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When musicians use Roman Numerals for chords (like I, IV and V) that reffers to the scale step that the chord's root is built upon. The scale has seven notes that can be sung in solfege - "do, re, mi, fa, so, la, ti, do". Those same notes can also be thought of as scale steps "1, 2, 3, 4, 5, 6, 7, 1". So, when we replace these numbers with Roman Numerals, they represent the triads built on those scale steps: I, II, III, IV, V, VI, VII, I. If you want to be even more exact, you can show the tonality of the chords like: I, IIm, IIIm, IV, V, VIm, VII°, I for the Major scale and Im, II°, bIII, IVm, V, bVI, bVII, I for the Minor scale.

Most popular music uses the three primary triads more than any of the others and those turn out to be the I, IV and V chords. In C Major that means the I chord is C, the IV chord is F and the V chord is G. In E Minor the I chord is Em, the IV chord is Am and the V chord is Bm or B (depending on which version of the minor scale you are using). So, when someone says "this is a I, IV, V tune" that means the piece will only use those three chords (and that it is probably based or loosly based on a blues form).

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