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Music Theory

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Music theory encompasses the nature and mechanics of music. It often involves identifying patterns that govern composers' techniques. In a more general sense, music theory also often distills and analyzes the elements of music – rhythm, harmony (harmonic function), melody, structure, Form, and texture. People who study these properties are known as music theorists.

Elements of Music

Music has many different elements. The main elements are: rhythm, melody, harmony, structure, timbre and texture. Each element -- and its sub-elements, if any -- is discussed below.

Melody

Main article: Melody
A melody is a series of pitches sounding in succession. In tonal Western music, the pitches of a melody are typically created with respect to scales or modes. The rhythm of a melody is often based on the inflections of language, the physical rhythms of dance, or simply periodic pulsation. Melody is typically divided into phrases within a larger overarching structure. The elements of a melody are composed of pitch, duration, and timbre.

Pitch

Main article: Pitch (music)
Pitch is determined by the sound's frequency of vibration, such as the note modern concert A is defined to be 440 Hz. Put differently, pitch is the relative aural highness or lowness of a given tone: the greater the frequency, the higher sounding the pitch.

The process of assigning pitches to note names is called Tuning. So 440 Hz is assigned to modern concert A.

The difference in frequency between two pitches is called an interval. The most basic interval is the octave; a note and another note with twice its frequency form an octave. For example, if the pitch with frequency 440 Hz is A, then the pitches with frequency 880 Hz, 1760 Hz as well as 220 Hz, 110 Hz, and 55 Hz are also A's.

Notes can be arranged into different scales and modes. Western music theory traditionally has 12 notes that might be included in a piece of music. In a scale, each note is called a half-step or semitone. Patterns of half and whole steps (2 half steps, or a tone) make up a scale in that octave. The scales most commonly encountered are the major, the harmonic minor, the melodic minor, and the natural minor.

In music written using the system of major-minor tonality, the key of a piece determines the scale used. Transposing a piece from C major to D major will make all the notes two semitones higher. Even in modern equal temperament, 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 on which the piece is being performed. This often affects the music's timbre, as well as having technical implications for the performers. However, changing the key in which a piece is performed may go unrecognized by the listener, since changing the key does not change the relationship of the individual pitches to each other.
Therefore, different keys are often considered equivalent and a matter of choice on the part of performers. This is especially true for popular and folk songs.

Rhythm

Main article: Rhythm
Rhythm is the arrangement of sounds in time. Meter animates time in regular pulse groupings, called measures or bars. The time signature or meter signature specifies how many beats 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. Syncopated rhythms are rhythms that accent unexpected parts of the beat. Playing simultaneous rhythms in more than one time signature is called polymeter. See also polyrhythm.

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 Palmqvist, Fred Lerdahl and Ray Jackendoff, Jonathan Kramer, Christopher Hasty, William Rothstein, and Joel Lester.

Harmony

Main article: Harmony
Harmony is the study of vertical sonorities in music. Harmony in Common practice music is usually analyzed through a roman numeral system; in Popular Music a system of chord symbols is used; and in post-tonal music, a variety of approaches are used, most frequently set theory. In Common Practice and Popular music, harmonies are generally tertian (with some notable exceptions), while post-tonal music frequently is based on varities of interval structures, leading to the use of set theory for analysis.

Consonance and Dissonance

Main article: Consonance and Dissonance
Consonance can be roughly defined as harmonies whose tones complement and increase each others' resonance, and dissonance as those which 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 progression) 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.

"Harmony" as used by music theorists can refer to any kind of simultaneity without a value judgement, in contrast with a more common usage of "in harmony" or "harmonious", which in technical language might be described as consonance.

Texture

Main article: Musical 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: monophony, heterophony, polyphony, homophony, or monody. The perceived texture of a piece may also be affected by the timbre of the instruments, the number of instruments used, and the interval between each musical line, among other things.

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.

Form or Structure

Main article: Form
Musical Form 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 Western music include the fugue, the invention, sonata-allegro, canon, strophic, theme and variations, and rondo. Popular Music often makes use of strophic form often in conjunction with Twelve bar blues.

Theories of Harmonization

Four-part writing

Four part chorale writing is used to teach and analyze the basic conventions of Common-Practice Period music. Johann Sebastian Bach's four voice chorales written for liturgial purposes serve as a model for students. These chorales exhibit a fusion of linear and vertical thinking, providing an excellent starting point for beginniners in music theory. 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 good voice leading. Though traditionally concieved as a vocal exercise, other common four-part writings could consist of a brass quartet (two Trumpets, French Horn, and Trombone) or a string quartet.

Music perception and cognition

Further information: Music cognition, Fred Lerdahl, Ray Jackendoff

Serial Composition and Set Theory

Further information: serialism, set theory (music), Arnold Schoenberg, Milton Babbitt, David Lewin, Allen Forte
Twelve Tone Serialism is a technique developed by Arnold Schoenberg to order and repeat all the 12 pitches of the Chomatic Scale with specific order. An ordered row of the 12 pitches is created, then all possible transformations are explored. The analytic techniques involve writing a 12x12 matrix of the tone row, and all of its forms (Transposition, Inversion, Retrograde, Retrograde Inversion) This technique is strongly related to the composers of the Second Viennese School, but also has been incorporated into the languages of many other composers. Serialism does not always appear in the strict 12-note form; many composers have explored with serialism using fewer than 12 notes, repeating tones inside of the row, serialism of microtonal scales. Also, composers such as Pierre Boulez and his teacher Oliver Messiaen explored integral serialism, or the serialization of all possible musical paramaters (pitch, rhythm, dynamics, etc.). Composers such as Igor Stravinsky and Milton Babbitt developed personal approaches to Serialism; Stravinsky using a method of Rotational Arrays, and Babbitt using Combinitorality of the rows. Set Theory is another approach to understanding atonal music that may or may not be serial. Although more akin to the mathematical field of Group Theory than mathematical Set Theory, 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 funcitional 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 Lewin in his transformational approach utilizing networks of related sets.

Musical semiotics

Further information: music semiology Jean-Jacques Nattiez

Music Subjects

Notation

Main article: Music notation
Music notation is the graphical representation of music. In standard Western notation, pitches are represented on the vertical axis and time is represented by notation symbols on the horizontal axis. Thus, notes are properly placed on the musical staff with appropriate time values to show musicians what note to play and when to play it.

Such notation makes up the contents of the musical staff, along with directions indicating the key, tempo, dynamics, accents, and rests, etc.

Mathematics

Main article: Music and mathematics
Music has been susceptible to analysis by mathematics, ever since Pythagoras noticed the relationships between the frequencies of different pitches. Mathematics has also been used as the basis for compositions, as in some 20th century styles.

Analysis

Main articles: Musical analysis and Schenkerian analysis


Analysis attempts to answer the question "How does this music work?" Music theorists may look at the chords used in a piece, and thus the chord progressions. "Why did the composer use this chord here? Why modulate there?" These are the types of questions one must ask himself when analyzing music. In serial music and the like, one may ask himself, "How is this variation drawing the composition as a whole toward a conclusion?" Some chords may be difficult to analyze, meaning it may be difficult to find out exactly what chord is being used. This is part of what makes theoretical analysis such a challenging and rewarding task.

Analysis may also take place in the way of looking at musical form. A music theorist may want to pick out the exposition, development, and recapitulation in a sonata-allegro piece, for study. Composers who analyze music regularly often find an increase in the quality of their musical compositions.

Ear training

Main article: 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 pitch (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.

Source

See also

Further reading

External links

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composer is a person who writes music. The term refers particularly to someone who writes music in some type of musical notation, thus allowing others to perform the music. This distinguishes the composer from a musician who improvises or plays a musical instrument.
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Rhythm (Greek ῥυθμός = 'flow', or in Modern Greek, 'style') is the variation of the length and accentuation of a series of sounds or other events.
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harmony is the use and study of pitch simultaneity, and therefore chords, actual or implied, in music. The study of harmony may often refer to the study of harmonic progressions, the movement from one pitch simultaneity to another, and the structural principles that govern such
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melody, also tune, voice, or line, is a series of linear events or a succession, not a simultaneity as in a chord (see harmony). However, this succession must contain change of some kind and be perceived as a single entity (possibly Gestalt) to be called a
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Structure is a fundamental and sometimes intangible notion covering the recognition, observation, nature, and stability of patterns and relationships of entities. From a child's verbal description of a snowflake, to the detailed scientific analysis of the properties of magnetic
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The term musical form refers to two related concepts:
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In music, texture is the overall quality of sound of a piece, most often indicated by the number of voices in the music and by the relationship between these voices (see types of texture below).
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melody, also tune, voice, or line, is a series of linear events or a succession, not a simultaneity as in a chord (see harmony). However, this succession must contain change of some kind and be perceived as a single entity (possibly Gestalt) to be called a
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melody, also tune, voice, or line, is a series of linear events or a succession, not a simultaneity as in a chord (see harmony). However, this succession must contain change of some kind and be perceived as a single entity (possibly Gestalt) to be called a
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Pitch is the perceived fundamental frequency of a sound. While the actual fundamental frequency can be precisely determined through physical measurement, it may differ from the perceived pitch because of overtones, or partials, in the sound.
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Western music is the genres of music originating in the Western world (Europe and its former colonies) including Western classical music, American Jazz, Country and Western, pop music and rock and roll.
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In music, a scale is a collection of musical notes that provides material for part or all of a musical work. Scales are ordered in pitch or pitch class, with their ordering providing a measure of musical distance.
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scale is an ordered series of musical intervals, which, along with the key or tonic, define the pitches. However, mode is usually used in the sense of scale applied only to the specific diatonic scales found below.
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inflection or inflexion is the modification or marking of a word (or more precisely lexeme) to reflect grammatical (that is, relational) information, such as gender, tense, number or person.
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See Language (journal) for the linguistics journal.


A language is a system of symbols and the rules used to manipulate them. Language can also refer to the use of such systems as a general phenomenon.
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worldwide view of the subject.
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Dance (from French danser, perhaps from Frankish) generally refers to movement used as a form of expression, social interaction or presented in a
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Pitch is the perceived fundamental frequency of a sound. While the actual fundamental frequency can be precisely determined through physical measurement, it may differ from the perceived pitch because of overtones, or partials, in the sound.
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In music, timbre, or sometimes timber, (from Fr. timbre; IPA /'tæmbəɹ/ as in the first two syllables of tambourine, or /'tɪmbəɹ/, like timber)[1]
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Pitch is the perceived fundamental frequency of a sound. While the actual fundamental frequency can be precisely determined through physical measurement, it may differ from the perceived pitch because of overtones, or partials, in the sound.
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note has two primary meanings: 1) a sign used in music to represent the relative duration and pitch of a sound; and 2) a pitched sound itself. Notes are the "atoms" of much Western music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis
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In music, there are two common meanings for tuning:
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In music theory, the term interval describes the difference in pitch between two notes. Although frequently used in connection with intervals, the term "distance" does not adequately describe the physics and subjective effects of two interacting frequencies.
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Perfect octave
Inverse unison
Name
Other names -
Abbreviation P8
Size
Semitones 12
Interval class 0
Just interval 2:1
Cents
Equal temperament 1200
Just intonation 1200 In music, an octave
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In music, a scale is a collection of musical notes that provides material for part or all of a musical work. Scales are ordered in pitch or pitch class, with their ordering providing a measure of musical distance.
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scale is an ordered series of musical intervals, which, along with the key or tonic, define the pitches. However, mode is usually used in the sense of scale applied only to the specific diatonic scales found below.
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Perfect octave
Inverse unison
Name
Other names -
Abbreviation P8
Size
Semitones 12
Interval class 0
Just interval 2:1
Cents
Equal temperament 1200
Just intonation 1200 In music, an octave
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In music theory, the major 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.

The simplest major scale is C major (figure 1), the only major scale not to require sharps or flats on the
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Minor Scale was a test conducted by the United States Defense Nuclear Agency (now part of the Defense Threat Reduction Agency) involving the detonation of several thousand tons of conventional explosives for the purpose of simulating the explosion of a small nuclear bomb.
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Minor Scale was a test conducted by the United States Defense Nuclear Agency (now part of the Defense Threat Reduction Agency) involving the detonation of several thousand tons of conventional explosives for the purpose of simulating the explosion of a small nuclear bomb.
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