Based on the well established importance of long, non-dispersive baroclinic Kelvin and Rossby waves, a resonance of tropical planetary waves is demonstrated. Three main basin modes are highlighted through joint wavelet analyses of sea surface height (SSH) and surface current velocity (SCV), scale-averaged over relevant bands to address the co-variability of variables: (1) a 1-year period quasi-stationary wave (QSW) formed from gravest mode baroclinic planetary waves which consists of a northern, an equatorial and a southern antinode, and a major node off the South American coast that straddles the north equatorial current (NEC) and the north equatorial counter current (NECC), (2) a half-a-year period harmonic, (3) an 8-year sub-harmonic. Contrary to what is commonly accepted, the 1-year period QSW is not composed of wind-generated Kelvin and Rossby beams but results from the excitation of a tuned basin mode. Trade winds sustain a free tropical basin mode, the natural frequency of which is tuned to synchronize the excitation and the ridge of the QSWs. The functioning of the 1-year period basin mode is confirmed by solving the momentum equations, expanding in terms of Fourier series both the coefficients and the forcing terms. The terms of Fourier series have singularities, highlighting resonances and the relation between the resonance frequency and the wavenumbers. This ill-posed problem is regularized by considering Rayleigh friction. The waves are supposed to be semi-infinite, i.e. they do not reflect at the western and eastern boundaries of the basin, which would assume the waves vanish at these boundaries. At the western boundary the equatorial Rossby wave is deflected towards the northern antinode while forming the NECC that induces a positive Doppler-shifted wavenumber. At the eastern boundary, the Kelvin wave splits into coastal Kelvin waves that flow mainly southward to leave the Gulf of Guinea. In turn, off-tropical waves extend as an equatorially trapped Kelvin wave, being deflected off the western boundary. The succession of warm and cold waters transferred by baroclinic waves during a cycle leaves the tropical ocean by radiation and contributes to western boundary currents. The main manifestation of the basin modes concerns the variability of the NECC, of the branch of the South Equatorial Current (SEC) along the equator, of the western boundary currents as well as the formation of remote resonances, as will be presented in a future work. Remote resonances occur at midlatitudes, the role of which is suspected of being crucial in the functioning of subtropical gyres and in climate variability.