We report experiments on turbulent Rayleigh-Bénard convection of air in a cylindrical large-scale facility with a diameter of 7 meters and Rayleigh numbers up to Ra approximately 10(12). The facility is used to explore the structure of the large-scale circulation for continuously varying aspect ratios between Gamma approximately 1 and Gamma approximately 10. Using autocorrelation functions derived from high-resolution time series of temperature and velocity near the cooling plate we demonstrate that the well-known single-roll structure (often called "wind") breaks down when the aspect ratio increases beyond the critical value Gamma(1) = 1.68+/-0.22. We further show that at Gamma(2) = 3.66+/-0.46 a second transition from an oscillatory two-roll structure to an unstable multi-roll structure takes place. The value of Gamma(2) represents a lower bound for the aspect ratio that is necessary to reach homogeneous convection--a turbulent state that is free from the influence of lateral walls.