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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
By carving out of the Greater Perfect System (which we may call simply the Complete System) overlapping octave sections, each beginning on a different note, the Greek theorists found these to correspond in their intervals to each of the seven different modes, as follows: Thus all scales came to be thought of theoretically as transpositions of the corresponding octave sections in the Complete System (Foundation Scale). Indeed, the entire system was considered as transposed and the individual tones retained their names regardless of pitch, i. e., in the Dorian mode the mese would always be the fourth note from the bottom, in the Phrygian the fifth, etc.
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As an example, let us transpose the Foundation Scale one tone above its natural pitch:
