The arguments in favour of identifying the primitive national Modes ([Greek: harmoniai]) with the [Greek: tonoi] or keys may be reinforced by some considerations drawn from the history and use of another ancient term, namely [Greek: systêma]. A System ([Greek: systêma]) is defined by the Greek technical writers as a group or complex of intervals ([Greek: 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 ([Greek: 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_ ([Greek: 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[1]. § 16. _The Standard Octachord System._ In the age of the great melic poets the lyre had no more than seven strings: but the octave was completed in the earliest times of which we have accurate information. The scale which is assumed as matter of common knowledge in the Aristotelian _Problems_ and the _Harmonics_ of Aristoxenus consists of eight notes, named as follows from their place on the lyre: Nêtê ([Greek: neatê] or [Greek: nêtê], lit. 'lowest,' our 'highest'). Paranêtê ([Greek: paranêtê], 'next to Nêtê'). Tritê ([Greek: tritê], _i.e._ 'third' string). Paramesê ([Greek: paramesê] or [Greek: paramesos], 'next to Mesê'). Mesê ([Greek: mesê], 'middle string'). Lichanos ([Greek: lichanos], _i.e._ 'forefinger' string). Parhypatê ([Greek: parypatê]). Hypatê ([Greek: hypatê], lit. 'uppermost,' our 'lowest'). It will be seen that the conventional sense of high and low in the words [Greek: hypatê] and [Greek: neatê] was the reverse of the modern usage.