A Tangled Mess
I've spent the last couple of weeks listening to various cables on my Sennheiser HD 600, and while I think I've noticed some differences between the cables, I'm certain I wouldn't be able to tell them apart in blind tests. Well...I might be able to pick out the stock HD 600 cable from the others---it sounded just a bit confused---but otherwise, the differences I think I might have heard are too small to reliably identify.

To put a finer point on the sonic characteristics I heard, it sometimes seemed that certain instruments or sounds in the mix were slightly more obvious on some cables than others. Sometimes I'd hear the high-hat more clearly with one particular cable, sometimes I'd hear the vocals a bit more forward or back, but the cables wouldn't act the same way with different music, and it seemed the harder I listened for the effect, the more it would disappear. (Sort of like when you stare at an image without moving your eyes for long enough and the image starts to disappear.)

I've also spent quite a bit of time reading about people's experiences with cables. Not just anybody though, people for whom I've got a great deal of respect. I found a good deal of commonality in their opinion: Cables may make a small difference in some cases, but for the most part it's the last thing you should worry about.

It seems the most common reason cables made marked differences when installed was when there was something wrong with the stock cable. Maybe it had become intermittent over time, or oxidation had corroded the connectors, but replacing the cable made the headphones usable again.

Of course, there were also many comments ranging away from this middle ground, but it always seemed to me that confirmation bias was playing a big role in the opinion. Either the listener was wowed by the huge changes made, or was ever more convinced that cables made no difference at all. No doubt a self-fulfilling prophecy in most cases.

Untangling the Issue
Still, I remain convinced that there are good reasons to purchase aftermarket cables. For starters, I'm certain I've heard differences, and after reading and talking to some trusted sources, it appears they too have all experienced small differences in the sound of cables. There's just too much anecdotal evidence to believe anything other than sometimes something is happening with cable swaps that is apparent to the listener. Additionally, most have a hard time expressing exactly what they're perceiving. It doesn't seem like it's as simple as tonal changes that might be seen in frequency response measurements.

I'd like to caution objectivists to understand that there are a lot of things that could account for a small audible difference that doesn't show up as a change in frequency response. For example, back in the early days of the CD, "perfect sound forever" was the rallying cry. Objectivists claimed CD players should be indistinguishable, but subjectivists heard differences. Later, the discovery of jitter timing errors would clarify the source of the differences heard. Objectivists should always bear in mind that you don't know what you don't know, and skepticism should target both subjective experience and objective evaluation.

I'd like to point out this recently published scientific paper, "Human Time-Frequency Acuity Beats the Fourier Uncertainty Principle." The paper's abstract states:

The time-frequency uncertainty principle states that the product of the temporal and frequency extents of a signal cannot be smaller than 1=(4pi). We study human ability to simultaneously judge the frequency and the timing of a sound. Our subjects often exceeded the uncertainty limit, sometimes by more than tenfold, mostly through remarkable timing acuity. Our results establish a lower bound for the nonlinearity and complexity of the algorithms employed by our brains in parsing transient sounds, rule out simple "linear filter" models of early auditory processing, and highlight timing acuity as a central feature in auditory object processing.

While I'm not capable of delving into the fine details of this paper, the gist of it is readily apparent: Our listening system is far more complex than we're currently able to understand, and is much more focused on the time-domain than previously thought. Here's an excerpt:

Early last century a number of auditory phenomena, such as residue pitch and missing fundamentals, started to indicate that the traditional view of the hearing process as a form of spectral analysis had to be revised. In 1951, Licklider [25] set the foundation for the temporal theories of pitch perception, in which the detailed pattern of action potentials in the auditory nerve is used [26, 28], as opposed to spectral or place theories, in which the overall amplitude of the activity pattern is evaluated without detailed access to phase information. The groundbreaking work of Ronken [22] and Moore [23] found violations of uncertainty-like products and argued for them to be evidence in favor of temporal models. However this line of work was hampered fourfold, by lack of the formal foundation in time-frequency distributions we have today, by concentrating on frequency discrimination alone, by technical difficulties in the generation of the stimuli, and not the least by lack of understanding of cochlear dynamics, since the active cochlear processes had not yet been discovered. Perhaps because of these reasons this groundbreaking work did not percolate into the community at large, and as a result most sound analysis and processing tools today continue to use models based on spectral theories. We believe it is time to revisit this issue.

Additionally, training and expertise in the art of listening has an effect on our hearing acuity. From the paper:

We further found that composers and conductors achieved the best results in task 5, consistently beating the uncertainty principle by factors of 2 or more, whereas performers were more likely to beat it only by a few percentage points. After debriefing subjects, it appears that the necessity of hearing multi-voiced music (both in frequency and in time) in one's head and coaching others to perform it led to the improved performance of conductors and composers.

The take-away points here are: The human hearing system is exquisite and evidently capable of beating what we think of as objective theoretical limits---we need to learn much more about the human hearing system in order to identify things to measure for evaluative purposes. There are aspects of hearing that require training and long experience---just because we don't perceive something doesn't mean there isn't something there to be perceived. Some people will be far more sensitive than others. And lastly, though not addressed in the paper, it seems to me that these subtle effects and our experience of them will not yield easily to definition, and each individuals experience of them will vary somewhat. When it comes to cables, YMMV (your milage may vary).

An Avenue for Exploration
I did manage to stumble into what seems to me as a particularly interesting avenue for further exploration and development. I had a discussion with Dr. Kevin Gilmore (who many of you know from his terrific work designing commercial and DIY electrostatic headphone amplifiers) in which he stated that the effectes of impedance matching with headphone cables could be of an order strong enough to influence the listening experience.

All cables have a characteristic impedance. For example, I use Canare 4E5C cable for my cable building needs. This cable has a 40 Ohm characteristic impedance. If I were to build a headphone cable for a Sennheiser HD 600, which has a 300 Ohm impedance, there would be a point at the headphones where the signal went from the 40 Ohm impedance in the cable to the 300 Ohm impedance of the driver. This impedance mismatch would cause a point of reflection for the signal. There is an instrument call a Time Domain Reflectometer that is able to send a signal down a cable and see the various points of reflection caused by impedance mismatches (and other things). The reflected signal from the impedance mismatch can, depending on the topology of the amplifier in use, have an effect on the signal from the amp. To properly impedance match the cable to the headphones in this example case, you would have to put a 40 Ohm resistor between the signal and ground at the headphone end of the cable. This would dramatically reduce the reflected signal.

A further twist on cable impedance matching is to impedance match the output of the amp to the cable. This works better for interconnects where the damping factor between the source and load isn't as important. For further information on this topic see this Headcase thread.

It seems to me this is a readily available avenue for further development by custom headphone cable makers.

Other Good Reasons for Aftermarket Headphone Cables
While the sonic improvements of headphone cables may be a contentious subject, there are a number of other good reasons to consider an aftermarket headphone cable.

• Balanced Drive - There are many balanced drive headphone amplifiers available today. Using one of these amps requires headphones to be re-cabled.
• Ergonomics - Your particular habits of use may be aided by a cable that is longer (for home and office) or shorter (for use with mobile devices) than the one supplied with your headphones.
• Cable Born Noise - Often improperly called "microphonic" noise, a stiff cable will transmit mechanical vibration up the cable to the ear pieces, which can often be heard. (The term "microphonic noise" is aplicable to active components, like tubes, which will create electrical noise through mechanical vibration of the tube.) Replacing stiff cables with softer more pliable cable will reduce cable-born mechanical noise.
• Esthetics - Styling has become more important to headphone users these days, and replacing stock cables with cooler looking aftermarket cables having nicer connectors can bolster pride of ownership. Sorry, I dont see anything wrong with this.
• Ridding Headphones of Extraneous internal Connections - Many headphones have multiple solder joints within the headphone that can be bypassed when rewired. This is especially true of single-sided entry designs where the incoming cable is often soldered to a small circuit board to split the left and right channel. An additional cable will go to the driver on that side, and another cable will go up through the headband to the driver on the opposite side. Custom headphone re-cablers will often re-cable this type of headphone with a "Y" cable to go directly into each earpiece, and internally connect the new conductors directly to the driver wire terminals thereby bypassing a number of previously existing solder joints.
• DIY Opportunity - Recabling headphones is a great way to express your DIY skills. I would strongly recommend spending quite a bit of time building interconnects and headphone extension cables before attempting to re-cable a pair of headphones, but re-wiring your cans is a really fun mid-level DIY project for those interested and properly skilled.

Summary
To say that headphone cables make a significant difference, or no difference at all, is, to my mind, an overly-simplistic view. Objectivists will claim no one has ever identified differences in cable in double-blind tests, ignoring the possibility of subtle effects that don't lend themselves to that type of observation. And enthusiastic subjectivists often want to contribute to the evolution of their rig by swapping cable around, naively ignoring the fact that there are hundreds of solder joints and conductors inside their gear that will have a combined effect much stronger than that of any particular interconnect between the various pieces of gear. The truth, as always, lies in some middle ground where the gear you choose is of primary importance, and once you find a system to your taste, some slight tweaks may be achieved with careful cable selection.

Further development is possible both in our understanding of the human hearing system and how it perceives sound, and in understanding what factors may come into play with cable construction that might yield a better listening experience. Easier to achieve improvements may also be available though fairly simple impedance matching techniques in the design of aftermarket headphone cables.

Aftermarket cables can also provide improvements in ergonomics, styling, cable-born noise control, and connector changes for your particular use.

My suggestion? The diminishing returns curve is steep with cables, don't over buy. I like the Cardas Headphone Cable and the Moon Audio Blue Dragon. There are numerous cable makers out there, many are good, but many more are just hobbyists with a soldering iron and a yen to be in business. With cables, the devil is in the details, I strongly suggest using cable makers with long years of experience and a good reputation. If you have headphones with a hard wired stock cable and would like to have them replaced, again, it is very important to find a reputable supplier who is very familiar and competent with this type of work. I'll happily recommend Moon Audio as one such supplier.

Disclaimer - Many of you may have noticed Moon Audio as a recent advertiser at InnerFidelity. I've been planning to do this article for a long time and had requested cables from Moon (and Cardas) long before they began advertising here. My desire to do this article and my conclusions have nothing to do with who advertises here.

Resources
If you have any cable questions I suggest searching for answers in the Head-Fi.org Cable and Accessories forum area.
I couldn't find a particular thread for full-size headphone recabling vendors (please feel free to provide a link in the comments if you know of one) but I did find a thread for IEM recabling suggestions here and here.