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Page 228
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Mixolydian
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Phrygian
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Dorian
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(Hypo)lydian

To assimilate these to Eratocles' regular species, we have to ignore the anomalous d in the Mixolydian and supply a missing a; delete the Dorian d, which exceeds the octave; and make an only slightly greater modification of the Phrygian, purging it of its top d' and changing the lower d down to c.
Eratocles also digested into his scheme a current Hypophrygian and a Locrian/Hypodorian mode. 'Hypolydian' is not attested as a Classical mode, and he may have devised this name for the sake of parallelism, so that Lydian, Phrygian, and Dorian each had a corresponding Hypo- species starting on the note a fourth higher in the abstract revolving scale. As Eratocles' Hypolydian is the Damonian Lydian, his Lydian 0228-005.gif must be based on some alternative form of Lydian, unless it is his own creation for the sake of the scheme.
Keys
Other expositors constructed Perfect Systems extending over a twelfth or more, by staggering the modal scales in such a way that similar interval-sequences could be aligned and they could all be fitted into one sequence. But then, to counteract the displacement of one mode relative to another, a system of notional keys (tonoi, 'pitches') was invented. These were different pitches at which the Perfect System as a whole could be set. The higher up the composite scale a particular modal scale lay, the lower the key it was declared to be played in, so that in actuality they all stayed in more or less the same register, as for practical purposes they had to. The keys were named after the modes they went with.
We do not know many details of the pre-Aristoxenian systems of this type, but we gather that there were several rival ones. Aristoxenus likens the situation to the chaos that characterized Greek local calendars, 'as when it is the tenth of the month in Corinth but the fifth in Athens and the eighth somewhere else'. He refers to one scheme in which the Hypodorian key, as the lowest, was followed by the Mixolydian, Dorian, Phrygian, and Lydian, at intervals of semitone, semitone, tone, tone; another in which there was a Hypophrygian below the Hypodorian; another in which the order was Hypo-

 
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