i know this is probably a stupid question but ive wondered this for a while. a I-IV-V chord progression say C F G would be C ionian right? now if u changed the progression to F G C (IV-V-I) would it be c ionian or f lydian? another example Em-Am-C. would this be E phrygian or C ionian? how about a Dm-G (II-V)? is hat a D dorian or G mixolydian? how do u determine what the mode is, by the first chord in the progression, the last chord, or the lowest roman numerical?
What characterizes a mode is the set of lengths between each note and the tonic (and therefore, the distance of every note with every other note).
1. a I-IV-V chord progression say C F G would be C ionian right?
Yes. The Ionian is the major scale and the notes you picked belong to that particular scale.
The distance between notes in a Major scale are (W-whole, H-half)
C W D W E h F W G w A w B h C
What "makes" the major scale is a Major third, Sixth and Seventh. What defines it is the sharp 7th that drives the ear back to the tonic.
However, you have not picked chords/notes that characterize that particular scale.
C Ionian is C D E F G A B C
The chords you picked actually support other scales. **(Though not strictly for every relationship... someone please correct me if I am wrong)**.
For example, you could play those chords and actually be on C Myxolydian if you had a passing tone that was Bb.
C Lydian is C D E F G A Bb C. Notice that it is basically a C major scale with a flatted 7th. This characterizes a Myxolydian scale. However, it is the case that the C major chord your picked has a natural B and so does the G major chord, though that sharps the F# which would turn your original scale into a Lydian. This is the point I was making earlier [see **].
Another way to think of the Myxoldyian (that is, instead of thinking of it as a major scale with a flatted 7th) is to consider the following:
G Myxolydian is G A B C D E F G
Notice that this keeps the Ionian relationship on G (shown on C above) except that the F is flatted (making it a Myxolydian).
2. now if u changed the progression to F G C (IV-V-I) would it be c ionian or f lydian?
In this case the progression could take on both forms because those modes are supported by those chords. The notes that create the C Ionian scale are the same exact notes that create the F Lydian scale, so it depends on which one is your tonic. If your tonic is C then you are still in C Major, just starting on F. On the other hand, may be that you are choosing to trick the listener by inducing an F Lydian. Classical composers use this technique often. In this particular case it would not sound too interesting because you're still using the same notes. (Sharping the F (F#) in passing notes and then playing G Major would sound more interesting, for example.)
3. another example Em-Am-C. would this be E phrygian or C ionian?
An Em chord is characterized by the F#. An Am chord is characterized by naturals (no F#). Therefore, you would not be strictly in either (which makes things more interesting).
A Phrygian scale is characterized by a minor with a flatted second step, so by making Em's F# an F you would satisfy the Am diatonics, but not the C Major's.
4. how about a Dm-G (II-V)? is hat a D dorian or G mixolydian?
Following the same logic, if your tonic is C, then you are in C Major. However, starting like this at Dm could put you into an odd minor scale with a (Lydianesque) sharp fourth.
A G Myxolydian would have a Major D, not a minor.
A D dorian would be like D minor with a sharp 6th (giving it that major flavor to an otherwise minor scale, something that guitarists like Santana exploit). Therefore, this could be seen as a D dorian (but the Dm chord induces a Bb which conflicts with a B natural in the D dorian and G myxolydian).
In short, follow your ears. The trick is to elegantly move the listener's ear from mode to mode without it sounding harsh. Like a good writer, you should be able to 'foreshadow' by playing non-diatonic passing notes so that when you change to the new mode it all makes sense ex-post.
hope this helps. Someone please correct me if I have made a mistake.
About the grammar, I don't buy it that typing "u" as opposed to "you" saves you much time. In any case, think of it this way: the utility in time saved you get from typing u instead of you is strictly smaller than the disutility you cause for others reading your bad-grammar post. Assuming that you are the typical internet user (that is, you derive utility from others' utility because it leads on average to more information on the internet), then there is no reason for you to type u instead of you. It also looks bad.