Universal key

Different notations
Chord function		Number	Roman numeral
Tonic	T	1	I
Subdominant	S	4	IV
Dominant	D	5	V

The universal key or universal scale is a concept employed in music theory in which specific notes or chord symbols in a key signature are replaced with numbers or Roman numerals, so that the relationships between notes or chords can be universally applied to any key signature.

For example, in the key of E-flat major, the notes of the scale would be replaced like so:

E♭ becomes scale degree 1
F becomes scale degree 2
G becomes scale degree 3
A♭ becomes scale degree 4
B♭ becomes scale degree 5
C becomes scale degree 6
D becomes scale degree 7

Triads (common practice style)

When used with chord symbols, the Roman numerals represent the root of a triad built on the associated scale step. In music theory based on the practices of the common practice period and its derivations the chord numerals are often written in upper case for chords in the major family, and in lower case for chords in the minor family, with the usual "m" or "—" minor chord quality suffix omitted outright:

E♭ becomes I
Fm⁷ becomes ii⁷
Gm⁷ becomes iii⁷
A♭maj⁷ becomes IV maj⁷
B♭⁷ becomes V⁷
Cm⁷ becomes vi⁷
D^ø7 becomes vii^ø7

When representing the triads rooted in a minor key, the upper or lower case of the numerals indicate both its chord quality and that the key is minor:

Cm⁷ becomes i⁷
D^ø7 becomes ii^ø7
E♭ becomes III
Fm⁷ becomes iv⁷
Gm⁷ becomes v⁷
A♭maj⁷ becomes VI maj⁷
B♭⁷ becomes VII⁷

A major drawback of using this method is its lack of use of accidentals. While in the numeric system, flats and sharps can be represented either by the use of fractions (e.g. an A natural in the scale above becomes 4+1⁄2) or, more commonly in written text, by inserting an accidental before the number (e.g. the same note becomes ♭5 or ♯4).

Triads (jazz and popular style)

In music theory aimed towards jazz and popular music, all triads are represented by upper case numerals, followed by a symbol to indicate if it is not a major chord (e.g. "m" for minor or "ø" for half-diminished):

E♭maj⁷ becomes I maj⁷
Fm⁷ becomes IIm⁷
Gm⁷ becomes IIIm⁷
A♭maj⁷ becomes IV maj⁷
B♭⁷ becomes V⁷
Cm⁷ becomes VIm⁷
D^ø7 becomes VII^ø7

When representing the triads rooted in a minor key, accidentals are used to indicate the chromatic alteration from the assumed major key roots indicated by numerals that don't have accidentals:

E♭ minor:

E♭m⁷ becomes Im⁷
Fm^ø7 becomes II^ø7
G♭maj⁷ becomes ♭IIImaj⁷ (the assumed pitch for the root of a III numeral in E♭ is G, and the ♭ is required to indicate that, in E♭ minor, this chord is rooted on G♭)
A♭m⁷ becomes IVm⁷
B♭m⁷ becomes Vm⁷
C♭maj⁷ becomes ♭VImaj⁷
D♭⁷ becomes ♭VII⁷

This will frequently result in numerals whose accidentals are different than those of the actual root note, as they are referring to a change from the assumed pitch and not an absolute pitch:

D minor:

Dm⁷ becomes Im⁷
Em^ø7 becomes II^ø7
Fmaj⁷ becomes ♭III maj⁷ (the assumed pitch for the root of a III numeral in D is F♯, and the ♭ is required to indicate that, in D minor, this chord is rooted on F)
Gm⁷ becomes IVm⁷
Am⁷ becomes Vm⁷
B♭maj⁷ becomes ♭VI maj⁷
C⁷ becomes ♭VII⁷

References

Triads (common practice style)

Triads (jazz and popular style)

Further reading

References