Beethoven's Heiliger Dankgesang (opus 132, third movement)
Beethoven composed the third movement of his A minor string quartet (opus 132) after recovering from a near-fatal illness. At the top of the manuscript he wrote this dedication: "Heiliger Dankgesang eines Genesenen an der Gottheit, in der Lydischen Tonart" ("Holy song of thanksgiving of a convalescent to the Deity, in the Lydian mode").
What Beethoven doesn't mention is that while he does begin with a "holy song of thanksgiving" in the Lydian mode, the piece alternates between Lydian mode and D major. To make this alternation visible, I've used colors to identify the pitches:
Because the passages in Lydian mode are slow, reverent and introspective, I've chosen relatively subdued colors for the pitches in that mode (F, C, G, D, A, E, B).
All twelve pitches are used in D major sections, and I've used vivid colors for the five added pitches that are not in the Lydian mode (F#, C#, G#, D#, A#).
(n.b. This color assignment is a variation of a technique I call Harmonic Coloring, which is described in more detail here and here.)
The Lydian sections are built from three elements: a hymn tune ...
... the harmonization of the hymn tune, and contrapuntal passages derived from fragments of the hymn tune.
In the opening section of the piece, each phrase of the hymn tune is preceded by a short contrapuntal passage. The points of imitation in these passages are highlighted by lines connecting the notes:
The background is a pitch staff that shows the colors and vertical positions of the notes used in each section of the piece (this is done to highlight the modulations between F Lydian and D major).
The hymn tune is shown with hollow shapes (here, the first violin has the tune) ...
... and the harmonization is shown in solid shapes.
Two or three minutes into the piece, two brightly-colored pitch lines appear (F-sharp and C-sharp), followed by the corresponding notes, presaging the modulation to D major ...
Things get more agitated as the modulation becomes imminent. N.b. The final F of the hymn tune never happens — it's replaced by an E, as part of an A major chord that serves as the dominant/V to the impending tonic/I of D major ...
... which arrives jumping for joy (Beethoven marks this section "Neue Kraft fülend" — "Feeling new strength") ...
... and revels in exuberant play ...
... before blossoming into an expansive, relaxed cadence ...
... and the modulation back to F Lydian.
In the second Lydian section, the first violin again has the hymn tune, but the other instruments no longer participate in a unified, homophonic harmonization. Some play slow notes that are reminiscent of the original chorale section, but others are more contrapuntal; all are syncopated ...
As in the first Lydian section, the second concludes with an explosive modulation ...
... to D major.
The second D major section follows the same form as the first, but with more ornamentation. And, like the first, it ends by modulating back to F Lydian for the third and final hymn section.
In this final section, the hymn tune is progressively fragmented more and more until, eventually, only the first three notes survive ...
... after which we are left floating with the clouds ...
(I'm puzzled by the discrepancy in the ending ...)