Music theory is the study of how
musicMusic is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
works. It examines the
languageLanguage may refer either to the specifically human capacity for acquiring and using complex systems of communication, or to a specific instance of such a system of complex communication...
and
notationMusic notation or musical notation is any system that represents aurally perceived music, through the use of written symbols.-History:...
of music. It seeks to identify patterns and structures in
composers'A composer is a person who creates music, either by musical notation or oral tradition, for interpretation and performance, or through direct manipulation of sonic material through electronic media...
techniques across or within genres, styles, or historical periods. In a grand sense, music theory distills and analyzes the fundamental parameters or elements of music—
rhythmRhythm may be generally defined as a "movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions." This general meaning of regular recurrence or pattern in time may be applied to a wide variety of cyclical natural phenomena having a periodicity or...
,
harmonyIn music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
(
harmonic functionIn tonal music theory, a diatonic function is the specific, recognized role of each of the 7 notes and their chords in relation to the diatonic key...
),
melodyA melody , also tune, voice, or line, is a linear succession of musical tones which is perceived as a single entity...
,
structureStructure is a fundamental, tangible or intangible notion referring to the recognition, observation, nature, and permanence of patterns and relationships of entities. This notion may itself be an object, such as a built structure, or an attribute, such as the structure of society...
,
formThe term musical form refers to the overall structure or plan of a piece of music, and it describes the layout of a composition as divided into sections...
,
textureIn music, texture is the way the melodic, rhythmic, and harmonic materials are combined in a composition , thus determining the overall quality of sound of a piece...
, etc. Broadly, music theory may include any statement, belief, or conception of or about music. A person who studies these properties is known as a
music theorist. Some have applied
acousticsAcoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
,
human physiologyHuman physiology is the science of the mechanical, physical, bioelectrical, and biochemical functions of humans in good health, their organs, and the cells of which they are composed. Physiology focuses principally at the level of organs and systems...
, and
psychologyPsychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...
to the explanation of how and why music is perceived.
Fundamentals of music
Music has many different fundamentals or elements. These include but are not limited to: pitch, beat or pulse, rhythm, melody, harmony, texture, allocation of voices, timbre or color, expressive qualities (dynamics and articulation), and form or structure. In addition to these "fundamentals" there are other important concepts employed in music both in
WesternWestern culture, sometimes equated with Western civilization or European civilization, refers to cultures of European origin and is used very broadly to refer to a heritage of social norms, ethical values, traditional customs, religious beliefs, political systems, and specific artifacts and...
and non-Western cultures including "Scales and/or Modes" and "Consonance vs. Dissonance."
Pitch
Pitch is a subjective sensation, reflecting generally the lowness (slower wave frequency) or highness (faster wave frequency) of a sound. In a musical context, some people have what is called "perfect pitch" and can assign an isolated tone to its place on a musical scale. Human perception of pitch can be comprehensively fooled to create
auditory illusionAn auditory illusion is an illusion of hearing, the aural equivalent of an optical illusion: the listener hears either sounds which are not present in the stimulus, or "impossible" sounds...
s. Despite these perceptual oddities, perceived pitch is nearly always closely connected with the
fundamental frequencyThe fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the lowest frequency of a periodic waveform. In terms of a superposition of sinusoids The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the...
of a note, with a lesser connection to
sound pressureSound pressure or acoustic pressure is the local pressure deviation from the ambient atmospheric pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water...
level, harmonic content (complexity) of the sound, and to the immediately preceding history of notes heard. In general, the higher the frequency of vibration, the higher the perceived pitch is, and lower the frequency, the lower the pitch. However, even for tones of equal intensity, perceived pitch and measured frequency do not stand in a simple linear relationship.
At and below about 1,000 Hz, the perceived pitch of a tone gets lower as sound pressure increases, but above approximately 2,000 Hz, the pitch increases as the sound gets louder.
In Western music, there have long been several competing pitch standards defining tuning systems. Most made a particular key sonorous, with increasingly remote ones more and more problematic; the underlying problem is related to the physics of vibrations.
In addition, fixing notes to standard frequencies (required for instrument makers) has varied as well. "Concert A" was set at 435 Hz by France in 1859 while in England, concert A varied between 439 and 452 Hz. A frequency of 440 Hz was recommended as the standard in 1939, and in 1955 the
International Organization for StandardizationThe International Organization for Standardization , widely known as ISO, is an international standard-setting body composed of representatives from various national standards organizations. Founded on February 23, 1947, the organization promulgates worldwide proprietary, industrial and commercial...
affirmed the choice. A440 is now widely, though not exclusively, used as the A above
middle CC or Do is the first note of the fixed-Do solfège scale. Its enharmonic is B.-Middle C:Middle C is designated C4 in scientific pitch notation because of the note's position as the fourth C key on a standard 88-key piano keyboard...
.
The difference in frequency between two pitches is called an
intervalIn music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...
. The most basic interval is the
unisonIn music, the word unison can be applied in more than one way. In general terms, it may refer to two notes sounding the same pitch, often but not always at the same time; or to the same musical voice being sounded by several voices or instruments together, either at the same pitch or at a distance...
, which is simply two of the same pitch, followed by the slightly more complex
octaveIn music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
, which indicates either a doubling or halving of the fundamental frequency.
Scales and Modes
Notes can be arranged into different scales and
modesIn the theory of Western music since the ninth century, mode generally refers to a type of scale. This usage, still the most common in recent years, reflects a tradition dating to the middle ages, itself inspired by the theory of ancient Greek music.The word encompasses several additional...
. Western music theory generally divides the octave into a series of 12 notes that might be included in a piece of music. This series of twelve notes is called a
chromatic scaleThe chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...
. In the chromatic scale, the interval between adjacent notes is called a half-step or
semitone. Patterns of half and whole steps (2 half steps, or a
tone) can make up a scale in that
octaveIn music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
. The scales most commonly encountered are the seven toned
majorIn music theory, the major scale or Ionian scale is one of the diatonic scales. It is made up of seven distinct notes, plus an eighth which duplicates the first an octave higher. In solfege these notes correspond to the syllables "Do, Re, Mi, Fa, Sol, La, Ti/Si, ", the "Do" in the parenthesis at...
, the harmonic minor, the melodic minor, and the natural minor. Other examples of scales are the
octatonic scaleAn octatonic scale is any eight-note musical scale. Among the most famous of these is a scale in which the notes ascend in alternating intervals of a whole step and a half step, creating a symmetric scale...
, and the pentatonic or five-toned scale, which is common in but not limited to
folk musicFolk music is an English term encompassing both traditional folk music and contemporary folk music. The term originated in the 19th century. Traditional folk music has been defined in several ways: as music transmitted by mouth, as music of the lower classes, and as music with unknown composers....
. There are scales that do not follow the chromatic 12-note pattern, for example in classical Ottoman, Persian,
IndianThe origins of Indian classical music can be found in the Vedas, which are the oldest scriptures in the Hindu tradition. Indian classical music has also been significantly influenced by, or syncretised with, Indian folk music and Persian music. The Samaveda, one of the four Vedas, describes music...
and Arabic music. Arabic and Persian classical traditions often make use of quarter-tones, half the size of a semitone, as the name suggests.
In music written using the system of major-minor
tonalityTonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840...
, the
key of a piece determines the scale used. (One way of showing how various keys relate to one another may be seen in the
circle of fifthsIn music theory, the circle of fifths shows the relationships among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys...
.) Transposing a piece from C major to D major will make all the notes two semitones (or one full step) higher. Even in modern
equal temperamentAn equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
, changing the key can change the feel of a piece of music, because it changes the relationship of the composition's pitches to the pitch range of the instruments that play the piece. This often affects the music's timbre, as well as having technical implications for the performers. However, performing a piece in one key rather than another may go unrecognized by the casual listener, since changing the key does not change the relationship of the individual pitches to each other.
Consonance and Dissonance
ConsonanceIn music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
can be roughly defined as harmonies whose tones complement and increase each others' resonance, and dissonance as those that create more complex acoustical interactions (called 'beats'). A simplistic example is that of "pleasant" sounds versus "unpleasant" ones. Another manner of thinking about the relationship regards stability; dissonant harmonies are sometimes considered to be unstable and to "want to move" or "resolve" toward consonance. However, this is not to say that dissonance is undesirable. A composition made entirely of consonant harmonies may be pleasing to the ear and yet boring because there are no instabilities to be resolved.
Melody is often organized so as to interact with changing harmonies (sometimes called a
chord progressionA chord progression is a series of musical chords, or chord changes that "aims for a definite goal" of establishing a tonality founded on a key, root or tonic chord. In other words, the succession of root relationships...
) that accompany it, setting up consonance and dissonance. The art of melody writing depends heavily upon the choices of tones for their nonharmonic or harmonic character.
Rhythm
RhythmRhythm may be generally defined as a "movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions." This general meaning of regular recurrence or pattern in time may be applied to a wide variety of cyclical natural phenomena having a periodicity or...
is the arrangement of sounds and silences in
timeTime is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
.
MeterMeter or metre is a term that music has inherited from the rhythmic element of poetry where it means the number of lines in a verse, the number of syllables in each line and the arrangement of those syllables as long or short, accented or unaccented...
animates time in regular pulse groupings, called
measures or barsIn musical notation, a bar is a segment of time defined by a given number of beats of a given duration. Typically, a piece consists of several bars of the same length, and in modern musical notation the number of beats in each bar is specified at the beginning of the score by the top number of a...
. The
time signatureThe time signature is a notational convention used in Western musical notation to specify how many beats are in each measure and which note value constitutes one beat....
or meter signature specifies how many
beatThe beat is the basic unit of time in music, the pulse of the mensural level . In popular use, the beat can refer to a variety of related concepts including: tempo, meter, rhythm and groove...
s are in a measure, and which value of written note is counted and felt as a single beat. Through increased stress and attack (and subtle variations in duration), particular tones may be accented. There are conventions in most musical traditions for a regular and hierarchical accentuation of beats to reinforce the meter.
SyncopatedIn music, syncopation includes a variety of rhythms which are in some way unexpected in that they deviate from the strict succession of regularly spaced strong and weak but also powerful beats in a meter . These include a stress on a normally unstressed beat or a rest where one would normally be...
rhythms are rhythms that accent unexpected parts of the beat. Playing simultaneous rhythms in more than one time signature is called polymeter. See also
polyrhythmPolyrhythm is the simultaneous sounding of two or more independent rhythms.Polyrhythm in general is a nonspecific term for the simultaneous occurrence of two or more conflicting rhythms, of which cross-rhythm is a specific and definable subset.—Novotney Polyrhythms can be distinguished from...
.
In recent years, rhythm and meter have become an important area of research among music scholars. Recent work in these areas includes books by
Bengt-Olov PalmqvistBengt-Olov Palmqvist [bɛŋkt- olov palmqvist] is a Swedish-Australian musicologist and music theorist, with particular expertise on the subject of rhythm, within music theory. He has published a series of work-books titled "Refinement of Rhythm", that are used widely as resources for rhythmic...
,
Fred LerdahlAlfred Whitford Lerdahl is the Fritz Reiner Professor of Musical Composition at Columbia University, and a composer and music theorist best known for his work on pitch space and cognitive constraints on compositional systems or "musical grammar[s]." He has written many orchestral and chamber...
and
Ray JackendoffRay Jackendoff is an American linguist. He is professor of philosophy, Seth Merrin Chair in the Humanities and, with Daniel Dennett, Co-director of the Center for Cognitive Studies at Tufts University...
, and
Jonathan KramerJonathan Donald Kramer , was a U.S. composer and music theorist.- Biography :...
.
Melody
A melody is a series of tones sounding in succession. The tones of a melody are typically created with respect to pitch systems such as
scalesIn music, a scale is a sequence of musical notes in ascending and descending order. Most commonly, especially in the context of the common practice period, the notes of a scale will belong to a single key, thus providing material for or being used to conveniently represent part or all of a musical...
or
modesIn the theory of Western music since the ninth century, mode generally refers to a type of scale. This usage, still the most common in recent years, reflects a tradition dating to the middle ages, itself inspired by the theory of ancient Greek music.The word encompasses several additional...
. The rhythm of a melody is often based on the
inflectionIn grammar, inflection or inflexion is the modification of a word to express different grammatical categories such as tense, grammatical mood, grammatical voice, aspect, person, number, gender and case...
s of
languageIn the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written...
, the physical rhythms of
danceDance is an art form that generally refers to movement of the body, usually rhythmic and to music, used as a form of expression, social interaction or presented in a spiritual or performance setting....
, or simply periodic pulsation. Melody is typically divided into phrases within a larger overarching structure. The elements of a melody are
pitchPitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...
, duration,
dynamicsIn music, dynamics normally refers to the volume of a sound or note, but can also refer to every aspect of the execution of a given piece, either stylistic or functional . The term is also applied to the written or printed musical notation used to indicate dynamics...
, and
timbreIn music, timbre is the quality of a musical note or sound or tone that distinguishes different types of sound production, such as voices and musical instruments, such as string instruments, wind instruments, and percussion instruments. The physical characteristics of sound that determine the...
.
Harmony
HarmonyIn music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
is the study of vertical sonorities in music. Vertical sonority refers to considering the relationships between pitches that occur together; usually this means at the same time, although harmony can also be implied by a melody that outlines a harmonic structure.
The relationship between two pitches is referred to as an
intervalIn music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...
. A larger structure involving more than two pitches is called a
chordA chord in music is any harmonic set of two–three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may for many practical and theoretical purposes be understood as chords...
. In common practice and popular music, harmonies are generally
tertianIn music theory, tertian describes any piece, chord, counterpoint etc. constructed from the interval of a third...
. This means that the interval of which the chords are composed is a third. Therefore, a root-position
triadIn music and music theory, a triad is a three-note chord that can be stacked in thirds. Its members, when actually stacked in thirds, from lowest pitched tone to highest, are called:* the Root...
(with the root note in the lowest voice) consists of the root note, a note a third above, and a note a third above that (a fifth above the root).
Seventh chordA seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a major triad with an added minor seventh...
s add a third above the top note of a triad (a seventh above the root). There are some notable exceptions. In
20th century classical music20th century classical music was without a dominant style and highly diverse.-Introduction:At the turn of the century, music was characteristically late Romantic in style. Composers such as Gustav Mahler and Jean Sibelius were pushing the bounds of Post-Romantic Symphonic writing...
, many alternative types of harmonic structure were explored. One way to analyze harmony in common practice music is through a
Roman numeral systemIn tonal music theory, a diatonic function is the specific, recognized role of each of the 7 notes and their chords in relation to the diatonic key...
; in popular music and
jazzJazz is a musical style that originated at the beginning of the 20th century in African American communities in the Southern United States. It was born out of a mix of African and European music traditions. From its early development until the present, jazz has incorporated music from 19th and 20th...
a system of chord symbols is used; and in post-tonal music, a variety of approaches are used, most frequently
set theoryMusical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard Hanson in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as Allen Forte , drawing...
.
The perception of pitch within harmony depends on a number of factors including the interaction of frequencies within the harmony and the roughness produced by the fast beating of nearby partials. Pitch perception is also affected by familiarity of the listener with the music, and cultural associations.
"Harmony" as used by music theorists can refer to any kind of
simultaneityIn music, a simultaneity is more than one complete musical texture occurring at the same time, rather than in succession. This first appeared in the music of Charles Ives, and is common in the music of Conlon Nancarrow and others....
without a value judgement, in contrast with a more common usage of "in harmony" or "harmonious", which in technical language might be described as
consonanceIn music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
.
Monophony is the texture of a melody heard only by itself. If a melody is accompanied by chords, the texture is homophony. In homophony, the melody is usually but not always voiced in the highest notes. A third texture, called polyphony, consists of several simultaneous melodies of equal importance.
Texture
Musical texture is the overall sound of a piece of music commonly described according to the number of and relationship between parts or lines of music:
monophonyIn music, monophony is the simplest of textures, consisting of melody without accompanying harmony. This may be realized as just one note at a time, or with the same note duplicated at the octave . If the entire melody is sung by two voices or a choir with an interval between the notes or in...
,
heterophonyIn music, heterophony is a type of texture characterized by the simultaneous variation of a single melodic line. Such a texture can be regarded as a kind of complex monophony in which there is only one basic melody, but realized at the same time in multiple voices, each of which plays the melody...
,
polyphonyIn music, polyphony is a texture consisting of two or more independent melodic voices, as opposed to music with just one voice or music with one dominant melodic voice accompanied by chords ....
,
homophonyIn music, homophony is a texture in which two or more parts move together in harmony, the relationship between them creating chords. This is distinct from polyphony, in which parts move with rhythmic independence, and monophony, in which all parts move in parallel rhythm and pitch. A homophonic...
, or
monodyIn poetry, the term monody has become specialized to refer to a poem in which one person laments another's death....
. The perceived texture of a piece may also be affected by the timbre of the instruments, the number of instruments used, and the distance between each musical line, among other things.
Timbre
Timbre, sometimes called "Color", or "Tone Color" is the quality or sound of a voice or instrument. The quality of timbre varies widely from instrument to instrument, or from voice to voice. The timbre of some instruments can be changed by applying certain techniques while playing. For example, the timbre of a trumpet changes when a mute is inserted into the bell, or a voice can change its timbre by the way a performer manipulates the vocal apparatus, (e.g. the vocal cords, mouth and diaphragm). Generally, there is no common musical notation that speaks specifically to a change in timbre, (as "pianissimo" would indicate "very soft" for a change in dynamics).
Expressive Qualities
Expressive Qualities are those elements in music that create change in music that are not related to pitch, rhythm or timbre. They include Dynamics and Articulation.
Dynamics
In music, the term "dynamics" normally refers to the softness or loudness of a sound or note: e.g. pianissimo or fortissimo. Until recently, most dynamics in written form were done so in Italian, but recently are sometimes written or translated into English. Another sense of the word refers to any aspect of the execution of events in a given piece; either stylistic (staccato, legato etc.) or functional (velocity) are also known as dynamics. The term is also applied to the written or printed musical notation used to indicate dynamics.
Articulation
Articulation is the manner in which the performer applies their technique to execute the sounds or notes—for example,
staccatoStaccato is a form of musical articulation. In modern notation it signifies a note of shortened duration and separated from the note that may follow by silence...
or
legatoIn musical notation the Italian word legato indicates that musical notes are played or sung smoothly and connected. That is, in transitioning from note to note, there should be no intervening silence...
. Articulation is often described rather than quantified, therefore there is room to interpret how to execute precisely each articulation. For example,
Staccato is often referred to as "separated" or "detached" rather than having a defined, or numbered amount by which the separation or detachment is to take place. Often the manner in which a performer decides to execute a given articulation is done so by the context of the piece or phrase. Also, the type or style of articulation will depend on the instrument and musical period, e.g. the classical period, but there is a generally recognized set of articulations that most all instruments (and voices) have in common. They are, in order of long to short:
legato ("smooth, connected");
tenuto ("pressed", "lengthened but detached");
marcato (heavily accented and detached);
staccato ("separated", "detached"); "martelé" (or "rooftop accent" or "teepee accent") for its written shape (short and hard). Any of these may be combined to create certain "in-between" articulations. For example,
portato is the combination of
tenuto and
staccato. Some instruments have unique methods by which to produce sounds, such as
spicatto for strings, where the bow bounces off the string.
Form or Structure
FormThe term musical form refers to the overall structure or plan of a piece of music, and it describes the layout of a composition as divided into sections...
is a facet of music theory that explores the concept of musical syntax, on a local and global level. The syntax is often explained in terms of phrases and periods (for the local level) or sections or genre (for the global scale). Examples of common forms of Western music include the
fugueIn music, a fugue is a compositional technique in two or more voices, built on a subject that is introduced at the beginning in imitation and recurs frequently in the course of the composition....
, the invention,
sonata-allegroSonata form is a large-scale musical structure used widely since the middle of the 18th century . While it is typically used in the first movement of multi-movement pieces, it is sometimes used in subsequent movements as well—particularly the final movement...
,
canonIn music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration . The initial melody is called the leader , while the imitative melody, which is played in a different voice, is called the follower...
, strophic, theme and variations, and
rondoRondo, and its French equivalent rondeau, is a word that has been used in music in a number of ways, most often in reference to a musical form, but also to a character-type that is distinct from the form...
. Popular Music often makes use of
strophic formStrophic form is the simplest and most durable of musical forms, elaborating a piece of music by repetition of a single formal section. This may be analyzed as "A A A..."...
many times in conjunction with
Twelve bar bluesThe 12-bar blues is one of the most popular chord progressions in popular music, including the blues. The blues progression has a distinctive form in lyrics and phrase and chord structure and duration...
.
Four-part writing
Four-part chorale writing is used to teach and analyze the basic conventions of "Common-Practice Period music", the time period lasting from approximately 1650 to 1900. In the German musicology tradition referred to as functional harmony.
Johann Sebastian Bach'sJohann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...
four voice chorales written for liturgical purposes serve as a model for students. These chorales exhibit a fusion of linear and vertical thinking. In analysis, the harmonic function and rhythm are analyzed as well as the shape and implications of each of the four lines. Students are then instructed to compose chorales, often using given melodies (as Bach would have done), over a given bass line, or to compose within a chord progression, following rules of
voice leadingIn musical composition, voice leading is the term used to refer to a decision-making consideration when arranging voices , namely, how each voice should move in advancing from each chord to the next.- Details :...
.
Though traditionally conceived as a vocal exercise for
SopranoA soprano is a voice type with a vocal range from approximately middle C to "high A" in choral music, or to "soprano C" or higher in operatic music. In four-part chorale style harmony, the soprano takes the highest part, which usually encompasses the melody...
,
AltoAlto is a musical term, derived from the Latin word altus, meaning "high" in Italian, that has several possible interpretations.When designating instruments, "alto" frequently refers to a member of an instrumental family that has the second highest range, below that of the treble or soprano. Hence,...
,
TenorThe tenor is a type of male singing voice and is the highest male voice within the modal register. The typical tenor voice lies between C3, the C one octave below middle C, to the A above middle C in choral music, and up to high C in solo work. The low extreme for tenors is roughly B2...
, and Bass, other common four-part writings could consist of a brass quartet (two
TrumpetThe trumpet is the musical instrument with the highest register in the brass family. Trumpets are among the oldest musical instruments, dating back to at least 1500 BCE. They are played by blowing air through closed lips, producing a "buzzing" sound which starts a standing wave vibration in the air...
s, French Horn, and
TromboneThe trombone is a musical instrument in the brass family. Like all brass instruments, sound is produced when the player’s vibrating lips cause the air column inside the instrument to vibrate...
) or a
string quartetA string quartet is a musical ensemble of four string players – usually two violin players, a violist and a cellist – or a piece written to be performed by such a group...
(including violin I, violin II, viola and cello).
There are seven chords used in four-part writing that are based upon each note of the scale. The chords are usually given Roman Numerals I, II, III, IV, V, VI and VII to refer to triadic (three-note) chords based on each successive note of the major or minor scale the piece is in. Chords may be analyzed in two ways. Case-sensitive harmonic analysis would state that major-mode chords (I, IV, V
7, etc.), including augmented (for example, VII
+), would be notated with upper-case Roman numerals, and minor-mode chords, including diminished (ii, iii, vi, and the diminished vii chord, vii
o), would be notated with lower-case Roman numerals. When a scale degree other than the root of the chord is in the bass, the chord is said to be in inversion, and this is indicated by numbers written above the roman numeral. With triads a 6 indicates first inversion, and 6 4 indicates second inversion. With seventh chords, 6 5 indicates first inversion, 4 3 indicates second inversion, and 4 2 indicates third inversion. ( I
6, IV
4/3,V
4/2 , etc.) Schenkerian harmonic analysis, patterned after the theories of
Heinrich SchenkerHeinrich Schenker was a music theorist, best known for his approach to musical analysis, now usually called Schenkerian analysis....
, would state that the mode does not matter in the final analysis, and thus all harmonies are notated in upper-case.
The skill in harmonizing a Bach chorale lies in being able to begin a phrase in one key and to modulate to another key either at the end of the first phrase, the beginning of the next one, or perhaps by the end of the second phrase. Each chorale often has the ability to modulate to various tonally related areas: the relative major (III) or minor (vi), the Dominant (V) or its relative minor (iii), the Sub-Dominant (IV) or its relative minor (ii). Other chromatic chords may be used, like the
diminished seventhA diminished seventh chord is a four note chord that comprises a diminished triad plus the interval of a diminished seventh above the root. Thus it is , or enharmonically , of any major scale; for example, C diminished-seventh would be , or enharmonically...
(made up of minor thirds piled on top of each other) or the
Secondary dominantSecondary dominant is an analytical label for a specific harmonic device, prevalent in the tonal idiom of Western music beginning in the common practice period...
(the Dominant's Dominant – a kind of major version of chord II). Certain standard cadences are observed, most notably II
b7 – V
7 – I. The standard collection of
J. S. Bach's chorales was edited by
Albert Riemenschneider Albert Riemenschneider was an American musician and Bach musicologist.Riemenschneider was born into a musical family. His father, Karl H. Riemenschneider,There are two conflicting sources about the name of his father: T. Riemenschneider & L...
and this collection is readily available,
e.g. here.
Music perception and cognition
Jackendoff and Lerdahl attempt to develop a "musical grammar". Using Jackendoff's background as a linguist and Lerdahl's compositional and theoretical background, a series of generative rules are defined to explain the hierarchical structure of tonal music. The rules focus on musical grouping, or methods in which rhythmic groups of notes, as well as formal hierarchies, are perceived by listeners. Three sets of rules are given: "Grouping Well-Formedness Rules", "Grouping Preference Rules" and "Transformational Rules". These rules are designed to interpret how listeners group structures in tonal music. These groupings then play into the segmentation of events by listeners, which in turn determine the hierarchical structure perceived by the listener. Although this theory is well developed and complete, it is by far not the only system designed to discuss music in this manner, and there is no acceptance of this theory as being the sole theory by which to discuss perception of music (see
Jonathan KramerJonathan Donald Kramer , was a U.S. composer and music theorist.- Biography :...
).
Serial composition and set theory
Twelve-tone techniqueTwelve-tone technique is a method of musical composition devised by Arnold Schoenberg...
was developed by
Arnold SchoenbergArnold Schoenberg was an Austrian composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School...
to order and repeat all the 12 pitches of the chromatic scale with specific order. From 1947, this technique has been alternatively designated in French and English sources by the word
serialismIn music, serialism is a method or technique of composition that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though his contemporaries were also working to establish serialism as one example of...
. An ordered row of the 12 pitches is created, then all possible transformations are explored. The analytic techniques involve writing a 12 × 12 matrix of the tone row, and all of its forms (transposition, inversion, retrograde, retrograde inversion, and possibly other mappings, such as the cycle-of-fourths or M5 transformation). This technique is primarily associated with the composers of the
Second Viennese SchoolThe Second Viennese School is the group of composers that comprised Arnold Schoenberg and his pupils and close associates in early 20th century Vienna, where he lived and taught, sporadically, between 1903 and 1925...
, but also has been incorporated into the languages of many other composers.
The term serialism does not necessarily refer only to twelve-tone technique, especially in the German language; many composers have explored serialism using fewer than 12 notes, repeating tones inside of the row, serialism of microtonal scales, permutational serialism (in which note order is not fixed), distributional serialism, and serial composition without pitches at all. Also, composers such as
Pierre BoulezPierre Boulez is a French composer of contemporary classical music, a pianist, and a conductor.-Early years:Boulez was born in Montbrison, Loire, France. As a child he began piano lessons and demonstrated aptitude in both music and mathematics...
explored integral serialism, or the serialization of all possible musical parameters (pitch, rhythm, dynamics, etc.).
Set TheoryMusical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard Hanson in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as Allen Forte , drawing...
is another approach to understanding atonal music that may or may not be serial. Although more akin to the mathematical field of
Group TheoryIn mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
than mathematical
Set TheorySet theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
, the nomenclature has become standard inside the musical community. Set theory represents the pitch classes as numbers to allow a methodology of examining music without tonic or triadic functional harmony. This technique allows for exploration of the construction of a serial tone row as well as less strict atonal works. This technique has been extended with a great deal of mathematical rigor to both tonal and atonal systems by
David LewinDavid Lewin was an American music theorist, music critic and composer. Called "the most original and far-ranging theorist of his generation" , he did his most influential theoretical work on the development of transformational theory, which involves the application of mathematical group theory to...
in his
transformational approachTransformational theory is a branch of music theory developed by David Lewin in the 1980s, and formally introduced in his most influential work, Generalized Musical Intervals and Transformations...
utilizing networks of related sets.
Notation
Musical notation is the symbolic representation of music (not to be confused with audio recording). Historically, and in the narrow sense, this is achieved with graphic symbols. Computer file formats have become important as well. Spoken language and hand signs are also used to symbolically represent music, primarily in teaching.
In standard Western music notation, music is represented graphically by notes placed on a
staffIn standard Western musical notation, the staff, or stave, is a set of five horizontal lines and four spaces that each represent a different musical pitch—or, in the case of a percussion staff, different percussion instruments. Appropriate music symbols, depending upon the intended effect,...
or staves with the vertical axis roughly corresponding to pitch and the horizontal axis roughly corresponding to time. Note head shapes, stems, flags, and ties are used to indicate duration. Additional symbols represent key, tempo, dynamics, accents, rests, etc.
Mathematics
Music and mathematics are strongly intertwined. As noted above, the concept of pitch and temperament are both strongly tied to mathematics, and acoustics in particular. Analysis often takes a mathematical route; musical set theory and
Transformational theoryTransformational theory is a branch of music theory developed by David Lewin in the 1980s, and formally introduced in his most influential work, Generalized Musical Intervals and Transformations...
are both steeped in mathematics.
Some methods of composition are mathematically based.
Iannis XenakisIannis Xenakis was a Romanian-born Greek ethnic, naturalized French composer, music theorist, and architect-engineer. He is commonly recognized as one of the most important post-war avant-garde composers...
developed several methods using
stochasticStochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
methods. The French school of
spectral musicSpectral music is a musical composition practice where compositional decisions are often informed by the analysis of sound spectra. Computer-based sound spectrum analysis using tools like DFT, FFT, and spectrograms...
uses mathematical analysis of sounds to develop compositional materials.
In music history mathematics were the foundation of the first understanding of tones, intervals, and scales developed by the Greeks between 530 and 500 BC. This discovery was based upon shortening a harp’s string by a half, creating an octave. Further, separating the same string into two-thirds or four equal parts produced intervals known as fifths and fourths, respectively. This discovery had a philosophical impact on the importance of mathematics, “It was the first consistent realization that there is a mathematical rationality in the universe and that the human mind can make sense of that rationality,” said Kitty Ferguson, the author of
The Music of Pythagoras. Recently, Princeton University music theorist
Dmitri TymoczkoDmitri Tymoczko is a composer and music theorist. His music, which draws on rock, jazz, and romanticism, has been performed by ensembles such as the Ansermet Quartet, the Brentano Quartet, Janus, Newspeak, the San Francisco Contemporary Players, the Pacifica Quartet, and Ursula Opens...
discovered that relationships between notes exist in multi-dimensional geometric forms, or orbifolds. Tymoczko made his discovery when writing down all possible two note chords in columns on a sheet of paper. After doing so Tymoczko observed the possibility that a pattern existed, Two-note chords, the minimalist form of a chord (as a chord is any combination any number of notes played simultaneously) is represented graphically by a Mobius strip, a two-dimensional surface embedded in a three-dimensional space. As the chords are composed of increasing numbers of notes, the geometric form they take on becomes increasingly sophisticated. Three-note chords are represented by twisted three-dimensional shapes, and four-note chords, four-dimensional shapes. These principles on tonal relationships apply to every genre of music and have been unintentionally practiced by theorists and composers since medieval times. The significance of this finding is rooted in teaching and applying music theory. The simplistic relationships of tones as geometric shapes allow students of music to understand the composition of complex musical scores. In doing so, students can apply the relationships used in preeminent examples of melodic composition more easily into their own writing. Tymoczko explains this simplicity as being It was this idea that lead to the study of mathematical music theory and explains his discovery of orbifolds and representations of these relationships. Tymoczko used these tools to as facilitators for his own compositions and an analysis of Western music in his book
A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice.
Analysis
Analysis is the effort to describe and explain music. Analysis at once is a catch-all term describing the process of describing any portion of the music, as well as a specific field of formal analysis or the field of stylistic analysis. Formal analysis attempts to answer questions of hierarchy and form, and stylistic analysis attempts to describe the style of the piece. These two distinct sub-fields often coincide.
Analysis of harmonic structures is typically presented through a roman numeral analysis. However, over the years, as music and the theory of music have both grown, a multitude of methods of analyzing music have presented themselves. Two very popular methods, Schenkerian analysis and Neo-Riemannian analysis, have dominated much of the field. Schenkerian analysis attempts to "reduce" music through layers of foreground, middleground, and, eventually and importantly, the background. Neo-Riemannian (or Transformational) analysis began as an extension of
Hugo RiemannKarl Wilhelm Julius Hugo Riemann was a German music theorist.-Biography:Riemann was born at Grossmehlra, Schwarzburg-Sondershausen. He was educated in theory by Frankenberger, studied the piano with Barthel and Ratzenberger, studied law, and finally philosophy and history at Berlin and Tübingen...
's theories of music, and then expanding Riemann's concepts of pitch and transformation into a mathematically rich language of analysis. While both theories originated as methods of analysis for tonal music, both have been extended to use in non-tonal music as well.
Ear training
Aural skills – the ability to identify musical patterns by ear, as opposed to by the reading of notation – form a key part of a musician's craft and are usually taught alongside music theory. Most aural skills courses train the perception of
relative pitchThe term relative pitch may denote:* the distance of a musical note from a set point of reference, e.g. "three octaves above middle C"* a musician's ability to identify the intervals between given tones, regardless of their relation to concert pitch * the skill used by singers to correctly sing a...
(the ability to determine pitch in an established context) and rhythm. Sight-singing – the ability to sing unfamiliar music without assistance – is generally an important component of aural skills courses.
Absolute pitchAbsolute pitch , widely referred to as perfect pitch, is the ability of a person to identify or re-create a given musical note without the benefit of an external reference.-Definition:...
or perfect pitch describes the ability to recognise a particular audio frequency as a given musical note without any prior reference.
Sources
- Benade, Arthur H. (1960). Horns, Strings, and Harmony. Science Study Series S 11. Garden City, New York: Doubleday & Company, Inc.
- Boretz, Benjamin
Benjamin Boretz is an American composer and music theorist.-Life and work:Boretz was born in Brooklyn, New York and graduated with a degree in music from Brooklyn College...
(1995). Meta-Variations: Studies in the Foundations of Musical Thought. Red Hook, New York: Open Space.
- Benward, Bruce, and Marilyn Nadine Saker (2009). Music in Theory and Practice, eighth edition, vol. 2. Boston: McGraw-Hill. ISBN 978-0-07-310188-0.
- Bent, Ian D., and Anthony Pople (2001). "Analysis." The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie
Stanley Sadie CBE was a leading British musicologist, music critic, and editor. He was editor of the sixth edition of the Grove Dictionary of Music and Musicians , which was published as the first edition of the New Grove Dictionary of Music and Musicians.Sadie was educated at St Paul's School,...
and John TyrrellJohn Tyrrell was born in Salisbury, Southern Rhodesia in 1942. He studied at the universities of Cape Town, Oxford and Brno. In 2000 he was appointed Research Professor at Cardiff University....
. London: Macmillan Publishers.
- Castan, Gerd (2009). "Musical Notation Codes". Music-Notation.info (Accessed 1 May 2010). (Accessed 1 May 2010)
- Harnsberger, Lindsey C. (1997). "Articulation". Essential Dictionary of Music: Definitions, Composers, Theory, Instrument and Vocal Ranges, second edition. The Essential Dictionary Series. Los Angeles: Alfred Publishing Co. ISBN 0882847287.
- Jackendoff, Ray
Ray Jackendoff is an American linguist. He is professor of philosophy, Seth Merrin Chair in the Humanities and, with Daniel Dennett, Co-director of the Center for Cognitive Studies at Tufts University...
and Fred LerdahlAlfred Whitford Lerdahl is the Fritz Reiner Professor of Musical Composition at Columbia University, and a composer and music theorist best known for his work on pitch space and cognitive constraints on compositional systems or "musical grammar[s]." He has written many orchestral and chamber...
(1981). "Generative Music Theory and Its Relation to Psychology." Journal of Music Theory.
- Josephs, Jess L. (1967). The Physics of Musical Sound. Princeton, Toronto, London: D. Van Nostrand Company, Inc.
- Kostka, Stefan, and Dorothy Payne (2004). Tonal Harmony, fifth edition. New York: McGraw-Hill.
- Kramer, Jonathan
Jonathan Donald Kramer , was a U.S. composer and music theorist.- Biography :...
(1988). The Time of Music. New York: Schirmer Books.
- Lerdahl, Fred
Alfred Whitford Lerdahl is the Fritz Reiner Professor of Musical Composition at Columbia University, and a composer and music theorist best known for his work on pitch space and cognitive constraints on compositional systems or "musical grammar[s]." He has written many orchestral and chamber...
(2001). Tonal Pitch Space. Oxford: Oxford University Press.
- Lewin, David
David Lewin was an American music theorist, music critic and composer. Called "the most original and far-ranging theorist of his generation" , he did his most influential theoretical work on the development of transformational theory, which involves the application of mathematical group theory to...
(1987). Generalized Musical Intervals and Transformations. New Haven: Yale University Press.
- Lloyd, Llewellyn S., and Hugh Boyle (1978). Intervals, Scales and Temperaments. New York: St. Martin's Press. ISBN 0-312-42533-3
- Stevens, S. S., J. Volkmann, and E. B. Newman (1937). "A Scale for the Measurement of the Psychological Magnitude Pitch". Journal of the Acoustical Society of America 8, no. 3:185–90.
Further reading
- Apel, Willi, and Ralph T. Daniel (1960). The Harvard Brief Dictionary of Music. New York: Simon & Schuster Inc. ISBN 0-671-73747-3
- Benward, Bruce, Barbara Garvey Jackson, and Bruce R. Jackson. (2000). Practical Beginning Theory: A Fundamentals Worktext, 8th edition, Boston: McGraw-Hill. ISBN 0697343979. [First edition 1963]
- Brown, James Murray (1967). A Handbook of Musical Knowledge, 2 vols. London: Trinity College of Music.
- Chase, Wayne (2006). How Music REALLY Works!, second edition. Vancouver, Canada: Roedy Black Publishing. ISBN 1-897311-55-9 (book)
- Hewitt, Michael (2008). Music Theory for Computer Musicians. USA: Cengage Learning. ISBN 13-978-1-59863-503-4.
- Lawn, Richard J., and Jeffrey L. Hellmer (1996). Jazz Theory and Practice. [N.p.]: Alfred Publishing Co. ISBN 0-882-84722-8.
- Owen, Harold (2000). Music Theory Resource Book. Oxford University Press. ISBN 0-19-511539-2.
- Seashore, Carl
Carl Emil Seashore was a prominent American psychologist.-Background:Seashore was born in Mörlunda, Hultsfred Municipality, Kalmar County, Sweden to Carl Gustav and Emily Sjöstrand. He emigrated with his family to the United States in 1870 and settled in Iowa. The name “Seashore” is a...
(1933). Approaches to the Science of Music and Speech. Iowa City: The University.
- Seashore, Carl (1938). Psychology of Music, New York, London, McGraw-Hill Book Company, Inc.
- Sorce, Richard (1995). Music Theory for the Music Professional. [N.p.]: Ardsley House. ISBN 1-880-15720-9.
- Taylor, Eric (1989). AB Guide to Music, vol 1. England: Associated Board of the Royal Schools of Music. ISBN 1-854-72446-0
- Taylor, Eric (1991). AB Guide to Music, vol 2. England: Associated Board of the Royal Schools of Music. ISBN 1-854-72447-9
- Yamaguchi, Masaya (2006). The Complete Thesaurus of Musical Scales, revised edition. New York: Masaya Music Services. ISBN 0967635306.