Blank (i)
The first part describes what the "first-time listener" finds "exasperating." The appositive elaboration - "the way thematic material drifts without apparent direction" - defines this quality. The blank must mean aimlessness, lack of direction, or disconnectedness.
- A. irreverence - Lack of respect; flippancy. Drifting without direction does not imply disrespect or mockery. Incorrect.
- B. desultoriness - Lack of consistency or method; disconnectedness; aimlessness. "An exasperating desultoriness" perfectly captures the quality of thematic material that "drifts without apparent direction." Correct.
- C. dogmatism - Authoritarian assertion of principles; rigidity of opinion. Dogmatism implies overbearing certainty and fixity - the opposite of drifting without direction. Incorrect.

Blank (ii)
The sentence pivots: what initially seemed exasperating "reveals itself, after repeated hearings, to be the very source of their _______ ." The blank must name a positive quality - the asset that the initially irritating trait turns out to be. If the initial perception was "desultoriness" (aimlessness), the re-evaluation must transform that into a virtue. The blank must mean something like depth, richness, or meaningful complexity.
- D. profundity - Deep insight; intellectual depth; richness of meaning. What first seemed aimless is later recognized as the source of the quartets' profundity - their depth emerges from the very quality that initially seemed like drift. Correct.
- E. tangents - Divergences from a central theme; digressions. "Tangents" is close to the meaning of Blank (i) - it would mean the initial irritation is the source of the digressions, which is circular and does not capture a re-evaluation from flaw to asset. Incorrect.
- F. meticulousness - Extreme care and precision. Meticulousness is the opposite of drifting without direction. If the music were meticulous, it would not strike the listener as desultory in the first place. Incorrect.