In music, harmony considers the process by which the composition of individual sounds, or superpositions of sounds, is analysed by hearing. Usually, this means simultaneously occurring frequencies, pitches, or chords, the study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the aspect of music, as distinguished from melodic line. In popular and jazz harmony, chords are named by their root plus various terms, in many types of music, notably baroque, romantic, modern, and jazz, chords are often augmented with tensions. A tension is an additional member that creates a relatively dissonant interval in relation to the bass. Typically, in the common practice period a dissonant chord resolves to a consonant chord. Harmonization usually sounds pleasant to the ear when there is a balance between the consonant and dissonant sounds, in simple words, that occurs when there is a balance between tense and relaxed moments. The term harmony derives from the Greek ἁρμονία, meaning joint, agreement, concord, from the verb ἁρμόζω, to fit together, the term was often used for the whole field of music, while music referred to the arts in general. In Ancient Greece, the term defined the combination of contrasted elements, in the Middle Ages the term was used to describe two pitches sounding in combination, and in the Renaissance the concept was expanded to denote three pitches sounding together. Aristoxenus wrote a work entitled Harmonika Stoicheia, which is thought the first work in European history written on the subject of harmony, the underlying principle behind these texts is that harmony sanctions harmoniousness by conforming to certain pre-established compositional principles. Current dictionary definitions, while attempting to give concise descriptions, often highlight the ambiguity of the term in modern use, ambiguities tend to arise from either aesthetic considerations or from the point of view of musical texture (distinguishing between harmonic and contrapuntal. The view that modern tonal harmony in Western music began in about 1600 is commonplace in music theory and this is usually accounted for by the replacement of horizontal writing, common in the music of the Renaissance, with a new emphasis on the vertical element of composed music. Modern theorists, however, tend to see this as an unsatisfactory generalisation, as Carl Dahlhaus puts it, It was not that counterpoint was supplanted by harmony but that an older type both of counterpoint and of vertical technique was succeeded by a newer type. And harmony comprises not only the structure of chords but also their movement, like music as a whole, harmony is a process. Descriptions and definitions of harmony and harmonic practice may show bias towards European musical traditions, pitch simultaneity in particular is rarely a major consideration. Nevertheless, emphasis on the precomposed in European art music and the written theory surrounding it shows considerable cultural bias, the conception of musics that live in oral traditions as something composed with the use of improvisatory techniques separates them from the higher-standing works that use notation. Yet the evolution of harmonic practice and language itself, in Western art music, is and was facilitated by this process of prior composition, some traditions of Western music performance, composition, and theory have specific rules of harmony. This model provides that the seventh and ninth are not dissonant
Barbershop quartets, such as this US Navy group, sing 4-part pieces, made up of a melody line (normally the lead) and 3 harmony parts.
Rameau's 'Traité de l'harmonie' (Treatise on Harmony) from 1722.
The harmonious major triad is composed of three tones. Their frequency ratio corresponds approximately 6:5:4. In real performances, however, the third is often larger than 5:4. The ratio 5:4 corresponds to an interval of 386 cents, but an equally tempered major third is 400 cents and a Pythagorean third with a ratio of 81:64 is 408 cents. Measurements of frequencies in good performances confirm that the size of the major third varies across this range and can even lie outside it without sounding out of tune. Thus, there is no simple connection between frequency ratios and harmonic function.