How to find the parent scale (prime form?) for a group of sibling modes?

Question

Reminder: I know just enough theory to be really annoying. this is everything I know about it. so far.

I've calculated all the possible modes and recently learned they all have names but what eludes me is how the parent scale is chosen for a group of sibling modes. Like Ionian has the most diatonic notes, or least accidentals (if we're talking C Ionian). what about all the others.. how do you determine which is the major (or primary?) scale of the group? and which are its modes?

confusing enough yet?

TL:DR:

for example, we know the first group given the modes:

legend:
a) number of degrees in the scale
b) modal sibling group (related interval patterns)
c) number of degrees with perfect 5ths in the scale
d) number of degrees in the diatonic scale
+-----------+---+---+---+---+-----------------------------+----------------+
|name       | a | b | c | d |  degrees                    |  intervals     |
+-----------+---+---+---+---+-----------------------------+----------------+
|Lydian     | 7 | 1 | 6 | 6 |  0,  2,  4,  6,7,  9,   11  |  2,2,2,1,2,2,1 |
|Mixolydian | 7 | 1 | 6 | 6 |  0,  2,  4,5,  7,  9,10     |  2,2,1,2,2,1,2 |
|Aeolian    | 7 | 1 | 6 | 4 |  0,  2,3,  5,  7,8,  10     |  2,1,2,2,1,2,2 |
|Locrian    | 7 | 1 | 6 | 2 |  0,1,  3,  5,6,  8,  10     |  1,2,2,1,2,2,2 |
|Ionian     | 7 | 1 | 6 | 7 |  0,  2,  4,5,  7,  9,   11  |  2,2,1,2,2,2,1 |
|Dorian     | 7 | 1 | 6 | 5 |  0,  2,3,  5,  7,  9,10     |  2,1,2,2,2,1,2 |
|Phrygian   | 7 | 1 | 6 | 3 |  0,1,  3,  5,  7,8,  10     |  1,2,2,2,1,2,2 |
+-----------+---+---+---+---+-----------------------------+----------------+
                               C # D # E F # G # A  #  B 
+-----------+---+---+---+---+-----------------------------+----------------+
|Ionythian  | 7 | 2 | 5 | 6 |  0,      4,5,  7,  9,10,11  |  4,1,2,2,1,1,1 |
|Aeolyrian  | 7 | 2 | 5 | 3 |  0,1,  3,  5,6,7,8          |  1,2,2,1,1,1,4 |
|Gorian     | 7 | 2 | 5 | 6 |  0,  2,  4,5,6,7,       11  |  2,2,1,1,1,4,1 |
|Aeolodian  | 7 | 2 | 5 | 5 |  0,  2,3,4,5,      9,10     |  2,1,1,1,4,1,2 |
|Doptian    | 7 | 2 | 5 | 3 |  0,1,2,3,      7,8,  10     |  1,1,1,4,1,2,2 |
|Aeraphian  | 7 | 2 | 5 | 5 |  0,1,2,      6,7,9,     11  |  1,1,4,1,2,2,1 |
|Zacrian    | 7 | 2 | 5 | 3 |  0,1,      5,6,  8,  10,11  |  1,4,1,2,2,1,1 |
+-----------+---+---+---+---+-----------------------------+----------------+

but what about the second group (probably a bad example given the mode named 'ionythian' but you get the gist? there are a lot of groups without modes starting with 'ion' as in Ionian).

Maybe should have used Aeolacrian, Zythian, Dyrian, Koptian, Thocrian, Aeolanian, Danian?

I thought a few things, calculating based on number of perfections (degrees whose perfect 5th is also in the mode) and diatonic notes (if 'C' was the root, how many of the modes degrees are in the major scale) but the number of perfections are the same (duh) and multiple modes have the highest number of matches to the major scale.

I read somewhere that the mode with the most degrees packed towards the root would be the victor (eg if one modes degrees started 1,2,3,... it would be chosen over another mode that started 1,3,5) but this means that Gorian would be chosen over Ionythian

Answer 1

In practice, the most popular scale is the parent. By that logic, Locrian sure as heck isn't the parent. There are also modes of the harmonic minor (e.g. Phrygian Dominant) and ascending melodic minor scales, with harmonic minor and ascending melodic minor being assumed to be the parents because they're that much more common. Even major pentatonic and minor pentatonic scales are modes of each other, with major pentatonic winning the "parent" race there (though maybe not by that much). The whole-half and half-whole diminished scales are modes of each other, with no distinct parent due to their pretty much equal lack of popularity.

So, for evenly unpopular enough mode families such as the diminished scales and your "Ionythian" family, there is no parent.

Answer 2

You mention the concept of the "prime form" of a pitch class set, and the idea of "the most degrees packed towards the root" which indeed describes the prime form. However, mixing up tonal concepts of keys and modes with set theory concepts of pitch class sets and prime forms is problematic. For one, the prime form of a pitch class set ignores direction, e.g. a minor triad and a major triad have the same prime form 0-3-7, because they both contain a minor third, a major third, and a perfect fifth. In fact, the prime form of your second list of "modes" would be the Ionythian mode starting from C but backwards, i.e.

C B A# A G F E

with intervals

1,1,1,2,2,1,4

and prime form

0,1,2,3,5,7,8

Answer 3

Somehow, I think if you approached modes from the basic angel 🧚 that I use, it may make more sense.

I have (for ever) regarded modes as the derivatives of a parent. So, using the parent of C major, its 'children' are D, E, F, G, A, and B as root/home/base notes. So from the parent C, we get D Dorian, E Phrygian, F Lydian, G Mixolydian, A Aeolian and B Locrian as the titles of the modes which are directly descended, or related to, the notes comprising the C major scale.

That's the modern way in which modes are considered, and far easier (for me, at least) to make any sense of them. This could be an easier concept to use rather than taking C and its parallel modes, which I find a longer job to assimilate.