As far as I have understood a Shepherd tone is a combination of overtones of different octaves between them, for instance F0, 2F0, 4F0 and 8F0. Is this true? I do not quite understand what the Shepherd EFFECT is.
Simply put, the Shepard effect is an auditory illusion where your brain is tricked into believing that a sound is continuously going up or down.
Wikipedia actually has a very good explanation of how an ascending Shepard tone is structured:
Overlapping notes that play at the same time are exactly one octave apart, and each scale fades in and fades out so that hearing the beginning or end of any given scale is impossible. As a conceptual example of an ascending Shepard scale, the first tone could be an almost inaudible C4 (middle C) and a loud C5 (an octave higher). The next would be a slightly louder C♯4 and a slightly quieter C♯5; the next would be a still louder D4 and a still quieter D5. The two frequencies would be equally loud at the middle of the octave (F♯4 and F♯5), and the eleventh tone would be a loud B4 and an almost inaudible B5 with the addition of an almost inaudible B3. The twelfth tone would then be the same as the first, and the cycle could continue indefinitely. (In other words, each tone consists of two sine waves with frequencies separated by octaves; the intensity of each is e.g. a raised cosine function of its separation in semitones from a peak frequency, which in the above example would be B4.)