The arguments in favour of identifying the primitive national Modes (harmoniai) with the tonoi or keys may be reinforced by some considerations drawn from the history and use of another ancient term, namely systÊma.

A System (systÊma) is defined by the Greek technical writers as a group or complex of intervals (to ek pleionÔn Ê henos diastÊmatÔn synkeimenon Ps. Eucl.). That is to say, any three or more notes whose relative pitch is fixed may be regarded as forming a particular System. If the notes are such as might be used in the same melody, they are said to form a musical System (systÊma emmeles). As a matter of abstract theory it is evident that there are very many combinations of intervals which in this sense form a musical System. In fact, however, the variety of systems recognised in the theory of Greek music was strictly limited. The notion of a small number of scales, of a particular compass, available for the use of the musician, was naturally suggested by the ancient lyre, with its fixed and conventional number of strings. The word for string (chordÊ) came to be used with the general sense of a note of music; and in this way the several strings of the lyre gave their names to the notes of the Greek gamut[8].