Computational Music Analysis

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This e-book offers an in-depth creation and review of present examine in computational track research. Its seventeen chapters, written by means of best researchers, jointly characterize the variety in addition to the technical and philosophical sophistication of the paintings being performed this day during this intensely interdisciplinary box. A large diversity of techniques are provided, applying options originating in disciplines similar to linguistics, details thought, details retrieval, trend attractiveness, desktop studying, topology, algebra and sign processing. some of the tools defined draw on well-established theories in tune conception and research, akin to Forte's pitch-class set concept, Schenkerian research, the equipment of semiotic research built by way of Ruwet and Nattiez, and Lerdahl and Jackendoff's Generative concept of Tonal Music

 

The e-book is split into six elements, protecting methodological concerns, harmonic and pitch-class set research, shape and voice-separation, grammars and hierarchical relief, motivic research and trend discovery and, eventually, class and the invention of certain patterns. 

 

As an in depth and up to date photo of present study in computational tune research, the ebook presents a useful source for researchers, academics and scholars in song thought and research, machine technological know-how, tune info retrieval and similar disciplines. It additionally offers a state of the art reference for practitioners within the song know-how industry.

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1. 1 beneficial properties We define an n-dimensional characteristic vector as a numerical illustration of the notes in a chord of their polyphonic context. n is fixed inside of a studying and alertness version, yet depends upon the utmost variety of voices V the version helps. Pitches are represented as MIDI be aware numbers, pitch periods as semitones, and intervals as entire notes. while utilizing a version designed for V voices, a chord can comprise 1 to V notes. The characteristic vector has 3 elements: 1. note-specific positive factors are various for the person notes within the chord. every one of those will get a default price of −1 for every word the chord is brief of V , that's, for notes c to V − 1, the place c is the variety of notes within the chord (using zero-based indexing); 2. chord-level gains are calculated in line with chord; three. polyphonic embedding positive aspects depend upon the mapping of notes to voices for the chord; each one mapping ends up in a distinct polyphonic embedding. v allow ntv be the chord notice mapped to voice v below the present mapping, nt−1 the former word in v, p(n) a note’s pitch, on(n) its onset time, and off(n) its offset time. for every voice v we calculate v : • the pitch proximity of ntv to nt−1 pitchProx(v) = 1 v )| + 1 ; |p(ntv ) − p(nt−1 (6. 1) v : • the inter-onset time proximity of ntv to nt−1 intOnProx(v) = 1 v )) + 1 ; (on(ntv ) − on(nt−1 v : • the offset-onset time proximity ntv to nt−1 (6. 2) 144 Tillman Weyde and Reinier de Valk offOnProx(v) = ⎧ ⎨ 1 v ))+1 (on(ntv )−off(nt−1 1 ⎩ (on(nv )−off(nv ))−1 t t−1 , v ) ≤ on(nv ) , if off(nt−1 t , v ) > on(nv ) ; if off(nt−1 t (6. three) v ), in • the pitch movements—that is, for every voice v, the adaptation p(ntv ) − p(nt−1 semitones; • the pitch–voice correlation ρ among the chord’s pitch ordering and voice ordering, as measured by means of the Pearson correlation coefficient: ρ pv (C) = ∑ pi vi − c p¯v¯ = s p sv ∑ pi vi − ∑ pi ∑ vi ∑ p2i − (∑ pi )2 ∑ v2i − (∑ vi )2 , (6. four) the place c is the variety of notes within the chord C, pi the pitch of notice i, and vi the voice assigned to notice i. If there's just one be aware, zero is back. the choice to version proximity as 1/distance instead of utilizing distance was once taken in an effort to emphasize changes among smaller distances. the full characteristic vector is defined in desk 6. 1 for the C2C version and in desk 6. 2 for the N2N version. positive aspects marked with an asterisk (*) are assigned a price of −1 for each notice the chord is brief of V . 6. three. 1. 2 Variable Chord Sizes A important challenge within the C2C strategy is that chords are of variable dimension, and traditional neural networks, like so much computer studying algorithms, use fixed-size vectors. We ponder techniques the following for pitch and time proximity: 1) representing every one voice individually, utilizing default values while there are not any notes in a voice; 2) averaging values over notes. technique 1 has the good thing about taking pictures all info within the voice task. in spite of the fact that, while no longer all voices are current, the voice beneficial properties are filled with default values. those values are open air the common diversity of values, yet this knowledge isn't particular to the neural community (or the other vector-based studying procedure used).

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