FM: Do rational ratios of carrier to modulator signals really produce harmonic spectra?
That paper (1973) is about more natural, simple and rich audio synthesis using FM (which later became Yamaha's very populer FM synthesis audio chips).

In that respect, the carrier frequency is taken very low compared to the modulating tone frequency, unlike in communication applications. Hence the the side lobes cross the zero frequency boundary and are reflected back into the positive band using simple trigonometry.

Another alternative to see this is to use positive and negative frequency version (exponential) of Fourier series analysis, to see that negative frequency side lobes penetrate into the positive (vice versa) band when the carrier frequency is insufficiently low. 

Note that the resulting Bessel spectra of the single tone modulated FM signal predicts that the side lobes about the carrier will be placed at the frequencies of:

$$f_n = f_c \pm n f_m $$
where $f_c$ is th carrier frqeuency, and $f_m$ is the single tone modulator. As you can see, if $f_c$ is sufficiently low, then for some $n$, the component at $f_n = f_c - n f_m$ will be less than $0$ Hertz and will be reflected into the positive frequency $f_r = n f_m - f_c$.

So the FM side lobes that reflect from negative frequencies and the already existing ones do mix up to create the final audio spectrum which can be harmonic or inharmonic depending on the carrier frequency and modulating tone frequency ratios. 

This was a genuine way of producing harmonically rich audio synthesis in legacy analog synthesizers.