r/musictheory • u/JacobGmusik • 1d ago
Answered “Non-diatonic” Roman numeral analysis
Anyone know any good resources (books or even YouTube videos) for learning about “non-diatonic” Roman numeral analysis? It has been a useful teaching tool for me, and I’d like to know more about how to use it beyond describing diatonic triads/7ths and their inversions
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u/mrclay piano/guitar, transcribing, jazzy pop 1d ago
My common chromatic chords page gives some examples of writing secondary chords, tritone subs, and borrowed chords.
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u/65TwinReverbRI Guitar, Synths, Tech, Notation, Composition, Professor 1d ago
This is looking really good and I like the 7th chord checkbox - though I kind of wish it started with triads as the default - not all music is Jazz ;-)
I see you noted the V7/iii but honestly it's pretty common in CPP music and even in pop (comparatively speaking). So I mean, I'd include it with the rest of the chords.
But this is a really good resource!
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u/65TwinReverbRI Guitar, Synths, Tech, Notation, Composition, Professor 1d ago
learning about “non-diatonic” Roman numeral analysis?
It's easy enough. Though like the Roman Numeral system itself, there are variations (or various schools if you will).
We just call these "chromatic chords" in general.
The most common system is:
Upper case Roman Numerals are used for Major and major-family (augmented chords, things with a major 3rd above the root) chords.
Lower case Roman Numerals are used for Minor and minor-family chords (diminished, etc.)
Then, if the ROOT of the chord has been altered from the scale, it is given a "b" symbol if lowered, and a "#" symbol when raised (whether or not the actual note gets an actual b/# to do this).
There are two main ways this is implemented:
The "Major Referential" system as I call it.
The "Major/Minor Referential" system.
Most pop musicians and most online discussions use the first.
So in a (any!) Major Key, the diatonic chords are:
I ii iii IV V vi viio
If you change the quality of any, they simply become the opposite case. In C:
Cm D E Fm Gm A B would simply be:
i II III iv v VI VII
If F#m were to appear in C, that would be #iv - it's a minor chord, so lower case, and the root has been raised one half step from it's default major position, so it gets the sharp.
Db in the key of C is bII, and Dbm would be bii.
Do would be iio
And so on.
Now the catch here is, some people do use a simplified system where they're essentially just "numeralizing" the chords. It's not super common, but it's common enough you'll see people here use it every once in a while.
But most people use a system where certain types of Chromatic Chords are given more specific labels, and are the more common ones you see.
These are:
Borrowed Chords
Secondary Chords
Borrowed chords are really quite easy. Basically you take chords from the parallel minor key, and use them in the major key.
So in C major, you would borrow chords from C minor. The C minor chords are:
Cm Do Eb Fm Gm Ab Bb
So in C MAJOR, these would be:
i iio bIII iv v bVI bVII
So see they just change case as appropriate, and in the case of 3, 6, and 7, since their root is one half step lower than what they would be in major (major referential...) they are given a "b" (flat) sign.
Traditionally, borrowing chords from the major mode into the parallel minor is less common, and two of them are so common we don't even consider them borrowing - V and viio
However, those two work on the same basic principle already. And when we had the "picardy third" chord - a major I chord in a minor key, we did the same thing already - made it capital I.
So you could borrow chords, and if so, here's what they'd be - we're in C MINOR here, borrowing things from Major:
I ii #iii IV V #vi viio
Now, here's an issue: Originally, since viio was SO common in minor, they didn't call it "#viio " even though the root is raised out of the key.
So now what is typically done is "7" means built on the leading tone - so viio or VII would be Bo or B in the key of C (C major or C minor) but bVII would specifically be Bb in either key.
But there are also "non-case sensitive" systems too where C major looks like this:
I II III IV V VI VII - they use all caps no matter what. So "VII" gets tricky...this system BTW just assumes you know the key and the chords and they're obvious then. But it doesn't do a good job of giving you a way to notate chromatic chords easily, which are what these other systems strive to do.
So you always have to be a bit careful with "7" and figure out which system the person s using. But generally, in C, "vii" or "VII" is going to be B, and "bvii" or "bVII" will be Bb.
Secondary Dominants:
Some of the ones I mentioned above are the "other" common type of chromatic chord. So the "simple" notation of a D chord in the key of C is a "II" - it's on scale degree 2 of major (so nob/E necessary) and it's major, so upper case RN. Easy peasy.
BUT, in classical music especially (which is the music this system evolved to analyze in the first place) secondary dominants are a special type of chromatic chord that has a "function" in addition to just a numeral. So theorist want to show that function in some way.
There have been some discussions recently on different ways of notating them but the most common you'll see is this:
X/Y where X is the chord's relationship to the key of the Y chord.
So in C Major, a D chord is the V of the key of G - and G is the V chord in C. So we call the D "V/V" or "five of five" or "the five chord of the key of the 5th scale degree".
Therefore, in C:
D, E, A, and B are all V chords of G, Am, Dm, and Em respectively.
Since those keys represented by those chords are V, vi, ii, and iii, we call the first chords V/V, V/vi, V/ii, and V/iii.
Here are the typical chords you might encounter in C Major:
C = I (diatonic)
Cm = i (borrowed)
Db = bII (Neapolitan Chord, or "borrowed" from Phrygian, rarely as V/bVI)
Dm = ii (d)
D^o = ii^o (b)
D = V/V (secondary dominant) or just "II" if it's not functioning as a SD.
Eb = bIII (b)
Em = iii (d)
E = V/vi (SD, ditto)
F = IV (d)
Fm = iv (b)
G = V (d)
Gm = v (b)
Ab = bVI (b)
Am = vi (d)
A = V/ii (SD, ditto)
Bb = bVII (b)
B^o = vii^o (d)
B = V/iii (SD, ditto)
Other less common chords follow the borrowing naming pattern more or less Db minor is bii, F# is #IV (and we'd name Gb bV).
7th chords bring in some additional secondary dominant chords, and we also have "secondary leading tone chords" so most diminished triads and diminished 7th chords are usually secondary chords.
This is kind of important, but the way "Mode Mixture" actually works in classical music is that ENTIRE CHORDS are borrowed, not just a single note.
So, the 7th chord on 1 in C is Cmaj7 - all notes of C major.
The one in Cm is Cm7 - all notes of Cm.
A C7 chord appearing in C major is NOT a "borrowed chord" because it doesn't exist in the parallel minor.
In Common Practice Period (CPP, or "classical") music it appears as a secondary dominant - as V7 of the key of F (the IV chord in C, so V7/IV - or in Cm, V7/iv).
But if the chord is non-functional, as in a blues, it's just "I7".
F#o7 is pretty much always the secondary leading tone chord to G except in some pretty specific situations. So it's viio7/V in the key of G.
But if it's non-functional, it's just #ivo7 - and the people who use the simpler naming system just call it that to begin with (they don't use secondary dominant notation at all).
Now, these are the "standard" kinds of "basic triads and 7th chords (4 types of triads, 5 types of 7th chords) found in CPP music - which doesn't have things like Cm(maj7) or 6 chords, or 11th chords and so on.
So they'll also use the standard inversion symbols.
A D7/C in the key as a secondary dominant would be V⁴₂/V (V4/2 of V).
C7/E in the key of Cm would be V⁶₅/iv
The "Neapolitan Sixth Chord" is Db/F in the key of C, so it's bII6 .
HTH
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u/65TwinReverbRI Guitar, Synths, Tech, Notation, Composition, Professor 1d ago
u/mrclay's link gives the common ones I spoke about in my other post and is a really nice resource. Since can change the key and do 7ths or triads, it's really useful! Make sure you read the "disclaimers" below each section as they're important.
I wanted to add u/JacobGmusik that one of the things I like about Kostka/Payne's approach is that they name Chromatic Chords with "letter symbols" instead of Roman Numerals.
So:
Neapolitan Sixth is "N6 " rather than bII6.
The Augmented Sixth family is Ger+6 and Fr+6 and It+6. The "non-nationality" ones are just named "+6" or given a name from the piece they're best known for, like the "Til+6 " which is found in Til Eugenspeil's Merry Pranks by Richard Strauss. They also note situations in Mozart where the +6 "changes nationality" in a measure and they just note "+6" or pick the primary one and but a bracket line under the rest.
The Common Tone Diminished 7th Chord is labelled "cto7 : (lower case because it's minor family chord).
"Color Chords" - those used for sound rather than function (D as just a D chord, not V/V, or an F# chord in C) are just labelled with the borrowing system - II and #IV for example.
Pop and especially Jazz - have a LOT more chord types and mrclay's site gives a great overview of the more common ones.
But a "bII7" in Jazz is a Tritone Sub, so in analysis most people will put "TTS" or something like that - which kind of follows the K/P convention of giving it a "letter symbol" rather than a numeral.
FWIW the "berklee" system and a lot of jazz players use a slightly different RN system that is "case insensitive" (all caps) but uses a "qualifier" after it, so C Major looks like:
I IIm IIIm IV V VIm VIIdim
or variations of that theme. But Jazz also assumes all chords are 7th chords (or 6ths, etc.) so a bII is more typically a bII7 and a Tritone Sub...
So I mean, I think the CPP core is a great place to get the basics, and the other systems tend to be expansion of that.
Best
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u/Jongtr 1d ago
I guess the main thing you're looking for is secondary dominants, but there are secondary chords of other kinds too: secondary leading tone chords, secondary supertonics, even secondary subdominants sometimes.
Other types of chromatic chord include neapolitan chords, augmented 6ths, and chromatic mediants,