The rotationally resolved n nu(1) (n=2-6) overtone transitions of the CH acetylenic stretching of propyne (CH3-C equivalent to C-H) have been recorded by using Fourier transform spectroscopy (n=2), various intracavity laser absorption spectrometers (n=3, 4, and 6) and cavity ring down spectroscopy (CRDS) (n=5). The 2 nu(1), 3 nu(1), and 6 nu(1) bands exhibit a well-resolved and mostly unperturbed J-rotational structure, whose analysis is reported. The 5 nu(1) band recorded by pulsed CRDS shows an unresolved rotational envelope. In the region of 12 700 cm(-1), an anharmonic interaction is confirmed between 4 nu(1) and 3 nu(1)+nu(3)+nu(5). The band at a higher wave number in this dyad exhibits a partly resolved K-structure, whose analysis is reported. The mixing coefficient of the two interacting states is determined consistently using different procedures. The 1/35 anharmonic resonance evidenced in the 4 nu(1) manifold induces weaker intensity borrowing from the 2 nu(1) and 3 nu(1) levels to the nu(1)+nu(3)+nu(5) and 2 nu(1)+nu(3)+nu(5) level, respectively, which have been predicted and identified. Several hot bands around the 2 nu(1), 3 nu(1), and 3 nu(1)+nu(3)+nu(5) bands arising from the nu(9)=1 and nu(10)=1 and 2 bending levels are identified and rotationally analyzed, also leading to determine x(1,9) [-20.3(3) cm(-1)], x(1,10) [-1.7975(75) cm(-1)], and x(3,10) [-6.56 cm(-1)]. The J-clumps of the P and R branches in the 6 nu(1) band at 18 499 cm(-1) show a Lorentzian homogeneous profile mostly J-independent with an average full width at half maximum (FWHM) of 0.17 cm(-1), attributed to arising from the intramolecular vibrational energy redistribution towards the bath of vibrational states. A detailed comparative examination of the fine structure in all investigated n nu(1) (n=2 to 7) overtone bands and the similar behavior of the cold and hot bands arising from nu(10)=1 definitively suggests that a highly specific low-order anharmonic coupling, still unidentified, dominates the hierarchy of interaction mechanisms connecting the n nu(1) levels to the background states.