Tube Amp for Sennheiser HD650 — Real Differences in Sound?

Hello fellow headphone enthusiasts, I’ll soon be getting the highly acclaimed Sennheiser HD650.

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I wanted to ask: is it worth getting a tube amplifier as well?

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At the moment I own and use a Fosi Audio ZH3 DAC/amp.

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More specifically, I’d like to know the actual difference between listening with and without a tube amp.

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I’m talking about everything related to the listening experience: timbre, frequency response, soundstage, imaging, and anything else.