相关论文: Modes in modern music from a topological viewpoint

We make some general observations about partial orders on quotient spaces, and explore their use in music theory, in two different contexts. In the first, we show that many of the most familiar chord and scale types in Western music appear…

Musical features and descriptors could be coarsely divided into three levels of complexity. The bottom level contains the basic building blocks of music, e.g., chords, beats and timbre. The middle level contains concepts that emerge from…

This paper focuses on the modeling of musical melodies as networks. Notes of a melody can be treated as nodes of a network. Connections are created whenever notes are played in sequence. We analyze some main tracks coming from different…

The buildup and release of a sense of tension is one of the most essential aspects of the process of listening to music. A veridical computational model of perceived musical tension would be an important ingredient for many music…

Topological features embedded in ancient braiding and knotting arts endow significant impacts on our daily life and even cutting-edge science. Recently, fast growing efforts are invested to the braiding topology of complex Bloch bands in…

Understanding the structural characteristics of harmony is essential for an effective use of music as a communication medium. Of the three expressive axes of music (melody, rhythm, harmony), harmony is the foundation on which the emotional…

Graphs can be leveraged to model polyphonic multitrack symbolic music, where notes, chords and entire sections may be linked at different levels of the musical hierarchy by tonal and rhythmic relationships. Nonetheless, there is a lack of…

Coherence and interestingness are two criteria for evaluating the performance of melody harmonization, which aims to generate a chord progression from a symbolic melody. In this study, we apply the concept of orderless NADE, which takes the…

The notion of a braided chord diagram is introduced and studied. An equivalence relation is given which identifies all braidings of a fixed chord diagram. It is shown that finite-type invariants are stratified by braid index for knots which…

Polyphonic music files were analyzed using the set of symbols that produced the Minimal Entropy Description which we call the Fundamental Scale. This allowed us to create a novel space to represent music pieces by developing: a) a method to…

Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. Although it can be treated purely as an algebraic subject, it is inherently topological in nature: the…

Most work on musical score models (a.k.a. musical language models) for music transcription has focused on describing the local sequential dependence of notes in musical scores and failed to capture their global repetitive structure, which…

One of the most significant attitudinal shifts in the history of music occurred in the Renaissance, when an emerging triadic consciousness moved musicians towards a new scalar formation that placed major thirds on a par with perfect fifths.…

The standard theory of musical scales since antiquity has been based on harmony, rather than melody. While recent analyses provide mixed support for a role of melody as well as harmony, we lack a comparative analysis based on cross-cultural…

Many people enjoy classical symphonic music. Its diverse instrumentation makes for a rich listening experience. This diversity adds to the conductor's expressive freedom to shape the sound according to their imagination. As a result, the…

Music can be represented in multiple forms, such as in the audio form as a recording of a performance, in the symbolic form as a computer readable score, or in the image form as a scan of the sheet music. Music synchronisation provides a…

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…

Musical gestures connect the symbolic layer of the score to the physical layer of sound. I focus here on the mathematical theory of musical gestures, and I propose its generalization to include braids and knots. In this way, it is possible…

Distances on symbolic musical sequences are needed for a variety of applications, from music retrieval to automatic music generation. These musical sequences belong to a given corpus (or style) and it is obvious that a good distance on…

Western music is an innately hierarchical system of interacting levels of structure, from fine-grained melody to high-level form. In order to analyze music compositions holistically and at multiple granularities, we propose a unified,…