Why hasn't anyone built a musical instrument based around the Doppler effect?

The Doppler Effect (an increase or decrease in pitch based on the speed of a moving object) is most commonly experienced when the pitch of a speeding car's horn ascends/descends as a vehicle approaches or departs a stationary viewer. This physical property of acoustics is used in Leslie Speaker cabinets, which create vibrato and chorus effects by rotating a "horn" attached to a speaker between 40-400RPM.

I propose to build the Dopplerphone, which will push the concepts mentioned above to the extreme, and combine them into a singular musical instrument that can be played polyphonically via keyboard. The Dopplerphone will use high speed motors to move speakers at several thousand RPM, in the hopes of creating new acoustic effects and exploring the extreme ranges of the Doppler effect. When a speaker emitting a stationary drone is rotating at a super-precise rate, will it be able to pla