Harmony

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This article is about musical harmony and harmonies. For
other uses of the term, see Harmony
(disambiguation).

"Disharmony" redirects here. For the episode of Angel,
see Disharmony
(Angel).

Barbershop quartets, such as this US Navy group,
sing melodies together. The pitches of the four melodies combine to clearly
define a tonal center and imply major and minor chords and seventh
chords.

In music, harmony is
the use of simultaneous pitches (tones, notes), or chords.[1]
The study of harmony involves chords and their construction and chord progressions and
the principles of connection that govern them.[2]
Harmony is often said to refer to the "vertical" aspect of music, as
distinguished from melodic line, or the "horizontal"
aspect.[3]
Counterpoint, which
refers to the interweaving of melodic lines, and polyphony, which refers to the
relationship of separate independent voices, are thus sometimes distinguished
from harmony.

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. Typically, in the classical Common practice
period a dissonant chord (chord with tension) will "resolve" 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.

Contents

1 Etymology and
definitions

2 Historical
rules

3 Types

4 Intervals

5 Chords and
tension

6 Perception of
harmony

7 Consonance and dissonance
in balance

8 See also

9 References

9.1 Footnotes

9.2 Notations

10 External
links

11 Further
reading

[edit]
Etymology and
definitions

The term harmony derives from the Greek ἁρμονία (harmonía), meaning
"joint, agreement, concord",[4]
from the verb ἁρμόζω (harmozo), "to fit together, to join".[5]
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.[6]
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.[6]

Rameau's 'Traité de l'harmonie'
(Treatise on Harmony) from 1722.

It was not until the publication of Rameau's 'Traité de l'harmonie'
(Treatise on Harmony) 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.[7]

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).[7]
In the words of Arnold
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.

—[7]

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.

—[8][9]

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 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
(or fourth) that does not alter in pitch throughout the course of a
composition.[10]
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.[11]

So although intricate combinations of pitches sounding simultaneously do
occur in Indian
classical music, 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,[12]
whereas in Western Music improvisation has been uncommon since the end of the
19th century,.[13]
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.[14]

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.

—[15]

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).[16]

[edit]
Historical rules

Some traditions of Western 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. This model provides that the minor seventh and ninth are not
dissonant (i.e., are consonant). 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 and cello, convey subtle harmony through
inference rather than full chordal structures. These works create a sense of
harmonies by using arpeggiated chords and implied basslines. The implied
basslines are created with low notes of short duration that many listeners
perceive as being the bass note of a chord; (see below):

Example of implied harmonies in J.S. Bach's Cello
Suite no. 1 in G, BWV 1007, bar 1.

[edit]
Types

Close position C major triad.

Open position C major triad.

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, 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).

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
"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 harmony and quintal harmony.

[edit]
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:

Root

Major Third

Minor third

Fifth

C

E

E♭

G

D♭

F

E

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

B

E♭

A

C♯

C

E

B♭

D

D♭

F

B

D♯

D

F♯

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, and in a
G7 (G dominant 7th) chord, the root G with each subsequent note (in this case B,
D and F) 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 always corresponds to a certain degree of the scale.
The "tonic", or 1st-degree note, can be any of the 12 notes (pitch classes) of
the chromatic scale. All the other notes fall into place. So, when C is the
tonic, the fourth degree, subdominant, is F. But when D is the tonic, the fourth
degree is G. So while the note names are intransigent, the intervals are not. In
layman's terms: the subdominant, "fourth" (four-step interval) is always a
fourth, no matter what the tonic 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 melody into the corresponding
key. When the intervals surpass the perfect Octave (12 semitones), these
intervals are named as "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 following:

2nd + Octave = 9th

3rd + octave = 10th

4th + Octave = 11th

5th + octave = 12th

6th + Octave = 13th

7th + octave = 14th

The reason the two numbers don't "add" correctly is that one note is counted
twice. 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. In tonal music, the term consonant also means
"brings resolution" (to some degree at least, whereas dissonance "requires
resolution").

The consonant intervals are considered to be the perfect Unison, Octave, Fifth, Fourth and Major and
Minor Third and sixth, and their compound forms. The Third and sixth are
historically considered Imperfect intervals while the former are considered
Perfect intervals . In classical music the perfect fourth above the bass may be
considered to be dissonant when its function is contrapuntal. Other
intervals, the second and the seventh (and their compound forms) are considered
Dissonant and require
resolution (of the produced tension) and usually preparation (depending on the
music style used).

[edit]
Chords and tension

Main article: Chord (music)

Main article: Consonance and
dissonance

In the Western tradition, in music after the seventeenth century, harmony is
manipulated using chords, which are
combinations of pitch classes. In tertian or tertial 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. (Note that chord members are named after their interval above the
root.) Dyads, the simplest chords,
contain only two members (see power chords).

In heavy metal music, "power chords"- a root,
fifth, and octave- are often performed by electric guitarists, typically with
the guitar plugged into a distortion effect.

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, giving a new, potentially dissonant member the interval of a seventh away
from the root and therefore called the "seventh" of the chord, and 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#, Bb),
etc. (For a more complete exposition of nomenclature see Chord (music).)

Continuing to stack thirds on top of a seventh chord produces extensions, and
brings in the "extended tensions" or "upper tensions" (those more than an octave
above the root when stacked in thirds), the ninths, elevenths, and thirteenths.
This creates the chords named after them. (Note that except for dyads and
triads, tertian chord types are named for the interval of the largest size and
magnitude in use in the stack, not for the number of chord members : thus a
ninth chord has five members, not nine.) Extensions beyond the thirteenth
reproduce existing chord members and are (usually) left out of the nomenclature.
Complex harmonies based on extended chords are
found in abundance in jazz, late-romantic music, modern orchestral works, film
music, etc.

Typically, in the classical Common practice
period a dissonant chord (chord with tension) will "resolve" 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. For this reason, usually tension is
'prepared' and then 'resolved'.[17]

Preparing tension means to place a series of consonant chords that lead
smoothly to the dissonant chord. In this way the composer ensures introducing
tension 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 tension of the
previous chords. The clearing of this tension usually sounds pleasant to the
listener, although this is not always the case in late-nineteenth century music,
such as Tristan und Isolde by Richard Wagner.[17]

[edit]
Perception of
harmony

Harmony is based on consonance, a concept whose definition has changed
various times during the history of Western music. In a psychological approach,
consonance is a continuous variable. Consonance can vary across a wide range. A
chord may sound consonant for various reasons.

One is lack of perceptual roughness. Roughness happens when partials
(frequency components) 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 roughness of two simultaneous harmonic complex tones depends on
the amplitudes of the harmonics and the interval between the tones. 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).

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.

The second reason is perceptual fusion. A chord fuses in perception if its
overall spectrum is similar to a harmonic series. 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 generally more prevalent than other sevenths (in spite of the
dissonance of the tritone interval) in mainstream tonal music. Of course these
comparisons depend on style.

The third reason is familiarity. 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.

Western music is based on major and minor triads. The reason why these chords
are so central is that they are consonant in terms of both fusion and lack of
roughness. they fuse because they include the perfect fourth/fifth interval.
They lack roughness because they lack major and minor second intervals. No other
combination of three tones in the chromatic scale satisfies these criteria.

[edit]
Consonance and
dissonance in balance

Post-nineteenth century music has evolved in the way that tension may be less
often prepared and less formally structured than in Baroque or Classical periods, thus
producing new styles such as post-romantic harmony, impressionism, pantonality,
Jazz and Blues, where dissonance may not be
prepared in the way seen in 'common practice' harmony. In a jazz or blues song,
the tonic chord may be a dominant seventh chord.

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.

—Frank Zappa, "The Real
Frank Zappa Book" page 181, Frank Zappa and Peter Occhiogrosso,
1990

[edit]
See also

Barbershop
music

Consonance and
dissonance

Chord
(music)

Chord sequence

Chromatic chord

Chromatic
mediant

Counterpoint

Harmonic
series

Harmonized scale

Homophony
(music)

List of
musical terminology

Mathematics
of musical scales

Musica
universalis

Peter
Westergaard's tonal theory

Prolongation

Physics of music

Tonality

Unified
field

Voice
leading

[edit]
References

[edit]
Footnotes

^ Malm, William
P. (1996). Music Cultures of the Pacific, the Near East, and Asia,
p.15. ISBN
0-13-182387-6. Third edition. "Homophonic texture...is more common in
Western music, where tunes are often built on chords (harmonies) that move in
progressions. Indeed this harmonic orientation is one of the major differences
between Western and much non-Western music."

^ Dahlhaus,
Car. "Harmony", Grove
Music Online, ed. L. Macy (accessed 24 February 2007), grovemusic.com (subscription access).

^
Jamini, Deborah (2005). Harmony and Composition: Basics to
Intermediate, p.147. ISBN
1-4120-3333-0.

^ '1. Harmony'
The Concise Oxford Dictionary of English Etymology in English Language
Reference accessed via Oxford Reference
Online (24th February 2007)

^ Harmonia, Henry George Liddell, Robert Scott, "A Greek-English
Lexicon", at Perseus

^ a
b
Dahlhaus, Carl. "Harmony", Grove
Music Online, ed. L. Macy (accessed 24 February 2007), grovemusic.com (subscription access).

^ 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 )

^ Harmony, §3:
Historical development. "Carl Dahlhaus", Grove
Music Online, ed. L. Macy (accessed 16 November 2007), grovemusic.com (subscription access).

^ see also
Whitall 'Harmony: 4. Practice and Principle', Oxford Companion to
Music

^ 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]

^ 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).

^ 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).

^ Rob C.
Wegman. "Improvisation, §II: Western art music", Grove
Music Online, ed. L. Macy (accessed 16 November 2007), grovemusic.com (subscription access).

^ 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).

^ 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).

^ see Whitall,
'Harmony'

^ a
b
Schejtman, Rod (2008). The Piano Encyclopedia's "Music Fundamentals
eBook", p.20-43 (accessed 10 March 2009). PianoEncyclopedia.com

[edit]
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
3-89221-056-X

[edit]
External links

Look up harmony in Wiktionary, the free
dictionary.

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

Posts about traditional and jazz harmony

Sonantometry as Natural Harmony Algebra

Chord
Harmonization Tool Online tool that automates chord progression analysis
to identify underlying scales and related chords

[edit]
Further reading

Prout, Ebenezer,
Harmony, its Theory and Practice (1889, revised 1901)

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Retrieved from "http://en.wikipedia.org/wiki/Harmony"

Categories: Harmony | Music
theory | Greek
loanwords | Concepts in
aesthetics

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