Se ha denunciado esta presentación.
Utilizamos tu perfil de LinkedIn y tus datos de actividad para personalizar los anuncios y mostrarte publicidad más relevante. Puedes cambiar tus preferencias de publicidad en cualquier momento.

Towards a Computational Model of Melody Identification in Polyphonic Music

159 visualizaciones

Publicado el

Slide de apresentação de artigo da disciplina de Inteligência Artificial sobre modelos de identificação de melodias.
"Towards a Computational Model of Melody Identification in Polyphonic Music"

Publicado en: Datos y análisis
  • You can ask here for a help. They helped me a lot an i`m highly satisfied with quality of work done. I can promise you 100% un-plagiarized text and good experts there. Use with pleasure! ⇒ www.HelpWriting.net ⇐
       Responder 
    ¿Estás seguro?    No
    Tu mensaje aparecerá aquí
  • Sé el primero en recomendar esto

Towards a Computational Model of Melody Identification in Polyphonic Music

  1. 1. Towards a Computational Model of Melody Identification in Polyphonic Music S ren Tjagvad Madsen1 , Gerhard Widmer2 Austrian Research Institute for Artificial Intelligence, Vienna1 ,Department of Computational Perception Johannes Kepler University, Linz2 IJCAI (International Joint Conference on Artificial Intelligence) Ronildo Oliveira da Silva 9 de janeiro de 2017
  2. 2. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion Contents 1 Introduction 2 Complexity and Melody Perception 3 A Computational Model 4 Experiments 5 Discussion So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 2 / 22
  3. 3. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion Introduction 1 Melody is a central dimension in almost all music. 2 It is not easy define the concept of ‘melody’. 3 In a way, which notes constitute the melody is defined by where the listeners perceive the most interesting things to be going on in the music. 4 This paper presents first steps towards a simple, robust computational model of automatic melody note identification. Based on results from musicology and music psychology. 5 We will introduce a simple, straightforward measure of melodic complexity based on entropy, present an algorithm for predicting the most likely melody note at any point in a piece. So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 3 / 22
  4. 4. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion Complexity and Melody Perception The basic motivation for our model of melody identification is the observation, that there seems to be a connection between the complexity of a musical line, and the amount of attention that will be devoted to it on the part of a listener. Show that the complexity or information content of a sequence of notes may be directly related to the degree to which the note sequence is perceived as being part of the melody. measure of complexity based only on note-level entropies; measures based on pattern compression and top-down heuristics derived from music theory. So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 4 / 22
  5. 5. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion A Computational Model The basic idea of the model consists in calculating a series of complexity values locally. Based on these series of local complexity estimates, the melody is then reconstructed note by note by a simple algorithm. The information measures will be calculated from the structural core of music alone: a digital representation of the printed music score like a MIDI (Musical Instrument Digital Interface). So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 5 / 22
  6. 6. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion The Sliding Window The algorithm operates by in turn examining a small subset of the notes in the score. A fixed length window is slid from left to right over the score. 1 offset of first ending note in current window 2 onset of next note after current window So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 6 / 22
  7. 7. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion The Sliding Window From the notes belonging to the same voice (instrument) in the window, we calculate a complexity value. We do that for each voice present in the window. So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 7 / 22
  8. 8. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion Entropy Measures in Musical Dimensions Shannon’s entropy [Shannon, 1948] is a measure of randomness or uncertainty in a signal. If the predictability is high, the entropy is low, and vice versa. uniformity, low prediction no uniformity, high prediction Let X = {x1, x2, ..., xn} p(x) = Pr(X = x) X could for example be the set of MIDI pitch numbers and p(x) would then be the probability (estimated by the frequency) of a certain pitch. So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 8 / 22
  9. 9. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion Entropy Measures in Musical Dimensions Let X = {x1, x2, ..., xn} and p(x) = Pr(X = x) then the entropy H(x) is defined as: H(X) = − x∈X p(x)log2p(x) p(x) would then be the probability (estimated by the frequency) of a certain pitch. So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 9 / 22
  10. 10. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion Entropy Measures in Musical Dimensions We are going to calculate entropy of ’features‘ extracted from the notes in monophonic lines. We will use features related to pitch and duration of the notes. 1 Pitch class (C): count the occurrences of different pitch classes present (the term pitch class is used to refer the ‘name’ of a note); 2 MIDI Interval (I): count the occurrences of each melodic interval present (e.g., minor second up, major third down, . . . ); 3 Note duration (D): count the number of note duration classes present, where note classes are derived by discretisation (a duration is given its own class if it is not within 10% of an existing class). So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 10 / 22
  11. 11. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion Entropy Measures in Musical Dimensions With each measure we extract events from a given sequence of notes, and calculate entropy from the frequencies of these events (HC , HI ,HD ). So far rhythm and pitch are treated separately. We have also included a measure HCID weighting the above three measures: HCID = 1 4 (HC + HI ) + 1 2 HD. Entropy is also defined for a pair of random variables with joint distribution: H(X, Y ) = − x∈X y∈Y p(x, y)log2[p(x, y)] So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 11 / 22
  12. 12. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion An Alternative: Complexity via Compression The entropy function is a purely statistical measure related to the frequency of events. No relationships between events is measured – e.g. the events abcabcabc and abcbcacab will result in the same entropy value. So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 12 / 22
  13. 13. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion Predicting Melody Notes The prediction period. The prediction period pi is thus the interval between the beginning of window wi and the beginning of wi+1. The average complexity value for each voice present in the windows in o(pi ) is calculated. Rank the voices according to their average complexity over o(pi ). Every note in wi gets its melody attribute set to true if it is part of the winning voice, and to false otherwise. So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 13 / 22
  14. 14. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion Predicting Melody Notes So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 14 / 22
  15. 15. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion The Musical Test Corpus The Musical Test Corpus 1 Haydn, F.J.: String quartet No 58 op. 54, No. 2, in C major, 1st movement 2 Mozart, W.A.: Symphony No 40 in G minor (KV 550), 1st movement So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 15 / 22
  16. 16. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion The Musical Test Corpus Annotating Melody Notes So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 16 / 22
  17. 17. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion The Musical Test Corpus Evaluation Method We can now measure how well the predicted notes correspond to the annotated melody in the score. We express this in terms of recall (R) and precision (P) values. Recall is the number of correctly predicted notes (true positives, TP) divided by the total number of notes in the melody. Precision is TP divided by the total number of notes predicted (TP + FP (false positives)). F(R, P) = 1 − 2RP R + P A high rate of correctly predicted notes will result in high values of recall, precision and F − measure (close to 1.0). So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 17 / 22
  18. 18. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion The Musical Test Corpus Results We performed prediction experiments with four different window sizes (1-4 seconds) and with the six different entropy measures. So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 18 / 22
  19. 19. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion The Musical Test Corpus Results So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 19 / 22
  20. 20. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion The Musical Test Corpus Results We can conclude that there is indeed a correlation between melody and complexity in both pieces. The precision value of 0.60 in the best symphony experiment with a resulting F- measure of 0.51 (window size 3 seconds) tells us that 60% of the predicted notes in the symphony are truly melody notes. In the string quartet, the second violin is alternating between a single note and notes from a descending scale, making the voice very attractive (lots of different notes and intervals) while the ‘real melody’ So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 20 / 22
  21. 21. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion Discussion In our opinion, the current results, though based on a rather limited test corpus, indicate that it makes sense to consider musical complexity as an important factor in computational models of melody perception. (MADSEN, 2015) So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 21 / 22
  22. 22. Introduction Complexity and Melody Perception A Computational Model Experiments Discussion Referêcias I MADSEN, G. W. S. T. Towards a Computational Model of Melody Identification in Polyphonic Music. 1st. ed. [S.l.]: IJCAI, 2015. So ren Gerhard Towards a Computational Model of Melody Identification in Polyphonic Music 22 / 22

×