# Harmonic Analysis of Polka, Op. 39, No. 14 by Tchaikovsky

I'm having some trouble identifying what's going on harmonically in this chromatic sections here.

i. Bar 2: What function does the chord spelled [C#EGBb] have? All I can say about it is that it's a fully diminished chord built on either the 1st, b3rd, #4th, or 6th scale degree. But I can't slot any of these into what I know about music theory.

ii Bar 10 (i.e. the last bar of line 2): The chord spelled [G#FB]. Enharmonically this would be an Fdim. But it's spelled with G# instead of Ab so I don't want to jump to that conclusion. Aside from that, I wouldn't know what harmonic purposes an Fdim could serve here.

Thanks

As background, I'm a hobbyist piano player who's trying to get a better understanding of what I'm playing.

Both chords in question are instances of common-tone diminished chords. These are chords that serve to prolong, expand, or, in this case, delay the arrival of a principal harmony with which there is a shared pitch — typically the root of the principal harmony.

In m. 2, the common tone is the. Bb between the first and second chords of that measure. In m. 10, the common tone is the F between the first and second chords. In both cases, the diminished chords are spelled enharmonically to make clear the chromatic motion in the bass.

More on common-tone chords can be found in:

• Thanks Aaron. This makes sense. What threw me here is that some of the texts I've seen specified that a common-tone diminished chord must be nested between two identical chords - e.g. an I6 on both sides. This didn't happen in this case. But I just found two sources saying that this CTo7 can happen with incomplete neighbor tones. Commented Nov 13, 2023 at 10:19

Bars 1-2 are basically this: one of the most common harmonic cliches throughout Common Practice music! The diminished chord is used as a chromatic link. It COULD have been used as a modulation to D minor, in which case we could have analyzed C♯dim7 as a rootless A7(♭9), the dominant of D minor. But in this case there's no modulation, it's just a passing chord.

I will focus on the request for a functional interpretation of the first question using Riemannian music theory which is the foundation of Functional Harmonic Theory. The C#o7 chord as was mentioned in another answer can be taken as an A7 chord (or an A7b9). The question is A7 of what key; it is A7 of either D major or D minor; in this case we can take it as A7 of D minor. The A7 however does not resolve to D minor, but rather it moves to Bb major. Bb major does in fact have a functional relationship to D minor; it is the Tonic Leittonwechsel of D minor (notice the term 'Tonic' in the name which is the key to understanding this progression). A7 to Bb major is actually a form of dominant to tonic progression in D minor. The Bb major triad is a variant of the D minor chord. Showing how that works is another topic however so we can just leave it there.

A7(b9) -> Bb Major is D -> T LTW