In jams, someone will say, "Let's play modal tunes." Kitchen Girl, Glory in the Meeting House, Santy Anna's Retreat, ... American fiddle tunes collections are full of 'em.
Let me explain modes in a different way, which will.
You can hear the difference between major and minor, right? Those are two modes, Ionian and Aeolian. The other modes sound different, too, but they don't sound like either of these. Listen to a couple and ask yourself whether they're major or minor. The answer is, "No, ... well, sort of."
We say ".. well, sort of" because that when we don't have names for things, we put them into boxes we do have names for. If you point to a spot on a rainbow, I'll tell you whether it's red, orange, yellow, green, blue, or purple. Cyan? Green. Plop a finger down on the neck of a fiddle or a fretless banjo, pluck the note, and someone will tell you you're playing "C" even if the frequency is 265 instead of 261.626
It's true for everything. Rattlesnake? Tastes like chicken. If you're British, you know you judge every vegetable based on how close it tastes to over-cooked Brussels sprouts.
There are, however, advantages to this approach above and beyond just the ability to make fun of it. Names let you talk to other folks about stuff. "Play me an A." "Hand me that green pick." "Let's play modal tunes."
Like the colors of the rainbow, or the continuum of note frequencies, there is an infinite variety of modes you could learn, but I can get you most of the way there for fiddle tunes by expanding your two boxes to four.
The two new modes you need are "mountain major" and "mountain minor": Myxolidian and Dorian. And yep, you can call it Myxolidian if you want, just like you can call it Ionian instead of "major." It'll get you more dates with music professors.
"Mountain major" tunes sound sort of major. "Mountain minor" tunes sound sort of minor.
To spot them in a jam if you play guitar or mandolin, watch the chords. A-major tunes have mostly A and E chords, with some Ds thrown in. A-minor tunes are Am, E, and Dm. A-myxolidian tunes have lots of A chords, but the big other chord is a G. It's major chords, but the sound is different from A Major. An A-dorian tune will be full of Am and G major chords. It's sort of minor-y, but all the G chords give the tune a very different feel from a D minor tune.
For both of the mountain modes, the predominant contrast chord to the tonic -- to the chord that names the key -- is the chord right under it, or the "seven chord," because its root is the seventh note of the scale. A D-myxolidian tune is full of D major and C majors; an E-dorian tune, full of E minors and G majors. Bluegrass and classical music are full of I-IV-V tunes. These are I-VII tunes.
Want to keep one tune in your head that makes this clear? Learn Cold Frosty Morning. It's in A, but the coarse is A-dorian, and the fine is A-myxolidian. The first part is A-minor and G-major, the second is A-major and G-major.
There. That was easy, right?
As a bonus, I'll throw in one more mode: Phyrigian. Listen to some flamenco. Why's it sound like that? It's in Phyrigian mode. Here, the chord to listen for is a major chord rooted on the note half a step up from the tonic. Too theoretical? If you're a guitar player, play E-F-E. Aha! Flamenco.
You can now distinguish five modes by ear: Aeolian, Ionian, Dorian, Phyrigian, and Myxolidian.
Can you tie that back to the music-theory stuff? Sure. Find a piano and run up and down a white-note scale starting on C. That's major. Start on A? That's minor: the "relative minor" of C, because it has the same number of sharps and flats. (In in this case, none.) Start on E? Phyrigian. On D? Dorian. On G? Myx.
Here's another way to say it: a minor scale has three fewer sharps than the major scale. Two fewer sharps? Dorian. One fewer sharp? Myxolidian. Four fewer sharps? Phyrigian.
So, what's the key signature of "D phyrigian"? D major has two sharps, so D Phyrigian would have two flats. (Think of a flat as a "negative sharp.")
Tommy Jarrel didn't look at tunes this way, but even the dual majors in math and music should now be happy.
Is this all? Heck no. Go out and find a copy of Bela Bartok's Mikrokosmos, Bartok's idea of how to teach beginners to play piano. Each step is a tiny little Bartok composition. Which, if you've ever listened to Bartok should be warning enough. By third page or so, he has you playing a piece with one sharp in the key signature. F-sharp? No. C-sharp. What mode is that? The rest of the book builds to complete little pieces in Lydian mode, Dorian mode, and others. He's teaching absolute beginners to hear outside the box of western classical music.
Weeks go by when the earworm stuck in my head is Balkan Beat Box's Hermetico, another none-of-the-above. The most common mode for klezmer, Balkan, and middle-eastern tunes is "D freygish" ("freygish" started life as "phyrigian"), also known as "D hijaz." The key signature has a B-flat, and E-flat, and ... an F-sharp. Once your brain forces you to listen to Hermetico enough times, if someone plays the Klezmatics' Mizmor Sher Lehanif, or Sherefe's Gole Sangam, you'll think, "D freygish!"
(Actually, you won't think that. You'll think, "Oh, hell. I'm going to be stuck with this one in my head for the next two weeks.")
But for us? Major, minor, mountain major, mountain minor.