: Modes of the "major scale" or modes of the "diatonic scale"? I'm doing some studying and I think I have a solid grasp on how the diatonic scale was formed, and how it naturally has 7 modes depending on which note you declare

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You do not necessarily need to talk about "modes of a major scale" when you just think the modes as interval-progression and refer to its actual name but include the corresponding root note:

so instead of saying: mixolydian from the c major scale
you could simply say: G mixolydian
or D dorian instead of dorian from the c major scale

I think the names of the modes generally refer to this interval progeressions:

I Ionian 1 2 3 4 5 6 7
II Dorian 1 2 ?3 4 5 6 ?7
III Phrygian 1 ?2 ?3 4 5 6 ?7
IV Lydian 1 2 3 ?4 5 6 7
V Mixolydian 1 2 3 4 5 6 ?7
VI Aeolian 1 2 ?3 4 5 ?6 ?7
VII Locrian 1 ?2 ?3 4 ?5 ?6 ?7

I am really not used to talk about: mixolydian of C melodic minor since then the definition in terms of intervals would break. You would then rather talk about degrees in terms of numbers (I, II , II etc.) but not refer to the "greek" names without adding the special interval like: Mixolydian ?6 in melodic minor.

I Melodic Minor 1 2 ?3 4 5 6 7
II Phrygian ?6 or Dorian ?2 1 ?2 ?3 4 5 6 ?7
III Lydian Augmented 5 1 2 3 ?4 ?5 6 7
IV Lydian Dominant 1 2 3 ?4 5 6 ?7
V Mixolydian ?6 1 2 3 4 5 ?6 ?7
VI Locrian ?2 * 1 2 ?3 4 ?5 ?6 ?7
VII Super Locrian * 1 ?2 ?3 ?4 ?5 ?6 ?7

*) updated; thanks to @TheChaz2 .0

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Simply put, using the term Major Scale is a bit more clear, and less confusing, than referring to the Diatonic Scale. The two terms are, basically, synonymous, but since the Natural Minor Scale is also diatonic (though, not usually referred to as the Diatonic Scale), if we refer to the, say, the 2nd mode (i.e. Dorian) of the Diatonic Scale, some may think we are referring to the scale that is derived from starting on the 2nd degree of the Natural Minor Scale.

However, if we were to define modes in relation to the Major Scale, we can be sure that we are being as clear as possible.

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This question is much deeper than I originally understood. The question is:

Why do we need to refer to a parent scale at all when talking about the modes? All of the 7 modes are diatonic scales, so why not simply refer to them as the "diatonic modes" and leave it at that? And if, for some reason, we do need to refer to a parent scale, why do we choose the major scale to be the parent scale instead of, say, the dorian scale?"

We have to refer to a parent scale because, among other things, modes are a mechanism for creating new scales. We start by choosing an interesting and less common scale, like harmonic major, and we see what happens when we start on a different root. We realize, "hey, if we start on the 5th scale degree, it sounds great over a dominant 7th (?9?13) chord!" When we see our friend later that day, we say "try playing the 5th mode of the harmonic major scale in measure 3." Referring to the parent scale helps us communicate clearly. It's how people tend to think about those less common modes--in terms of more common parent scales.

Given how important the first mode is, it receives a special designation: we call it the "parent scale" for all of the other modes. But for the case of the diatonic modes, aren't all of them already well known? Yes, but there's still a reason why we don't choose dorian to be the parent scale/the 1st mode. The major scale has a very special status (even more special than other parent scales like harmonic major, melodic minor, etc.).

The major scale is special because we use it to define every other scale. Browsing through the names listed in this post, we see things like phrygian ?6, lydian ?2, and dorian ?5. What do those numbers refer to? These numbers/alterations refer to the notes of the major scale. When we say:

natural minor scale has a flat third, a flat sixth, and a flat seventh

what we really mean is:

natural minor scale has a flat third, a flat sixth, and a flat seventh compared to the major scale

The major scale serves as our benchmark or baseline. That's why, given the 7 diatonic modes, we choose it to be the parent scale.

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Diatonic means related to the seven notes we call a major or minor scale. These notes all have intervals between them of a tone or a semitone. Except the harmonic minor, possessing an augmented second. If you are considering 'diatonic' to equate to 'major', that's where you stumbled ! Because there are not 7 modes, but 21. (We can't count chromatics, pentatonics, whole tone, blues scales as diatonic).

Yes, of the 'major scale' there is a total of seven modes related to it. The most used these days is the ubiquitous major scale.

They probably are called modes of the major scale because modes of the minor scale exist also. No, obviously not the Aeolian mode/scale - as it has the same notes as the parent major. But - the notes from the harmonic and melodic scales also will have their own diatonic rooted modes, all of them different from those of the major, which just happens to be known as the Ionian mode as well.

So, to summarise, they need to be called modes of something specific, and the reference or datum point, or parent, if you like, is the basic, best known, most used major scale. It needs a name, too, so is christened Ionian.

As an afterthought, why do you find Aeolian silly as a mode? It happens to be one of the scales/keys that is diatonic, so has as much right and reason to be included in that family. Is it because it's a minor mode? But so is Dorian and Phrygian.