Hexachord

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Hexachord ostinato, in cello, which opens Die Jakobsleiter by Arnold Schoenberg, notable for its compositional use of hexachords
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In music, a hexachord (also hexachordon) is a six-note series, as exhibited in a scale or tone row. The term was adopted in this sense during the Middle Ages and adapted in the 20th century in Milton Babbitt's serial theory. The word is taken from the Greek : ἑξάχορδος, compounded from ἕξ (hex, six) and χορδή (chordē, string [of the lyre], whence "note"), and was also the term used in music theory up to the 18th century for the interval of a sixth ("hexachord major" being the major sixth and "hexachord minor" the minor sixth). [2] [3]

Music form of art using sound

Music is an art form and cultural activity whose medium is sound organized in time. General definitions of music include common elements such as pitch, rhythm, dynamics, and the sonic qualities of timbre and texture. Different styles or types of music may emphasize, de-emphasize or omit some of these elements. Music is performed with a vast range of instruments and vocal techniques ranging from singing to rapping; there are solely instrumental pieces, solely vocal pieces and pieces that combine singing and instruments. The word derives from Greek μουσική . See glossary of musical terminology.

Musical note sign used in musical notation, a pitched sound

In music, a note is the pitch and duration of a sound, and also its representation in musical notation. A note can also represent a pitch class. Notes are the building blocks of much written music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis.

In music, a tone row or note row, also series or set, is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometimes found.

Contents

Middle Ages

The hexachord as a mnemonic device was first described by Guido of Arezzo, in his Epistola de ignoto cantu. [4] In each hexachord, all adjacent pitches are a whole tone apart, except for the middle two, which are separated by a semitone. These six pitches are named ut, re, mi, fa, sol, and la, with the semitone between mi and fa. These six names are derived from the first syllable of each half-verse of the first stanza of the 8th-century Vesper hymn Ut queant laxis resonare fibris / Mira gestorum famuli tuorum, etc. [5] Melodies with a range wider than a major sixth required the device of mutation to a new hexachord. For example, the hexachord beginning on C and rising to A, named hexachordum naturale, has its only semitone between the notes E and F, and stops short of the note B or B. A melody moving a semitone higher than la (namely, from A to the B above) required changing the la to mi, so that the required B becomes fa. Because B was named by the "soft" or rounded letter B, the hexachord with this note in it was called the hexachordum molle (soft hexachord). Similarly, the hexachord with mi and fa expressed by the notes B and C was called the hexachordum durum (hard hexachord), because the B was represented by a squared-off, or "hard" B. Starting in the 14th century, these three hexachords were extended in order to accommodate the increasing use of signed accidentals on other notes. [6]

Guido of Arezzo Italian monk, inventor of musical notaticulo

Guido of Arezzo was an Italian music theorist of the Medieval era. He is regarded as the inventor of modern musical notation that replaced neumatic notation. His text, the Micrologus, was the second most widely distributed treatise on music in the Middle Ages.

Semitone musical interval

A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale. For example, C is adjacent to C; the interval between them is a semitone.

Ut queant laxis psalm

"Ut queant laxis" or "Hymnus in Ioannem" is a Latin hymn in honor of John the Baptist, written in Horatian Sapphics and traditionally attributed to Paulus Diaconus, the eighth-century Lombard historian. It is famous for its part in the history of musical notation, in particular solmization. The hymn belongs to the tradition of Gregorian chant.

The introduction of these new notes was principally a product of polyphony, which required the placing of a perfect fifth not only above the old note B, but also below its newly created variant, this entailing, as a result of the ‘original sin‘ committed by the well-meant innovation B, the introduction of the still newer respective notes F and E, with as consequences of these last C and A, and so on. The new notes, being outside the gamut of those ordinarily available, had to be "imagined", or "feigned" (it was long forbidden to write them), and for this reason music containing them was called musica ficta or musica falsa. [7]

Polyphony

In music, polyphony is one type of musical texture, where a texture is, generally speaking, the way that melodic, rhythmic, and harmonic aspects of a musical composition are combined to shape the overall sound and quality of the work. In particular, polyphony consists of two or more simultaneous lines of independent melody, as opposed to a musical texture with just one voice, monophony, or a texture with one dominant melodic voice accompanied by chords, which is called homophony.

Perfect fifth musical interval

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.

Musica ficta was a term used in European music theory from the late 12th century to about 1600 to describe pitches, whether notated or added at the time of performance, that lie outside the system of musica recta or musica vera as defined by the hexachord system of Guido of Arezzo.

20th century

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Allen Forte in The Structure of Atonal Music [9] redefines the term hexachord to mean what other theorists (notably Howard Hanson in his Harmonic Materials of Modern Music: Resources of the Tempered Scale [10] ) mean by the term hexad, a six-note pitch collection which is not necessarily a contiguous segment of a scale or a tone row. David Lewin used the term in this sense as early as 1959. [11] Carlton Gamer uses both terms interchangeably. [12]

Allen Forte American musicologist

Allen Forte was an American music theorist and musicologist. He was Battell Professor Emeritus of the Theory of Music at Yale University and specialized in 20th-century atonal music and music analysis.

Howard Hanson 20th-century American composer, conductor, educator and music theorist

Howard Harold Hanson was an American composer, conductor, educator, music theorist, and champion of American classical music. As director for 40 years of the Eastman School of Music, he built a high-quality school and provided opportunities for commissioning and performing American music. In 1944, he won a Pulitzer Prize for his Symphony No. 4, and received numerous other awards including the George Foster Peabody Award for Outstanding Entertainment in Music in 1946.

David Benjamin 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 music.

See also

In music and music theory, a hexatonic scale is a scale with six pitches or notes per octave. Famous examples include the whole tone scale, C D E F G A C; the augmented scale, C D E G A B C; the Prometheus scale, C D E F A B C; and the blues scale, C E F G G B C. A hexatonic scale can also be formed by stacking perfect fifths. This results in a diatonic scale with one note removed.

Guidonian hand

In Medieval music, the Guidonian hand was a mnemonic device used to assist singers in learning to sight-sing. Some form of the device may have been used by Guido of Arezzo, a medieval music theorist who wrote a number of treatises, including one instructing singers in sightreading. The hand occurs in some manuscripts before Guido's time as a tool to find the semitone; it does not have the depicted form until the 12th century. Sigebertus Gemblacensis in c. 1105–10 did describe Guido using the joints of the hand to aid in teaching his hexachord. The Guidonian hand is closely linked with Guido's new ideas about how to learn music, including the use of hexachords, and the first known Western use of solfege.

In music using the twelve tone technique, combinatoriality is a quality shared by twelve-tone tone rows whereby each section of a row and a proportionate number of its transformations combine to form aggregates. Much as the pitches of an aggregate created by a tone row do not need to occur simultaneously, the pitches of a combinatorially created aggregate need not occur simultaneously. Arnold Schoenberg, creator of the twelve-tone technique, often combined P-0/I-5 to create "two aggregates, between the first hexachords of each, and the second hexachords of each, respectively."

Sources

  1. Arnold Whittall, The Cambridge Introduction to Serialism, Cambridge Introductions to Music (New York: Cambridge University Press, 2008): 23. ISBN   978-0-521-86341-4 (hardback) ISBN   978-0-521-68200-8 (pbk).
  2. William Holder, A Treatise of the Natural Grounds and Principles of Harmony (London: Printed by J. Heptinstall, for John Carr, at the Middle-Temple-Gate, in Fleet-Street, 1694): 192. Facsimile reprint, New York: Broude Brothers, 1967.
  3. Ephraim Chambers, Cyclopædia: or, an Universal Dictionary of Arts and Sciences , 2 vols. (London: Printed for J. and J. Knapton [and 18 others], 1728): 1, part 2:247.
  4. Guido d'Arezzo, "Epistola de ignotu cantu [ca. 1030]", abridged translation by Oliver Strink in Source Readings in Music History, selected and annotated by Oliver Strunk, 5 vols. (New York: W. W. Norton, 1965): 1:121–25. Latin test in Martin Gerbert, Scriptores ecclesistici de musica sacra potissimum, 3 vols. (St. Blasien, 1784), 2:43–46, 50. See also Clause V. Palisca, "Introduction" to Guido's Micrologus, in Hucbald, Guido, and John on Music: Three Medieval Treatises, translated by Warren Babb, edited, with introductions by Claude V. Palisca, index of chants by Alejandro Enrique Planchart, 49–56, Music Theory Translation Series 3 (New Haven and London: Yale University Press, 1978): esp. 49–50. ISBN   0-300-02040-6.
  5. Guido d'Arezzo, "Epistola de ignotu cantu [ca. 1030]", abridged translation by Oliver Strink in Source Readings in Music History, selected and annotated by Oliver Strunk, 5 vols. (New York: W. W. Norton, 1965): 1:121–25. Citation on p. 124.
  6. Jehoash Hirshberg, "Hexachord", The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publishers, 2001).
  7. Andrew Hughes and Edith Gerson-Kiwi, "Solmization [solfatio, solmifatio]", The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publishers, 2001): §4, "Expansion of the Hexachord System".
  8. George Perle, Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern, sixth edition, revised (Berkeley: University of California Press, 1991): 145. ISBN   978-0-520-07430-9.
  9. Allen Forte, The Structure of Atonal Music (New Haven and London: Yale University Press, 1973).[ page needed ] ISBN   0-300-01610-7 (cloth) ISBN   0-300-02120-8 (pbk).
  10. Howard Hanson, Harmonic Materials of Modern Music: Resources of the Tempered Scale (New York: Appleton-Century-Crofts, 1960): [ page needed ].
  11. David Lewin, "Re: Intervallic Relations Between Two Collections of Notes", Journal of Music Theory 3, no. 2 (November 1959): 298–301, citation on 300.
  12. Carlton Gamer, "Some Combinational Resources of Equal-Tempered Systems", Journal of Music Theory 11, no. 1 (Spring 1967): 32–59. The term "hexad" appears just once, in a table on p. 37; the word "hexachord" also occurs once, on p. 41.

Further reading

International Standard Book Number Unique numeric book identifier

The International Standard Book Number (ISBN) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.

Stanley John Sadie was an influential and prolific British musicologist, music critic, and editor. He was editor of the sixth edition of the Grove Dictionary of Music and Musicians (1980), which was published as the first edition of The New Grove Dictionary of Music and Musicians.

Related Research Articles

In the theory of Western music, a mode is a type of musical scale coupled with a set of characteristic melodic behaviors. Musical modes have been a part of western musical thought since the Middle Ages, and were inspired by the theory of ancient Greek music. The name mode derives from the Latin word modus, "measure, standard, manner, way, size, limit of quantity, method".

In music, an accidental is a note of a pitch that is not a member of the scale or mode indicated by the most recently applied key signature. In musical notation, the sharp, flat, and natural symbols, among others, mark such notes—and those symbols are also called accidentals.

In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones. For instance, the interval from F up to the B above it is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B. According to this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. A tritone is also commonly defined as an interval spanning six semitones. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B and B–F. In twelve-equal temperament, the tritone divides the octave exactly in half.

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In music theory, a trichord is a group of three different pitch classes found within a larger group. A trichord is a contiguous three-note set from a musical scale or a twelve-tone row.

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The Aeolian mode is a musical mode or, in modern usage, a diatonic scale also called the natural minor scale. On the white piano keys, it is the scale that starts with A. Its ascending interval form consists of a key note, whole step, half step, whole step, whole step, half step, whole step to return.

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Interval vector

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Ionian mode is a musical mode or, in modern usage, a diatonic scale also called the major scale.

Diatonic and chromatic

Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900.

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In medieval music theory, the terms color and coloration are used in four distinct senses, two of which relate to the notation and structuring of note durations, the third to florid ornamentation, and the fourth to the quality of chromatic music.