Wall speed controls for ceiling fans

Hello,
I'm a little confused on how (and how efficiently) speed controls for ceiling fans work. I understand that there are two types of speed controls--capacitor based controls (with discrete speed levels) and triac based controls (which can be continuous). I'm using the Hunter Vista fan, which has a capacitor-based 3-speed control built in. So, a few questions:
1) How do capacitor based speed controls work? I was under the impression that an induction motor's speed was fixed by its design and the AC frequency.
2) Are the capacitor based speed controls more energy efficient than the solid state controls? In particular, I understand that triac based lighting dimmers use a small amount of power themselves. Does this hold true for triac based fan speed controls, and not hold true for capacitor based fan speed controls?
3) Will a wall capacitor based speed control work as well as the built-in capacitor based speed control on the fan itself? I ask because in the wall there are just hot and neutral, while the fan motor has 4 wires going to it.
4) Is every "rotary action" discrete fan speed control going to be capacitor based, or are some actually triac based? In particular I'm interested in the Hampton Bay 750 450 discrete speed control, I'll have to call them tomorrow to double check.
Thanks, Wayne
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On 1/25/2005 6:17 PM US(ET), Wayne Whitney took fingers to keys, and typed the following:

considered a single hot wire that has a switch inserted in it to operate the fan. The one wire is white because it is more convenient to run a single length of wire cable (blk-wh-neutral) to the switch rather than two black wires.

--
Bill

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Yes, this is often true (although the white wire should be marked black), so I should rephrase my question to "only the hot wire in the wall versus 4 wires that go to the motor". In my case, there is neutral in the switch box, if it matters.
Cheers, Wayne
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