ProtegeManiac
Headphoneus Supremus
I added emphasis.
You can know pretty clearly how it will go, if you know the impedance curve of the headphone and the output impedance of the amplifier. As you approach ideal power transfer you will see "boosts" (so points with higher load impedance + higher source impedance will lead to "boosts" of the frequency response). And it isn't explicitly tied to "the bass" either - it is simply the inter-relationship of load impedance and source impedance. Many single-driver systems have a resonance in their mid-bass and that's why "it affects the bass" is such a common explanation. A lot of IEMs or multi-driver systems have much different looking impedance curves, and their FR will respond accordingly to higher source Z. Examples:
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If the amplifier has atypical frequency response, is current/voltage limited, or is doing something else, that can also have an impact on the sound. So this isn't the only variable. But "high output impedance" does not equate to "unpredictable changes to bass response" - that's far too generalized of a statement.
Didn't know that bit, thanks. But again that assumes he'd have the data...or, well, just using an amp that won't require having to account for these interactions.