More on modes

The relationship between the Greek and Ecclesiastical modal nomenclatures
is a confusing topic and I think somewhat more complex than the result of
simple intervallic inversion, though this is a good way to remember the
orders.

In the natural key (C major, no accidentals), the order of the Greek modes
(ascending) is Mixolydian (B), Lydian (c), Phrygian (d), Dorian (e),
Hypolydian (f), Hypophrygian (g) and Hypodorian (a). The corresponding
interval patterns (ascending) are (in generalized diatonic tuning):
M S T T S T T T
L T T S T T T S
P T S T T T S T
D S T T T S T T
HL T T T S T T S
HP T T S T T S T
HD T S T T S T T

Retrograding these interval patterns or doing the equivalent operation of
inverting the scales around the octave yields the following pairs:
M HL
L D
P P
D L
HL M
HP HD
HD HP

It is true that the order of the M L P D HL modes is reversed to HL D P L
M,
but the HP and HD modes do not fit the pattern unless the HD mode is taken
an octave lower to low A (on proslambanomenos). Then the inversion pattern
fits exactly. However, I do not think this is the way the system developed
historically, though I admit that the effect is the same.

Although the modes may be thought of as sections of the diatonic scale
starting on different notes, the Greeks actually transposed all their modes
to the same register. Thus there developed a set of pitch keys named after
the modes which they transposed into the central two octave range. The
Dorian key and mode were the center point. The Phrygian key was a tone
higher so that the sequence D-d now fell on the notes that formerly
represented the E mode. The Hypolydian was a tone higher still (two tones
in all) and the Mixolydian a semitone above this. Similarly, the Hypolydian
key was a semitone below the Dorian (to bring the sequence f-f' into the
center range), the Hypophrygian a tone and 1/2, and the Hypodorian a tone
below this.

These pitch keys ran in the ascending order HD HP HL D P L M which
corresponds to the Ecclesiastical modes Aeolian or Hypodorian (A),
Hypophrygian (B), Ionian or Hypolydian (c), Dorian (d), Phrygian (e)
Lydian (f), and Mixolydian (g). In other words, the ecclesiastical modes
are in the order of the pitch keys, the Greek in the order of their
starting notes.

This is a simplified account as there was another series of late Greek
pitch
keys interleaved between these (so that keys stood at semitonal intervals)
and the entire system was transposed so that the f mode (Hypolydian still)
was
the center rather than the e mode (Dorian). The topic is further
complicated by there being more than one set of ecclesiastical names
depending upon the writer and the period.

--John