相关论文: Motivic Rhythms
The harmonic number $H_k=\sum_{j=1}^k1/j(k=1,2,3\cdots)$ play an important role in mathematics. Let $p>3$ be a prime. In this paper, we establish a number of congruences with the form $\sum_{k=1}^{p-1}k^mH_k^n(\mod p^2)$ for…
We present a hybrid neural network and rule-based system that generates pop music. Music produced by pure rule-based systems often sounds mechanical. Music produced by machine learning sounds better, but still lacks hierarchical temporal…
We deal with the fragment of modal logic consisting of implications of formulas built up from the variables and the constant `true' by conjunction and diamonds only. The weaker language allows one to interpret the diamonds as the uniform…
In this article we further the study of the relationship between pure motives and noncommutative motives. Making use of Hochschild homology, we introduce the category NNum(k)_F of noncommutative numerical motives (over a base ring k and…
Using the definition of quasiperiodic function as a motivation, we introduce the idea of quasiperiodic music and detail the composition process of a quasiperiodic music piece, Raindrops in A minor. We also discuss connections between…
Creating a pop song melody according to pre-written lyrics is a typical practice for composers. A computational model of how lyrics are set as melodies is important for automatic composition systems, but an end-to-end lyric-to-melody model…
Much like most of cognition research, music cognition is an interdisciplinary field, which attempts to apply methods of cognitive science (neurological, computational and experimental) to understand the perception and process of composition…
I argue that data becomes temporarily interesting by itself to some self-improving, but computationally limited, subjective observer once he learns to predict or compress the data in a better way, thus making it subjectively simpler and…
In this paper we construct extensions of the Mixed Hodge structure on the fundamental group of a pointed algebraic curve. These extensions correspond to the regulator of certain explicit motivic cohomology cycles in the self product of the…
We introduce the notion of multi-pattern, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach lies in the fact that this offers a way to compose two multi-patterns in order to produce a longer one. This…
The rational points of a smooth curve $X$ over a number field $k$ map to the set of augmentations of the associated motivic algebra. An expectation, related to Kim's conjecture, is that for $X$ hyperbolic, the set of augmentations which…
This article is about discrete periodicities and their combinatorial structure. It describes the unique structure caused by the alteration of a pattern in a repetition. That alteration of a pattern could be "heard" as the disturbance that…
A combination of three or more tones played together is called a chord. In the chromatic scale, chords which are consonant are of particular interest and can be divided into several groups, two main ones being the major and minor chords.…
The term melodic template or skeleton refers to a basic melody which is subject to variation during a music performance. In many oral music tradition, these templates are implicitly passed throughout generations without ever being…
This paper formalises the concept of learning symbolic rules from multisource data in a cardiac monitoring context. Our sources, electrocardiograms and arterial blood pressure measures, describe cardiac behaviours from different viewpoints.…
Two semisimple algebraic groups of the same type are said to be motivic equivalent if the motives of the associated projective homogeneous varieties of the same type are isomorphic. We give general criteria of motivic equivalence in terms…
Every art form ultimately aims to invoke an emotional response over the audience, and music is no different. While the precise perception of music is a highly subjective topic, there is an agreement in the "feeling" of a piece of music in…
This is the text of an introductory lecture delivered at the IHES summer school on motives in July, 2006.
The origins of consonance in human music has long been contested, and today there are three primary hypotheses: aversion to roughness, preference for harmonicity, and learned preferences from cultural exposure. While the evidence is…
We use motivic colimits to construct power operations on the homotopy groups of normed motivic spectra admitting a (normed) map from HF_2. We establish enough of their standard properties to prove that the motivic dual Steenrod algebra is…