Roman Numerals for Musical Analysis

CHARLES FRANCIS LEINBERGER, PH.D.
Roman Numerals for Musical Analysis

Use this table to determine possible Roman numerals of a chord once you know the type of chord, its root, and on what scale degree the root is located.
For many chords, there is more than one possible Roman numeral. Which one is best depends on the chord's resolution. How does that chord fit into its harmonic context?
If I forgot any, please let me know at CHARLESL@UTEP.EDU!

		Triads				Seventh Chords
Scale Degree		+	M	m	d	M⁷₊₅ (+M⁷)	Mm⁷₊₅ (+m⁷)	M⁷ (MM⁷)	⁷ (Mm⁷)	⁷_♭5 (Mm⁷_♭5) or Fr⁷ (Fr⁺⁶)	m^M7 (mM⁷)	m⁷ (mm⁷)	^ø7 (dm⁷)	°⁷ (dd⁷)
1	Tonic		I	i				I^M7	V⁷/IV		i^M7	i⁷			1
			I
			V/iv						V⁷/iv
♯1	Raised Tonic				vii°/ii									vii°⁷/ii	♯1
♭2	Lowered Supertonic		N (♭II)					N^M7 (♭II^M7)	Gr⁺⁶/I, It⁺⁶/I						♭2
2	Supertonic		V/V	ii	vii°/♭III				V⁷/V	Fr⁷ (Fr⁺⁶)		ii⁷	vii^ø7/♭III	vii°⁷/♭III	2
					ii°								ii^ø7
					vii°/III								vii^ø7/III	vii°⁷/III
♯2	Raised Supertonic				vii°/iii									vii°⁷/iii	♯2
♭3	Lowered (Minor) Mediant	♭III+	♭III			♭III^M7₊₅		♭III^M7	V⁷/♭VI						♭3
♭3	Lowered (Minor) Mediant	III+	III			III^M7₊₅		III^M7	V⁷/VI						♭3
3	Mediant		V/vi	iii	vii°/IV				V⁷/vi			iii⁷	vii^ø7/IV	vii°⁷/IV	3
3	Mediant		V/vi	iii	vii°/iv				V⁷/vi			iii⁷	vii^ø7/IV	vii°⁷/iv	3
4	Subdominant		V/♭VII	iv				IV^M7	V⁷/♭VII		iv^M7	iv⁷	Till Eulenspiegel		4
			IV						IV⁷
			V/VII	iv					V⁷/VII
♯4	Raised Subdominant				vii°/V								vii^ø7/V	vii°⁷/V	♯4
5	Dominant	V+	V	v	vii°/♭VI		V⁷₊₅		V⁷	Fr⁷/I (Fr⁺⁶/I)		v⁷	vii^ø7/♭VI	vii°⁷/♭VI	5
5	Dominant	V+	V	v	vii°/VI		V⁷₊₅		V⁷	Fr⁷/I (Fr⁺⁶/I)		v⁷	vii^ø7/VI	vii°⁷/VI	5
♯5	Raised Dominant				vii°/vi									vii°⁷/vi	♯5
♭6	Lowered (Minor) Submediant		♭VI					♭VI^M7	Gr⁺⁶, It⁺⁶, V⁷/N (V⁷/♭II)				Tristan		♭6
♭6	Lowered (Minor) Submediant		VI					VI^M7	Gr⁺⁶, It⁺⁶, V⁷/N (V⁷/♭II)				Tristan		♭6
6	Submediant		V/ii	vi	vii°/♭VII				V⁷/ii			vi⁷	vii^ø7/♭VII	vii°⁷/♭VII	6
					♯vi°								♯vi^ø7
					vii°/VII								vii^ø7/VII	vii°⁷/VII
♭7	Subtonic		♭VII						♭VII⁷						♭7
			V/♭III						V⁷/♭III
			VII						VII⁷
			V/III						V⁷/III
7	Leading Tone		V/iii		vii°				V⁷/iii				vii^ø7	vii°⁷	7
7	Leading Tone		Fate		vii°				V⁷/iii				vii^ø7	vii°⁷	7
Scale Degree		+	M	m	d	M⁷₊₅ (+M⁷)	Mm⁷₊₅ (+m⁷)	M⁷ (MM⁷)	⁷ (Mm⁷)	⁷_♭5 (Mm⁷_♭5) or Fr⁷ (Fr⁺⁶)	m^M7 (mM⁷)	m⁷ (mm⁷)	^ø7 (dm⁷)	°⁷ (dd⁷)
		Triads				Seventh Chords

Blue cells indicate diatonic Roman numerals in major keys. Some of these chords also have a chromatic Roman numeral in minor keys.

Yellow cells indicate diatonic Roman numerals in minor keys only (natural, harmonic, or melodic).

Green cells indicate diatonic Roman numerals in either major or minor keys (blue + yellow = green).

Therefore, major keys include diatonic Roman numerals in Blue and Green. Minor keys include diatonic Roman numerals in Yellow and Green.

Purple cells indicate chromatic Roman numerals in major keys only. All chromatic Roman numerals are dependent upon the chord resolving logically.

Orange cells indicate chromatic Roman numerals in minor keys only. All chromatic Roman numerals are dependent upon the chord resolving logically.

Dark gray cells indicate chromatic Roman numerals in either major or minor keys. All chromatic Roman numerals are dependent upon the chord resolving logically.

Therefore, major keys include chromatic Roman numerals in Purple and Gray. Minor keys include chromatic Roman numerals in Orange and Gray.

Light gray cells include Roman numerals for chords that are traditionally non-Roman numeralal, but have been given programmatic meaning, such as Fate (Tchaikovsky: Fourth Symphony in F Minor), Till Eulenspiegel (Richard Strauss: Till Eulenspiegels lustige Streiche), and Tristan (Richard Wagner: Tristan und Isolde).

Empty cells indicate that there are no logical Roman numerals for particular chord types on a those scale degrees.

Abbreviations used on this table:
Chord	Intervals Above the Root
Chord	Third	Fifth	Seventh
+ = Augmented Triad	Major	Augmented
M = Major Triad	Major	Perfect
m = minor Triad	Minor	Perfect
d = Diminished Triad	Minor	Diminished
M⁷₊₅ = Augmented-Major seventh chord (+M⁷)	Major	Augmented	Major
Mm⁷₊₅ = Augmented-minor seventh chord (+m⁷)	Major	Augmented	Minor
M⁷ = Major-Major seventh chord (MM⁷)	Major	Perfect	Major
⁷ = Major-minor seventh chord (Mm⁷)	Major	Perfect	Minor
⁷_♭5 = Major-minor seventh chord with diminished fifth (Mm⁷_♭5) or Fr⁷ (French seventh), often appears in second inversion as Fr⁺⁶	Major	Diminished	Minor
m^M7 = minor-major seventh chord (mM⁷)	Minor	Perfect	Major
m⁷ = minor-minor seventh chord (mm⁷)	Minor	Perfect	Minor
^ø7 = diminished-minor seventh chord (half-diminished) (dm⁷)	Minor	Diminished	Minor
°⁷ = diminished-diminished seventh chord (fully-diminished) (dd⁷)	Minor	Diminished	Diminished

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Modulation Types for Musical Analysis
Examples of Modulation Types for Musical Analysis (PDF)
Dr. Edward Murphy's "Sonata Form" Essay
Instrument Transpositions for Musical Analysis
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This page was updated 12 April 2020.