Triode mode has plate impedance and lower distortion which makes it sound more sterile as compared to big bad pentode operation. Ultra-linear is partway between triode and pentode operation, the sound is also partway between the two. There is less advantage to running a EL84 in fixed bias as compared to cathode bias due to the grid bias voltage. Comparing a 6V6 to a EL84 at 250V, the 6V6 needs a bias voltage of -15V compared to the -11V that the EL84 needs. That 4V difference is added heat and power developed by the cathode resistor, the EL84 will waste less potential audio power than the 6V6 in a cathode biased circuit. Mind you it is more sensitive due to the added power used by the heaters. It was designed to be more sensitive so an added gain stage was not needed to drive it. By eliminating one gain stage the manufacturer saved money. As our amps run higher voltages the bias voltage is also higher, with more losses in cathode mode as we go higher. Some would debate the tube as being a poor design. It was introduced to the world in the Mullard Model 510 and helped kick off the hifi craze of the 50's and 60's. An example of this is the amplifiers built by H.H. Scott, the 222 and 299 series of amplifiers. I happen to have a 299 that still works to this day. Wonderful sounding amplifier, mind you it used the higher voltage 7189 variant of the EL84.