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

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

• This approach assumes some cause-and-effect things that aren't necessarily true. As far as I know, the "church modes" didn't have "children" deriving from a "parent," they just were a collection. The way you're thinking of this is being colored a bit by starting every mode on C. Another way of understanding the church modes is to start each one on a different pitch, and for certain pitches column "D" can be 7 for all of them. That is, instead of conceiving of them as mutating the Ionian mode, instead they share the same pitches and just "center" them differently. Nov 20 at 13:50
• Have you read this (or watched the accompanying video)? Prime Form at ianring.com Nov 20 at 16:14
• Does this answer your question? How to find the root note of a scale? Nov 20 at 16:38
• @PiedPiper I'm not nuts about the proposed dupe. While the question might have overlap, the existing answer is so simplistic as to be no help to yarns here (though maybe the one the OP over there needed to hear)... Nov 20 at 22:55
• @AndyBonner That doesn't mean this isn't a duplicate; it means the other question should receive better answers. Nov 21 at 7:44

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.

• i'm coming to this conclusion slowly i think Nov 21 at 7:30
• +1 Music theory is descriptions of musical practices, and a theoretical i.e. descriptional concept of "parent" exists i.e. is meaningful to people only as far as someone has a communicational need to describe something to another person by using such a concept. Whatever is the most well-known to the recipient of communication, is a good candidate to be referred to as a "parent" scale. Nov 21 at 9:26

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
```

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.

• but how do you find the parent for the modes Aeolacrian, Zythian, Dyrian, Koptian, Thocrian, Aeolanian, Danian? which one is the parent? Nov 20 at 16:01
• @yarns Although this is sort of what I proposed, I feel like there's one key thing here that could confuse you: there's nothing special about Ionian. Except for centuries of preferential treatment. There's no procedural reason that it's a "parent"; it's just a handy way of understanding the modes. If we lived in a universe where Dorian was the most common, we might be talking about whether Dorian were a "parent" of Ionian. So I would pose significant challenge to this answer and say that there is not such a thing as a "parent mode," except as a handy learning concept. Nov 20 at 18:43
• @AndyBonner - of course, you're right. But Ionian has become the datum point, like it or not. To use another only muddies the water even more! And the reason is probably that these days, a great(er) percentage of pieces use Ionian as a basis, can't deny that. And - 'handy learning concept' - we all desperately need those..!
– Tim
Nov 21 at 10:10
• yeah i cant find any connection between major and diatonic like why does it start at C? just because we had to start somewhere... but i can't find any way to distinguish a mode from its siblings, every thing i try usually has two modes with the same properties. if only i had a genie and a lamp haha, my OCD is glitching every time i decide to just pick one. there's likely an angle i haven't considered but i think i'll end up going with the 'whichever has the most degrees closest to the root' formula. unfortunately the way i designed my app requires a "prime", even if there isn't one in theory! Nov 22 at 14:12