*Fo* is an harmonic component, and it is the first of the sequence, so in my opinion we can call it

**h1**, and so on, h2, h3,...

In this way their numbering become very obvious and simple, and math help us.

If we consider the octave intervals of the harmonic series, we note that their numbers are:

h1 = Fo, base frequency

h2 = first octave

h4 = second octave

h8 = third octave

h16 = fourth octave

so, obviously

the first octave includes 1 harmonic component

the second octave includes 2 harmonic components

the third octave includes 4 harmonic components

the fourth octave includes 8 harmonic components

Not only, for example the octave of h3 is h6, the octave of h5 is h10, and so on.

it is very obvious but really charming for me!

What do you think?