Harmony
In music, harmony is the concept of combining different sounds in order to create new, distinct musical ideas. Theories of harmony seek to describe or explain the effects created by distinct pitches or tones coinciding with one another; harmonic objects such as chords, textures and tonalities are identified, defined, and categorized in the development of these theories. Harmony is broadly understood to involve both a "vertical" dimension and a "horizontal" dimension, and often overlaps with related musical concepts such as melody, timbre, and form.
A particular emphasis on harmony is one of the core concepts underlying the theory and practice of Western music. The study of harmony involves the juxtaposition of individual pitches to create chords, and in turn the juxtaposition of chords to create larger chord progressions. The principles of connection that govern these structures have been the subject of centuries worth of theoretical work and vernacular practice alike.
Drawing both from music theoretical traditions and the field of psychoacoustics, its perception in large part consists of recognizing and processing consonance, a concept whose precise definition has varied throughout history, but is often associated with simple mathematical ratios between coincident pitch frequencies. In the physiological approach, consonance is viewed as a continuous variable measuring the human brain's ability to 'decode' aural sensory input. Culturally, consonant pitch relationships are often described as sounding more pleasant, euphonious, and beautiful than dissonant pitch relationships, which can be conversely characterized as unpleasant, discordant, or rough.
In popular and jazz harmony, chords are named by their root plus various terms and characters indicating their qualities. 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. The notion of counterpoint seeks to understand and describe the relationships between melodic lines, often in the context of a polyphonic texture of several simultaneous but independent voices. Therefore, it is sometimes seen as a type of harmonic understanding, and sometimes distinguished from harmony.
Typically, in the classical common practice period, a dissonant chord "resolves" to a consonant chord. Harmonization usually sounds pleasant when there is a balance between consonance and dissonance. This occurs when there is a balance between "tense" and "relaxed" moments. Dissonance is an important part of harmony when it can be resolved and contribute to the composition of music as a whole. A misplayed note or any sound that is judged to detract from the whole composition can be described as disharmonious rather than dissonant.
Etymology and definitions
The term harmony derives from the Greek ἁρμονία harmonia, meaning "joint, agreement, concord", from the verb ἁρμόζω harmozō, " 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. 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 or from the point of view of musical texture and "contrapuntal" ). According to A. Whittall:
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 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:
Descriptions and definitions of harmony and harmonic practice often show bias towards European musical traditions, although many cultures practice vertical harmony. In addition, South Asian art 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 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 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, 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 identifies this clearly:
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 remained unchanged regardless of the nature of the performance.
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.File:Bach cello harmony.JPG|center|thumb|upright=1.8|Example of implied harmonies in J.S. Bach's Cello Suite no. 1 in G, BWV 1007, bars 1–2. or
Types
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 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 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 and the second two notes 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, above it.The following are common intervals:
| Root | Major third | Minor third | Fifth |
| C | E | E | G |
| D | F | F | A |
| D | F | F | A |
| E | G | G | B |
| E | G | G | B |
| F | A | A | C |
| F | A | A | C |
| G | B | B | D |
| A | C | C | E |
| A | C | C | E |
| B | D | D | F |
| B | D | D | F |
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 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 be serving the harmonic function of the third of a D♭ minor chord, a borrowed chord within the scale.
Therefore, the combination of notes with their specific intervals—a chord—creates harmony. For example, in a C chord, there are three notes: C, E, and G. The note C is the root. The notes E and G provide harmony, and in a G7 chord, the root G with each subsequent note provide the harmony.
In the musical scale, there are twelve pitches. Each pitch is referred to as a "degree" of the scale. The names A, B, C, D, E, F, and G are insignificant. The intervals, however, are not. Here is an example:
| 1° | 2° | 3° | 4° | 5° | 6° | 7° | 8° |
| C | D | E | F | G | A | B | C |
| D | E | F | G | A | B | C | D |
As can be seen, no note will always be the same scale degree. The tonic, or first-degree note, can be any of the 12 notes of the chromatic scale. All the other notes fall into place. For example, when C is the tonic, the fourth degree or subdominant is F. When D is the tonic, the fourth degree is G. While the note names remain constant, they may refer to different scale degrees, implying different intervals with respect to the tonic. The great power of this fact is that any musical work can be played or sung in any key. It is the same piece of music, as long as the intervals are the same—thus transposing the melody into the corresponding key. When the intervals surpass the perfect Octave, these intervals are called compound intervals, which include particularly the 9th, 11th, and 13th Intervals—widely used in jazz and blues Music.
Compound Intervals are formed and named as follows:
- 2nd + Octave = 9th
- 3rd + Octave = 10th
- 4th + Octave = 11th
- 5th + Octave = 12th
- 6th + Octave = 13th
- 7th + Octave = 14th
The consonant intervals are considered the perfect unison, octave, fifth, fourth and major and minor third and sixth, and their compound forms. An interval is referred to as "perfect" when the harmonic relationship is found in the natural overtone series. The other basic intervals are called "imperfect" because the harmonic relationships are not found mathematically exact in the overtone series. In classical music the perfect fourth above the bass may be considered dissonant when its function is contrapuntal. Other intervals, the second and the seventh are considered Dissonant and require resolution and usually preparation.
The effect of dissonance is perceived relatively within musical context: for example, a major seventh interval alone may be perceived as dissonant, but the same interval as part of a major seventh chord may sound relatively consonant. A tritone sounds very dissonant alone, but less so within the context of a dominant seventh chord.