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Musical system of ancient Greece : ウィキペディア英語版
Musical system of ancient Greece

The musical system of ancient Greece evolved over a period of more than 500 years from simple scales of tetrachords, or divisions of the perfect fourth, to ''The Perfect Immutable System'', encompassing a span of fifteen pitch keys (see ''tonoi'' below)
Any discussion of ancient Greek music, theoretical, philosophical or aesthetic, is fraught with two problems: there are few examples of written music, and there are many, sometimes fragmentary theoretical and philosophical accounts. This article provides an overview that includes examples of different kinds of classification while also trying to show the broader form evolving from the simple tetrachord to system as a whole.
==''Systêma ametabolon'', an overview of the tone system==
At about the turn of the 5th to 4th century BCE the tonal system, systema teleion, had been elaborated in its entirety. As an initial introduction to the principal names of the divisions of the system and the framing tetrachords, a depiction of notes and positional terms follows. Please note, this is an as yet not completely translated version of a German illustration, hence, ''b'' in the illustration is B and ''h'', B.
Greek theorists conceived of scales from higher pitch to lower (the opposite of modern practice), and the largest intervals were always at the top of the tetrachord, with the smallest at the bottom. The 'characteristic interval' of a tetrachord is the largest one (or the 'tone' in the case of the 'tense/hard diatonic' genus). The image shows the descending two octaves of tones with corresponding modern note symbols and ancient Greek vocal, and instrumental, note symbols in the central columns. The modern note names are merely there for an orientation as to the intervals. They do not correspond to ancient Greek pitches or note names. The section delimited by a blue brace is the range of the central octave. The range is approximately what we today depict as follows:
The Greek note symbols originate from the work of Egert .
The Greater Perfect System (systêma teleion meizon) was composed of four stacked tetrachords called the (from bottom to top) Hypatôn, Mesôn, Diezeugmenôn and Hyperbolaiôn tetrachords (see the right hand side of the diagram). Each of these tetrachords contains the two fixed notes that bound it.
The octaves are each composed of two like tetrachords (1–1–½) connected by one common tone, the 'Synaphé''. At the position of the ''Paramése'', which should be the connecting (''Synaphé'') tone, the continuation of the system encounters a boundary (at b-flat, b). To retain the logic of the internal divisions of the tetrachords (see below for more detail) such that ''méson'' not consist of three whole tone steps (b-a-g-f), an interstitial note, the ''diázeuxis'' ('dividing') was introduced between ''Paramése'' and ''Mése''. The tetrachord ''diezeugménon'' is the 'divided'. To bridge this inconsistency, the system allowed moving the ''Néte'' one step up permitting the construction of the ''synemmenón'' ('connecting') tetrachord (see the far left of the diagram).
The use of the synemmenón tetrachord effected a modulation of the system, hence the name ''systema metabolon'', the modulating system also
the Lesser Perfect System. It was considered apart, built of three stacked tetrachords—the Hypatôn, Mesôn and Synêmmenôn. The first two of these are the same as the first two tetrachords of the Greater Perfect (right side diagram), with a third tetrachord placed above the Mesôn (left side diagram). When viewed together, with the Synêmmenôn tetrachord placed between the Mesôn and Diezeugmenôn tetrachords, they make up the Immutable (or Unmodulating) System (systêma ametabolon).
In sum, it is clear that the ancient Greeks conceived of a unified system with the octave as the unifying structure (interval). The very last (deepest) tone no longer belongs to the system of tetrachords reflected in its name, the ''Proslambanomenós'', the adjoined.
Below elaborates the mathematics that led to the logic of the system of tetrachords just described.


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