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Say I have a chord progression in C major:

I V vi

C G Am

When I play each of these chords can I potentially play the scale of each chord over it? So for C I'd play C major, for G I'd play G major, for Am I'd play A minor scale. I'm thinking this is possible because secondary dominants work this way by establishing a temporary key on whatever chord you're currently on. But does this happen in practice where people modulate to a different key on each chord change?

Edit: I was confused that a scale can be played over a chord. I thought the moment you play a scale then you're in a new key. I forgot that in order to establish a new key you need to atleast play a progression in the new key. It's just that I saw a video and they were playing different scales over each chord and it mixed me up. I forgot a scale wasn't the same as a key.

Yes, sort of, but it's probably better to call it a tonicization rather than changing keys.

Importantly, consider the implications of changing the scale to tonicize each chord.

If you play scales C major, G major, A minor (in this last case let's assume you get the proper raised leading tone in there so harmonic or melodic minor), you will create tonicize each chord. Which means you would relabel...

C:I I/V i/vi
C G Am

On the other hand, if you keep it diatonic and really get the sense of your original chord symbols, you would play all in C major. I don't like describing it this way but the scales will be C major, G Mixolydian, A Aeolian...

I V vi
C G Am

...if you play it that way you should get the feel of a deceptive progression.

You can do it either way, but the effect of where the tonal center lies will change.

EDIT

You changed it to I vi V. Either way demonstrates the concept.

The only difference with this is that the diatonic version should have a feel of a half-cadence, or just an opening progression depending on the phrasing.

The chromatic approach - using G major on the G chord - will have the feel of temporarily changing the tonal focus to G, a tonicization.

It seems like you are asking a series of questions about the interaction of diatonic and chromatic.

Secondary dominants and tonicization is one way to achieve chromaticism.

You may also want to look at chromatic non-chord tones. This will add chromatic notes, but importantly they are harmonically un-essential so they will not cause a tonicization. Chromatic NCT's are a nice way to spice up vanilla diatonicism.

I often wonder whether before asking your questions you've actually tried out the theoretical ideas in practice. If not, why not. There isn't a lot of theory involved here. What sounds good (to you or others) is what the result will be.

In answer - say you're in C, and the chords are C, G, Am F. Over c, use C scale,, over G use G scale, etc., there are not many notes that will need to change. For the G chord, there's only an F/F# difference. For the F, there's only B/Bb difference. Depending where you place those accidentals will determine whether they will fit into the melody or not. So, basically, this is another theory based question that has very little bearing on the reality of music playing. Please, instead of bombarding us with 'what might happen if...', get playing and discover by listening to what is happening when you actually try these ideas out on piano, or whatever.

Not really as suggested by modern theorists. The (clock) time is too short. To establiah a new key, one usually must use noted that were not in the previous key. One can use non-tonic chords in any key; you notation shows that, C-G-Am is a C-major (or A-minor) chord progression. Were one to play, C-E7-Am, things might be a bit ambiguous; the G# is not in the key of C but is in the key of Am (and A and G and D). However, were the Am followed (not to unusually by) Dm-G7-C or even D7-G7-C, that would emphasize the F from the G7 and contradict the establishment of Am. To confirm Am, one would usually follow thing by a B0-E7-Am which uses F# a couple of times and no F natural.

There is a duration effect. One should spend more than a beat or even a few bars in the new key, then "neutralize" (Schoenberg's term, not a bad term for this effect) the note in the old key (F in the case being discussed) and emphasize the new note (F#). This is termed "modulation" (which to me seems, analogously with FM vs AM, to describe a short digression but that train left the airport over 1000 years ago.) Short digressions are usually termed "tonicizations" (why not "tonicickizations" like in "picknicking"?).

No, secondary dominants don't do that. They might establish a temporary tonic on the chord they lead TO.

But try. In your example - C, Am, G - try playing some melodies. When you get to the G, does F# or F♮ fit better? I think it will depend on whether you feel you've modulated to G, or whether G keeps its identity as V of C major.

Let's look at an example that includes a secondary dominant. C, D7, G. It might be a bit more obvious. G7, or G(maj7)? The former keeps us in C major, the latter suggests we've modulated to G major. Both are fine.

It's also fine to play a succession of maj7 chords, implying the major scale of each. C(maj7), D(maj7), E♭(maj7) ... Use the scales C major, D major, E♭ major ... Not functional harmony any more (we can discard that 'circle of 5ths' thing :-) But nice and funky (or dreamy, depending on style)!