Roman Chord Notation

[crimson]

I'm starting to get familiar with roman chord notation among other things, but one thing I haven't figured out is what the following means: ii⁶

I know that V^6/4 is the dominant chord in second inversion, and that there are intervals of a 6th and a 4th above the root, but the above one still bugs me. I know ii is the supertonic. Does it simply mean that there's only a sixth above the root and nothing else?

[stevel]

Originally Posted by crimson

I'm starting to get familiar with roman chord notation among other things, but one thing I haven't figured out is what the following means: ii⁶

I know that V^6/4 is the dominant chord in second inversion, and that there are intervals of a 6th and a 4th above the root, but the above one still bugs me. I know ii is the supertonic. Does it simply mean that there's only a sixth above the root and nothing else?

No.

Here's how it works:

A Root Position chord gets a Roman Numeral. In most cases, minor chords (or chords including the minor third as the lowest interval, such as diminished, minor 7, etc.) get a lower case RN. Major (augmented, etc.) get upper case RNs.

Thus, in a Major key, the RN for the chords are:

I ii iii IV V vi vii^o

and in minor

i ii^o III iv V VI vii^o

The V and the vii^o
obviously have the 7th scale degree raised to make a LT.

If the chord is in First Inversion, it gets a superscript 6:

I⁶ means a I chord, in first inversion. In the key of C that would be C-E-G with an E (the third) in the Bass.

If the chord is in Second Inversion, its gets a superscript 6, and a subscript 4, like:

6
I
4

This, in C, would be C-E-G with a G (the fifth) in the Bass.

So root position, first inversion, and second inversion would be:

I I6 I6/4 (and it is typically written in text this way, and from now on, if I write x/y it means the x is superscript, and the y subscript).

For 7th chords, it is:

RP V⁷
FI V6/5
SI V4/3
TI V4/2 (or just 2 in some older texts).

7th chords are easy to remember: 7:6-5:4-3:2 (and that's why even newer texts sometimes use 2 for third inversion).

9th chords are rare in tonal music, and typically, most appear in Root Position, so there's no standardization for inversional symbols.

RP V⁹

First Inversion, if allowed, would look like V7/6/5 or something, and adding the 7 there could be really confusing!

Now, for the reasoning behind these numbers (skip to the end if you don't want to read all this, though it does answer part of your question - there's more about RN down there and an Important Note):

The numbers come from Figured Bass numerals (Thorough Bass). In that system, only the Bass line is written for the accompanimental instrument (melodies may be given to other instruments though). The person "realizes" the Bass Part by playing the written notes with their left hand (usually it was done on harpsichord, but lute and such were used) and using the "figures" written under the bass notes (which is why it's called figured bass) determines which intervals to play above the written note.

For example, if I wanted to tell you to play a C Major chord, I would write a C note, and then put the figures 5/3 in the music. That tells you to put a 5th and a 3rd above the written note. In a sense, the written note is "1", so you know 1-3-5 makes up a major chord right? That's all it's telling you.

However, in this style, the performer improvises the upper parts of the chord based on stylistic conventions. They will play the 5th above the 3rd, or the 3rd above the 5th, add in duplicates of the written note, and so on. So, C with 5/3 might be played C-E-G; C-G-E; C-C-E-G-C, etc. - whatever voicing the player chooses.

Now, If I take the chord E-G-C, you'll see that there's a 3rd and a 6th above the bass note. The E would be written, and the player would see the 6 and 3 and know to put the notes that are a 6th (C) and 3rd (G) somewhere above the written note.

You know this is a C chord in first inversion. So even though E is the written bass note, the Root is C, so in the key of C, we call this a I. What this means is, when you see 6/3, you know that the written note is the third of the chord.

Now, like all good lazy musicians, there wasn't time to map out every single interval, so they came up with shortcuts or "abbreviations". For Triads, rather than writing 5/3 on RP, they wrote nothing. So a C note with no figures means RP (just like today, when we say "C", we assume we mean C Major unless someone specifically says "C Minor".

First inversion, instead of 6/3, became just 6 (the 3 is implied). And SI remains 6/4.

RP - full: 5/3, abr: [ ] (nothing)
FI - full:6/3, abr: 6
SI - full: 6/4, abr: same

For 7th chords, think about it G7 is G B D F - that's a 3rd, 5th, and 7th above the written G. And B D F G is a 3rd, 5th, and 6th, etc. So:

RP - full: 7/5/3, abr: 7
FI - full: 6/5/3, abr: 6/5
SI - full: 6/4/3, abr: 4/3
TI - full: 6/4/2, abr: 4/2

So you notice when we use Roman Numerals, we just append the abbreviated figured bass symbol to the numeral.

Now, a couple of things I should mention:
1. In FB, intervals are diatonic - if you get E in A minor with no figures, that's RP - E-G-B. You used DIATONIC notes - the ones form the key signature. To make this chord E-G#-B, you need to show the accidental. So they developed this system to include accidentals - either a sharp, flat, or natural sign, a plus sign, or a slash through a numeral. For example, if, in A minor, we want the V chord in third inversion, we have to write a D (the bass note of a third inversion E7 chord) and put 4+/2.

That tells us we should put a 2, raised 4, and 6 above the D (we know 6/4/2 because 4/2 is the abr. for 6/4/2). So, in the key of A minor, which has no sharps or flats, you get D-E-G-B, and raise the note that's the fourth above the written D, thus D-E-G#-B.

There were other shortcuts too - for example, an accidental by itself (where a numeral would normally be) always means to adjust the third above the written bass note. So in minor keys, you see a lot of single accidental signs everywhere there's a V chord because you need to raise the 3rd of the V chord (which is the 3rd above the written bass note when that chord is in root position).

Sometimes, in FB, full figured are used - for instance, after a 6/4 you'll often see 5/3 even though it's not super necessary.

Another cool thing is that you can notate 9th chords, or really, any combination. For example, you'll often see 4 - 3 which means a RP chord with a 4th above the written bass note, like CFG - 4 by itself is an abr. for 5/4/1, and then the 3 makes 5/3/1, so you've got a 4-3 suspension - so sometimes even melodic lines are shown with numerals.

Back to Roman Numerals:

So our system uses:

RP - I
FI - I⁶
SI - I6/4
for triads, and

RP - V⁷
FI - V6/5
SI - V4/3
TI - V4/2
for 7th chords pretty much exclusively.

If a note it altered, as in the case of a V chord in minor, we don't put it in the "Inversion Symbols" (which evolved from figured bass) because the uppercase or lowercase RN shows it.

For example, if we use a minor I in a major key, we just put "i". If we use a Major iv chord in a minor key, we just put "IV".

If something becomes diminished or augmented, same deal:

If you use ii^o in major rather than the normal ii, you just add the diminished symbol: ii^o.

If you use V+ instead of the normal V in major, you just add the +: V⁺.

If some other interval is altered, then that is shown in the Inversion Symbols - V in Major with a flatted 9th is written V^b9 (and in minor we use it to to avoid confusion with V⁹). This is pretty rare occurrence though because the system is so elegant - RN, case, and Inversion symbols.

I should note here Crimson that the Inversion Symbols only tell you what inversion it is, not specifically which notes to play (and really, these symbols are used for analysis, not for instructions on what to play or write - except in theory classes). So I⁶ in C really just means C/E. But in Jazz, you play from C/E, and in classical music, you either play from notes (imagine that, playing music from notes!) or you realize figured bass, which is E with 6.

If the ROOT of a chord is altered, we show that in RN. For instance:

i in C major is C - Eb - G.
i⁶ in C major is Eb - G - C.

But the ROOT is still C, so the RN is still I/i.

But if you use an Ab chord in C Major, the root of your normal vi chord (A-C-E) has been lowered, so we put a flat sign before the numeral:

bVI in major means a Major triad (Uppercase RN) built on lowered scale degree 6. Likewise, the Neapolitan, which is built on lowered 2, and is a major chord, is bII (though often now simply "N"). If you could have a minor Neapolitan chord, it would be bii.

In minor, you will encounter a half-diminished (m7b5) chord built on raised 6, we call that #vi%7 (% means h-d or m7b5, it's really a degree symbol with a slash through it).

HOWEVER, vii^o is SO common in minor, that even though it's built on raised 7, we don't put #vii^o
, we just put vii^o. So in minor, there's vii^o
built on the LT (like Bn-D-F in Cm), and VII built on normal 7 (like Bb-D-F in cm).

Other than that, they're pretty striaghtforward.

Another aside (sorry) - we DO NOT put "II" for a major chord on the supertonic when it is acting as a secondary dominant. We put V/V (which means the V of the key of the V). Likewise, something like what I've seen called #iv^o7 (F# A C Eb in C) here is called vii^o7/V - again, assuming it's a secondary leading tone chord - which it typically is.

There are some "Roman Numeral" symbols you should know about:

N means Neapolitan - a major triad built on b2. In FI in would be N⁶.

The Augmented 6th family has names:
Ger+6; Fr+6, and It+6 for German, French, and Italian augmented 6ths.

And there are chords that many call "common tone diminished 7ths" or ct^o7 - these are diminished 7th chords that are not secondary chords, but neighboring chords, like C-D#-F#-A that resolves to C E G C in C major.

Important Note:
Some people use other systems:
1. They use ALL Uppercase RN and understand that you know that "II" in a minor key is a diminished triad. They only pur alterations on the chord if it is out of ordinary (so a minor v in a minor key would be Vb - the b implying the third of the chord is lowered as in figured bass, or a dinished ii in Major would be II^b5 or II^5b). You can see where this can get confusing - however, I will say that this system uses the "inversion symbols" more like real figured bass. But if they're going to do that, why use the RN at all!

2. I've seen here, a,b,c,d appended to a RN for inversions. It seems to be largely British, and maybe only in pre-collegiate level courses. I can tell you I've never seen a university textbook written (by a university professor) using them - it seems a little "pop" to me, and we've already got enough systems already. But if the Brits are like the Americans, where we're dumbing down everything, I guess this is like ebonics for music theory. At any rate, Ia means RP, Ib means first inversion, etc. I'm not yet sure if this system alters case too, and if a is "assumed" on RP chords. Maybe someone else can chime in on that.

3. Many people erroneously think Nashville Numbering System (NNS) is Roman Numeral (I think something like Sibelius included it and they didn't do any research) but it's not. It uses Arabic Numerals (1, 2 rather than I II) - they mean the same thing - 1 is the chord built on scale degree 1. This is a system for PLAYING, not for analysis, and it's only practiced by a relatively small population (in fact, until about 3-4 years ago, I had only ever heard it referenced once in my life, and then about 2-3 years ago, I heard my 2nd reference - now I hear it more and more - ahhh, the internet - spreading misinformation with information!).

Sorry for the length, but wanted to be fairly thorough.

HTH,
Steve

[stevel]

Originally Posted by crimson

I'm starting to get familiar with roman chord notation among other things, but one thing I haven't figured out is what the following means: ii⁶

I know that V^6/4 is the dominant chord in second inversion, and that there are intervals of a 6th and a 4th above the root, but the above one still bugs me. I know ii is the supertonic. Does it simply mean that there's only a sixth above the root and nothing else?

Oh crap.

I should mention Crimson - V6/4 MAY NOT mean a second inversion V chord.

There are two styles of notating a Cadential Tonic-Six-Four chord.

The first is:

I6/4 - V(7).

The second is

V6/4 - V(7) or V6/4 - V5/3

Both are attempts to reconcile the fact that, in C, G-C-E in a cadential situation is really acting as an embellishment to the V chord rather than a "true" standalone tonic chord.

The people who use the former notation (with the I there) will often put a bracket under the whole I6/4-V combo, with a V RN to shoe it's all part of an elaborated Dominant harmony. The latter has the numeral "V" so they figure that's good enough. In Figured Bass, in C, we'd see a G note written, and the figures like this:
6 - 5
4 - 3
G----

So they will also put "V6/4" - with dashes leading from the 6 to a 5, and then the 4 to a 3 to show that the 6th and 4th above the V chord's bass note both resolve down to the 5th and 3rd of the V chord.

You will see standalone V6/4 chords in non-cadential situations though. Usually theorists put parentheses around these to show their weaker harmonic function, like

I - (V6/4) - I⁶ shows the V chord in SI inversion is really just acting like a passing chord between RP and FI of a tonic chord.

Other 6/4 chords don't have this cadential situation problem - so just be sure that if you see I6/4-V, or V6/4 - V, you check to see if it's a cadence and then you understand that those two notes - the 6 and 4 are written above the ROOT of the DOMINANT chord in that key.

Best,
Steve

[crimson]

Wow, thanks again for the thorough explanation. It sure clarified things. Maybe now I'm less likely to lose track of stuff when reading theory texts