into, Stochastic, Deterministic, Chaotic and Artificial Intelligence methods. These methods some times interact therefore we could have a method integrating both stochastic and deterministic functions. A further division could be made between algorithms dedicated to sound-synthesis (like Granular synthesis) and algorithms for event-generation (like MIDI). However, this distinction is vague, at least within the electroacoustic music practices.
Stochastic
"Stochastic" is a term comes from mathematics which designates such a process, "in which a sequence of values is drawn from a corresponding sequence of jointly distributed random variables" (Webster's). Xenakis gives his explanation about stochastic processes in his book, Formalized Music. Thought and Mathematics in Composition. “. [A stochastic process is] . . . an asymptotic evolution towards a stable state, towards a kind of goal, of stochos [Greek word of aim / goal], whence comes the adjective "stochastic.” ” [10] In stochastic algorithmic composition, a decision is taken according to the output of random generators. However, much information can be gathered from the output of a random generator in order to make the final music result more meaningful. Stochastic processes work in parallel with probability distribution tables. A probability distribution table determines the occurrence of a random event, by monitoring how many times an event occurred within a specific number range (e.g. the times a random output is between the ranges of 10 to 20). A Markov chain is an example of such a process in which the output event is determined by the state of an event in the immediate past. It is obvious that using stochastic procedures to generate music information, a great importance has to be given in the weighting of the distribution table in order to get interesting results.
Deterministic
An algorithmic composition using deterministic or rule-based procedures does not involve random generation of numbers, but instead uses a set of rules to generate the score or other musical information. Hiller’s The Illiac Suite for a String Quarter is an example of this process. A deterministic algorithm describes a grammar in which the compositional process must follow. A grammar is a term comes from the Linguistic theory which designates a formal system of rules by which a possible sentence of a language is generated [11]. Some other examples of using this process are William’s Shottstaedt automatic species counterpoint program and Kemal’s Ebcioglu CHORAL system, which generates four-part chorales in the style of J.S. Bach following approximately 350 different rules [4].
Chaotic
Chaotic algorithmic composition describes a method fundamentally different than the previously discussed. The core difference is that a chaotic algorithm exhibits non-linearity in oppose to the linear behaviors of the stochastic and deterministic methods. A very small change in the input can result in a large scale unpredictable change in the output. As the name probably suggests, this type of algorithm is connected to the theory of Chaos. Stephen H. Kellert in his book In the Wake of Chaos gives a nice definition about the Chaos Theory. “…the qualitative study of unstable aperiodic behavior in deterministic nonlinear dynamical systems.” [7]. The theory of Chaos states that any system, no matter how complicated, can be modeled by using very simple mathematical equations. Although the word ‘Chaos’ prompts the mind into a kind of absolute disorder in a system, the theory implies the opposite, that there is a hidden order within the system that waits to be found.
One part of the Chaos theory also deals with Fractals. Fractals are also referred to as 1/f noise, widely known as pink noise. In pink noise, as the frequency increases the probability of a given frequency decreases [9]. In addition, the average occurrence of the last 10 events seems to have the same important to the final result as the occurrence of the last 100 events. This memory property makes fractals very attractive to algorithmic music composition, as the result of a fractal algorithm can have a non-linear behavior, but at the same time to be always connected with the initial starting properties. [9]
Artificial Intelligent
Algorithmic composition with AI uses both deterministic and AI algorithms to generate musical information. AI is similar to deterministic systems in respect that both are using a set of predetermined grammar, but AI has the additional ability to learn from the composer - programmer inputs. Examples of such procedures can be found in David Cope's system called Experiments in Musical Intelligence (EMI). This system is based on a large database of musical style descriptions of different compositional approaches, however it is able to update this database or to create additional elements into it by analyzing scores of a specific composer [3]. A recent approach to AI and algorithmic composition comes from genetic programming algorithmic models. These types of algorithms generate both their own musical materials as well as they create their own database and grammar [5]. The composer - programmer defines a set of function for the algorithm and describes the desirable final result. The algorithm then searches for the more suitable function(s) in order to produce a result as similar as possible to the composer’s pre-defined desirable output.
Final words
In my brief research, I have just scratched the surface of such a vast subject. Algorithmic composition is not a single method for composing music, but rather it is a collection of different compositional strategies, each one with different properties The beauty of algorithmic composition is that allows a composer to employ his/hers personalized algorithmic models, based on his/her preferences and current creative needs. It can provide a complete separation between the composer and the compositional process, in case where the composer is not the programmer, thus providing the ability for someone to work faster on a higher level for the development of a musical idea. Genetic programming goes a step forward, by disconnecting the algorithm even by the composition process itself, thus proving an almost autonomous music system. This can serve as a model for the evolution of completely new musical forms, as the interaction of different musical elements within the algorithm can be possible. The simplification of music composition due to such an algorithm would allow more creative people to join the process of making music and the criteria for a good piece of music would be limited to the originality of the idea and not to the technical details behind it. To some extent, this is already happening with today’s music sequencers. Although we have not found a complete algorithmic representation of all music yet, there have been many innovative and radical ideas developed for music composition in the 20th century that are moving towards this direction. In the near future, a more robust compositional algorithmic model might be found that will allow exploring music even further and push our creativity to the limits.
REFERENCES:
[1] The Grove Concise Dictionary of Music edited by Stanley Sadie
© Macmillan Press Ltd., London.
[2] http://ced.appstate.edu/intercollege/3850/studwork
/medieval/guide/comp/guido.htm
[3] Cope, David. New Directions in Music. 4th ed. (Dubuqe, Iowa: W. C. Brown, 1984).
[4] Grout, Donald Jay, and Claude V. Palisca. A History of Western Music. 5th ed.
[5] Horner, A., and D. Goldberg. 1993. "Machine Tongues XVI: Genetic Algorithms and Their Application to FM Matching Synthesis." Computer Music Journal, 17(4):17-29.
[6] http://sunsite.univie.ac.at/Mozart/dice/ - Mozart dice game
[7] Stephen H. Kellert , In the Wake of Chaos
[8] Alpern, Adam. "Techniques for Algorithmic Composition of Music." http://hamp.hampshire.edu/~adaF92/algocomp/algocomp95.html .
[9] Curtis, Roads The Computer Music Tutorial.
[10] Xenakis, Iannis. Formalized Music. Thought and Mathematics in Composition. (Indiana University Press, 1971).
[11] Burns, Kristine, H. "Algorithmic Composition, a Definition." http://music.dartmouth.edu/~wowem/hardware
/algorithmdefinition.html. Florida International University, 1997.
BIBIBLIOGRAPHY:
Composing with genetic algorithms.
http://www.ee.umd.edu/~blj/algorithmic_composition
/icmc.95.html
Genetic algorithms as a method for GS Regulation.
http://www.music.mcgill.ca/~ich/research
/ICMC94_paper.html
Roads, Curtis, The Computer Music Tutorial
Boulanger, Richard, The Csound Book
Dimitris Barnias 2004
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