Foundations on Music Theory Print

Arpeggio

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Uses#

Any instrument may employ arpeggiation, but arpeggios are more commonly used on instruments which serve the role of melodic lead or ornamentation. Arpeggios may be used as an alternative to continuous portamento for instruments which are not able to achieve that, or which have limitations in achieving portamento over multiple notes of a scale, such as keyboards, fretted instruments, and monophonic instruments like the flute. Arpeggios are commonly used in many music genres and are particularly highlighted in genres with significant focus on melody and ornamentation, such as flamenco and neo-classical. Arpeggios are an important part of jazz improvisation. On guitar, sweep-picking is a technique used for rapid arpeggiation, which is most often found in rock music and heavy metal music. Along with scales, arpeggios are a form of basic technical exercise that students use to develop intonation and technique. They can also be used in call and response ear training dictations, either alone or in conjunction with harmony dictations. Some synthesizers contain arpeggiators, which are step sequencers designed to facilitate the playing of arpeggios, as well as non-arpeggiated sequences also. In early video game music, arpeggios were often the only way to play a chord since sound hardware usually had a very limited number of oscillators, or voices. Instead of tying them all up to play one chord, one channel could be used to play an arpeggio, leaving the rest for drums, bass, or sound effects. A prominent example was the music of games and demos on Commodore 64’s SID chip, which only had three oscillators (see also Chiptune). This technique was highly popular amongst European video game music composers for systems in the 1980s like the NES, with many transferring their knowledge from their days of composing with the Commodore 64.

Atonality

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History#

While music without a tonal center had been previously written, for example Franz Liszt’s Bagatelle sans tonalité of 1885, it is with the coming of the twentieth century that the term atonality began to be applied to pieces, particularly those written by Arnold Schoenberg and The Second Viennese School. The term “atonality” was coined in 1907 by Joseph Marx in a scholarly study of tonality, which was later expanded into his doctoral thesis. Their music arose from what was described as the “crisis of tonality” between the late nineteenth century and early twentieth century in classical music. This situation had arisen over the course of the nineteenth century due to the increasing use of ambiguous chords, improbable harmonic inflections, and more unusual melodic and rhythmic inflections than what was possible within the styles of tonal music. The distinction between the exceptional and the normal became more and more blurred. As a result, there was a “concomitant loosening” of the synthetic bonds through which tones and harmonies had been related to one another. The connections between harmonies were uncertain even on the lowest chord-to-chord level. On higher levels, long-range harmonic relationships and implications became so tenuous, that they hardly functioned at all. At best, the felt probabilities of the style system had become obscure. At worst, they were approaching a uniformity, which provided few guides for either composition or listening. The first phase, known as “free atonality” or “free chromaticism”, involved a conscious attempt to avoid traditional diatonic harmony. Works of this period include the opera Wozzeck (1917–1922) by Alban Berg and Pierrot lunaire (1912) by Schoenberg. The second phase, begun after World War I, was exemplified by attempts to create a systematic means of composing without tonality, most famously the method of composing with 12 tones or the twelve-tone technique. This period included Berg’s Lulu and Lyric Suite, Schoenberg’s Piano Concerto, his oratorio Die Jakobsleiter and numerous smaller pieces, as well as his last two string quartets. Schoenberg was the major innovator of the system. His student, Anton Webern, however, is anecdotally claimed to have begun linking dynamics and tone color to the primary row, making rows not only of pitches but of other aspects of music as well. However, actual analysis of Webern’s twelve-tone works has so far failed to demonstrate the truth of this assertion. One analyst concluded, following a minute examination of the Piano Variations, op. 27, that while the texture of this music may superficially resemble that of some serial music … its structure does not. None of the patterns within separate nonpitch characteristics makes audible (or even numerical) sense in itself. The point is that these characteristics are still playing their traditional role of differentiation. Twelve-tone technique, combined with the parametrization (separate organization of four aspects of music: pitch, attack character, intensity, and duration) of Olivier Messiaen, would be taken as the inspiration for serialism. Atonality emerged as a pejorative term to condemn music in which chords were organized seemingly with no apparent coherence. In Nazi Germany, atonal music was attacked as “Bolshevik” and labeled as degenerate (Entartete Musik) along with other music produced by enemies of the Nazi regime. Many composers had their works banned by the regime, not to be played until after its collapse at the end of World War II. After Schoenberg’s death, Igor Stravinsky used the twelve-tone technique. Iannis Xenakis generated pitch sets from mathematical formulae, and also saw the expansion of tonal possibilities as part of a synthesis between the hierarchical principle and the theory of numbers, principles which have dominated music since at least the time of Parmenides.

Melody

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Function and elements#

Johann Philipp Kirnberger argued: The Norwegian composer Marcus Paus has argued: Given the many and varied elements and styles of melody “many extant explanations of melody confine us to specific stylistic models, and they are too exclusive.” The melodies existing in most European music written before the 20th century, and popular music throughout the 20th century, featured “fixed and easily discernible frequency patterns”, recurring “events, often periodic, at all structural levels” and “recurrence of durations and patterns of durations”. Composers also allotted a structural role to “the qualitative dimensions” that previously had been “almost exclusively reserved for pitch and rhythm”. Kliewer states, “The essential elements of any melody are duration, pitch, and quality (timbre), texture, and loudness. Though the same melody may be recognizable when played with a wide variety of timbres and dynamics, the latter may still be an “element of linear ordering.”

Music theory

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Mesopotamia#

Several surviving Sumerian and Akkadian clay tablets include musical information of a theoretical nature, mainly lists of intervals and tunings. The scholar Sam Mirelman reports that the earliest of these texts dates from before 1500 BCE, a millennium earlier than surviving evidence from any other culture of comparable musical thought. Further, “All the Mesopotamian texts about music are united by the use of a terminology for music that, according to the approximate dating of the texts, was in use for over 1,000 years.”

Musical instrument classification

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Classification criteria#

The criteria for classifying musical instruments vary according to point of view, time, and place. The many different approaches consider aspects such as the physical characteristics of the instrument (shape, construction, material composition, physical condition, etc.), the manner in which the instrument is played (plucked, bowed, etc.), the means by which the instrument produces sound, the quality or timbre of the sound produced by the instrument, the tonal and dynamic range of the instrument, the musical function of the instrument (rhythmic, melodic, etc.), and the place of the instrument in an orchestra or other ensemble.

Musical note

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Distinguishing duration#

A note can have a note value that indicates the note’s duration relative to the musical meter. In order of halving duration, these values are: Longer note values (e.g. the longa) and shorter note values (e.g. the two hundred fifty-sixth note) do exist, but are very rare in modern times. These durations can further be subdivided using tuplets. Furthermore, a tie can combine two notes together to create a more specific duration which cannot be represented by a single note’s value. A rhythm is formed from a sequence in time of consecutive notes and rests (the space between notes) of various durations. Rhythms are agnostic to pitches, so if a melody is transposed to a different scale, its rhythm will remain constant.

Pitch (music)

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Pitch and frequency#

Pitch is an auditory sensation in which a listener assigns musical tones to relative positions on a musical scale based primarily on their perception of the frequency of vibration (audio frequency). Pitch is closely related to frequency, but the two are not equivalent. Frequency is an objective, scientific attribute which can be measured. Pitch is the subjective perception of a sound wave by the individual person, which cannot be directly measured. However, this does not necessarily mean that people will not agree on which notes are higher and lower. The oscillations of sound waves can often be characterized in terms of frequency. Pitches are usually associated with, and thus quantified as, frequencies (in cycles per second, or hertz), by comparing the sounds being assessed against sounds with pure tones (ones with periodic, sinusoidal waveforms). Complex and aperiodic sound waves can often be assigned a pitch by this method. According to the American National Standards Institute, pitch is the auditory attribute of sound allowing those sounds to be ordered on a scale from low to high. Since pitch is such a close proxy for frequency, it is almost entirely determined by how quickly the sound wave is making the air vibrate and has almost nothing to do with the intensity, or amplitude, of the wave. That is, “high” pitch means very rapid oscillation, and “low” pitch corresponds to slower oscillation. Despite that, the idiom relating vertical height to sound pitch is shared by most languages. In most cases, the pitch of complex sounds such as speech and musical notes corresponds very nearly to the repetition rate of periodic or nearly-periodic sounds, or to the reciprocal of the time interval between repeating similar events in the sound waveform. Pitch depends to a lesser degree on the sound pressure level (loudness, volume) of the tone, especially at frequencies below 1,000 Hz and above 2,000 Hz. The pitch of lower tones gets lower as sound pressure increases. For instance, a tone of 200 Hz that is very loud seems one semitone lower in pitch than if it is just barely audible. Above 2,000 Hz, the pitch gets higher as the sound gets louder. and W. Snow. Later investigations, e.g. by A. Cohen, have shown that in most cases the apparent pitch shifts were not significantly different from pitch‐matching errors. When averaged, the remaining shifts followed the directions of Stevens’s curves but were small (2% or less by frequency, i.e. not more than a semitone). File:C3 131 Hz oscillogram.png Lower pitches have lower frequency. C 3 , an octave below middle C. The frequency is half that of middle C (131 Hz). (Scale: 1 square is equal to 1 millisecond) File:Middle C, or 262 hertz, on a virtual oscilloscope.png Oscillogram of middle C (262 Hz) (pure tone) File:C5 523 Hz oscillogram.png Higher pitches have higher frequency. Oscillogram of C 5 , an octave above middle C. The frequency is twice that of middle C (523 Hz).

Tonality

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Etymology#

The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840. According to Carl Dahlhaus, however, the term tonalité was only coined by Castil-Blaze in 1821. Although Fétis used it as a general term for a system of musical organization and spoke of types de tonalités rather than a single system, today the term is most often used to refer to major–minor tonality, the system of musical organization of the common practice period. Major–minor tonality is also called harmonic tonality (in the title of Carl Dahlhaus, translating the German harmonische Tonalität), diatonic tonality, common practice tonality, functional tonality, or just tonality.

Transposing instrument

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Ease of switching instruments#

Some instruments are constructed in a variety of sizes, with the larger versions having a lower range than the smaller ones. Common examples are clarinets (the high E clarinet, soprano instruments in C, B and A, the alto in E, and the bass in B), flutes (the piccolo, transposing at the octave, the standard concert-pitch flute, and the alto flute in G), saxophones (in several octaves in B and E), and trumpets (the common instrument in B, instruments in C, D and E, and the piccolo trumpet transposing at the octave). Music is often written in transposed form for these groups of instruments so that the fingerings correspond to the same written notes for any instrument in the family, even though the sounding pitches will differ. A musician who plays several instruments in a family can thus read music in the same way regardless of which particular instrument is being used. Instruments that transpose this way are often said to be in a certain “key” (e.g., the “B clarinet” or “clarinet in B”). This refers to the concert pitch that is heard when a written C is played on the instrument in question. Playing a written C produces a concert B on a B clarinet, a concert A on an A clarinet, and a concert C on a C clarinet (this last example is a non-transposing instrument).