Consonance and dissonance in the context of "Barbershop music"

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths which are "pure" or perfect, with ratio ${\displaystyle 3:2}$. This is chosen because it is the next harmonic of a vibrating string, after the octave (which is the ratio ${\displaystyle 2:1}$), and hence is the next most consonant "pure" interval, and the easiest to tune by ear. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is ≈ 702 cents wide.

The system dates back to Ancient Mesopotamia;. (See Music of Mesopotamia § Music theory.) It is named, and has been widely misattributed, to Ancient Greeks, notably Pythagoras (sixth century BC) by modern authors of music theory. Ptolemy, and later Boethius, ascribed the division of the tetrachord by only two intervals, called "semitonium" and "tonus" in Latin (256:243 × 9:8 × 9:8), to Eratosthenes. The so-called "Pythagorean tuning" was used by musicians up to the beginning of the 16th century. "The Pythagorean system would appear to be ideal because of the purity of the fifths, but some consider other intervals, particularly the major third, to be so badly out of tune that major chords [may be considered] a dissonance."

In Western music theory, a chord is a group of notes played together for their harmonic consonance or dissonance. The most basic type of chord is a triad, so called because it consists of three distinct notes: the root note along with intervals of a third and a fifth above the root note. Chords with more than three notes include added tone chords, extended chords and tone clusters, which are used in contemporary classical music, jazz, and other genres.

Chords are the building blocks of harmony and form the harmonic foundation of a piece of music. They provide the harmonic support and coloration that accompany melodies and contribute to the overall sound and mood of a musical composition. The factors, or component notes, of a chord are often sounded simultaneously but can instead be sounded consecutively, as in an arpeggio.

In music, tension is the anticipation music creates in a listener's mind for relaxation or release. For example, tension may be produced through reiteration, increase in dynamic level, gradual motion to a higher or lower pitch, or (partial) syncopations between consonance and dissonance.

Experiments in music perception have explored perceived tension in music, and perceived emotional intensity.

Minimal music (also called minimalism) is a form of art music or other compositional practice that employs limited or minimal musical materials. Prominent features of minimalist music include repetitive patterns or pulses, steady drones, consonant harmony, and reiteration of musical phrases or smaller units. It may include features such as phase shifting, resulting in what is termed phase music, or process techniques that follow strict rules, usually described as process music. The approach is marked by a non-narrative, non-teleological, and non-representational approach, and calls attention to the activity of listening by focusing on the internal processes of the music.

The approach originated on the West Coast of the United States in the late 1950s and early 1960s, particularly around the Bay Area, where La Monte Young, Terry Riley and Steve Reich were studying and living at the time. After the three composers moved to the East Coast, their music became associated with the New York Downtown music scene of the mid-1960s, where it was initially viewed as a form of experimental music called the New York Hypnotic School. In the Western art music tradition, the American composers Moondog, La Monte Young, Terry Riley, Steve Reich and Philip Glass are credited with being among the first to develop compositional techniques that exploit a minimal approach. The movement originally involved dozens of composers, although only five (Young, Riley, Reich, Glass, and later John Adams) emerged to become publicly associated with American minimal music; other lesser known pioneers included Dennis Johnson, Terry Jennings, Richard Maxfield, Pauline Oliveros, Phill Niblock, and James Tenney. In Europe, the music of Louis Andriessen, Karel Goeyvaerts, Michael Nyman, Howard Skempton, Éliane Radigue, Gavin Bryars, Steve Martland, Peter Michael Hamel, Henryk Górecki, Arvo Pärt and John Tavener exhibits minimalist traits.

Resolution in Western tonal music theory is the move of a note or chord from dissonance (an unstable sound) to a consonance (a more final or stable sounding one).

Dissonance, resolution, and suspense can be used to create musical interest. Where a melody or chordal pattern is expected to resolve to a certain note or chord, a different but similarly suitable note can be resolved to instead, creating an interesting and unexpected sound. For example, the deceptive cadence.

A suspended chord (or sus chord) is a musical chord in which the (major or minor) third is omitted and replaced with a perfect fourth or a major second. The lack of a minor or a major third in the chord creates an open sound, while the dissonance between the fourth and fifth or second and root creates tension. When using popular-music symbols, they are indicated by the symbols "sus4" and "sus2". For example, the suspended fourth and second chords built on C (C–E–G), written as C and C, have pitches C–F-G and C–D-G, respectively.

Suspended fourth and second chords can be represented by the integer notation {0, 5, 7} and {0, 2, 7}, respectively.