Reading Roman Numerals on Lead Sheets

Roman numerals on lead sheets indicate the relative position of a chord in a key.

Students sometimes ask me for an explanation of the Roman numerals they see on lead sheets. Briefly, Roman numerals indicate the relative position of a chord in a key. A key is a set of relationships between a scale and its chords. The scale helps generate a melody and a chord or chord progression helps generate the harmony. 

Every key in music has 7 chords that “belong” to it. That means that you can play any of these chords in a song,
and they will sound good to the ear. The reason they sound good is that all of the notes in the chords are
contained in that one scale.
 
In my teaching methodology, I call these chords full diatonic chords. In the major key, the root of each chord
mirrors each note of the major scale. In C major, these notes are C D E F G A and B. The chords that are supported
by these notes are C Dm Em F G Am Bdim. They are represented by Roman Numerals I II III IV V VI and VII.

In the so-called Nashville numbering system, they are identified as 1 2 3 4 5 6 and 7. The chords are almost
identical to traditional chord harmonies with the exception of the VII chord, which is Bb and not Bdim. 
 
Play these chords above in different orders and see how they sound. The reason they will be pleasing to the ear is
that all of the notes in each chord are contained in the C scale. Once you know the type of chord built on the notes of one scale, you can apply what you’ve learned to another scale and read Roman numerals for that scale. 

So, if you picked up music in F major, the Roman numerals you would see: I, iim, iiim, IV, V, vim, and viidim would translate to: F, Gm, Am, Bb, C, Dm, Edim. In my teaching, I have eliminated the lower case Roman numerals in favor of the upper case Roman numerals.