The phrase "melancholy strain" typically refers to a mood, feeling, or tone characterized by sadness, pensiveness, and often a sense of longing or wistful reflection. Here's a breakdown of the terms:

• Melancholy: A thoughtful sadness, often with a hint of longing. It's a contemplative and somewhat wistful state of mind. The Oxford Learner's Dictionary defines it as "a feeling of being very sad and without hope" Oxford Learner's Dictionary
• Strain: In this context, "strain" refers to a specific quality, tone, or undercurrent. Merriam-Webster defines it as "a particular tendency, quality, or tone." Merriam-Webster

Therefore, "melancholy strain" suggests a pervading sense of sadness or a melancholic tone present in something, such as a piece of music, writing, or even a person's demeanor.