text: Connectionist sequence models (e.g., RNNs) applied to musical sequences suffer from two known problems: First, they have strictly "absolute pitch perception". Therefore, they fail to generalize over musical concepts which are commonly perceived in terms of relative distances between pitches (e.g., melodies, scale types, modes, cadences, or chord types). Second, they fall short of capturing the concepts of repetition and musical form. In this paper we introduce the recurrent gated autoencoder (RGAE), a recurrent neural network which learns and operates on interval representations of musical sequences. The relative pitch modeling increases generalization and reduces sparsity in the input data. Furthermore, it can learn sequences of copy-and-shift operations (i.e. chromatically transposed copies of musical fragments)---a promising capability for learning musical repetition structure. We show that the RGAE improves the state of the art for general connectionist sequence models in learning to predict monophonic melodies, and that ensembles of relative and absolute music processing models improve the results appreciably. Furthermore, we show that the relative pitch processing of the RGAE naturally facilitates the learning and the generation of sequences of copy-and-shift operations, wherefore the RGAE greatly outperforms a common absolute pitch recurrent neural network on this task.
  @cite_19: We introduce a method for imposing higher-level structure on generated, polyphonic music. A Convolutional Restricted Boltzmann Machine (C-RBM) as a generative model is combined with gradient des- cent constraint optimisation to provide further control over the genera- tion process. Among other things, this allows for the use of a “template” piece, from which some structural properties can be extracted, and trans- ferred as constraints to the newly generated material. The sampling pro- cess is guided with Simulated Annealing to avoid local optima, and to find solutions that both satisfy the constraints, and are relatively stable with respect to the C-RBM. Results show that with this approach it is possible to control the higher-level self-similarity structure, the meter, and the tonal properties of the resulting musical piece, while preserving its local musical coherence.
  @cite_23: We present GESMI (Generative Electronica Statistical Modeling Instrument), a software system that generates Electronic Dance Music (EDM) using evolutionary methods. While using machine learning, GESMI rests on a corpus analysed and transcribed by domain experts. We describe a method for generating the overall form of a piece and individual parts, including specific patterns sequences, using evolutionary algorithms. Lastly, we describe how the user can use contextually-relevant target features to query the generated database of strong individual patterns. As our main focus is upon artistic results, our methods themselves use an iterative, somewhat evolutionary, design process based upon our reaction to results.
  @cite_2: Chord sequences play a fundamental role in music analysis and generation. This paper considers the task of chord sequence generation for electronic dance music, specifically for pieces in the sub-genre of trance. These pieces contain repetitive harmonic sequences with a specific semiotic structure and coherence. The paper presents a formal representation for the semiotic structure of chord sequences, and describes a method for ranking the instances of a semiotic pattern using a statistical model trained on a corpus. Examples of generated chord sequences for a full trance piece are presented.
  @cite_5: 
  @cite_13: Stylistic composition is a creative musical activity, in which students as well as renowned composers write according to the style of another composer or period. We describe and evaluate two computational models of stylistic composition, called Racchman-Oct2010 (random constrained chain of Markovian nodes, October 2010) and Racchmaninof-Oct2010 (Racchman with inheritance of form). The former is a constrained Markov model, and the latter embeds this model in an analogy based design system. Racchmaninof-Oct2010 applies a pattern discovery algorithm called SIACT and a perceptually validated formula for rating pattern importance, to guide the generation of a new target design from an existing source design. A listening study is reported concerning human judgments of music excerpts that are, to varying degrees, in the style of mazurkas by Frederic Chopin (1810–1849). The listening study acts as an evaluation of the two computational models and a third, benchmark system, called Experiments in Musical Intelligence. Judges’ responses indicate that some aspects of musical style, such as phrasing and rhythm, are being modeled effectively by our algorithms. Judgments are also used to identify areas for future improvements. We discuss the broader implications of this work for the fields of engineering and design, where there is potential to make use of our models of hierarchical repetitive structure.
  @cite_20: 
summary: For structured sequence generation, Markov chains together with pre-defined repetition structure schemes were employed in @cite_13 , where specific methods for handling transitions between repeating segments were proposed; in @cite_5 , where an approach to a controlled creation of variations was introduced; in @cite_2 , where chords were generated, obeying a pre-defined repetition structure. In @cite_19 , a convolutional restricted Boltzmann machine was employed, and different structural properties were imposed using differentiable soft-constraints and gradient descent optimization. A constrained variable neighborhood search to generate polyphonic music obeying a tension profile and the repetition structure from a template piece was proposed in @cite_20 . In @cite_23 , Markov chains and evolutionary algorithms were used to generate repetition structure for Electronic Dance Music.