Glossary, Roman Numeral Function
Roman numeral function or functional analysis is a representation of a piece of music that shows how the theory works the same for all keys (see transposition). Within a given key, we can convert from chord names or mode names to Roman numerals, then change the key, then convert the numerals back to chords or modes, and now we have transposed a piece while maintaining all of the the relationships between all of the chords, keeping the structure of the piece the same, just moving all of the notes up or down by a set number of semitones. (See Interactive Key Slider and Keys for a breakdown of all chords in all keys.)
In Roman numeral function, capital numerals (I, IV, V) are used for major or augmented modes or chords, and minor modes and chords (i, ii, iii, vi) are represented with lowercase numerals. The degree symbol means diminished (the presence of a ♭3 and a ♭5) and a plus means augmented (the presence of a major third and an augmented major fifth or tritone). See Diatonic Modes & Chords for a ground-up explanation of modes and some examples in the major diatonic scale.