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six different notes, or in some cases only two or three.41 These notes form a closed system, characterized by a particular structure and hierarchy and suspended in a tonal void. So far as that melody is concerned, other notesincluding 'the same' notes in another octavedo not exist. To define the melody's tonality or modality it will not be sufficient to say that it is in E flat major (or whatever modern scale the notes may fit). It is necessary to specify its ambitus, what segment of the theoretical scale is actually employed, how many notes above and below the predominant or tonic note, and their relative importance in the melody.
Ancient Greek music requires this kind of analysis if its modal variety is to be understood and the character of individual specimens appreciated. Particularly in the earlier period there is evidence for melodies of limited compass. The airs of Olympus and Terpander are reported to have used only a small number of notes as compared with those of later composers, and more specifically to have been 'simple and three-note'.42 'Three-note', trichorda, could be interpreted as meaning that there were only three notes in what later were tetrachords, in other words that the fourths were divided by only one infix and the scale was pentatonic.43 But it may mean literally that some of these old ritual tunes used only three notes. After all, according to Bruno Nettl,
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Cultures with more complex scale systems nevertheless tend to have some songs with only two or three tones, and this is also true of European folk cultures. In most cases (in Europe and elsewhere) these are children's songs, game songs, lullabies, and old ritual melodies.44
If the first interpretation is correct, the reference may still be to melodies with as few as five distinct notes and an ambitus of less than an octave. One of the ceremonial tunes attributed to Olympus, the Spondeion or Libatory, was apparently based on the five notes e f a b 0173-001.gif.45 In e f a we recognize the fourth with infix, and it seems
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41 C. Engel, An Introduction to the Study of National Music (London, 1866). 120-3, Nettl, FTM 45f.; C. Sachs, The Rise of Music in the Ancient World (New York, 1943), 31-9 and WM 59-72.
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42 Ps.-Plut. De mus. 1137ab.
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43 See above. p. 163. According to Clement, Strom. 1. 76. 5, Agnis (Hyagnis) the Phrygiana legendary prehistoric figureinvented 'the trichord and the diatonic scale'; but it is not entirely clear whether 'trichord' here is adjectival, referring to a type of scale, or a noun, the instrument that bore this name (above, p. 80).
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44 Op. cit. 45.
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45 Ps.-Plut. De mus. 1135ab, 1137b-d; Barker, GMW i. 255f. The note-values given here serve merely to characterize the intervals of the scale: we do not know the proper pitch.

 
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