Circular dichroism (CD) spectroscopy is widely used to characterize the structures of DNA G-quadruplexes. CD bands at 200-300 nm have been empirically related to G-quadruplexes having parallel or antiparallel sugar-phosphate backbones. We propose that a more fundamental interpretation of the origin of the CD bands is in the stacking interactions of neighboring G-quartets, which can have the same or opposing polarities of hydrogen bond acceptors and donors. From an empirical summation of CD spectra of the d(G)5 G-quadruplex and of the thrombin binding aptamer that have neighboring G-quartets with the same and opposite polarities, respectively, the spectra of aptamers selected by the Ff gene 5 protein (g5p) appear to arise from a combination of the two types of polarities of neighboring G-quartets. The aptamer CD spectra resemble the spectrum of d(G3T4G3), in which two adjacent quartets have the same and two have opposite polarities. Quantum-chemical spectral calculations were performed using a matrix method, based on guanine chromophores oriented as in d(G3T4G3). The calculations show that the two types of G-quartet stacks have CD spectra with features resembling experimental spectra of the corresponding types of G-quadruplexes.