Construct a dream-like low-fidelity musical piece, which acts as a time capsule, transporting listeners back to a realm of nostalgia. It should be a blend of comforting melodies, understated vinyl scratches, and mellow beats. Embody the essence of a warm, rainy day spent in a retro coffee house, intertwining a calming symphony of sounds which bring out feelings of peace and serenity. The aim is to weave together a comforting reverie, with each component enhancing the overall dreamy and lo-fi vibe. Consider the integration of mild piano harmonies, spectral synth layers, and discreet ambient noises to heighten the atmospheric immersion. The final musical piece should unravel naturally, coaxing the listeners into a calming mental state, at a tempo of 60 beats per minute.