Using Newton's theorem of revolving orbits one can easily obtain orbits for central forces containing inverse cube terms, such as $$F(r)=F_0(r)+\frac{(1-k^2)|B|}{r^3},$$ from known orbits for $F_0$. When the known orbit is closed so it is the new orbit as long as $k$ is a rational number. Wikipedia article calls "harmonic" the orbits with $k$ an integer and "subharmonic" the orbits with $k$ an inverse of an integer. In the figure bellow I plotted some closed orbits for some values of $k$ obtained from an elliptical orbit in a gravitational field. Then I have some questions which I did not find the answer.
i) Why these terms "harmonics" and "subharmonics"? In other words, is there a relation with harmonic motion?
ii) Is the first harmonic equal to the first subharmonic as the wiki article suggests?
iii) When I look to plots bellow I see $m$ "loops" for the $m$th harmonic and $n$ "petals" (such as flower's petals) for the $n$th subharmonic. Are there corresponding technical terms?
iv) The $k=m/n$ which is neither harmonic nor subharmonic have $m$ loops and $n$ petals. Is there something better that justifies an eventual superposition of the $m$th harmonic and the $n$th subharmonic?
v) Do the set of all harmonics and all subharmonics form, in some sense, a complete basis in the same sense the normal modes or harmonics form for waves?
