I had thought that "as the speed decreases, the torque decreases with the square of the speed and the horsepower decreases with the cube of the speed" applies to the characteristics of the load, i.e.
VARIABLE TORQUE LOADS:
Load types require reduced torque when driven at speeds less than the base speed of the load. Conversely, such loads may require increased torque when driven at speeds greater than the base speed of the load. These are classified as variable torque loads. Many variable torque loads decrease with the square of the speed. This is characteristic of centrifugal pumps, and certain types of fans and blowers. Typically, as the speed decreases, the torque decreases with the square of the speed and the horsepower decreases with the cube of the speed.
CONSTANT TORQUE LOADS
With constant torque loads, the torque loading is not a function of speed. Typical applications are: Traction drives, Compressors, Conveyors, Positive displacement pumps and Hoists. As the speed changes, the load torque remains constant and the horsepower changes linearly with speed. Constant torque loads cause motors to draw relatively high current at low speeds when compared to variable torque applications. This is why the same size drive may have a lower HP rating for Constant Torque applications.
Many VFDs can be set up with VT or CT type settings. Base speed is their RPM at the nameplate motor rated Hz (usually 60Hz): Many 3 phase inverter rated motors are rated for a CT ratio of around 10:1, they can deliver constant torque below their base speed of 60Hz down to around 5-6Hz. AC Vector motors (CT ratio around 1000-2000:1) provide full torque essentially down to ~0 RPM. They loose horsepower in a 1:1 ratio below their base speed, they maintain HP above the base speed to around 2X their base speed. They maintain full torque below base speed (as noted above), they loose torque in a somewhat linear fashion above to 1.5-2X their base speed (non-linear above that). As you mentioned, most manufactures rate their inverter (4 pole) motors to a maximum RPM around 2X their base speed, smaller (2-5HP) vector motors nameplate often go to 4-5K. Yikes. Most of the smaller Vector rated AC motors are TENV, and do not have the usual overheating problems with lower or above base speed of cooling associated with the usual forced air cooling units.
One intriguing idea I was considering for my lathe was to use a 6 pole 1200 RPM vector motor instead of a 4 pole 1800 RPM. A 6 Pole 1200 RPM vector motor provides higher full load torque (~150% of 4 pole) and maintains constant horsepower to about 2X base speed, so a usable working RPM range of 0-2400 RPM. Unfortunately the 6 pole motors are 1-2 frame sizes bigger then their 1800 RPM version, and did not fit in my application.
Great reference I saw posted elsewhere on [FONT=&]Feed your VFD with the right power[/FONT]:
http://machinedesign.com/motorsdrives/feed-your-vfd-right-power
Mark