Music theory

Music theory is a field of study that describes the elements of music and includes the development and application of methods for analyzing and composing music, and the interrelationship between the notation of music and performance practice, theory. Broadly, theory may include any statement, belief, or conception of or about music (Boretz, 1995). A person who studies or practices music theory is a music theorist.

Some music theorists attempt to explain the techniques composers use by establishing rules and patterns. Others model the experience of listening to or performing music. Though extremely diverse in their interests and commitments, many Western music theorists are united in their belief that the acts of composing, performing, and listening to music may be explicated to a high degree of detail (this, as opposed to a conception of musical expression as fundamentally ineffable except in musical sounds). Generally, music theory works are both descriptive and prescriptive, that is they both attempt to define practice and to influence later practice. Thus, music theory generally lags behind practice in important ways, but also points towards future exploration and performance.

Musicians study music theory in order to be able to understand the relationships that a composer or songwriter expects to be understood in the notation, and composers study music theory in order to be able to understand how to produce effects and to structure their own works. Composers may study music theory in order to guide their precompositional and compositional decisions. Broadly speaking, music theory in the Western tradition focuses on harmony and counterpoint, and then uses these to explain large scale structure and the creation of melody.

Sound
Music theory describes how sounds, which travel in waves, are notated, and how what is sounded, or played, is perceived by listeners. The study of how humans interpret sound is called psychoacoustics, while the cognitive aspects of how perceived sounds are interpreted into musical structures is studied in music cognition. In music, sound waves are usually measured not by length (or wavelength) or period, but by frequency.

Every object has a resonant frequency which is determined by the object's composition. The different frequencies at which the sound producers of many instruments vibrate are given by the harmonic series. The resonators of musical instruments are designed to exploit these frequencies. Different instruments have different timbres due to variation in the size and shape of the instrument as well as the choice of materials from which the parts of the instrument are constructed.

A note is generally perceived as a sound on a single pitch. Notes have a regular wave beat on the eardrum that humans (and perhaps animals as well) find pleasing. This may be in part due to the fact that from the moment the hearing function becomes available to an unborn child, there is the regular rhythm of the mother's heartbeat.

Often the fundamental aspects of sound and music are described as pitch, duration, intensity, and timbre.

Pitch
Musical sounds are composed of pitch, duration, and timbre. Pitch is determined by the sound's frequency of vibration, such as A440, which vibrates at 440 Hz. Pitches may be related by interval, their relative distance from a reference pitch. Tuning is the process of assigning pitches to notes. The difference in pitch between two notes is called an interval. Notes, in turn, can be arranged into different scales and modes. The most common scales are major, harmonic minor, melodic minor, and pentatonic.

In music written using the system of major-minor tonality, the key of a piece determines the pitch level or frequency of each note. A piece in the key of D major will put all the notes two semitones higher than a piece in the key of C major. Changing the key can dramatically change the feel of the 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 timbre as well as technical implications for the performers. However, key changes may also go unrecognized by the listener, because changing the key does not change the relationship of the individual pitches to each other. Therefore, different keys can in many cases be considered equivalent and a matter of choice on the part of performers. This is especially true for popular and folk songs.

Rhythm
Rhythm is the arrangement of sounds in time. Meter animates time in regular pulse groupings, called measures (or bars in British English). 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 parts of the beat not already stressed by counting. 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 Fred Lerdahl and Ray Jackendoff, Jonathan Kramer, Christopher Hasty, William Rothstein, and Joel Lester.

Melody
Melody is the unfolding in musical time of a principal single line of pitches. This line can be sounded alone, unaccompanied, known as monophony. It can also be accompanied by chords, known as homophony, where it is usually (but not always) present in the highest notes. A third texture, called polyphony, consists of several simultaneous melodies of equal importance. Counterpoint is the study of combining such independent melodies. The Gradus ad Parnassum by Johann Joseph Fux is a distillation of the principles of counterpoint and was used as an instructional manual for many composers, including Mozart and Beethoven.

Melodic rhythm is often rooted in the accent patterns of language or the animating rhythms of dance.

In much of Western music, melody is often the most identifiable element. Melodies will often imply certain scales or modes.

Harmony, consonance, & dissonance
Harmony occurs when two or more pitches are sounded simultaneously, although harmony can be implied when pitches are sounded successively rather than simultaneously (as in arpeggiation). Two simultaneous pitches form an interval. Three or more pitches sounded simultaneously are called chords, though the term is often used to indicate a particular organization of pitches, such as the triad, rather than just any three or more pitches.

Consonance can be roughly defined as harmonies whose tones complement and augment 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.

Brief audio (MIDI) musical examples of the interaction and effect of consonance and dissonance upon each other can be found here: "The effect of context on dissonance'" and here: "The role of harmony in music"

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 judgment, in contrast with a more common usage of "in harmony" or "harmonious", which in technical language might be described as consonance.

Texture
Musical texture is the overall sound of a piece of music commonly described according to the number 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 playing these parts and the harmony and rhythms used, among other things.

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, etc.

Analysis
See: Musical analysis and Schenkerian analysis.

Music perception and cognition
See: Fred Lerdahl and Ray Jackendoff.

12-tone and set theory
See: serialism, set theory (music), Milton Babbitt, David Lewin, and Allen Forte.

Musical semiotics
See: Jean-Jacques Nattiez.

Ear training

 * Main article: ear training. 

A key skill learned in Music Theory is the ability to recognize pitches, scale progressions, and intervals. There are many uses for having a good ear, including finding the leading tone, melodic line, bass line, and key for pieces of music. The basic approach to beginning training with the ear is to play two pitches one after the other and be able to tell the interval between the two. Common intervals are the Major Third, Perfect Fourth, Perfect Fifth, Major Sixth, and the Octave. One possible way to learn to recognize these intervals is to associate the sound with a commonly known song or pop culture sound. For example, Twinkle, Twinkle, Little Star starts with a rising Perfect Fifth interval; Francis Lai's theme music for the film Love Story begins with a rising and falling Minor Sixth; a Major Sixth can be associated with the NBC jingle or the song My Bonnie Lies over the Ocean; and Somewhere Over the Rainbow commences with a rising Octave.

Four-part writing
Four-part writing served for several hundred years as the foundation of musical practice in Europe. Historically, this is due to the primacy of choral music in the western tradition. The basic principle of four-part writing is to create four simultaneous lines that obey the rules of harmony and voice leading.

Four-part writing is sometimes referred to as an SATB arrangement, that is, an arrangement for the four vocal parts: Soprano, Alto, Tenor and  Bass lines. However, it is not necessary that these specific voice parts be present for a composition to be considered to be four-part. In men's choral music, four-part pieces are most commonly expressed as TTBB (Tenor I, Tenor II, Baritone, Bass), while a string quartet uses two violins, a viola and a cello.

Source

 * Boretz, Benjamin (1995) Meta-Variations: Studies in the Foundations of Musical Thought. Red Hook, New York: Open Space.