# Harmony and roman numeral analysis: how to deal with chromaticism?

I recently started playing piano.

While learning and performing new pieces, I found that it helps me a lot to have some certainty of what's going on with the notes, the chords, and the harmony.

I decided to learn these as my first 3 pieces: Beethoven's Bagatelle No. 25 in A minor and Piano Sonata No. 14 in C-sharp minor Op. 27 No. 2, and Chopin's Prelude Op. 28 No. 4.

I have no issues with the first two. I understand what's going on in the harmony, and roman numeral analysis was straight-forward. Chopin's prelude Op.28 No. 4, in the other hand, confuses me. I don't even know where to start in order to understand the function of each chord.

Here is the piece in question:

And the first measures:

It starts with i - V: Em to B7sus4 (i think?), and from there it goes through a series of subtle chromatic movements, involving only one note of each chord, slowly moving semitone by semitone. That's where I get lost. The functions of the chords stop being obvious to me.

How do you perform harmony and roman numeral analysis on works like this, with so much chromaticism going on? Where do you start? How is the function of the chords deduced/derived?

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Hi JC, I'm part way through preparing an answer for you - it is proving a little harder than expected. In the meantime, I found this online, which is pretty interesting! mathemusicality.wordpress.com/2007/08/05/… – Bob Broadley Jul 24 '14 at 16:17
@BobBroadley Thanks Bob! I really appreciate it. And what an interesting article, great read. – Archundia Jul 24 '14 at 16:25

Although much of the harmony here is triadic, few of the chords function in a conventional way. It is possible to give each chord a "name"; for instance, the first 13 bars could be notated as these chords (with a little enharmonic licence):

Em / / / | B7sus4 / B7 / | B7b5 / Bm7b5 Dm7b5 | E7 / Em7 Edim7 |

Am7 / F#m7b5 ?? | F#m7b5 / D#dim7 ?? | D7 / / / | Dm7 / Bm7b5 Bdim7 |

Cmaj7+ Am / / | B7sus4 B7 F#m7b5 (Am) | B7 / F#m7b5 (Am) | B7 / / / (implied) | Em …

At this point, we could try to analyse these chords in terms of key, however this quickly becomes problematic, for two main reasons:

• few of these chords feel strongly associated with the tonic, E Minor; it makes little sense to analyse them in terms of this key.
• although there are a number of dominant 7th chords, we never cadence in any key (except the final return to E Minor in bars 12-13), so no modulations are effected, making it unhelpful to analyse chords in terms of any other key, either.

So, although we may be able to describe each of the chords in this harmonic progression, and even relate them to one or more keys (using roman-numeral notation, for instance), this would neither describe how we perceive this progression, or how it is constructed. Instead, we need to view this chord sequence as the result of a series of simultaneous (mostly) chromatic descending "voices". (@Pat Muchmore gives a good explanation of this in his answer.)

However, we do feel some "harmonic-signposts" along the way. Essentially the first 13 bars function as a single i-iv-V-i cadence, embellished by many chromatic passing notes. Bar 1 is clearly chord i; with some decoration, bars 9-10 are basically chord iv and bars 11-12 are chord V; we cadence strongly back to i in E Minor at bar 13. (Possibly the D7, bVII7, chord in bars 7-8 could be considered pre-cadential too…)

This article, which I already mentioned in comments above, clearly shows the chromatic and step-wise movement of the "voices" in this harmonic progression. Although it is a rather "tongue-in-cheek" article, suggesting an approach to "create-your-own-Chopin-Prelude", it does show that the harmonic movement in this Prelude can be viewed at a variety of different background "rates", which progressively become closer to the actual Prelude, as further embellishments are made.

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Could this be thought of as polyphonic rather than harmonic? Would it make more sense to analyze each voice? – empty Jul 24 '14 at 18:42
@KevinJohnsrude, I see what you mean about the movement of "lines" within these chords, but no this is not polyphonic music; these "lines" are certainly not independent, being mostly part of block-chords. They are only "lines" or "voices" in the sense of voice-leading. – Bob Broadley Jul 24 '14 at 18:45
@KevinJohnsrude, but you could, I suppose, analyse the movement of the "voices" within the chord progression, as though they were independent lines - this is effectively what the article I link to does. – Bob Broadley Jul 24 '14 at 18:56

The term for chord connections like this, where each note of the chords changes (usually chromatically, almost always step-wise) one-by-one, is linear harmony. It's quite common in Liszt, Scubert, Schumann, etc. Roman numeral analysis is mostly pointless during linear harmony passages, most analysts will either just label it as linear harmony until the next functional chord is found, or will use Neo-Riemannian analysis to describe the harmonic movement. Neo-Riemannian analysis is complicated if you haven't already heard studied it, and it mostly only works for the portions of the linear harmony passage that has triads, but you might find it interesting enough to look up.

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+1 Pat, this is really helpful. As these chords are predominately triadic, I started writing an answer to show JC how he could analyse them, but yes, I found this approach to be pretty meaningless. Glad you posted this answer; it made me decide to rethink… I don't know anything about Neo-Riemannian analysis - I'll definitely check it out... – Bob Broadley Jul 24 '14 at 17:05
The article "Introduction to Neo-Riemannian Theory" from the Journal of Music Theory by Richard Cohn is an excellent starting point. I'll try a link that I found to a PDF, but you might need to access it via a library or other scholarly institution. recherche.ircam.fr/equipes/repmus/mamux/… – Pat Muchmore Jul 24 '14 at 17:58
Thanks, Pat. I'll check out that link. As it happens, I realised I know a little about this, having stumbled across info while reading about Tonnetz, but I could definitely do with learning about this analytical approach in detail. – Bob Broadley Jul 24 '14 at 18:02
Thanks again, Pat. I was able to open the whole PDF, despite it being a JSTOR article. I've only read the first few pages, and the rest will have to wait until I have a little more time, but it is already very enlightening, and has already explained the need for this analytical approach in a more convincing manner than other sources I've seen. – Bob Broadley Jul 24 '14 at 18:13
Well, he practically invented it, so I would hope he could make a relatively compelling case! :) – Pat Muchmore Jul 24 '14 at 19:43