Still though as my proof shows, for high impedance headphones, it just isn't going to matter.
The total impedance on the output side is: ZOut + Zconnections + Zcable + Zheadphone. These are all in series and thus are all added together in the end. Please enlighten us why you would obsess over the Zcable term and not demand Zheadphone be of the best possible hand picked value?
Think what you want, but just because "Better" is possible, doesn't mean it matters to the human ear. If "Better" results in no audible change, I would contend it really isn't better. If you want to properly model everything and do measurement on headphone cables, I'd love to see them. Without one single manufacturer doing this, anyone would be crazy to buy these $500-$5000 cables. Keep in mind you'd need to completely model the circuit, not just measure the headphone cable. Also, maybe pass a squarewave and plot the FFT of the acoustical output of the headphone driver.
Now if you want to talk about 4 ohm speakers connected to an amp with .2 ohm ouptut, yes it maybe possible that a cable might make a very small audible difference due to the low impedance values present in the circuit (probably the only expensive cable that might cause a small difference as power cords and interconnects are pure BS). We are talking here though of the HD800 with a driver impedance of 320ohms.
You're certainly right with your view that 0.5, 1 or 4 ohms due to the cable's resistivity doesn't matter for a 450 ohm headphone like the HD 800. The fact that cables do make an audible difference with it nonetheless (in my humble experience) clearly shows that resistance and impedance of cables aren't responsible for the sonic differences. The same may apply to capacitance and inductance, although they can have an audible impact – but they don't define a cable's sonic characteristic in the first place.
One word to the damping factor. Above ohm values are certainly low enough to not cause more than a marginally reduced damping factor, hence a purely academic impact on the sound. But what is the damping factor actually for? It serves for fighting an unwanted frequency-response hump at the fundamental resonant frequency of dynamic transducers due to a corresponding interaction with the there impedance hump. And what's actually the cause of the latter? Back EMF (where EMF stands for electromotive force). A voice-coil not only is moved by the current flowing through it, it also produces current by being moved. And that's exactly what's happening at the resonant frequency: The long decay after the electrical signal has already stopped causes an alternating current within the voice-coil. Which in turn is seen as an impedance rise by the amplifier. At other frequencies this effect is marginal at best, therefore not accompanied by an impedance rise. But there are exceptions, to be noticed in some impedance-response graphs, hinting at mechanical or reflective resonances of a kind and intensity affecting voice-coil movement. They even appear on planar magnetic drivers which otherwise don't have an explicit fundamental resonance reflected in the impedance response.
Back to cables. I began experimenting with homegrown cables, with interesting results, for HD 600 and 650. The first time I have replaced the standard cable with an aftermarket cable was with the HD 650. The Zu Mobius enhanced transparency, clarity, detail and finally the musical enjoyment significantly – and surpassed my own designs. Later I also experimented with a Silver Dragon, which offered some more treble sparkle, somewhat at the expense of naturalness and warmth. Its third-generation version was my first choice later with the HD 800. And it made clear that it was a silver cable: more treble sparkle, more detail and clarity, with only a small, tolerable loss of organicalness. Note that my HD 800 is modified, has much less treble glare than originally, so the choice of silver shouldn't be seen as a misconfiguration. But inspired by other Head-Fiers I wanted to try a DHC «Clone» (the «Complement»'s little brother). What a disappointment! It sounded dull and lackluster, sacrificed detail. No matter how I try to compensate for it by equalizing, I haven't managed to get satisfying results. It also shows that cable characteristics are not caused by frequency-response phenomena, at least not in the first place, although they sometimes sound like it. And it shows that the cable at hand is specifically designed to remove the HD 800's treble glare – apparently at the expense of detail and transparency.
I haven't stopped there – suddenly I decided that I like the stock cable better nonetheless. It took some EQ fine-tuning, though, and the change of mind was also influenced by EQ experiments due to the new configuration with the Chord Hugo as source (instead of McCormack UDP-1 and Bel Canto DAC2). The Silver Dragon was later delegated to be connected to the HiFiMan HE1000. And that was clearly the most significant cable effect of my audio career – and revealed how bad (dull, grainy, intransparent) the HE1000's original cable is.
I certainly understand the reservation against cable-sound reports of people who aren't sensitive to this kind of sonic subtleties and moreover have a rather rigid scientific orientation. (In turn I'm rather insensitive to MP3 compression effects myself, at least at high bit rates, and haven't detected any effect from power cables and conditioners so far). It's indeed hard to believe how effectively immeasurable signal differences could cause audible differences. But those who are interested may read some of Rob Watts' essays on this forum (in Mojo, Hugo/TT and DAVE threads). The developer of said Chord DACs who is so kind to share all of his secret recipes with us offers a lot of
insight how much more
sensitive the human hearing is than what's commonly acknowledged. According to his
experience during the development of DAVE humans can detect modulation noise in the range of –350 dB and equally low harmonic distortion. Once you're familiar with DAVE you'll immediately believe it, because it takes care about this new insight and sounds correspondingly exquisite, probably more transparent down to the lowest tones than any other DAC on the planet. According to Rob even solder joints have an audible impact, every single electronics component anyway (that includes cables).
Many Head-Fiers certainly are familiar with the HD 800 damping mods – and how they reduce treble intensity. The mechanism behind that is clear: predominantly high frequencies are absorbed by the damping materials, whereas lower frequencies (= larger wave lengths) are barely affected, since the damping layers are too thin for them. So the actual performance of the damping is a reduction of reflected high-frequency sound waves, therefore a relative increase of the usable, direct sound waves from the membrane. Now when you look at the measuring graphs, the results are not so impressive. There's certainly something going on, but it's not entirely positive – or if, it's rather marginal. But the fact that the treble is significantly reduced and less glaring to the ears makes the mod mandatory to me. Granted, my own mod uses different materials than the Anaxilus mod (velvet instead of foam or felt or velours, which is much better in my book, just less user-friendly), but I think the relative dullness after applying the mod is a common experience. Nevertheless, the waterfall plots astonishingly don't show a shortening of decay to the expected degree. – This example is meant to show that measurability of audible effects is overrated. Some very cheap headphones and IEMs show best measuring values, but fail to sound accordingly. That said, of course I believe that audible effects have to be reflected in the measurements, but it seems that our now horizon about what there's to be measured is too narrow.
Just installed a superdupont mod I got in eBay. Fantastic, a much more pleasing listen. Not nearly as harsh. I totally recommend it.
And its impact is measurable. Weird, that.
I absolutely believe you. But you could have achieved the same result with active equalizing, plus even more (e.g. extended low bass).