The low-frequency Raman signals of single-wall carbon nanotubes (SWNTs), appearing in the range of 100-300 cm-1, have been interpreted as radial-breathing mode (RBM) comprising pure radial Eigenvectors. Here, we report that the majority of the low-frequency, as well as the intermediate-frequency signals of SWNTs are radial-tangential modes (RTMs) coexisting radial and tangential Eigenvectors, while only the first peak at the low-frequency side is the RBM. Density functional theory simulation for a SWNT of ~2 nm in diameter shows that dozens of RTMs exhibit following the RBM (~150 cm-1) up to G-mode (~1592 cm-1) in order with Landau regulation. We specify the RBM and the RTM on Raman spectra obtained from SWNTs, where both appear as a prominent peak between 149 cm-1 and 170 cm-1 and as ripple-like peaks between 166 cm-1 and 1440 cm-1, respectively. We report that the RTMs have been regarded as RBM (~300 cm-1) and ambiguously named as intermediate-frequency mode (300-1300 cm-1) without assignment. The RTMs gradually interlink the RBM and the G-mode resulting in the symmetric Raman spectra in intensity. We reveal high-resolution transmission microscope evidence for a helical structure of SWNTs informing the typical diameter of commercial SWNTs to be 1.4-2 nm.