The spectrum of the vibrating string consists of multiples of the fundamental frequency F0. These specific modes of vibration can be classified according to the number of nodes. There are generally two different types of framework conditions. There can be either nodes or anti-nodes at the edge. Physically, this corresponds to either a closed end or an open end. Let us consider the simplest mode of vibration having two open ends. It has one node in the middle and one anti-node per each of the two edges. Let us now bend this vibration to form a semicircle. Rotating this semicircle around the Z axis will result in a sphere. There is an azimuthal nodal line at the equator of the vibrating sphere. We can perform the same steps for the following resonant frequency, which has two nodes. Let us bend the vibration to a semicircle and again, let the semicircle rotate around the Z axis. This results in a vibrating sphere having two azimuthal nodal lines. We can repeat this on and on. Bending and rotating the vibration with L nodes results in a vibrating sphere with L nodal lines. By definition, these sphere vibrations are rotationally symmetric. They are also their own reflection. The result is that the vibration of the Z axis is a constant. These vibrations are rotationally symmetric. They are also their own reflection. Positioning the mirror plane exactly in the middle will result in an identical mirror image. L specifies the total number of azimuthal nodal lines. There is no nodal line for L equals zero. There is one nodal line for L equals one. However, this exceptionally symmetrical vibration does not reveal the full range of possibilities, because we can also rotate the nodal line on the sphere. Let's rotate that nodal line to the right or reflect it to the left. There are now two new modes of vibration on the spherical surface with one nodal line. Those are vibrations with an azimuthal nodal line that is rotating clockwise or anti-clockwise. In the case of two nodal lines, there is an option to rotate not just one, but both nodal lines to the right and reflect their image to the left. In the case of three nodal lines, we can rotate first one line, then two, then all three nodal lines to the right and reflect their image to the left. There are thus two L plus one potential modes of vibration on the spherical surface with L nodal lines. We can generate any number of basic modes on the two-dimensional spherical surface by adding and rotating nodal lines, starting from the simplest vibration.