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I try to practice playing some scales every day: C major, G major and A minor pentatonic. Recently I stopped trying to think as much of the position ("string 2 fret 3, string 3 fret 0, string 3 fret 2 ...") while playing and instead think the notes I play ("C, D, E, ...") to associate the position and movement with the name of the note. Then I realised that I have very little connection to the note's "function" in the scale, so maybe it would be beneficial to consciously think "root, second, third, ..." instead?

What would be most beneficial to think while practicing scales?

Similarly, when playing chord progressions from some song: Would I benefit from moving from thinking "C, F, Am, G" to thinking "I, IV, vi, V"?

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Once you get past playing scales with open strings, shapes and patterns will take over. At that point, the number each note has will be the same for each scale in each pattern. At that point, it's worth knowing the names of the notes from more of an academic point of view.

Chords, once you know their names, which is always a good idea, will be more useful if you think in RN terms. the problem I have with some people I play with is that they learn a sequence in one specific key, and that's it. They cannot easily transpose to any other key - unless the old capo comes out.... Thinking in terms of RN will mean you'll understand where something is going in far more terms than learning something parrot-fashion.

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With a bit of practice, you will be able to think both ways at the same time. I tend to think C,F,Am,G when playing and I,IV,vi,V when composing. A bit of both when improvising. The Roman Numeral (or equivalent) notation has the advantage of being the same in any key; one just sets I and goes from there.

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