This paper describes an analytical and experimental investigation of the dynamic response and performance of a special type of centrifugal pendulum vibration absorber used for reducing torsional vibrations in rotating systems. This absorber has the property that it behaves linearly out to large amplitudes, and thus experiences no frequency detuning. Previous analytical work on such tautochronic absorbers has considered the response, dynamic stability, and performance of single- and multi-absorber systems. In particular, it is known that these absorbers, when perfectly tuned to the order of the applied torque, do not exhibit hysteretic jumps in the response, but multi-absorber systems can experience instabilities that destroy the symmetry of their synchronous response. In this work we extend the theory to include linear de-tuning of the absorbers, which can be used as a design parameter to influence absorber performance, both in terms of rotor vibration reduction and operating range. This paper reviews the basic analysis, which employs scaling and averaging, and extends it to include the detuning. In addition, systematic experiments of systems with one and two absorbers are carried out. The experimental results are unique in that the test facility is capable of varying the excitation order, thereby allowing one to obtain order-response curves that are useful for design purposes. The experimental results are found to be in excellent agreement with the analytical predictions, and these clearly demonstrate the tradeoffs faced when selecting absorber tuning.