Set theory (music)Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. Other theorists, such as Allen Forte, further developed the theory for analyzing atonal music, drawing on the twelve-tone theory of Milton Babbitt. The concepts of musical set theory are very general and can be applied to tonal and atonal styles in any equal temperament tuning system, and to some extent more generally than that.
Transposition (music)In music, transposition refers to the process or operation of moving a collection of notes (pitches or pitch classes) up or down in pitch by a constant interval. The shifting of a melody, a harmonic progression or an entire musical piece to another key, while maintaining the same tone structure, i.e. the same succession of whole tones and semitones and remaining melodic intervals. For example, one might transpose an entire piece of music into another key.
SerialismIn music, serialism is a method of composition using series of pitches, rhythms, dynamics, timbres or other musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though some of his contemporaries were also working to establish serialism as a form of post-tonal thinking. Twelve-tone technique orders the twelve notes of the chromatic scale, forming a row or series and providing a unifying basis for a composition's melody, harmony, structural progressions, and variations.
Chromatic scaleThe chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the chromatic scale, while other instruments capable of continuously variable pitch, such as the trombone and violin, can also produce microtones, or notes between those available on a piano. Most music uses subsets of the chromatic scale such as diatonic scales.
Quarter toneA quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (orally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, and have 24 different pitches. Quarter tones have their roots in the music of the Middle East and more specifically in Persian traditional music. However, the first evidenced proposal of the equally-tempered quarter tone scale, or 24 equal temperament, was made by 19th-century music theorists Heinrich Richter in 1823 and Mikhail Mishaqa about 1840.
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".
Pitch (music)Pitch is a perceptual property of sounds that allows their ordering on a frequency-related scale, or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre. Pitch may be quantified as a frequency, but pitch is not a purely objective physical property; it is a subjective psychoacoustical attribute of sound.
Accidental (music)In music, an accidental is a note of a pitch (or pitch class) that is not a member of the scale or mode indicated by the most recently applied key signature. In musical notation, the sharp (), flat (), and natural () symbols, among others, mark such notes—and those symbols are also called accidentals. In some kinds of musical style, there are also the half sharp as well as half flat, sometimes also called quarter tone. (See koron.
12 equal temperament12 equal temperament (12-ET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 ( ≈ 1.05946). That resulting smallest interval, the width of an octave, is called a semitone or half step. Twelve-tone equal temperament is the most widespread system in music today. It has been the predominant tuning system of Western music, starting with classical music, since the 18th century, and Europe almost exclusively used approximations of it for millennia before that.
Tone rowIn music, a tone row or note row (Reihe or Tonreihe), also series or set, is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometimes found. Tone rows are the basis of Arnold Schoenberg's twelve-tone technique and most types of serial music. Tone rows were widely used in 20th-century contemporary music, like Dmitri Shostakovich's use of twelve-tone rows, "without dodecaphonic transformations.
AtonalityAtonality in its broadest sense is music that lacks a tonal center, or key. Atonality, in this sense, usually describes compositions written from about the early 20th-century to the present day, where a hierarchy of harmonies focusing on a single, central triad is not used, and the notes of the chromatic scale function independently of one another. More narrowly, the term atonality describes music that does not conform to the system of tonal hierarchies that characterized European classical music between the seventeenth and nineteenth centuries.
TonalityTonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is called the tonic. The root of the tonic chord forms the name given to the key, so in the key of C major, the note C can be both the tonic of the scale and the root of the tonic chord (when it is C–E–G). The tonic can be a different note in the same scale, when the work is said to be in one of the modes of the scale.
C (musical note)C or Do is the first note and semitone of the C major scale, the third note of the A minor scale (the relative minor of C major), and the fourth note (G, A, B, C) of the Guidonian hand, commonly pitched around 261.63 Hz. The actual frequency has depended on historical pitch standards, and for transposing instruments a distinction is made between written and sounding or concert pitch. It has enharmonic equivalents of B and D. In English the term Do is used interchangeably with C only by adherents of fixed Do solfège; in the movable Do system Do refers to the tonic of the prevailing key.
Scale (music)In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale. Often, especially in the context of the common practice period, most or all of the melody and harmony of a musical work is built using the notes of a single scale, which can be conveniently represented on a staff with a standard key signature.
OctaveIn music, an octave (octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems". The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class.
Interval (music)In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord. In Western music, intervals are most commonly differences between notes of a diatonic scale. Intervals between successive notes of a scale are also known as scale steps. The smallest of these intervals is a semitone.
Triad (music)In music, a triad is a set of three notes (or "pitch classes") that can be stacked vertically in thirds. Triads are the most common chords in Western music. When stacked in thirds, notes produce triads. The triad's members, from lowest-pitched tone to highest, are called: the root Note: Inversion does not change the root. (The third or fifth can be the lowest note.
