Harmony in music is the simultaneous use of different pitches to make chords. Harmonics are wavelengths or frequencies related to one another by simple proportions. The study of harmony involves harmonic progressions and the structural principles that govern them.^[1] Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic line, or the "horizontal" aspect.^[2] Counterpoint and polyphony are thus sometimes distinguished from harmony.

Definitions, origin of term, and history of use

The term harmony derives from the Greek ἁρμονία (harmonía), meaning "joint, agreement, concord",^[3] from the verb ἁρμόζω (harmozo), "to fit together, to join".^[4] 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: a higher and lower note.^[5] Nevertheless, it is unclear whether the simultaneous sounding of notes was part of ancient Greek musical practice; "harmonía" may have merely provided a system of classification of the relationships between different pitches. 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.^[5]

It was not until the publication of Rameau's 'Traité de l'harmonie' in 1722 that any text discussing musical practice made use of the term in the title, though that work is not the earliest record of theoretical discussion of the topic. The underlying principle behind these texts is that harmony sanctions harmoniousness (sounds that 'please') by conforming to certain pre-established compositional principles.^[6]

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).^[6] In the words of Arnold Whitall:

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.

—^[6]

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 (of contrapuntal) 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 (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.

—^[7][8]

Descriptions and definitions of harmony and harmonic practice may show bias towards European (or Western) musical traditions. For example, South Asian art music (Hindustani and Karnatak) 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 (or fourth) that does not alter in pitch throughout the course of a composition.^[9] 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 Rāgas, which combines both melodic and modal considerations and codifications within it.^[10] So although intricate combinations of pitches sounding simultaneously in Indian classical music do occur they are rarely studied as teleological harmonic or contrapuntal progressions, which is the case with notated Western music. This contrasting emphasis (with regard to Indian music in particular) manifests itself to some extent in the different methods of performance adopted: in Indian Music improvisation takes a major role in the structural framework of a piece,^[11] whereas in Western Music improvisation has been uncommon since the end of the 19th century,^[12]. Where it does occur in Western music (or has in the past), the improvisation will either embellish pre-notated music or, if not, draw from musical models that have previously been established in notated compositions, and therefore employ familiar harmonic schemes.^[13]

There is no doubt, nevertheless, that the 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 quite 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.

—^[14]

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 alike of individual pre-constructed works in which pitches (and to some extent rhythms) remained unchanged regardless of the nature of the performance).^[15]

Historical rules

Some traditions of music performance, composition, and theory have specific rules of harmony. These rules are often held to be based on natural properties such as Pythagorean tuning's law whole number ratios ("harmoniousness" being inherent in the ratios either perceptually or in themselves) or harmonics and resonances ("harmoniousness" being inherent in the quality of sound), with the allowable pitches and harmonies gaining their beauty or simplicity from their closeness to those properties. While Pythagorean ratios can provide a rough approximation of perceptual harmonicity, they cannot account for cultural factors.^{[citation needed]}

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. Early music also forbade usage of the tritone, as its dissonance was associated with the devil, and composers often went to considerable lengths, via musica ficta, to avoid using it. In the newer triadic harmonic system, however, the tritone became permissible, as the standardization of functional dissonance made its use in dominant chords desirable.

Although most harmony comes about as a result of two or more notes being sounded simultaneously, it is possible to strongly imply harmony with only one melodic line through the use of arpeggios or hocket. Many pieces from the baroque period for solo string instruments, such as Bach's Sonatas and partitas for solo violin, convey subtle harmony through inference rather than full chordal structures; see below:

Types

Carl Dahlhaus (1990) distinguishes between coordinate and subordinate harmony. Subordinate harmony is the hierarchical tonality or tonal harmony well known today, while 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, such as frequently in the music of Alban Berg, George Perle, Arnold Schoenberg, Béla Bartók, and Edgard Varèse's Density 21.5.

Other types of harmony are based upon the intervals used in constructing the chords used in that harmony. Most chords used in western music are based on "tertial" 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 harmony and quintal harmony.

Intervals

An interval is the relationship between two separate musical pitches. For example, in the melody "Twinkle Twinkle Little Star", the first two notes (the first "twinkle") and the second two notes (the second "twinkle") are at the interval of one 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:

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, with the notes "E" and "G" providing 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:

As can be seen, no note always corresponds to a certain degree of the scale. The "root", or 1st-degree note, can be any of the 12 notes of the scale. All the other notes fall into place. So, when C is the root note, the fourth degree is F. But when D is the root note, the fourth degree is G. So while the note names are intransigent, the intervals are not. In layman's terms: a "fourth" (four-step interval) is always a fourth, no matter what the root note is. The great power of this fact is that any song can be played or sung in any key—it will be the same song, as long as the intervals are kept the same, thus transposing the harmony into the corresponding key.

When the intervals surpass the Octave (12 semitones), these intervals are named as "Extended intervals", which include particularly the 9th, 11th, and 13th Intervals, widely used in Jazz and Blues Music.

Extended Intervals are formed and named as following:

• 2nd Interval + Octave = "Ninth" Interval / 9th
• 4th Interval + Octave = "Eleventh" Interval / 11th
• 6th Interval + Octave = "Thirteenth" Interval / 13th

Apart from this categorization, intervals can also be divided into consonant and dissonant. As explained in the following paragraphs, consonant intervals produce a sensation of relaxation and dissonant intervals a sensation of tension.

The consonant intervals are considered to be the Unison, Octave, Fifth, Fourth and Major and Minor Third. However, harmonically the Fourth interval is considered as a dissonance even though it is the inversion of a Fifth, therefore all the previous intervals are named as Perfect Consonant Intervals while the Fourth is categorized as Imperfect Consonant Interval.

All the other intervals, such as the 7th, 9th, 11th, and 13th are considered Dissonant and require resolution (of the produced tension) and usually preparation (depending on the music style used).

Chords & tensions

In the Western tradition there are certain basic harmonies. A basic chord consists of three notes: the root, the third above the root, and the fifth above the root (which happens to be "the minor third above the third above the root"). So, in a C chord, the notes are C, E, and G. In an A-flat chord, the notes are Ab, C, and Eb. In many types of music, notably baroque and jazz, basic chords are often augmented with "tensions". A tension is a degree of the scale which, in a given key, hits a dissonant interval. The most basic, common example of a tension is a "seventh" (actually a minor, or flat seventh) — so named because it is the seventh degree of the scale in a given key. While the actual degree is a flat seventh, the nomenclature is simply "seventh". So, in a C7 chord, the notes are C, E, G, and Bb. Other common dissonant tensions include ninths, elevenths, and thirteenths. In jazz, chords can become very complex with several tensions.

Typically, a dissonant chord (chord with a tension) will "resolve" to a consonant chord. A good 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 "tension" and "relax" moments. Because of this reason, usually tensions are 'prepared' and then 'resolved'. ^[16]

Preparing a tension means to place a series of consonant chords that lead smoothly to the dissonant chord. In this way the composer ensures to build up the tension of the piece smoothly, without disturbing the listener. Once the piece reaches its sub-climax, the listener needs a moment of relaxation to clear up the tension, which is obtained by playing a consonant chord that resolves the tensions of the previous chords. The clearing of this tension usually sounds pleasant to the listener. ^[16]

Consonance and dissonance in balance

As Frank Zappa explained it, "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."[2] In other words, a composer cannot ensure a listener's liking by using exclusively consonant sounds. However, an excess of tension may disturb the listener. The balance between the two is essential.

Contemporary music has evolved in the way that tensions are less prepared and less structured than in Baroque or Classical periods, thus producing new styles such as Jazz and Blues, where tensions are usually not prepared.

See also

• Barbershop music
• Consonance and dissonance
• Chord (music)
• Chord sequence
• Chromatic chord
• Chromatic mediants
• Counterpoint
• Harmonic series
• Homophony (music)
• Mathematics of musical scales
• Musica universalis
• Peter Westergaard's tonal theory
• Physics of music
• Tonality
• Unified field
• Voice leading

Further reading

• Ebenezer Prout -- Harmony (1889, Revised 1901).
• Persichetti, Vincent (1961). Twentieth-century Harmony: Creative Aspects and Practice. New York: W. W. Norton. ISBN 0-393-09539-8. OCLC 398434.
• Arnold Schoenberg -- Harmonielehre. Universal Edition, 1911. Trans. by Roy Carter as Theory of Harmony. University of California Press, 1978
• Arnold Schoenberg -- Structural Functions of Harmony. Ernest Benn Limited, second (revised) edition, 1969. Ed. Leonard Stein.
• Walter Piston -- Harmony, 1969. ISBN 0-393-95480-3.
• Edward Aldwell & Carl Schachter -- Harmony and Voice Leading, 3rd Edition, 2003. ISBN 0-15-506242-5.
• Copley, R. Evan (1991). Harmony, Baroque to Contemporary, Part One (2nd ed.). Champaign: Stipes Publishing. ISBN 0-87563-373-0.
• Copley, R. Evan (1991). Harmony, Baroque to Contemporary, Part Two (2nd ed.). Champaign: Stipes Publishing. ISBN 0-87563-377-3.
• Kholopov, Yuri, "Harmony. Practical Course". In 2 Vol., Moscow: Kompozitor, 2003. ISBN 5-85285-619-3.

References

Footnotes

1. ^ Dahlhaus, Car. "Harmony", Grove Music Online, ed. L. Macy (accessed 24 February 2007), grovemusic.com (subscription access).
2. ^ Jamini, Deborah (2005). Harmony and Composition: Basics to Intermediate, p.147. ISBN 1412033330.
3. ^ '1. Harmony' The Concise Oxford Dictionary of English Etymology in English Language Reference accessed via Oxford Reference Online (24th February 2007)
4. ^ Harmonia, Henry George Liddell, Robert Scott, "A Greek-English Lexicon", at Perseus
5. ^ ^{a b} Dahlhaus, Carl. "Harmony", Grove Music Online, ed. L. Macy (accessed 24 February 2007), grovemusic.com (subscription access).
6. ^ ^{a b c} Arnold Whittall, "Harmony", The Oxford Companion to Music, ed. Alison Latham, (Oxford University Press, 2002) (accessed via [Oxford Reference Online], 16 November 2007 is gayubview=Main&entry=t114.e3144 )
7. ^ Harmony, §3: Historical development. "Carl Dahlhaus", Grove Music Online, ed. L. Macy (accessed 16 November 2007), grovemusic.com (subscription access).
8. ^ see also Whitall 'Harmony: 4. Practice and Principle', Oxford Companion to Music
9. ^ Regula Qureshi. "India, §I, 2(ii): Music and musicians: Art music", Grove Music Online, ed. L. Macy (accessed 16 November 2007), grovemusic.com (subscription access). and Catherine Schmidt Jones, 'Listening to Indian Classical Music', Connexions, (accessed 16 November 2007) [1]
10. ^ Harold S. Powers/Richard Widdess. "India, §III, 2: Theory and practice of classical music: Rāga", Grove Music Online, ed. L. Macy (accessed 16 November 2007), grovemusic.com (subscription access).
11. ^ Harold S. Powers/Richard Widdess. "India, §III, 3(ii): Theory and practice of classical music: Melodic elaboration", Grove Music Online, ed. L. Macy (accessed 16 November 2007), grovemusic.com (subscription access).
12. ^ Rob C. Wegman. "Improvisation, §II: Western art music", Grove Music Online, ed. L. Macy (accessed 16 November 2007), grovemusic.com (subscription access).
13. ^ Robert D Levin. "Improvisation, §II, 4(i): The Classical period in Western art music: Instrumental music", Grove Music Online, ed. L. Macy (accessed 16 November 2007), grovemusic.com (subscription access).
14. ^ Bruno Nettl. "Improvisation, §I, 2: Concepts and practices: Improvisation in musical cultures", Grove Music Online, ed. L. Macy (accessed 16 November 2007), grovemusic.com (subscription access).
15. ^ see Whitall, 'Harmony'
16. ^ ^{a b} Schejtman, Rod (2008). The Piano Encyclopedia's "Music Fundamentals eBook", p.20-43 (accessed 10 March 2009). PianoEncyclopedia.com

Notations

• Dahlhaus, Carl. Gjerdingen, Robert O. trans. (1990). Studies in the Origin of Harmonic Tonality, p.141. Princeton University Press. ISBN 0-691-09135-8.
• van der Merwe, Peter (1989). Origins of the Popular Style: The Antecedents of Twentieth-Century Popular Music. Oxford: Clarendon Press. ISBN 0-19-316121-4.
• Nettles, Barrie & Graf, Richard (1997). The Chord Scale Theory and Jazz Harmony. Advance Music, ISBN 389221056X

External links

• Chord Geometry - Graphical Analysis of Harmony Tool
• Interactive Lessons about harmonizing melodies and scales using different Musical Styles
• Harmonic Progressions with demos and how to harmonize a melody
• General Principles of Harmony by Alan Belkin
• Morphogenesis of chords and scales Chords and scales classification
• A Beginner's Guide to Modal Harmony
• LucyTuning
• Sonantometry as Natural Harmony Algebra

Categories: Harmony | Greek loanwords

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