Roman Numeral Notation

Roman Numeral Notation (RNN) is useful generally in understanding musical harmony, particularly for harmonising music, even more particularly for harmonising music liable to be transposed to another key  -  for example: where a singer's range can not cover a song in its original key, annotating the accompaniment with RNN simplifies transposing it to a new key.

Instead of or in addition to annotating with actual chords, a roman numeral shows which chord is intended:  a I for the chord 'rooted' (based) on the keynote, or tonic, a ii for the chord rooted on the next note up the scale, the supertonic, and so on.  It is common, but not universal, to use upper case roman numerals for major chords and lower for minor chords.

This table gives the RNN for all the Major keys  -  a similar one can be drawn up for the Minor keys, and both can also be used to transpose chord variants such as seventh chords:

To transpose a chord, in the starting key's column, find which row the chord is in, move along that row to the destination key's column, and that is the transposed chord.  For example:

• iii  -  A Minor (Am) in F Major transposes to D Sharp Minor (D#m) in B Major.
• V7  -  C Major 7 (CM7 or C7) in F Major transposes to F Sharp Major 7 (F#M7 or F#7) in B Major.

If such tables simplify transposition, given their ease of use, why bother with RNN?

1. If you don't have a table handy, there is no substitute for the notation.  There are 12 × 11 × 6 = 792 possible direct chord transpositions in the table, but using RNN as an intermediate stage, the second stage is always simply the reverse of one the first possible stages, so there are effectively only 12 × 6 = 72 transpositions.  This much more manageable number can be reduced still further by noting the repetitive, cyclical, vertical (stepping by seconds A to G) and horizontal (stepping by fifths F-C-G-D-A-E-B) patterns in the table.
2. RNN reduces the chances of making transposition errors that would change the character of a piece.  Transpositions are correct if the starting and ending chords have the same RNN.  Thus, by making them explicit, RNN clarifies harmonic roles that would otherwise be more obscure.  Incidentally, a guitarist using a capo to get different keys with one chord family is just a special case where not only the RNN and harmonic roles of chords remain constant, but conveniently also the fingering patterns.
3. It can be useful in transposing between guitar tunings, for example Open C and Open G.

So RNN is worth learning, especially as an adult singer's vocal range remains more or less constant, and folk music tends to use just a handful of the twelve possible keys  -  it's fairly easy to get used to translating between RNN and these few real keys, possibly even well enough to translate on sight in real time.