rian, [G: a (d') a' ] dominant, F.
Hypophrygian, [G: c (e') b' ] dominant, A.
Hypolydian, [G: c' (f') c''] dominant, A.
Hypo-mixolydian, [G: d' (g') d''] dominant, C.

It is easy to see that these so-called new modes are simply
new versions of the first four; although they are lowered a
fourth beneath the authentic modes (hence the _hypo_), the
_keynote remains the same_ in each instance. Still later two
more modes were added to this list, the Ionic, [G: c' c'']
dominant, G, which corresponded to the ancient Greek Lydian;
and the Aeolian, [G: a' a''] dominant, E, which, strange to say,
was the only one of these newer modes which corresponded to
its Greek namesake. Naturally these two newly admitted modes
were also accompanied by their lower pitched attendant modes,
the Hypoionic, [G: g (c') g'] dominant, E, and the Hypoaeolian,
[G: e' (a') e''] dominant, C.

SUMMARY

Mode. Key. Dominant.

Dorian. D A
Hypodorian. D F
Phrygian. E C
Hypophrygian. E A
Lydian. F C
Hypolydian. F A
Mixolydian. G D
Hypo-mixolydian. G C
Aeolian. A E
Hypoaeolian. A C
Ionian. C G
Hypoionian. C E

Dominants

[G: a' f' c' {a (a')} c' a d' c' e' c' g' e']

Now all these lower, or derived modes, Hypodorian, Hypophrygian,
Hypolydian, etc., received the name Plagal modes, because
there was but one tonic or keynote in the scale; consequently
a melody starting on any degree of the scale would invariably
return to the same tonic or keynote. They differed from the
authentic modes, inasmuch as in the latter a melody might end
either on the upper or lower tonic or keynote. Thus the melody
itself was said to be either authentic or plagal, according
to whether it had one or two tonics. The theme of Schumann's
"Etudes symphoniques" is authentic, and the first variation
is plagal.

Between the sixth and tenth centuries there was much confusion
as to the placing of these modes, but they finally stood as
given above. The Greek names were definitely accepted in the
eleventh century, or thereabouts; previously, they were known
also as the first, second, third, etc., up to the twelfth,
church tones or Gregorian modes.

At this point it is necessary to refer again to Ambrose.
Apar