Tetrachord

A tetrachord ( ancient Greek for "four-string") is a four-tone sequence with the frame interval of a pure fourth . The term is taken from music theory in ancient Greece and is occasionally used to describe the construction of scales. Of the various forms common in ancient Greece, only the so-called diatonic tetrachord has found its way into western music theory. This tetrachord is composed of two whole tones and one semitone , whereby the following variants are possible: whole tone-whole tone-semitone, whole tone-semitone-whole tone and semitone-whole tone-whole tone.

The classical diatonic scales ( major , minor , church tones ) can be composed of two tetrachords with the same structure by adding a further whole tone, provided that the same relationships are used that were the basis of the ancient Greek scales. A distinction must be made between two cases:

The two tetrachords are not connected and the additional whole tone lies in the middle between them.
The two tetrachords are connected by a common tone and the additional whole tone is added above or below.

Examples

In the C major scale (cdefgahc) the two unconnected tetrachords have the interval structure: whole tone-whole tone-semitone. The whole step fg lies between the first tetrachord (cdef) and the second (gahc).
In the natural A minor scale (ahcdefga), the two tetrachords have the structure: whole tone-semitone-whole tone. The first tetrachord (ahcd) is connected to the second (defg) by the common tone d and an additional whole tone step ga is added at the top.

Usage today

If tetrachords are used to describe scales in today's music didactic literature, then only unconnected tetrachords are used. A general music theory, for example, describes the minor scale as being composed of two unconnected tetrachords: “In contrast to the major scale, the two tetrachords of the minor scale are constructed differently from each other.” Reinhard Amon writes: “Almost all seven-note scales (major, minor, Hungarian scales, blues scale ) are made up of two superimposed tetrachords. The bottom note of the first forms an octave with the top note of the second as a frame. "

This approach is not without its problems. While working with various unconnected tetrachords, for example with the natural minor scale, still works smoothly. For example, with the Lydian scale, the difficulty arises that the lower "tetrachord" would span an excessive fourth ( tritone ). This would be in stark contrast to the ancient Greek term tetrachord, in which a consonant frame interval (fourth) is filled with variable nuances. In the ancient Greek sense, the Lydian scale can only be understood as a combined combination of the two similar tetrachords gahc 'and c'-d'-e'-f' with f added below.

In order to explain “Hungarian scales” ( gypsy minor and major ), in addition to the diatonic ones mentioned above, “chromatic” tetrachords have to be used, which consist of two semitones and a minor third or excessive second ( hiatus ). The Gypsy major (c-des-efg-as-b-c ') can then easily be explained as being composed of the two tetrachords c-des-ef and g-as-b-c' , both of which follow the same pattern (semitone -Hiatus semitone). With the gypsy minor (cd-es-fis-g-a -flat -b-c '), however, an analogous explanation no longer works satisfactorily. The lower “tetrachord” would have a different structure than the upper one and a (“forbidden”) tritone as a frame interval.

Such problems, which are often "solved" in the literature by restricting them to unproblematic examples and discreetly hiding critical cases, can easily be avoided if one thinks about the ancient Greek principle, according to which the tetrachords are usually connected by a common tone and only exceptionally to avoid the tritone separated by an interposed whole tone. In this sense, the Gypsy minor could easily be explained as consisting of the connected and identically built tetrachords d-es-fis-g and g-a-flat-hc ′ , which are completed to an octave by the note c below .

history

Ancient Greece

Main article → The sound system of ancient Greece .

In the music of ancient Greece, in addition to the diatonic, the chromatic and the enharmonic appeared as tone genders. However, these are not to be equated with our current terms of diatonic , chromatic and enhharmonic .

The tetrachord played an important role in the music theory of ancient Greece . In the diatonic tetrachord there was a whole step from the initial tone, another whole step and finally a half step down. The half step was always at the lower end of the tetrachord. There are two such ancient Greek tetrachords on the white keys of the modern piano : edch and agfe. Combined, these two tetrachords make a descending diatonic ladder. Putting tetrachords together was a fundamental thought in music theory in ancient Greece. In addition to the diatonic tetrachord, there was also a chromatic tetrachord with the step sequence minor third , semitone, semitone and an enharmonic tetrachord with the step sequence major third, quarter tone , quarter tone. Some of the oldest sources on the tetrachords go back to Greek philosophers and mathematicians. More information can be found in the descriptions of the Greek philosophers and mathematicians. Philolaos - music theory section , Archytas - music section , Aristoxenos - harmonics section , Euclid - music theory section .

middle Ages

See also: Music of the Middle Ages

Music theorists of the Middle Ages, namely the influential Hucbald von Saint-Amand , took up the ancient Greek concept of the tetrachord, but in a different form. Now the four-tone sequences were no longer imagined in descending order, but in ascending order, limited to diatonic proportions and the semitone steps were not exclusively placed below, but optionally below, in the middle or above. The tetrachords obtained were expanded to form hexachords or, as in ancient Greece, combined to form modal ladders, the so-called church scales . The church key Dorian consisted of two tetrachords with the step sequence whole tone, semitone, whole tone (on the white keys of the piano: defg and ahcd).

20th century

In the 20th century , ethnomusicologists adopted the term. They called excerpts from pentatonic ladders with the frame interval of a fourth “tetrachords”, although these excerpts did not consist of four, but only three tones. Two three-tone "tetrachords" formed a pentatonic scale (on the black keys of the piano, for example, c sharp-dis-f sharp and g sharp-a sharp-c sharp). With this meaning, the term tetrachord was used in particular to explain Japanese tone systems, for example by Fumio Koizumi . The melodic analysis of oriental modes, such as the Iranian Dastgah system, is largely based on a tetrachordic perspective.

Remarks

↑ According to Duden, both "the" and "the" tetrachord are possible.
↑ Here, however, the term tetrachord, in a generous extension of the ancient Greek definition, is also used for four-tone sequences that do not have a pure fourth as a frame interval, e.g. B. fgah or cis-def.
↑ In addition to the “classical” scales, there are also newer scale formations that meet the usual definition of “diatonic”, but cannot be composed of tetrachords in the traditional sense. This includes the altered scale , the upper "tetrachord" of which would contain two semitones, while the lower "tetrachord" would only consist of whole-tone steps.
^ Willibald Gurlitt , Hans Heinrich Eggebrecht (ed.): Riemann Music Lexicon (subject part) . B. Schott's Sons, Mainz 1967, p. 930 .
^ Wieland Ziegenrücker: General music theory . 1st edition. B. Schott's Sons, Mainz 1979, ISBN 3-442-33003-3 , p. 88 .
↑ Reinhard Amon: Lexicon of Harmony . 2nd Edition. Doblinger, Vienna 2015, ISBN 978-3-902667-56-4 , pp. 305 .
↑ Harvard Dictionary of Music , 2nd edition, Heinemann (London 1976), keyword “Tetrachord”.
^ The New Grove Dictionary of Music and Musicians , Macmillan (London 1980), keyword "Tetrachord".
↑ The respective direction of movement (downwards in Greek antiquity, upwards in the Middle Ages) is only discussed in the Harvard Dictionary of Music , not in Riemann or New Grove .

[1] According to Duden, both "the" and "the" tetrachord are possible.

[2] Here, however, the term tetrachord, in a generous extension of the ancient Greek definition, is also used for four-tone sequences that do not have a pure fourth as a frame interval, e.g. B. fgah or cis-def.

[3] In addition to the “classical” scales, there are also newer scale formations that meet the usual definition of “diatonic”, but cannot be composed of tetrachords in the traditional sense. This includes the altered scale , the upper "tetrachord" of which would contain two semitones, while the lower "tetrachord" would only consist of whole-tone steps.

[4] Willibald Gurlitt , Hans Heinrich Eggebrecht (ed.): Riemann Music Lexicon (subject part) . B. Schott's Sons, Mainz 1967, p. 930 .

[5] Wieland Ziegenrücker: General music theory . 1st edition. B. Schott's Sons, Mainz 1979, ISBN 3-442-33003-3 , p. 88 .

[6] Reinhard Amon: Lexicon of Harmony . 2nd Edition. Doblinger, Vienna 2015, ISBN 978-3-902667-56-4 , pp. 305 .

[7] Harvard Dictionary of Music , 2nd edition, Heinemann (London 1976), keyword “Tetrachord”.

[8] The New Grove Dictionary of Music and Musicians , Macmillan (London 1980), keyword "Tetrachord".

[9] The respective direction of movement (downwards in Greek antiquity, upwards in the Middle Ages) is only discussed in the Harvard Dictionary of Music , not in Riemann or New Grove .