Imagine playing in the key of C Major (CDEFGABC) but instead of playing from C to C', play from D to D'. (DEFGABC) In relation to the key of C Major, that is known as the Dorian modal scale (b3, b7). It is a scale rooted on the second note (AKA the second 'scale degree' or 'ii') of whatever key the song is in. (In the case of C Major, the second scale degree is D.) Modal scales sounds odd because they seem as if their 'flavor' or 'feel' is pulling toward something else. (The D Major scale normally has an F# and C#, but the D Dorian modal scale lowers the third (F#) and seventh (C#) notes of the D Major scale by one half step (F, C) in order to conform to what you could probably call the 'parent' key signature of C Major.)
[For those of you who know your Major and minor chords (AKA 'triads'; chords comprised of three stacked notes separated by Major or minor thirds- three or four half steps) if you go back and look at the D Dorian scale, you'll notice that while it's in the key of C Major, the first, third, and fifth scale degrees of the mode would form a D minor chord (D F A). One of the reasons that someone would choose to play in a mode is where, in the case of a lead guitarist (or any member of the band, for that matter): the band is holding on a particular chord, they're playing a solo and they want to stay in the general area of that chord. They could choose to continue playing in the key of the song, or they could play in the mode that the chord is based on. For example, in the case of a song is C Major, where the band is holding on a G Major chord, they could solo within a G Mixolydian mode, and as long as the last note they played before the band changed chords is one of the notes in the G Major chord (depending on the sound they're going for, of course), it'll blend very well, and sound pleasing AND interesting to the ear, because the center of the song's key in relation to the person playing was, in a manner of speaking, temporarily shifted. (This change is also called a shift of 'tonal center'.) )
The Phrygian mode would be as if you were playing from E to E' in C Major. (Starting on the third scale degree or 'iii'.) (EFGABCDE) The E Major scale normally has an F#, G#, C#, and D# but the E Phrygian modal scale has a lowered second (F#), third (G#), sixth (C#), and seventh (D#) scale degree so as to conform to the song's key. (You might also see this scale described as something like "b2, b3, b6, b7"). Again, if you look at the notes of the E Phrygian modal scale, you'll notice that the first, third, and fifth notes form an E minor triad (E G B). That being said, if the band is playing in C Major and is holding on an E minor chord, the lead guitarist can solo within an E Phrygian scale, AND, again, as long as the last note before the chord changes is a member of that chord- that triad- it'll sound good. (That being said, when the chord changes, if they just change modes so that they are soloing over the correct scale, it'll STILL sound good AND interesting! So, as an example, if a band is playing in C Major, they hold on a D minor chord (D Dorian mode) then move to E minor (E Phrygian), as long as you change to the correct mode (C Major -> D Dorian -> E Phrygian) you'll be just fine.
Moving on, the Lydian mode (based on the fourth scale degree, or 'IV') would be as if playing from F to F' in the key of C Major. (FGABCDEF') The key of F Major normally has a Bb, but the Lydian scale raises the fourth scale degree (Bb) by a half step (B).
So, as an example: C Major -> F Major (F Lydian) -> G Major (Mixolydian) -> C Major (Ionian).
(The Major scale is actually a mode, too ('I'), but it's not in relation to any other key signature, really, so you don't need to worry about that. Also, the minor scale is a mode as well, known as the Aeolian mode; it's based off of the sixth scale degree, or 'vi')
Next, the A Aeolian scale, based off of the sixth scale degree ('vi'; ABCDEFGA'), actually looks pretty familiar already, now doesn't it? It's an A minor scale. That's because the Aeolian scale is also called the 'minor scale'. A Major has a C#, F#, and G#, but in an Aeolian scale the third (C#), sixth (F#), and seventh (G#) scales degrees are lowered one half step (C, F, G) so the scale conform to the key. Now don't go around calling songs in A minor as if they're in 'A Aeolian', but though I don't remember exactly why from my music theory classes, it's not quite true.
I almost forgot to talk about this one (having briefly mentioned it earlier): The Mixolydian mode. (GABCDEFG') It's a scale based off of the fifth scale degree (or 'V') of the song's key signature. The key of G Major has an F# in it, but the Mixolydian mode lowers the seventh scale degree (F# -> F) in order to conform to the key. The first, third, and fifth notes in the scale outline a G Major chord, so you know you can use it to solo over a chord built upon the fifth scale degree (so, in the key of C Major, you can use the Mixolydian scale to solo over a G Major chord).
Finally, we get to the last mode: The Locrian mode (vii^o). (Imagine that "o" as a tiny 'o' just above and to the right of the last 'i'.) (BCDEFGAB) B Major actually has five sharps: C#, D#, F#, G#, and A#, but the Locrian scale lowers all five of those (b2, b3, b5, b6, b7) to conform to the key. It is described as the "most unstable" mode, musically speaking, because there is such a strong pull toward other modes or chords (perhaps, most strongly, the Ionian mode ('I')/C Major).
Something you may not have realized that the Roman numerals I was using in my description of each mode (i.e. I, V, vi, vii^o) are actual music terms called 'Diatonics'; diatonics have to do with chords whose notes are all in same key. (When a song changes from one key signature to another, the chords, and inherently, the diatonics, follow the new key.)
Here's another way to look those Roman numerals:
In the key of C Major-
I - CEG
ii - DFA
iii - EGB
IV - FAC
V - GBD
vi - ACE
vii^o - BDF
If you're familiar with what the different kinds of triads are, you'll see the following pattern:
I - Major
ii - minor
iii - minor
IV - Major
V - Major
vi - minor
vii^o - diminished
With that in mind, you'll also notice from the lowercase and uppercase letters go with particular types of chords; lowercase Roman numerals go with minor triads, and uppercase Roman numerals go with Major triads.
In case you're wondering, there is, in fact, a diatonics pattern for minor key signatures:
i - ACE
ii^o - BDF
III - CEG
iv - DFA
V* - EG#B (* - I'll get to why there's a G# right after this)
VI - FAC
vii^o - G#BD
Now the reason that the G is raised a half step (when it normally would not be in the key of A minor) is because by raising the seventh scale degree of the V and vii^o chords (and just the chords themselves; not a minor scale, which I'll get to shortly) in a minor key, it helps to clearly define the 'tonal center' of the song so that the seventh scale degree, regardless of key signature, is always wanting to pull that last half step up to 'A'.
The reason I said that you'd only raised the seventh scale degree of the scale when forming or outlining the V or vii^o chords, is because there are actually minor scales where you'd raise it; the fact of the matter is, there are three different kinds of minor scales:
There's
1) The Natural ("Pure") minor scale (ABCDEFGA)
2) The Harmonic minor scale (ABCDEFG#A)
and
3) The Melodic minor scale (ABCDEF#G#A' - A'GFEDCBA)
[The Melodic minor scale is played a certain way when going up, and a certain way when going down. These variations on the Natural minor scale also have their own diatonics, which I've noted below:
Harmonic minor diatonics
i - ACE
ii^o BDF
III+* - CEG# (* - the "+" means it's an augmented chord; two stacked Major thirds)
iv - DFA
V - EG#B
VI - FAC
vii^o - G#BD
Melodic minor diatonics
(ascending diatonics)
i - ACE
ii - BDF#
III+ - CEG#
IV - DF#A
V - GBD
VI - FAC
vii^o - G#BD
(descending diatonics)
i - ACE
VII - GBD
VI - FAC
v - EGB
iv - DFA
III - CEG
ii^o - BDF
i - ACE]
Another something to think about that'll help enrich your solos is that even though you're playing in a mode, you can still play chords and arpeggios within that mode. Another thing you could try is take a melody that you played in one mode and play it in another!
I hope this was a big help to anyone wanting to learn more about music theory, so that they can apply it to enriching their playing, as well as their band's sound!

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