Algorithmic composition

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Algorithmic composition is the technique of using algorithms to create music.

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Algorithms (or, at the very least, formal sets of rules) have been used to compose music for centuries; the procedures used to plot voice-leading in Western counterpoint, for example, can often be reduced to algorithmic determinacy. The term can be used to describe music-generating techniques that run without ongoing human intervention, for example through the introduction of chance procedures. However through live coding and other interactive interfaces, a fully human-centric approach to algorithmic composition is possible. [1]

Some algorithms or data that have no immediate musical relevance are used by composers [2] as creative inspiration for their music. Algorithms such as fractals, L-systems, statistical models, and even arbitrary data (e.g. census figures, GIS coordinates, or magnetic field measurements) have been used as source materials.

Models for algorithmic composition

Compositional algorithms are usually classified by the specific programming techniques they use. The results of the process can then be divided into 1) music composed by computer and 2) music composed with the aid of computer. Music may be considered composed by computer when the algorithm is able to make choices of its own during the creation process.

Another way to sort compositional algorithms is to examine the results of their compositional processes. Algorithms can either 1) provide notational information (sheet music or MIDI) for other instruments or 2) provide an independent way of sound synthesis (playing the composition by itself). There are also algorithms creating both notational data and sound synthesis.

One way to categorize compositional algorithms is by their structure and the way of processing data, as seen in this model of six partly overlapping types: [3]

Translational models

This is an approach to music synthesis that involves "translating" information from an existing non-musical medium into a new sound. The translation can be either rule-based or stochastic. For example, when translating a picture into sound, a JPEG image of a horizontal line may be interpreted in sound as a constant pitch, while an upwards-slanted line may be an ascending scale. Oftentimes, the software seeks to extract concepts or metaphors from the medium, (such as height or sentiment) and apply the extracted information to generate songs using the ways music theory typically represents those concepts. Another example is the translation of text into music, [4] [5] which can approach composition by extracting sentiment (positive or negative) from the text using machine learning methods like sentiment analysis and represents that sentiment in terms of chord quality such as minor (sad) or major (happy) chords in the musical output generated.

Mathematical models

Mathematical models are based on mathematical equations and random events. The most common way to create compositions through mathematics is stochastic processes. In stochastic models a piece of music is composed as a result of non-deterministic methods. The compositional process is only partially controlled by the composer by weighting the possibilities of random events. Prominent examples of stochastic algorithms are Markov chains and various uses of Gaussian distributions. Stochastic algorithms are often used together with other algorithms in various decision-making processes.

Music has also been composed through natural phenomena. These chaotic models create compositions from the harmonic and inharmonic phenomena of nature. For example, since the 1970s fractals have been studied also as models for algorithmic composition.

As an example of deterministic compositions through mathematical models, the On-Line Encyclopedia of Integer Sequences provides an option to play an integer sequence as 12-tone equal temperament music. (It is initially set to convert each integer to a note on an 88-key musical keyboard by computing the integer modulo 88, at a steady rhythm. Thus 123456, the natural numbers, equals half of a chromatic scale.) As another example, the all-interval series has been used for computer-aided composition. [6]

Knowledge-based systems

One way to create compositions is to isolate the aesthetic code of a certain musical genre and use this code to create new similar compositions. Knowledge-based systems are based on a pre-made set of arguments that can be used to compose new works of the same style or genre. Usually this is accomplished by a set of tests or rules requiring fulfillment for the composition to be complete. [7]

Grammars

Music can also be examined as a language with a distinctive grammar set. Compositions are created by first constructing a musical grammar, which is then used to create comprehensible musical pieces. Grammars often include rules for macro-level composing, for instance harmonies and rhythm, rather than single notes.

Optimization approaches

When generating well defined styles, music can be seen as a combinatorial optimization problem, whereby the aim is to find the right combination of notes such that the objective function is minimized. This objective function typically contains rules of a particular style, but could be learned using machine learning methods such as Markov models. [8] Researchers have generated music using a myriad of different optimization methods, including integer programming, [9] variable neighbourhood search, [10] and evolutionary methods as mentioned in the next subsection.

Evolutionary methods

Evolutionary methods of composing music are based on genetic algorithms. [11] The composition is being built by the means of evolutionary process. Through mutation and natural selection, different solutions evolve towards a suitable musical piece. Iterative action of the algorithm cuts out bad solutions and creates new ones from those surviving the process. The results of the process are supervised by the critic, a vital part of the algorithm controlling the quality of created compositions.

Evo-Devo approach

Evolutionary methods, combined with developmental processes, constitute the evo-devo approach for generation and optimization of complex structures. These methods have also been applied to music composition, where the musical structure is obtained by an iterative process that transform a very simple composition (made of a few notes) into a complex fully-fledged piece (be it a score, or a MIDI file). [12] [13]

Systems that learn

Learning systems are programs that have no given knowledge of the genre of music they are working with. Instead, they collect the learning material by themselves from the example material supplied by the user or programmer. The material is then processed into a piece of music similar to the example material. This method of algorithmic composition is strongly linked to algorithmic modeling of style, [14] machine improvisation, and such studies as cognitive science and the study of neural networks. Assayag and Dubnov [15] proposed a variable length Markov model to learn motif and phrase continuations of different length. Marchini and Purwins [16] presented a system that learns the structure of an audio recording of a rhythmical percussion fragment using unsupervised clustering and variable length Markov chains and that synthesizes musical variations from it.

Hybrid systems

Programs based on a single algorithmic model rarely succeed in creating aesthetically satisfying results. For that reason algorithms of different type are often used together to combine the strengths and diminish the weaknesses of these algorithms. Creating hybrid systems for music composition has opened up the field of algorithmic composition and created also many brand new ways to construct compositions algorithmically. The only major problem with hybrid systems is their growing complexity and the need of resources to combine and test these algorithms. [17]

Another approach, which can be called computer-assisted composition, is to algorithmically create certain structures for finally "hand-made" compositions. As early as in the 1960s, Gottfried Michael Koenig developed computer programs Project 1 and Project 2 for aleatoric music, the output of which was sensibly structured "manually" by means of performance instructions. In the 2000s, Andranik Tangian developed a computer algorithm to determine the time event structures for rhythmic canons and rhythmic fugues, [18] [19] which were then worked out into harmonic compositions Eine kleine Mathmusik I and Eine kleine Mathmusik II; for scores and recordings see. [20]

See also

Related Research Articles

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<span class="mw-page-title-main">Markov chain</span> Random process independent of past history

A Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). Markov processes are named in honor of the Russian mathematician Andrey Markov.

A hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent Markov process. An HMM requires that there be an observable process whose outcomes depend on the outcomes of in a known way. Since cannot be observed directly, the goal is to learn about state of by observing . By definition of being a Markov model, an HMM has an additional requirement that the outcome of at time must be "influenced" exclusively by the outcome of at and that the outcomes of and at must be conditionally independent of at given at time . Estimation of the parameters in an HMM can be performed using maximum likelihood estimation. For linear chain HMMs, the Baum–Welch algorithm can be used to estimate parameters.

In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it – that is, the Markov chain's equilibrium distribution matches the target distribution. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution.

Stochastic is the property of being well-described by a random probability distribution. Stochasticity and randomness are distinct, in that the former refers to a modeling approach and the latter refers to phenomena; these terms are often used synonymously. In probability theory, the formal concept of a stochastic process is also referred to as a random process.

The notion of musical similarity is particularly complex because there are numerous dimensions of similarity. If similarity takes place between different fragments from one musical piece, a musical similarity implies a repetition of the first occurring fragment. As well, eventually, the similarity does not occur by direct repetition, but by presenting in two set of relations, some common values or patterns. Objective musical similarity can be based on musical features such as:

Generative music is a term popularized by Brian Eno to describe music that is ever-different and changing, and that is created by a system.

Markov decision process (MDP), also called a stochastic dynamic program or stochastic control problem, is a model for sequential decision making when outcomes are uncertain.

Texture synthesis is the process of algorithmically constructing a large digital image from a small digital sample image by taking advantage of its structural content. It is an object of research in computer graphics and is used in many fields, amongst others digital image editing, 3D computer graphics and post-production of films.

A stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities.

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<span class="mw-page-title-main">Computational creativity</span> Multidisciplinary endeavour

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In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it. Generally, this assumption enables reasoning and computation with the model that would otherwise be intractable. For this reason, in the fields of predictive modelling and probabilistic forecasting, it is desirable for a given model to exhibit the Markov property.

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<span class="mw-page-title-main">Musical phrasing</span> Expressive shaping of note sequences

Musical phrasing is the method by which a musician shapes a sequence of notes in a passage of music to allow expression, much like when speaking English a phrase may be written identically but may be spoken differently, and is named for the interpretation of small units of time known as phrases. A musician accomplishes this by interpreting the music—from memory or sheet music—by altering tone, tempo, dynamics, articulation, inflection, and other characteristics. Phrasing can emphasise a concept in the music or a message in the lyrics, or it can digress from the composer's intention, aspects of which are commonly indicated in musical notation called phrase marks or phrase markings. For example, accelerating the tempo or prolonging a note may add tension.

A phrase is a substantial musical thought, which ends with a musical punctuation called a cadence. Phrases are created in music through an interaction of melody, harmony, and rhythm.

Stochastic chains with memory of variable length are a family of stochastic chains of finite order in a finite alphabet, such as, for every time pass, only one finite suffix of the past, called context, is necessary to predict the next symbol. These models were introduced in the information theory literature by Jorma Rissanen in 1983, as a universal tool to data compression, but recently have been used to model data in different areas such as biology, linguistics and music.

<span class="mw-page-title-main">Andranik Tangian</span> Soviet-German polymath (born 1952)

Andranik Semovich Tangian (Melik-Tangyan) ; born March 29, 1952) is a Soviet Armenian-German mathematician, political economist and music theorist. He is professor of the Institute for Economics (ECON) of the Karlsruhe Institute of Technology.

<span class="mw-page-title-main">Shlomo Dubnov</span> Musician

Shlomo Dubnov is an American-Israeli computer music researcher and composer. He is a professor in the Music Department and Affiliate Professor in Computer Science and Engineering and a founding faculty of the Halıcıoğlu Data Science Institute in the University of California, San Diego, where he has been since 2003. He is the Director of the Center for Research in Entertainment and Learning (CREL) at UC San Diego's Qualcomm Institute.

References

  1. ↑ The Oxford Handbook of Algorithmic Music. Oxford Handbooks. Oxford, New York: Oxford University Press. 2018-02-15. ISBN   9780190226992.
  2. ↑ Jacob, Bruce L. (December 1996). "Algorithmic Composition as a Model of Creativity". Organised Sound . 1 (3): 157–165. doi:10.1017/S1355771896000222. hdl: 1903/7435 . S2CID   15546277.
  3. ↑ Papadopoulos, George; Wiggins, Geraint (1999). "AI Methods for Algorithmic Composition: A Survey, a Critical View and Future Prospects" (PDF). Proceedings from the AISB'99 Symposium on Musical Creativity, Edinburgh, Scotland: 110–117.
  4. ↑ Davis, Hannah (2014). "Generating Music from Literature". Proceedings of the EACL Workshop on Computational Linguistics for Literature: 1–10. arXiv: 1403.2124 . Bibcode:2014arXiv1403.2124D. doi:10.3115/v1/W14-0901. S2CID   9028922.
  5. ↑ "Generating Music from Text".
  6. ↑ Mauricio Toro, Carlos Agon, Camilo Rueda, Gerard Assayag. "GELISP: A Framework to Represent Musical Constraint Satisfaction Problems and Search Strategies." Journal of Theoretical and Applied Information Technology 86 (2). 2016. 327–331.
  7. ↑ Brown, Silas (1997). "Algorithmic Composition and Reductionist Analysis: Can a Machine Compose?". CamNotes. Cambridge University New Music Society. Retrieved 28 October 2016.
  8. ↑ Herremans, D.; Weisser, S.; Sörensen, K.; Conklin, D. (2015). "Generating structured music for bagana using quality metrics based on Markov models" (PDF). Expert Systems with Applications. 42 (21): 7424–7435. doi:10.1016/j.eswa.2015.05.043. hdl: 10067/1274260151162165141 .
  9. ↑ Cunha, Nailson dos Santos; Anand Subramanian; Dorien Herremans (2018). "Generating guitar solos by integer programming" (PDF). Journal of the Operational Research Society . 69 (6): 971–985. doi:10.1080/01605682.2017.1390528. S2CID   51888815.
  10. ↑ Herremans, D.; Sörensen, K. (2013). "Composing fifth species counterpoint music with a variable neighborhood search algorithm" (PDF). Expert Systems with Applications. 40 (16): 6427–6437. doi:10.1016/j.eswa.2013.05.071.
  11. ↑ Charles Fox 2006 Genetic Hierarchical Music Structures (American Association for Artificial Intelligence)
  12. ↑ Ball, Philip (2012). "Algorithmic Rapture". Nature . 188 (7412): 456. doi: 10.1038/488458a .
  13. ↑ Fernandez, JD; Vico, F (2013). "AI Methods in Algorithmic Composition: A Comprehensive Survey". Journal of Artificial Intelligence Research . 48: 513–582. arXiv: 1402.0585 . doi: 10.1613/jair.3908 .
  14. ↑ S. Dubnov, G. Assayag, O. Lartillot, G. Bejerano, "Using Machine-Learning Methods for Musical Style Modeling Archived 2017-08-10 at the Wayback Machine ", IEEE Computers, 36 (10), pp. 73–80, October 2003.
  15. ↑ G. Assayag, S. Dubnov, O. Delerue, "Guessing the Composer's Mind : Applying Universal Prediction to Musical Style", in Proceedings of International Computer Music Conference, Beijing, 1999.
  16. ↑ Marchini, Marco; Purwins, Hendrik (2011). "Unsupervised Analysis and Generation of Audio Percussion Sequences". Exploring Music Contents. Lecture Notes in Computer Science. Vol. 6684. pp. 205–218. doi:10.1007/978-3-642-23126-1_14. ISBN   978-3-642-23125-4.
  17. ↑ Harenberg, Michael (1989). Neue Musik durch neue Technik? : Musikcomputer als qualitative Herausforderung für ein neues Denken in der Musik. Kassel: Bärenreiter. ISBN   3-7618-0941-7. OCLC   21132772.
  18. ↑ Tangian, Andranik (2003). "Constructing rhythmic canons" (PDF). Perspectives of New Music . 41 (2): 64–92. Retrieved January 16, 2021.
  19. ↑ Tangian, Andranik (2010). "Constructing rhythmic fugues (unpublished addendum to Constructing rhythmic canons)". IRCAM, Seminaire MaMuX, 9 February 2002, Mosaïques et pavages dans la musique (PDF). Retrieved January 16, 2021.
  20. ↑ Tangian, Andranik (2002–2003). "Eine kleine Mathmusik I and II". IRCAM, Seminaire MaMuX, 9 February 2002, Mosaïques et pavages dans la musique . Retrieved January 16, 2021.

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