I can't quantify these phase angles (they are not my theory, this is basic electronics), but the patents do make specific claims based on mathematical formulas, and they are huge; see http://www.freepatentsonline.com/5956410.pdf which claims that: "[for a cable with total distributed capacitance of 90pF] using the impedance meter it was shown that at a frequency of 80Hz the impedance phase angle was found to be -85.46 degrees, and at a frequency of 431Hz the phase angle was found to be -87.37 degrees". He then mathematically calculates power losses at 80Hz as being 7.92% and at 431Hz 4.41% - if true, these are significant losses; read the whole patent if you have more technical questions. Of special interest to me here is that total capacitance of 90pF in that cable under test... why? because this is very low as is, and if you look at the specs of very pricey cables, like Nordost's Odin, which measure about 9pF/foot or 90pF for a 10ft run, then one begins to wonder: do expensive cables also really suffer from such extreme phase issues??? That's HUGE, if true. MIT basically claim that there is exactly one frequency where the power transfer is optimal, and everywhere else there are losses, small or large: "The parallel capacitance of the cable is predisposed to store a greater magnitude of electrical energy than at other frequencies. Furthermore, the series distributed inductance of the cable is also predisposed to store a greater magnitude of electrical energy at certain frequencies than others."
These claims then lead to those MIT articulation-pole designs and another patent http://www.freepatentsonline.com/6658119.pdf which explains those designs (btw, it was claimed by others recently that this patent is now in the public domain), and wherein it is also claimed that the networks are chosen such that their phase angle is around -45 degrees at the chosen frequency, to compensate for the cable's positive phase angle deviation at the same frequency. The end goal, they claim, is to produce a "more uniform audio output". On the other hand, they also do admit that "in other embodiments the network can be designed to emphasize certain frequencies".
Peter
The claims are not huge - they are minimal. The phase angles you referring are capacitor phase angles of a low capacitance value unloaded cable - not the phase of audio signals! And if you compare the amount of difference of the energy stored in the cable (few nJ) with the total signal energy involved in the quoted 50V excitation delivered to a typical 4-8 ohm speaker you will conclude that you are in the -120 to -130dB zone - something we already know. The big question is still "Do these minimal electrical differences affect sound quality?"
The main objective of the patent is not to make science - it is to prevent others to use this technique in cable manufacturing.