Music Theory: Modes regarding tonal center

mwd

Power User
Is it correct to say that the notes A B C D E F G played over a Cmaj chord would be the 6th mode of a Cmaj scale but played over an Am chord would be the first mode of an Am scale?

Looking for the correct theory and terms.
 
That is correct.

The sixth mode is Aeolian, which is just another name for natural minor, meaning b3, b6, b7. It kind of depends on what tonal center is in the tune though. If the song (or section) is in C major as a whole, such as a I-VI-IV-ii-V, then you would still consider playing that pitch collection (A-A, no flats or sharps) as being in C major even if you play it as a mode.

However, if you were to alter any pitches, such as to make it Harmonic Minor (b3, b6, #7), and play that over the Am, then it is a very different result which you would consider to be a new scale instead of a mode of C major.
 
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