harmony

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.

Historical rules

Early Western religious music often features parallel perfect intervals; these intervals would preserve the clarity of the original plainsong. These works were created and performed in cathedrals, and made use of the resonant modes of their respective cathedrals to create harmonies. As polyphony developed, however, the use of parallel intervals was slowly replaced by the English style of consonance that used thirds and sixths. The English style was considered to have a sweeter sound, and was better suited to polyphony in that it offered greater linear flexibility in part-writing.

Types

Carl Dahlhaus (1990) distinguishes between coordinate and subordinate harmony. Subordinate harmony is the hierarchical tonality or tonal harmony well known today. Coordinate harmony is the older Medieval and Renaissance tonalité ancienne, "The term is meant to signify that sonorities are linked one after the other without giving rise to the impression of a goal-directed development. A first chord forms a 'progression' with a second chord, and a second with a third. But the former chord progression is independent of the later one and vice versa." Coordinate harmony follows direct (adjacent) relationships rather than indirect as in subordinate. Interval cycles create symmetrical harmonies, which have been extensively used by the composers Alban Berg, George Perle, Arnold Schoenberg, Béla Bartók, and Edgard Varèse's Density 21.5.

Close harmony and open harmony use close position and open position chords, respectively. See: Voicing (music) and Close and open harmony.

Other types of harmony are based upon the intervals of the chords used in that harmony. Most chords in western music are based on "tertian" harmony, or chords built with the interval of thirds. In the chord C Major7, C–E is a major third; E–G is a minor third; and G to B is a major third. Other types of harmony consist of quartal and quintal harmony.

A unison is considered a harmonic interval, just like a fifth or a third, but is unique in that it is two identical notes produced together. The unison, as a component of harmony, is important, especially in orchestration. In pop music, unison singing is usually called doubling, a technique the Beatles used in many of their earlier recordings. As a type of harmony, singing in unison or playing the same notes, often using different musical instruments, at the same time is commonly called monophonic harmonization.

Intervals

An interval is the relationship between two separate musical pitches. For example, in the melody "Twinkle Twinkle Little Star", between the first two notes (the first "twinkle") and the second two notes (the second "twinkle") is the interval of a fifth. What this means is that if the first two notes were the pitch C, the second two notes would be the pitch G—four scale notes, or seven chromatic notes (a perfect fifth), above it.

The following are common intervals:

When tuning notes using an equal temperament, such as the 12-tone equal temperament that has become ubiquitous in Western music, each interval is created using steps of the same size, producing harmonic relations marginally 'out of tune' from pure frequency ratios as explored by the ancient Greeks. 12-tone equal temperament evolved as a compromise from earlier systems where all intervals were calculated relative to a chosen root frequency, such as just intonation and well temperament. In those systems, a major third constructed up from C did not produce the same frequency as a minor third constructed up from D♭. Many keyboard and fretted instruments were constructed with the ability to play, for example, both of G♯ and A♭ without retuning. The notes of these pairs (even those where one lacks an accidental, such as E and F♭) were not the 'same' note in any sense.

Using the diatonic scale, constructing the major and minor keys with each of the 12 notes as the tonic can be achieved using only flats or sharps to spell notes within said key, never both. This is often visualized as traveling around the circle of fifths, with each step only involving a change in one note's accidental. As such, additional accidentals are free to convey more nuanced information in the context of a passage of music and the other notes that make it up. Even when working outside diatonic contexts, it is convention, if possible, to use each letter in the alphabet only once in describing a scale.

A note spelled as F♭ conveys different harmonic information to the reader versus a note spelled as E. In a tuning system where two notes spelled differently are tuned to the same frequency, those notes are said to be enharmonic. Even if identical in isolation, different spellings of enharmonic notes provide meaningful context when reading and analyzing music. For example, even though E and F♭ are enharmonic, the former is considered to be a major third up from C, while F♭ is considered to be a diminished fourth up from C. In the context of a C major tonality, the former is the third of the scale, while the latter could (as one of numerous possible justifications) be serving the harmonic function of the third of a D♭ minor chord, a borrowed chord within the scale.

Chords and tension

In the Western tradition, in music after the seventeenth century, harmony is manipulated using chords, which are combinations of pitch classes. In tertian harmony, so named after the interval of a third, the members of chords are found and named by stacking intervals of the third, starting with the "root", then the "third" above the root, and the "fifth" above the root (which is a third above the third), etc. (Chord members are named after their interval above the root.) Dyads, the simplest chords, contain only two members (see power chords).

A chord with three members is called a triad because it has three members, not because it is necessarily built in thirds (see Quartal and quintal harmony for chords built with other intervals). Depending on the size of the intervals being stacked, different qualities of chords are formed. In popular and jazz harmony, chords are named by their root plus various terms and characters indicating their qualities. To keep the nomenclature as simple as possible, some defaults are accepted (not tabulated here). For example, the chord members C, E, and G, form a C Major triad, called by default simply a C chord. In an A♭ chord (pronounced A-flat), the members are A♭, C, and E♭.

In many types of music, notably baroque, romantic, modern and jazz, chords are often augmented with "tensions". A tension is an additional chord member that creates a relatively dissonant interval in relation to the bass. Following the tertian practice of building chords by stacking thirds, the simplest first tension is added to a triad by stacking, on top of the existing root, third, and fifth, another third above the fifth, adding a new, potentially dissonant member a seventh away from the root (called the "seventh" of the chord) producing a four-note chord called a "seventh chord".

Depending on the widths of the individual thirds stacked to build the chord, the interval between the root and the seventh of the chord may be major, minor, or diminished. (The interval of an augmented seventh reproduces the root, and is therefore left out of the chordal nomenclature.) The nomenclature allows that, by default, "C7" indicates a chord with a root, third, fifth, and seventh spelled C, E, G, and B♭. Other types of seventh chords must be named more explicitly, such as "C Major 7" (spelled C, E, G, B), "C augmented 7" (here the word augmented applies to the fifth, not the seventh, spelled C, E, G♯, B♭), etc. (For a more complete exposition of nomenclature see Chord (music).)

Perception

A number of features contribute to the perception of a chord's harmony.

Tonal fusion

Tonal fusion contributes to the perceived consonance of a chord, describing the degree to which multiple pitches are heard as a single, unitary tone. Chords which have more coinciding partials (frequency components) are perceived as more consonant, such as the octave and perfect fifth. The spectra of these intervals resemble that of a uniform tone. According to this definition, a major triad fuses better than a minor triad and a major-minor seventh chord fuses better than a major-major seventh or minor-minor seventh. These differences may not be readily apparent in tempered contexts but can explain why major triads are generally more prevalent than minor triads and major-minor sevenths are generally more prevalent than other sevenths (in spite of the dissonance of the tritone interval) in mainstream tonal music.

In organ registers, certain harmonic interval combinations and chords are activated by a single key. The sounds produced fuse into one tone with a new timbre. This tonal fusion effect is also used in synthesizers and orchestral arrangements; for instance, in Ravel's Bolero #5 the parallel parts of flutes, horn and celesta resemble the sound of an electric organ.

Roughness

When adjacent harmonics in complex tones interfere with one another, they create the perception of what is known as "beating" or "roughness". These precepts are closely related to the perceived dissonance of chords. To interfere, partials must lie within a critical bandwidth, which is a measure of the ear's ability to separate different frequencies. Critical bandwidth lies between 2 and 3 semitones at high frequencies and becomes larger at lower frequencies. The roughest interval in the chromatic scale is the minor second and its inversion, the major seventh. For typical spectral envelopes in the central range, the second roughest interval is the major second and minor seventh, followed by the tritone, the minor third (major sixth), the major third (minor sixth) and the perfect fourth (fifth).

Familiarity

Familiarity also contributes to the perceived harmony of an interval. Chords that have often been heard in musical contexts tend to sound more consonant. This principle explains the gradual historical increase in harmonic complexity of Western music. For example, around 1600 unprepared seventh chords gradually became familiar and were therefore gradually perceived as more consonant.

Individual characteristics such as age and musical experience also have an effect on harmony perception.

Neural correlates of harmony

The inferior colliculus is a mid-brain structure which is the first site of binaural auditory integration, processing auditory information from the left and right ears. Frequency following responses (FFRs) recorded from the mid-brain exhibit peaks in activity which correspond to the frequency components of a tonal stimulus. The extent to which FFRs accurately represent the harmonic information of a chord is called neural salience, and this value is correlated with behavioral ratings of the perceived pleasantness of chords.

In response to harmonic intervals, cortical activity also distinguishes chords by their consonance, responding more robustly to chords with greater consonance.

Consonance and dissonance in balance

The creation and destruction of harmonic and 'statistical' tensions is essential to the maintenance of compositional drama. Any composition (or improvisation) which remains consistent and 'regular' throughout is, for me, equivalent to watching a movie with only 'good guys' in it, or eating cottage cheese.