For example, if I buy a Fiio A1 and run my Macbook headphone jack out into the A1, and the A1 into my headphones, is the practical output impedance the output impedance of the Macbook (~10), the output impedance of the A1 (<0.2), or some calculated combination of the two?
I'm debating whether better amping could help my DT 770s, given that their sound signature is notoriously sensitive to both under-amping and output impedance.
The headphones (or speakers - this applies to both) will only "see" the output impedance of the amplifier. So if the amplifier's output impedance is 100 ohms, 1 million ohms, whatever, that's what the load sees. The amplifier's input side is itself a "load" on the source device's output, and the source will accordingly "see" the amplifier's input side impedance as its load. For analog audio you generally want the output device (e.g. the source) to be lower impedance than the input device (e.g. the amp), and most equipment is designed so that at minimum you will have something like 5:1 and it may be 100:1 or higher. This is done primarily for noise rejection, and isn't anything you generally need to worry about. Usually the bigger concern is output voltage relative to input sensitivity - if the source's output is very "hot" (like say 2-3V) and the receiving device's input is very sensitive (like say sensitivity is insanely high, like 2mV) its very easy to drive into clipping and/or have very little usable range on a volume control with such a setup.
Source/amp impedance relationship isn't something to worry heavily about, because generally speaking modern devices (and even not so modern devices) will adhere to "best practices" in terms of the low/high relationship. As far as headphones and the amplifier go, output impedance will interact with frequency response IF the driver/load is relatively reactive (meaning the impedance changes a lot wrt frequency), and as you approach more ideal power transfer you will have increases (in magnitude) in frequency response; there is no "true" or "right" configuration for such a load - its simply reactive and will always react to output impedance.
Here's an article, with graphs, that explains that in more detail:
http://en.goldenears.net/index.php?mid=KB_Columns&document_srl=1389
It isn't just BA IEMs that can experience reactive loads - some dynamic cans are relatively reactive too (the Sennheiser HD 580/600/6XX/650 family are a very popular example), which leads to "they sound very different on different amps" - it isn't mystical though, there's an explanation for whats going on. Here's a modeled (and normalized) response plot of the HD 650 with different output impedances to give you some idea:
(this comes from here: http://personalaudio.ru/raa/otchety/naushniki/sennheiser-hd-650/)
At 300 ohm output impedance, the increase on the low-end is around 1.9 dB (which is audible, but not "huge").
By contrast something that's much more resistive, like a planar magnetic, will behave consistently with respect to output impedance:
(from here: http://personalaudio.ru/raa/otchety/naushniki/fostex-t50-rp/)
There is no "right" or "wrong" to this - the T50rp aren't "better" than the HD 650 as a result of this, its just a characteristic on either side, and one of them as a result has more interaction with amplifier selection than the other.
As far as the DT770's themselves, Stillhart is absolutely right that there are various SKUs of the DT770 with different impedance values (and I'm personally convinced Beyer does this just to create confusion
), and PersonalAudio.ru appears to have measured and modeled all of them:
32R:
(http://personalaudio.ru/raa/otchety/naushniki/beyerdynamic-dt-770-32-ohm/)
80R Pro:
(http://personalaudio.ru/raa/otchety/naushniki/beyerdynamic-dt-770-pro-80-ohm/)
250R:
(http://personalaudio.ru/raa/otchety/naushniki/beyerdynamic-dt-770-pro-250-ohm/)
600R:
(http://personalaudio.ru/raa/otchety/naushniki/beyerdynamic-dt-770-600-ohm/)
32R Limited Ed:
(http://personalaudio.ru/raa/otchety/naushniki/beyerdynamic-dt-770-pro-32-ohm-le/)
None of them would classify as "hyper sensitive" in my book - the 600R are showing around .5 dB of shift between 0 and 300R, while the 80R are showing 1.7 dB and shifts at two points on the scale. In any case, none of that is "massive," so as I said, I wouldn't regard them as "hyper sensitive" to changes in output impedance. Certainly I'd expect the 80R would be audibly different if you had side-by-side with a very high Zout (e.g. 300R or even higher, like the current-drive Bakoon amplifiers) vs a very low Zout (like 1ohm), but 1-2 dB differences aren't "huge." Also note that you're going to need fairly significant changes in output impedance to get into those 1-2 dB shifts (and realize I'm using imprecise language here: there isn't a "right answer" to this, so it isn't like high impedance is "wrong" and low impedance is "right" - they're just different, so the "shifts" are relative to low impedance output amplifier) - a lot of modern headphone amplifiers either have fairly low output impedance (for various reasons) or get somewhere around the IEC's spec 120R output (Beyer's headphone amplifiers have tended towards the IEC model, for example) - some OTL tube amps may go higher, and the Bakoon current-drive amplifiers have very high output impedance, but generally the only place you're likely to see "high output impedance" in that 300+ ohm range would be from older receivers/integrated amps. What sounds best to you is entirely subjective, but there's "what's happening" based on measurements.
