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Speaking of Functional harmony; If a song is in key C, then we call the C major scale from E to E is a Phyrigan mode. Good, what if a song is in key Am, which is actually relative of C and also Am scale can be called aeolian here) what happens?

I mean if somewhere in the song we want to play a Phyrigan in key of Am, are we going to play the same (from E to E) notes as we played as if we were in key of C ? Or let me put it other way; In key of Am and the the tonal center is in Em is that correct to play the Pyhrigan there?

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Well yes, but it won't make any sense.

All of the modes you've mentioned are diatonic to C major. That means that regardless of the tonal center, you're only playing natural notes that also exist in the C major scale.

When you're playing music in a given key, you are tonicizing one note over another. Meaning, the "Do", or tonic note exists in your melodic line the same as it would in your harmony (as a I chord). When you play E phrygian, you are tonicizing E. The notes are the same as those in C major, but if the rest of the music is tonicizing C, then playing a line tonicizing E is not going to make a whole lot of sense!

You should think about modes not as different starting points on a scale, but as different alterations to a scale. If you're playing a piece of music in A minor, you might play an A phrygian solo over a pedal tone, but the notes are not going to be diatonic to C major or A minor! You will alter the 2nd of A minor, by flatting it. The notes will be diatonic to F major starting on A, but realize that F doesn't really have anything to do with the music you are playing--that's just one way to figure out what notes are in a mode.

The other way of figuring out which notes are in a mode is by learning the scale alterations. This will clarify other things for you as well. The simplest examples are lydian, where the 4th note of the major scale is raised; mixolydian, where the 7th note of the major scale is lowered, or dorian, where the 3rd and the 7th of the major scale are flatted. You already know Aeolian/natural minor, where the 3rd, 6th, and 7th notes of the major scale are flatted.

This question/answer will be helpful to you: http://music.stackexchange.com/a/6890/133

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Why not make any sense to play E Phrygian over am key? Isnt that's what modes for, as long as I emphasis the Em chord tones during e Pygrigan –  Spring Aug 14 '12 at 20:35
    
If you emphasize the Em chords, then you aren't playing in Am anymore, you've changed keys to E. –  NReilingh Aug 15 '12 at 2:36
    
please read the question well, "In key of Am and the tonal center is in Em is that correct to play the Pyhrigan there?" –  Spring Aug 15 '12 at 8:04
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@Spring: Yngwie is playing the notes of an A harmonic minor scale which uses the same note material as E dominant phrygian (or E mixolydian b2 b6) scale. –  Ulf Åkerstedt Aug 19 '12 at 18:09
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@Ulf is completely correct. I find that guitar players tend to confuse the issue of modes since they spend so much time practicing scale permutations. What Yngwie is playing there is not what I would necessarily call modal--he's in A harmonic minor, but starting on E in order to play over a V-I resolution. He's not tonicizing E--rather, E has dominant function in that context. It would only really be modal playing if E was being fully tonicized. –  NReilingh Aug 20 '12 at 3:47

Let me rephrase your question:
Is the set of notes used for the E phrygian scale the same as the set of notes used for the A natural minor (or A aeolian) scale?

Answer: Yes.

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