First of all, let’s take care of the specific analysis business. Mixture chords are in bold.
m. 1-13 in C major:
I I V⁴₂/V V6 V6 bVII bVII V⁴₂/IV IV6 iv6 V7 iv6 V7 iv6 V7 iv6 V7 i V
m. 167-174 in C major:
i bVI bII (?) bVII bIII iv7 vii°⁴₂ V64/V vii°7/V V7 I
The opening theme in measures 1-13 and its subsequent repetitions/variations later on seemed to tell a story. The textbook purpose of a mixture chord is to evoke emotion and surprise by clouding the stability of the tonic area, often creating tension and tonal insecurity. I suppose this remains true for Beethoven in the Waldstein sonata, but for me, the mixture chords functioned more like mood setters for a good story. A story which I’m now going to tell you.
Our story starts with a journey. Beethoven opens with a series of fast eighth notes at an even but lively pace - The protagonist is traversing a new road, in a new land he’s never been to. Almost immediately, we move to a borrowed chord – V⁴₂/V, followed by V6. This motion doesn’t stray very far from C major, but it does wander far enough from tonic early enough as to prepare the listener for some unexpected tonic areas (aka mixture chords). The protagonist is eager to explore this new place, but feels somewhat unsure of what to expect. A little “birdcall motive” (measures 3-4, 7-8, 158-159, 162-163, and others) of falling 16th-note scalar passages seems both to encourage and forewarn the protagonist. We move to the first mixture chord - bVII, Bb major – which isn’t so much a surprise as a continuation of the protagonist’s mixed excitement and uncertainty. Another borrowed chord takes us to F major, and we hear the birdcall again (m. 7-8). But this time, the bird has become distinctly aware of some nearby danger, and frantically flies down at the protagonist – indicated by the quick V7 - iv6 harmonies and 16th-note runs in the right hand between F and B, a tritone apart. Eventually the bird’s erratic flight forces the protagonist off the road (m. 11) and a cautious unison arpeggio of C minor (i) in the next two measures illustrates the dust settling, as both traveler and bird wait to see if the coast is clear. The return to C major in measure 14 lets us know that all is well.
Many measures later (156 -174) we find the protagonist and bird resting together by the road, having become friends on the journey and experienced some interesting tonal areas and met some new theme material along their way. In measure 156 the opening music is repeated, as if the two friends are remembering their meeting and reflecting on it. In measure 167 the cautious C minor chord is repeated, but instead of resting on G as in measure 13, Beethoven holds a unison Ab (bVI). It seems that now, instead of waiting once more for the dust to settle and to watch for danger, the traveler, having experienced it already and now looking back, sees this moment as a life lesson, to look back on and appreciate. The cautious motive of measures 167-168 is repeated in 169-170, but this time Db major (bII) is arpeggiated, followed by unison Bb (bVII). It seems as if the traveler is saying, “You know, this has been an eventful journey, but a good one. I’m glad I started down this road.” And with those thoughts, he meanders happily back to C major through a harp figure in measures 171-173, from bIII to secondary dominants and eventually a nice V7 – I authentic cadence.
It’s strange to describe a piece this way - birds and traveling and stange new places... well, you know, I did go to China over winter term - but I think the story is a better illustration of the effect the mixture chords have, rather than saying “the Le in the bass adds tension to a tense measure”. While they do add “surprise” and “tonal variation” it’s much easier to comprehend from a narrative with the emotions built in.
I hope this covers everything from the questions… see you Monday!