Music Generation as a Probabilistic FunctionBen WestThe goal of this project was to generate short clips (8-10 notes) of music. Tempo was ignored, as wasthe octave of the note. Rather than using a standard neuronal model, a transition tab le was created andthen used along with a random coefficient to determine the best note to play.JustificationMusic generation is generally considered one of the most "human" traits. Therefore, any model whichattempts to mimic human function should be able to compose music, however this has not been thecase3.The same input (CE) can lead to multiple outputs(CEC, CEB or CEA in this case). Since it's aone-to-many map, it is difficult to determine whethera note is "right" or notStandard models run into many problems,but most of them relate to the fact that "good"music is hard to define objectively. Thisproject attempted to get around this byassuming that the better a phrase is, themore frequently it's used. Therefore, the"reward" to the model is how frequently themodel-generated output is used in humanmusic4.DataFinding good data and parsing it was one of the most difficult parts of this project. Data was retrievedfrom wikifonia.org in the MusicXML format under a creative commons license. This was then parsed asfollows:* Each measure was considered independently* Each note in the measure was recorded as a value 1-12 depending on its pitch* Tab-delimited files were created, each of which contained measures of a certain length* The note was ignored if it was part of a chord* Note length and any rests were ignoredIn total about 35,000 notes were found to be of good quality. The major groups used for tablegeneration were 2,104 two-note phrases, 2,151 three-note phrases, and 2,549 four-note phrases,giving just under 20,000 notes for computation.Table GenerationA method mentioned by (2) was used. A 12x12 table was created, where the (i,j) entry correspondedto the likelihood that note i is followed by note j.This method was further refined in two ways.One way involved creating multi-note keys. This means that the (x1,x2,...,xn) entry corresponds to thelikelihood that phrase (x1,...,xn -1) is followed by note xn.Another method used multi-note phrases for both the key and the value. This means that the([x1,...,xn],[y1,...,ym]) entry corresponds to the likelihood that phrase (x1,...,xn) is followed by phrase(y1,...,ym). Unfortunately, the small input set made using this for high values of n or m impossible(there are 12i possible combinations of notes in a measure i notes long, but there were, for example,only 517 8-note phrases).Music GenerationThe note x at time t was selected as follows: Where R is a random variable, and n is the set of all 12 notes. By changing the value of R a more or lessadventurous piece can be created; the author found best results when R was approximately half ofPr(x(t-1), ni) on average.x(0) was selected by random.A sample piece generated through this method can be found here: http://www.geocities.com/bwsithspawn00/firstgen.midThis was improved on by allowing x to be a phrase, as opposed to a single note. Phrases of lengths 1-4were tested; unfortunately 5+ note measures were so rare that the transition table was sparse to thepoint that most 4 note measures had no following note weights.Sample pieces generated by this method can be found on the web again:Two note phrase table: http://www.geocities.com/bwsithspawn00/gen2metas.midThree note phrase table: http://www.geocities.com/bwsithspawn00/gen3metas.midFour note phrase table: http://www.geocities.com/bwsithspawn00/gen4metas.midThe final variation let both x and n be phrases. Again, data set constraints kept x and n to two noteseach.A sample piece generated through this method can be found here: http://www.geocities.com/bwsithspawn00/gen22.midSuccess?In one word, no. Assuming that some phrases are more aesthetically pleasing than others, thesephrases should appear more frequently4. Therefore, how pleasing a phrase is can be determinedreasonably objectively by measuring how frequently it's used by human composers.For example, the simplest variant used in this project looked only at the previous note to determine thenext note. If this note-by-note process was repeated to create a phrase of eight notes, the success ofthe process is proportional to the number of human composers who used that eight-note phrase.All methods were, at best, equal to randomly selecting notes, with the exception of the phrase x phrasemethod, which gave a 30% improvement to random.AverageNumber ofHuman-generatedphrases foundwith phrase ofa given lengthModel 2 3 4RandomSelection3.03 5.32 2.33Plain Table 3.02 5.25 2.23Four noteindexed table3.04 5.33 1.942x2 phraseindexed andvalued tablen/a n/a 3.01ConclusionsMusic composition is hard, even in the simple constraints considered in this project. In addition,something which may appear obvious upon reflection but was not clear to me at the beginning of thisproject is that a two-note measure is radically different from the first two notes of a four-note measure.This is, presumably, why all the models failed except for the one which looked only at four-notemeasures.I think the phrase-phrase map has promise, and would like to see it applied to a larger data set toconfirm or deny this hypothesis.The transition table may be a naive method of generating music, but it does make music which is notunbearable. In addition, the true benefit of this model may not be in itself but rather in that it cansupport other models in telling them how sucessful their output is. The transition table can be seen as aglorified distance function in this respect.Works Cited1. Chen, C.C.J., and R. Miikkulainen. "Creating melodies with evolving recurrent neural networks."Neural Networks, 2001. Proceedings. IJCNN'01. International Joint Conference on 3 (20 01).2. Mozer, M.C. "Neural network music composition by prediction: Exploring the benefits ofpsychoacoustic constraints and multiscale processing." Musical Networks: Parallel Distributed Perceptionand Performance (1999).3. Papadopoulos, G., and G. Wiggins. "I methods for algorithmic composition: A survey, a critical viewand future prospects." AISB Symposium on Musical Creativity (1999).4. Pearce, M.T., and G. Wiggins. "Towards a framework for the evaluation of machine compositions."Proceedings of the AISB Symposium on Artificial Intelligence and Creativity in the Arts and Sciences(2001): 22-32.5. Todd, P.M. "Frankensteinian Methods for Evolutionary
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