Traditionally, a tetrachord is a series of four tones filling in the interval of a perfect fourth, a 4:3 frequency proportion. In modern usage a tetrachord is any four-note segment of a scale or tone row. The term tetrachord derives from ancient Greek music theory. It literally means four strings, originally in reference to harp-like instruments such as the lyre or the kithara, with the implicit understanding that the four strings must be contiguous. The lyre is a stringed musical instrument well known for its use in Classical Antiquity and later Ancient Greek music theory distinguishes three genera of tetrachords. These genera are characterised by the largest of the three intervals of the tetrachord:
- Diatonic
- A diatonic tetrachord has a characteristic interval that is less than or equal to half the total interval of the tetrachord (or 249 cents). The cent is a logarithmic unit of measure used for musical intervals. This characteristic interval is usually slightly smaller (approximating to 200 cents), becoming a whole tone. A major second () also called a whole step or a whole tone, is a Musical interval that occurs between the first and second degrees of a Classically, the diatonic tetrachord consists of two intervals of a tone and one semitone. 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
- 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. A minor third ( is the smaller of two commonly occurring musical intervals compounded of two steps of the Diatonic scale.
- Enharmonic
- An enharmonic tetrachord has a characteristic interval that is greater than four-fifths the total tetrachord interval (greater than 398 cents). In modern Music and notation, an enharmonic equivalent is a Note ( enharmonic tone) interval ( enharmonic interval) or Classically, the characteristic interval is a major third (otherwise known as a ditone), and the two smaller intervals are quartertones. A major third ( is one of two commonly occurring Musical intervals that span three Diatonic scale degrees the other being the Minor third. A quarter tone is an interval about half as wide (aurally or logarithmically as a Semitone, which is half a Whole tone.
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.
Contents |
About
Modern music theory makes use of the octave as the basic unit for determining tuning: ancient Greeks used the tetrachord for this purpose. In Music, an octave ( is the the use of which is "common in most musical systems 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. A major second () also called a whole step or a whole tone, is a Musical interval that occurs between the first and second degrees of a 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). The perfect fourth () is a Musical interval which spans four scale degrees The perfect fifth ( is the Musical interval between a note and the note seven Semitones above it on the musical scale
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 Middle East is a Subcontinent with no clear boundaries often used as a synonym to Near East, in opposition to Far East. India, officially the Republic of India (भारत गणराज्य inc-Latn Bhārat Gaṇarājya; see also other Indian languages) is a country Folk music can have a number of different meanings including Traditional music: The original meaning of the term "folk music" was synonymous The diatonic tetrachord, however, and particularly the shade built around two tones and a semitone, became the dominant tuning in European music.
Permutations
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. Due to historical confusion Lydian mode can refer to two very different Musical modes or Diatonic scales Greek Lydian mode The Lydian mode
- Dorian mode
- A rising scale of tone, semitone and tone, C D E♭ F, or D E F G. Due to historical confusion Dorian mode or Doric mode can refer to two very different Musical modes or Diatonic scales Greek
- Phrygian mode
- A rising scale of a semitone followed by two tones, C D♭ E♭ F, or E F G A. The Phrygian mode can refer to two different Musical modes or Diatonic scales the ancient Greek Phrygian mode and the Mediaeval Phrygian mode
Medieval music scholars misinterpreted Greek texts, and, therefore, medieval and some modern music theory uses these names for different modes than those for which they were originally intended.
Pythagorean tunings
Here are the traditional Pythagorean tunings of the diatonic and chromatic tetrachords:
Diatonic hypate parhypate lichanos mese 4/3 81/64 9/8 1/1 | 256/243 | 9/8 | 9/8 | -498 -408 -204 0 cents
Chromatic hypate parhypate lichanos mese 4/3 81/64 32/27 1/1 | 256/243 | 2187/2048 | 32/27 | -498 -408 -294 0 cents
Since there is no reasonable Pythagorean tuning of the enharmonic genus, here is a representative tuning due to Archytas:
Enharmonic hypate parhypate lichanos mese 4/3 9/7 5/4 1/1 | 28/27 |36/35| 5/4 | -498 -435 -386 0 cents
Originally, the lyre had only four strings, so only a single tetrachord was needed. Pythagorean tuning is a system of Musical tuning in which the Frequency relationships of all intervals are based on the ratio 32. Archytas (Ἀρχύτας 428 BC – 347 BC was an Ancient Greek Philosopher, Mathematician, Astronomer, Statesman, and strategist The lyre is a stringed musical instrument well known for its use in Classical Antiquity and later Larger scales are constructed from conjunct or disjunct tetrachords. Conjunct tetrachords share a note, while disjunct tetrachords are separated by a disjunctive tone of 9/8 (a Pythagorean major second). Alternating conjunct and disjunct tetrachords form a scale that repeats in octaves (as in the familiar diatonic scale, created in such a manner from the diatonic genus), but this was not the only arrangement. In Music theory, a diatonic scale (from the Greek διατονικος, meaning " through tones" also known as the heptatonia prima and
The Greeks analzyed genera using various terms, including diatonic, enharmonic, and chromatic, the latter being the color between the two other types of modes which were seen as being black and white. Scales are constructed from conjunct or disjunct tetrachords: the tetrachords of the chromatic genus contained a minor third on top and two semitones at the bottom, the diatonic contained a minor second at top with two major seconds at the bottom, and the enharmonic contained a major third on top with two quarter tones at the bottom, all filling in the perfect fourth (Miller and Lieberman, 1998) of the fixed outer strings. A minor third ( is the smaller of two commonly occurring musical intervals compounded of two steps of the Diatonic scale. 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 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 A major third ( is one of two commonly occurring Musical intervals that span three Diatonic scale degrees the other being the Minor third. A quarter tone is an interval about half as wide (aurally or logarithmically as a Semitone, which is half a Whole tone. The perfect fourth () is a Musical interval which spans four scale degrees However, the closest term used by the Greeks to our modern usage of chromatic is pyknon or the density ("condensation") of chromatic or enharmonic genera. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Condensation is the change of the physical state of aggregation (or simply state of matter from gaseous phase into liquid phase
| Didymos chromatic tetrachord | 16:15, 25:24, 6:5 |
| Eratosthenes chromatic tetrachord | 20:19, 19:18, 6:5 |
| Ptolemy soft chromatic | 28:27, 15:14, 6:5 |
| Ptolemy intense chromatic | 22:21, 12:11, 7:6 |
| Archytas enharmonic | 28:27, 36:35, 5:4 |
- (ibid)
Variations
Arabic and Indian
Arabic and Indian music divide the tetrachord differently than the Greek. Arabic music or Arab music ( Arabic: موسيقى عربية;) includes several genres and styles of Music ranging from Arabic classical For example, al-Farabi presented ten possible intervals used to divide the tetrachord (Touma 1996, p. TemplateInfobox Muslim scholars --> Abū Nasr Muhammad ibn al-Farakh al-Fārābi ( Nastaliq:) or Abū Nasr al-Fārābi 19):
| 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 () also called a whole step or a whole tone, is a Musical interval that occurs between the first and second degrees of a 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 A quarter tone is an interval about half as wide (aurally or logarithmically as a Semitone, which is half a Whole tone.
Uses
Milton Babbitt's serial theory extends the term tetrachord to mean a four-note segment of a twelve-tone row.
Allen Forte in his The Structure of Atonal Music redefines the term tetrachord to mean what other theorists call a tetrad, a set of four pitches or pitch classes, rather than a series of four contiguous pitches within a scale or tone row. In music theory a tetrad is a set of four notes When these four notes form a Tertian chord they are more particularly and more commonly referred to as a Seventh chord
See also
Source
- Chalmers, John H. In music theory a tetrad is a set of four notes When these four notes form a Tertian chord they are more particularly and more commonly referred to as a Seventh chord An all-interval tetrachord is a Tetrachord from which any Interval class can be extracted by means of various inversions. A jins ( Arabic: جنس; plural ajnās, اجناس) is a set of three four or five stepwise pitches used to build an Arabic Jr. Divisions of the Tetrachord. Frog Peak Music, 1993. Frog Peak Music is a Composer 's collective that produces and distributes experimental works and functions as a home for its artists ISBN 0-945996-04-7
- Habib Hassan Touma (1996). The Music of the Arabs, trans. Laurie Schwartz. Portland, Oregon: Amadeus Press. ISBN 0-931340-88-8.
- Miller, Leta E. and Lieberman, Frederic (1998). Lou Harrison: Composing a World. Oxford University Press. ISBN 0-19-511022-6.
| Pitch segments | edit |
| Trichord | Tetrachord | Pentachord | Hexachord | |
Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic