Discrete Fourier transform over a ringIn mathematics, the discrete Fourier transform over a ring generalizes the discrete Fourier transform (DFT), of a function whose values are commonly complex numbers, over an arbitrary ring. Let R be any ring, let be an integer, and let be a principal nth root of unity, defined by: The discrete Fourier transform maps an n-tuple of elements of R to another n-tuple of elements of R according to the following formula: By convention, the tuple is said to be in the time domain and the index j is called time.
ChromaticismChromaticism is a compositional technique interspersing the primary diatonic pitches and chords with other pitches of the chromatic scale. In simple terms, within each octave, diatonic music uses only seven different notes, rather than the twelve available on a standard piano keyboard. Music is chromatic when it uses more than just these seven notes. Chromaticism is in contrast or addition to tonality or diatonicism and modality (the major and minor, or "white key", scales).
HarmonyIn music, harmony is the process by which individual sounds are joined or composed into whole units or compositions. More concretely, harmony often refers to the effects created by distinct musical pitches or tones coinciding with one another. These effects are variously identified, defined, and categorized as harmonic objects like chords, textures and tonalities. Harmony is broadly understood to involve both a "vertical" dimension (frequency-space) and a "horizontal" dimension (time-space), and often overlaps with related musical concepts such as melody, timbre, and form.
Music genreA music genre is a conventional category that identifies some pieces of music as belonging to a shared tradition or set of conventions. It is to be distinguished from musical form and musical style, although in practice these terms are sometimes used interchangeably. Music can be divided into genres in varying ways, such as popular music and art music, or religious music and secular music. The artistic nature of music means that these classifications are often subjective and controversial, and some genres may overlap.
Extended chordIn music, extended chords are certain chords (built from thirds) or triads with notes extended, or added, beyond the seventh. Ninth, eleventh, and thirteenth chords are extended chords. The thirteenth is the farthest extension diatonically possible as, by that point, all seven tonal degrees are represented within the chord (the next extension, the fifteenth, is the same as the root of the chord). In practice however, extended chords do not typically use all the chord members; when it is not altered, the fifth is often omitted, as are notes between the seventh and the highest note (i.
Music theoryMusic theory is the study of the practices and possibilities of music. The Oxford Companion to Music describes three interrelated uses of the term "music theory": The first is the "rudiments", that are needed to understand music notation (key signatures, time signatures, and rhythmic notation); the second is learning scholars' views on music from antiquity to the present; the third is a sub-topic of musicology that "seeks to define processes and general principles in music".
Quartal and quintal harmonyIn music, quartal harmony is the building of harmonic structures built from the intervals of the perfect fourth, the augmented fourth and the diminished fourth. For instance, a three-note quartal chord on C can be built by stacking perfect fourths, C–F–B. { \override Score.TimeSignature #'stencil = ##f \relative c' { \clef treble \time 4/4 1 } } Quintal harmony is harmonic structure preferring the perfect fifth, the augmented fifth and the diminished fifth.
Musical instrumentA musical instrument is a device created or adapted to make musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is through purpose that the object becomes a musical instrument. A person who plays a musical instrument is known as an instrumentalist. The history of musical instruments dates to the beginnings of human culture. Early musical instruments may have been used for rituals, such as a horn to signal success on the hunt, or a drum in a religious ceremony.
Musical noteIn music, a note is the representation of a musical sound. Notes can represent the pitch and duration of a sound in musical notation. A note can also represent a pitch class. Notes are the building blocks of much written music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis. The term note can be used in both generic and specific senses: one might say either "the piece 'Happy Birthday to You' begins with two notes having the same pitch", or "the piece begins with two repetitions of the same note".
Music historyMusic history, sometimes called historical musicology, is a highly diverse subfield of the broader discipline of musicology that studies music from a historical point of view. In theory, "music history" could refer to the study of the history of any type or genre of music (e.g., the history of Indian music or the history of rock). In practice, these research topics are often categorized as part of ethnomusicology or cultural studies, whether or not they are ethnographically based.
