In music, a dyad (less commonly, diad) is a set of two notes or pitches that, in particular contexts, may imply a chord.
Dyads can be classified by the interval between the notes. For example, the interval between C and E is a major third, which can imply a C major chord, made up of the notes C, E and G. When the pitches of a dyad occur in succession, they form a melodic interval. When they occur simultaneously, they form a harmonic interval.
The harmonic series is built over a fundamental pitch, and the rest of the partials in the series are called overtones. The second partial is an octave above the fundamental and the third pitch is a fifth, so if C is the fundamental pitch the second note is C an octave higher and then the next pitch would be G. The harmonic series has more fifths than just this one, for example the fourth to the sixth, the sixth to the ninth and the seventh to the eleventh partial are all a fifth away from each other, though the latter is of a slightly different size than the former ones.
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In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant.
Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo, chord progression, form, and meter. The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory. While music theory has no axiomatic foundation in modern mathematics, the basis of musical sound can be described mathematically (using acoustics) and exhibits "a remarkable array of number properties".
A chord, in music, is any harmonic set of pitches/frequencies consisting of multiple notes (also called "pitches") that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and other types of broken chords (in which the chord tones are not sounded simultaneously) may also be considered as chords in the right musical context. In tonal Western classical music (music with a tonic key or "home key"), the most frequently encountered chords are triads, so called because they consist of three distinct notes: the root note, and intervals of a third and a fifth above the root note.