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Encyclopedia > Tetrachord

The tetrachord is a concept of music theory borrowed from ancient Greece. The name means four strings, and refers to the Greek lyre. Traditionally, the lowest and highest strings of the lyre were tuned at the interval of a perfect fourth, or a just ratio of 3:4. The two middle strings were tuned to various divisions of this set interval to create different musical modes. The series of these four tones defines the tetrachord. Greek music theory distinguished between three genera of tetrachords. These genera are characterised by the largest of the three intervals of the tetrachord: 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. ... A lyre is a stringed musical instrument well known for its use in Classical Antiquity. ... In music theory, an interval is the relationship between two notes or pitches, the lower and higher members of the interval. ... The perfect fourth or diatessaron, abbreviated P4, is one of two musical intervals that span four diatonic scale degrees; the other being the augmented fourth, which is one semitone larger. ...

Diatonic
A diatonic tetrachord has a characteristic interval that is equal to, or less than half the total interval of the tetrachord (or 249 cents). This characteristic interval is usually slightly smaller (approximating to 200 cents), becoming a whole tone, Classically, the diatonic tetrachord consists of two intervals of a tone and one semitone.
Chromatic
A chromatic tetrachord has a characteristic interval that is greater than half the total interval of the tetrachord, yet not as great as four-fifths of the interval (between 249 and 398 cents). Classically, the characteristic interval is a minor third (approximately 300 cents), and the two smaller intervals are equal semitones.
Enharmonic
An enharmonic tetrachord has a characteristic interval that is greater than four-fifths the total tetrachord interval (greater than 398 cents). Classically, the characteristic interval is a major third (otherwise known as a ditone), and the two smaller intervals are quartertones.

As the three genera simply represent ranges of possible intervals within the tetrachord, various shades (chroai) of tetrachord with specific tunings were specified. Once the genus and shade of tetrachord are specified the three internal intervals could be arranged in six possible permutations. In Music theory, the diatonic major scale (also known as the Guido scale), from the Greek diatonikos or to stretch out, is a fundamental building block of the European-influenced musical tradition. ... The cent is a logarithmic unit of measure used for musical intervals. ... A major second is one of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the minor second, which is one semitone smaller, and the augmented second, which is one semitone larger. ... A semitone (also known in the USA as a half step) is a musical interval. ... The chromatic scale is the scale that contains all twelve pitches of the Western tempered scale. ... A minor third is the smaller of two commonly occurring musical intervals that span three diatonic scale degrees. ... In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ... A major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ... A quarter tone is an interval half as wide (aurally, or logarithmically) as a semitone, which is half a whole tone. ...


Modern music theory makes use of the octave as the basic unit for determining tuning: ancient Greeks used the tetrachord for this purpose. The octave was recognised by ancient Greece as a fundamental interval, but it was seen as being built from two tetrachords and a whole tone. Ancient Greek music always seems to have used two identical tetrachords to build the octave. The single tone could be placed between the two tetrachords (between perfect fourth and perfect fifth) (termed disjunctive), or it could be placed at either end of the scale (termed conjunctive). In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... A major second is one of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the minor second, which is one semitone smaller, and the augmented second, which is one semitone larger. ... The perfect fourth or diatessaron, abbreviated P4, is one of two musical intervals that span four diatonic scale degrees; the other being the augmented fourth, which is one semitone larger. ... The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ...


Scales built on chromatic and enharmonic tetrachords continued to be used in the classical music of the Middle East and India, but in Europe they were maintained only in certain types of folk music. The diatonic tetrachord, however, and particularly the shade built around two tones and a semitone, became the dominant tuning in European music. A map showing countries commonly considered to be part of the Middle East The Middle East is a region comprising the lands around the southern and eastern parts of the Mediterranean Sea, a territory that extends from the eastern Mediterranean Sea to the Persian Gulf. ... Europe is conventionally considered one of the seven continents of Earth which, in this case, is more a cultural and political distinction than a physiographic one, leading to various perspectives about Europes borders. ... Folk Music, in the original sense of the term, is music by and of the common people. ...


The three permutations of this shade of diatonic tetrachord are:

Lydian mode
A rising scale of two whole tones followed by a semitone, or C D E F.
Phrygian mode
A rising scale of tone, semitone and tone, C D E♭ F, or D E F G.
Dorian mode
A rising scale of a semitone followed by two tones, C D♭ E♭ F, or E F G A.

Medieval music scholars misinterpreted Greek texts, and, therefore, mediaeval and some modern music theory uses these names for different modes than those for which they were originally intended. Due to historical confusion, Lydian mode can refer to two very different musical modes or diatonic scales. ... Due to historical confusion, Phrygian mode can refer to two very different musical modes or diatonic scales. ... Due to historical confusion, Dorian mode can refer to two very different musical modes or diatonic scales. ...


Arab and Indian music divide the tetrachord differently than the Greek. For example, al-Farabi presented ten possible intervals used to divide the tetrachord (Touma 1996, p.19): Arab music is the music of Arabic-speaking people or countries, especially those centered around the Arabian Peninsula. ... Al Farabi (870-950) was born of a Turkish family and educated by a Christian physician in Baghdad, and was himself later considered a teacher on par with Aristotle. ...

Ratio: 1/1 256/243 18/17 162/149 54/49 9/8 32/27 81/68 27/22 81/64 4/3
Note name: c d e f
Cents: 0 90 98 145 168 204 294 303 355 408 498

Since there are two tetrachords and a major tone in an octave, this creates a 25 tone scale as used in the Arab tone system before the quarter tone scale. A major second is one of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the minor second, which is one semitone smaller, and the augmented second, which is one semitone larger. ... The modern Arab tone system, or system of musical tuning, is based upon the theoretical division of the octave into twenty-four equal divisions or 24-tone equal temperament, the distance between each successive note being a quarter tone (50 cents). ... A quarter tone is an interval half as wide (aurally, or logarithmically) as a semitone, which is half a whole tone. ...


In musical set theory, a tetrachord is a collection of four pitch classes, often one of the three ordered tetrachords in a tone row or set form. Tetrachords may be used to create derived rows and invariance. Musical set theory is an atonal or post-tonal method of musical analysis and composition which is based on explaining and proving musical phenomena, taken as sets and subsets, using mathematical rules and notation and using that information to gain insight to compositions or their creation. ... Look up Collection on Wiktionary, the free dictionary In common usage, a collection is any group of items that has one or more properties in common, usually brought together for some specific purpose. ... In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ... In music using the twelve tone technique a derived row is a tone row whose entirety of twelve tones is constructed from a segment or portion of the whole, the generator. ... In music using the twelve tone technique invariance describes the portions of rows which have been so designed that they remain invariant under the allowable transformations (inversion, retrograde, retrograde-inversion, multiplication). ...


See also

The word monad comes from the Greek word μονάς (from the word μόνος, which means one, single, unique) and has had many meanings in different contexts in philosophy, mathematics, computing and music: Among the Pythagoreans (followers of Pythagoras) the monad was the first thing that came... In music, a dyad is any two notes or pitches, more commonly known as an interval. ... In music, especially in musical set theory, a trichord is a collection of three pitch classes, often one of the four ordered trichords in a tone row or set form. ... In music, a hexachord is a collection of six tones. ...

Source

  • Chalmers, John. Divisions of the tetrachord. Frog Peak Publications.
  • Habib Hassan Touma (1996). The Music of the Arabs, trans. Laurie Schwartz. Portland, Oregon: Amadeus Press. ISBN 0931340888.

External links

  • Greek Esoteric Music Theory: The Elemental Tetrachord
Collections of pitch classes edit
Monad | Dyad | Trichord | Tetrachord | Pentachord | Hexachord

en:Tetrachord In common usage, a collection is any group of items that has one or more properties in common. ... In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ... The word monad comes from the Greek word μονάς (from the word μόνος, which means one, single, unique) and has had many meanings in different contexts in philosophy, mathematics, computing and music: Among the Pythagoreans (followers of Pythagoras) the monad was the first thing that came... In music, a dyad is any two notes or pitches, more commonly known as an interval. ... In music, especially in musical set theory, a trichord is a collection of three pitch classes, often one of the four ordered trichords in a tone row or set form. ... In music, a hexachord is a collection of six tones. ...


  Results from FactBites:
 
Tetrachord - Definition, explanation (668 words)
A diatonic tetrachord has a characteristic interval that is equal to, or less than half the total interval of the tetrachord (or 249 centss).
A chromatic tetrachord has a characteristic interval that is greater than half the total interval of the tetrachord, yet not as great as four-fifths of the interval (between 249 and 398 cents).
Since there are two tetrachords and a major tone in an octave, this creates a 25 tone scale used in the Arab tone system before the quarter tone scale.
ZARLINO (3687 words)
The main characteristics of this tetrachord are therefore a "small" semitone (s) of 90 cents (the equal temperament semitone is by definition 100 cents) and two "large" tones of 204 cents (T).
Since the four degrees of the diatono tetrachord are taken, by definition, from the same series of pure fifths, the two intermediate degrees of the sintono must form part of a series which is higher by a comma.
the tetrachords, are not affected in the sense that their ratios one to another are maintained, both for the extreme strings and stepwise from degree to degree.
  More results at FactBites »

 
 

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