We present a detailed spectroscopic study of Herschel 36 A (H36A), the main stellar component of the massive multiple system Herschel 36 in the Hourglass Nebula, based on high-resolution optical spectra obtained along an 11 years span. The three stellar components present in the spectrum of H36A are separated by means of a spectral disentangling technique. Individual spectral classifications are improved, and high precision orbital solutions for the inner and the outer orbits are calculated. H36A is confirmed to be a hierarchical triple system composed of a close massive binary (Ab1+Ab2, O9.5 V+B0.7 V) in wide orbit around a third O-type star (Aa, O7.5 Vz). The inner-pair orbit is characterized by a period of 1.54157 +/- 0.00006 days, and semi-amplitudes of 181.2 +/- 0.7 and 295.4 +/- 1.7 km/s. The outer orbit has a period of 492.81 +/- 0.69 days, and semi-amplitudes of 62.0 +/- 0.6 and 42.4 +/- 0.8 km/s. Inner and outer orbits are not coplanar, having a relative inclination of at least 20 degrees. Dynamical minimum masses of 20.6 +/- 0.8 Msun, 18.7 +/- 1.1 Msun, and 11.5 +/- 1.1 Msun are derived for the Aa, Ab1, and Ab2 components, respectively, in reasonable agreement with the theoretical calibrations.