Final answer:
Nadezhda von Meck's relationship with Tchaikovsky was that of a patron.
Step-by-step explanation:
The relationship between Nadezhda von Meck and Tchaikovsky was that of patron. Nadezhda von Meck was a wealthy Russian patroness who provided financial support to Tchaikovsky, allowing him to focus on his compositions and musical career. She admired Tchaikovsky's work and funded his life, providing him with a regular income, without expecting any romantic or personal attachment.