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Performing musicians often use Numeric Analysis to denote the chord changes of a song, often in a chart. The three main forms of Numerical notation are Classical Roman Numeral Analysis, 'Berklee' Roman Numeral Analysis, and the Nashville Notation system.
Roman Numeral Analysis applies a roman numeral to each of the diatonic chords, in order from the root. There are actually two different forms of Roman Numeral Analysis commonly in use - classical, and Berklee. The drawmusic.com website has a nice comparison of 'Pop' (Berklee) vs. 'classical' Roman systems. We'll mainly use the classical system on this website. (Berklee system support coming later!)
There are seven diatonic chords in each key, so we use the numerals 'I' (or, in the case of minor keys, 'i') through vii (or 'VII').
Major chords are written with Capital Roman Numerals (such as 'I'), and minor chords are writen as lowercase Roman Numerals (such as 'i').
When the interval between the first (root) and third notes of the chord is 4 half-steps (a 'major third' interval), the chord is a Major chord, and gets a capital-letter roman numeral (in major keys: I, IV, or V; in minor keys: III, VI, or VII). When the interval between the first (root) and third notes of the chord is 3 half-steps (a 'minor third'), the chord is a minor chord, and gets a lower-case roman numeral (in major keys: ii, iii, or vii; in minor keys: I, IV, or V).
In the special case where interval between the first (root) and third notes of the chord is 3 half-steps, and the interval from the third to the fifth notes is also 3 half-steps - that's a diminished chord! The diminished chord also gets a lower-case roman numeral, usually followed by the 'diminished' symbol (⚬). This '⚬' symbol can be confusing however, as it's ALSO commonly used to refer to a 'diminished seventh' chord. In major keys, we get vii⚬, and in minor keys we get ii⚬.
NOTE: This is the simplest interpretation of classical Roman Numeral analysis. There are several variations commonly used, particularly for minor keys. In fact, the simple interpretation of minor key Roman Numeral Analysis given here is rarely used in practice.
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