Related papers: Musical Chords by the Numbers

Harmony in visual compositions is a concept that cannot be defined or easily expressed mathematically, even by humans. The goal of the research described in this paper was to find a numerical representation of artistic compositions with…

The identification of structural differences between a music performance and the score is a challenging yet integral step of audio-to-score alignment, an important subtask of music information retrieval. We present a novel method to detect…

We consider incomplete pairwise comparison matrices and determine exactly when they have a consistent completion and, if not, when they have a nearly consistent completion. We use the maximum 3-cycle product as a measure of inconsistency…

In current applied research the most-used route to an analysis of composition is through log-ratios -- that is, contrasts among log-transformed measurements. Here we argue instead for a more direct approach, using a statistical model for…

Systems such as Microsoft Songsmith automatically assign chords and harmony to a melody by minimizing the dissonance across all chord changes. Although this produces harmonious music, it is not what practicing musicians do. In this paper, I…

We study the convergence of certain subseries of the harmonic series corresponding to increasing sequences of integers whose digits in a certain base are not uniformly distributed. We also discuss the case of irregular sequences, where the…

We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of…

Interpreting experimental data in high school experiments can be a difficult task for students, especially when there is large variation in the data. At the same time, calculating the standard deviation poses a challenge for students. In…

Many music theoretical constructs (such as scale types, modes, cadences, and chord types) are defined in terms of pitch intervals---relative distances between pitches. Therefore, when computer models are employed in music tasks, it can be…

Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…

Chord diagrams are used by guitar players to show where and how to play a chord on the fretboard. They are useful to beginners learning chords or for sharing the hand positions required to play a song.However, the diagrams presented on…

Western tonality provides a hierarchy of stability among melodic scale-degrees, from the maximally stable tonic to unstable chromatic notes. Tonal stability has been linked to emotion, yet systematic investigations of the associations…

A song's backbone is its chord progressions, a series of chords that improve the harmony and add to the overall composition. For individuals ranging from beginners to creative artists, comprehending and implementing music theory grammar for…

While there is no a priori definition of good singing voices, we tend to make consistent evaluations of the quality of singing almost instantaneously. Such an instantaneous evaluation might be based on the sound spectrum that can be…

Audio-to-score alignment is a long-standing challenge in music information retrieval and arguably the most widely applicable alignment task for music research. Alignment algorithms match two versions of a piece of music, and for this to…

Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both…

For the tasks of automatic music emotion recognition, genre recognition, music recommendation it is helpful to be able to extract mode from any section of a musical piece as a perceived amount of major or minor mode (majorness) inside that…

This paper presents an investigation of perceptual similarity between music tracks focusing on each individual instrumental part based on a large-scale listening test towards developing an instrumental-part-based music retrieval. In the…

In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…

Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with…