Stiffness is the resistance of an elastic body to deformation by an applied force along a given degree of freedom when a set of loading points and boundary conditions are prescribed on the elastic body. It is an extensive material property.
Anders Sunde Wroldsen says that in general, the spring stiffness has no influence on the axial and lateral initial stiffness of the beam whereas prestress influences both initial stiffness and the change in stiffness with deformation. "Buckling load and deformation at buckling is sensitive to both prestress and spring stiffness. When designing a tensegrity beam or mast both prestress and spring stiffness should be considered to ensure the desired structural properties." See his 2007 PdD thesis "Modelling and Control of Tensegrity Structures ."
Specific Stiffness Chart Used in Tensegrity Modelling
The following chart shows specific stiffness of typical materials
Tunable Stiffness in Tensegrities
One unique property of tensegrity structures is the ability to change shape without changing stiffness, and on the other hand also to change stiffness without changing shape (Skelton et al., 2001a). These structures have in general a low structural damping, leading to challenges with respect to vibration in some applications. Having small displacement control one can avoid both high internal stresses and reduce vibrations, by small changes in stiffness and/or geometry. Piezoelectric actuators could be suitable for small displacement control. 
Tensegrities Have a High Stiffness-to-mass Ratio
A compressive member loses stiffness as it is loaded, whereas a tensile member gains stiffness as it is loaded. Stiffness is lost in two ways in a compressive member. In the absence of any bending moments in the axially loaded members, the forces act exactly through the mass center, the material spreads, increasing the diameter of the center cross section; whereas the tensile member reduces its cross-section under load. In the presence of bending moments due to offsets in the line of force application and the center of mass, the bar becomes softer due to the bending motion. For most materials, the tensile strength of a longitudinal member is larger than its buckling (compressive) strength. (Obviously, sand, masonary, and unreinforced concrete are exceptions to this rule.) Hence, a large stiffness-to-mass ratio can be achieved by increasing the use of tensile members. 
Links and References
 "An Introduction to the Mechanics of Tensegrity Structures", by Skelton, Helton, Adhikari, Pinaud, Chan. © 2002 by CRC Press LLC  "Modelling and Control of Tensegrity Structures", by Anders Sunde Wroldsen, Doctoral Dissertation, 2007