Hi Charles,
Of course the numbers you are referring to are taken from the 'scale' with numbers 1 though 7. As I understand it, a number (numeral) refers to a whole chord. So ...
I = 1 3 5 (of your numbers) .. a major chord based on the 'root', without specifying the key the music is written in.
II = a minor chord based on the second note of the scale (2 of your numbers), without specifying the key the music is written in.
III = a minor chord based on the third note of the scale (3 of your numbers), without specifying the key the music is written in.
IV = a major chord based on the fourth note of the scale (4 of your numbers), without specifying the key the music is written in.
V = a 7th chord based on the fifth note of the scale (5 of your numbers), without specifying the key the music is written in.
VI = a minor chord based on the sixth note of the scale (6 of your numbers), without specifying the key the music is written in.
VII = a diminished chord based on the seventh note of the scale (7 of your numbers), without specifying the key the music is written in.
So like tonic Sol Fa, if you know the chords of a piece using this method you could play it in any key (assuming you know the 'scale' notes of that key. For me, if it was F#, forget it!).
So if your chords, playing in the key of C, were C, Am, Dm, G7 .. then remember that as I, VI, II, V. And that is all you would have to remember. If playing the tune in the key of F these chords would translate into F, Dm, Gm, C7. Or, in tonic Sol Fa the chords are Doh, La(m), Ray(m), Soh(7). If I had learnt them in the first place, I think the 'Numerals' are easier to remember.
But I wonder how some of the other chords would be represented? Just a plain G for instance (rather than G7)?
Hugh