structural:summarization, information:extraction
Etymology and definitions

The term harmony derives from the Greek ἁρμονία harmonia, meaning "joint, agreement, concord", from the verb ἁρμόζω harmozō, "(Ι) fit together, join". Aristoxenus wrote a work entitled Elements of Harmony, which is thought the first work in European history written on the subject of harmony. In this book, Aristoxenus refers to previous experiments conducted by Pythagoreans to determine the relationship between small integer ratios and consonant notes (e.g., 1:2 describes an octave relationship, which is a doubling of frequency). While identifying as a Pythagorean, Aristoxenus claims that numerical ratios are not the ultimate determinant of harmony; instead, he claims that the listener's ear determines harmony.

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 (for example the view that only pleasing concords may be harmonious) or from the point of view of musical texture (distinguishing between harmonic (simultaneously sounding pitches) and "contrapuntal" (successively sounding tones)). According to A. Whittall:

While the entire history of music theory appears to depend on just such a distinction between harmony and counterpoint, it is no less evident that developments in the nature of musical composition down the centuries have presumed the interdependence – at times amounting to integration, at other times a source of sustained tension – between the vertical and horizontal dimensions of musical space.

The view that modern tonal harmony in Western music began in about 1600 is commonplace in music theory. This is usually accounted for by the replacement of horizontal (or contrapuntal) composition, 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. According to Carl Dahlhaus:

It was not that counterpoint was supplanted by harmony (Bach's tonal counterpoint is surely no less polyphonic than Palestrina's modal writing) but that an older type both of counterpoint and of vertical technique was succeeded by a newer type. And harmony comprises not only the ("vertical") structure of chords but also their ("horizontal") movement. Like music as a whole, harmony is a process.

Descriptions and definitions of harmony and harmonic practice often show bias towards European (or Western) musical traditions, although many cultures practice vertical harmony. In addition, South Asian art music (Hindustani and Carnatic music) is frequently cited as placing little emphasis on what is perceived in western practice as conventional harmony; the underlying harmonic foundation for most South Asian music is the drone, a held open fifth interval (or fourth interval) that does not alter in pitch throughout the course of a composition. Pitch simultaneity in particular is rarely a major consideration. Nevertheless, many other considerations of pitch are relevant to the music, its theory and its structure, such as the complex system of Ragas, which combines both melodic and modal considerations and codifications within it.

So, intricate pitch combinations that sound simultaneously do occur in Indian classical music – but they are rarely studied as teleological harmonic or contrapuntal progressions – as with notated Western music. This contrasting emphasis (with regard to Indian music in particular) manifests itself in the different methods of performance adopted: in Indian Music, improvisation takes a major role in the structural framework of a piece, whereas in Western Music improvisation has been uncommon since the end of the 19th century. Where it does occur in Western music (or has in the past), the improvisation either embellishes pre-notated music or draws from musical models previously established in notated compositions, and therefore uses familiar harmonic schemes.

Emphasis on the precomposed in European art music and the written theory surrounding it shows considerable cultural bias. The Grove Dictionary of Music and Musicians (Oxford University Press) identifies this clearly:

In Western culture the musics that are most dependent on improvisation, such as jazz, have traditionally been regarded as inferior to art music, in which pre-composition is considered paramount. 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, which permitted the study and analysis by theorists and composers of individual pre-constructed works in which pitches (and to some extent rhythms) remained unchanged regardless of the nature of the performance.