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Review of Dmitri Tymoczko, A Geometry of Music: Harmony and

Review of Dmitri Tymoczko, A Geometry of Music: Harmony and 2025

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The document discusses the concept of voice leadings as generalized key signatures in Western music theory, particularly focusing on how key signatures can be understood as collections of paths in pitch-class space. It explores the relationship between traditional musical notation and voice leading, presenting a systematic approach to understanding these concepts through mathematical frameworks. The paper outlines three virtues of voice leadings—avoiding voice crossings, maximizing common tones, and minimizing size—and demonstrates methods for finding minimal voice leadings between chords. Additionally, it introduces interscalar path matrices to derive key signatures for both diatonic and acoustic scales, emphasizing their significance in music theory.

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What is the theory of music and harmony?

What is harmony in music theory? Harmony is created with intervals or chords and occurs when two or more notes are played simultaneously or consecutively. In Western music, harmony is shaped by chord systems and how chords sound together within a certain key. Harmony functions vertically as well as horizontally.

What is the theory of singing harmony?

People sing in harmony by picking notes that blend well with the melody, usually following the chords of the song. It takes practice to get a feel for how different notes work together. What are the rules for singing harmony? The basic rule is to choose notes that complement the melody and fit the chord progression.

What is the definition of the musical harmony?

harmony, in music, the sound of two or more notes heard simultaneously.

What is the science of musical harmony?

A particular emphasis on harmony is one of the core concepts underlying the theory and practice of Western music. The study of harmony involves the juxtaposition of individual pitches to create chords, and in turn the juxtaposition of chords to create larger chord progressions.

What is the geometry of music theory?

Four-note chords in geometrical music theory the collections of notes form a tetrahedron, with the colours indicating the spacing between the individual notes in a sequence. In the blue spheres, the notes are clustered; in the warmer colours, they are farther apart.

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What is the principle of harmony in music?

Harmony, in music, consists of multiple notes played at once; this usually involves two or more notes or chords, which is three or more notesoften referred to as a triad. A chord being built of stacked thirds is referred to as a triadic, with a bottom note being the root, a third, and a fifth.

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