Roman Numeral Analysis

Roman Numeral Analysis uses the scale-degree location of the root of a chord to describe its position, and in doing so also describes the chords function. In more complex harmonic situations, the diatonic scale (Ionian mode) is used to define the diatonic posts. These will serve as harmonic targets for non-diatonic passing and approach chords.

Diatonic Posts - examples in C
SCALE DEGREE	1	2	3	4	5	6	7
ROMAN NUMERAL DIATONIC CHORD	I I^maj7	IIm II^min7	IIIm III^min7	IV IV^maj7	V V⁷	VIm VI^min7	VII^o VII^m7b5
KEY of C	C C^maj7	Dm D^min7	Em E^min7	F F^maj7	G G⁷	Am A^min7	B^o B^m7b5

Non-diatonic chords fall into a number of categories.
Modal Interchange can occur with chords based on the following scale degrees:

Available Modal Interchange Chords
scale degree	1	b2	2	b3	3	4	#4	/	b5	5	b6	6	b7	7
roman numeral	I	bII	II	bIII	III	IV	#IV	/	bV	V	bVI	VI	bVII	VII
available quality	maj7 min7 7 m7b5	maj7	min7 7 m7b5	maj7 min7 7	min7 m7b5	maj7 min7 7	m7b5	/	maj7	maj7 min7 7 m7b5	maj7 7	min7 m7b5	maj7 min7 7	min7 m7b5

Secondary Dominants resolve through the cycle of fifths to a diatonic target.

Secondary Dominants - examples in C
A7Dm	B7Em	C7F	D7G	E7Am
^V7/_IIIIm	^V7/_IIIIIIm	^V7/_IVIV	^V7/_VV	^V7/_VIVIm

Substitute Dominants [Sub V7] [Tritone Substitution] resolve down by half-step to a diatonic target.

Substitute Dominants - examples in C
Db7C	Eb7Dm	F7Em	Gb7F	Ab7G	Bb7Am
^subV7/_II	^subV7/_IIIIm	^subV7/_IIIIIIm	^subV7/_IVIV	^subV7/_VV	^subV7/_VIVIm

Passing and Approach diminished chords move between or toward diatonic posts by half-step root motion. This root motion can be hidden in the way the chord symbol is written, or hidden as an internal voice. There is always a chromatic connection with a diminished seventh chord and its target.

Ascending Diminished Seventh Chords - examples in C
	C^maj7		C#^o7		D^min7		D#^o7			E^m7		E^o7 [app. only]		F^maj7		F#^o7		G7		G#^o7		A^min7		A#^o7		^G/_B		B^o7 [app. only]		C^maj7
	I^maj7		#I^o7		II^min7		#II^o7			III^m7 also ^C/_E ^I/_3rd		III^o7		IV^maj7		#IV^o7		V7 also ^C/_G I/_5th		#V^o7		VI^min7		#VI^o7		^V/_3rd		VII^o7		I^maj7

Descending Diminished Seventh Chords - examples in C
	C^maj7		C^o7 [app. only]		^G/_B		Bb^o7		A^min7		Ab^o7		G7		Gb^o7		F^maj7		F^o7 [app. only]		E^m7		Eb^o7		D^min7		Db^o7			C^maj7
	I^maj7		I^o7		^V/_3rd		bVII^o7		VI^min7		bVI^o7		V7 also ^C/_G I/_5th		bV^o7		IV^maj7		IV^o7		III^m7 also ^C/_E ^I/_3rd		bIII^o7		II^min7		bII^o7			I^maj7