Hypolydian Hyperlydian (Like Hypophrygian) /━━━━━━━━━━━━━━━━━━━━━\ /━━━━━━━━━━━━━━━━━━━━━\ F G A B c d e f a b c´ d´ e´ f´ g´ ╲▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁╱ Lydian (It is evident from this table that the Hypodorian corresponds to the Hyperphrygian, and the Hypophrygian to the Hyperlydian; hence there are only seven _different_ modes.) A common relationship was thus clearly recognized between the three scales of each group, which may be thought of as having one common tonic. It may be noted, however, that the Hypodorian probably had an independent existence before being associated with the Dorian, as is indicated by its own ethnological name of 'Æolian,’ and as such was supposed to be of great antiquity. The Hyperdorian enjoyed an independent existence as 'Mixolydian.’ Its invention has been variously ascribed to Sappho, Damon and Pythocleides. We have seen how, by joining two tetrachords, the Greeks constructed their Dorian scale (octachord). By joining _additional_ tetrachords to this scale at either end they obtained their double octave scale or 'Perfect Immutable System’: [Illustration: Music] It should be noted, however, that the new tetrachords are added _conjunctively_, i. e., so that one of their notes (e) coincides with the terminal notes of the original octave, while the two tetrachords making up that octave were placed in juxtaposition with a whole tone step between them. This was called the tone of disjunction (_diezeuxis_). For purposes of modulation (_metabole_) they now laid across the middle of this system an additional diatonic tetrachord (from d to a) in such a way that one of its tones (b♭) came half way between the two notes of the _diezeuxis_.[37] The low A was added to round out the octave. (It is a curious fact that what we call _low_ the Greeks called _high_ and _vice versa_.) The two tetrachords _Meson_ and _Hypaton_, together with the conjunctive (_Synemmenon_), were also considered as an independent system called the Lesser Perfect System. The relation of these systems as well as the names of the individual notes are set forth on the accompanying table. DOUBLE OCTAVE SCALE, or PERFECT IMMUTABLE SYSTEM