Overlooked correspondance between the harmonic series and musical intervals?

For example: The very important interval of major 9th can be heard if we multiply the frequency of the fundamental by 9! Same for the interval of major 13th ie major 6th if we multiply by 13! Thanks to an equiry by Zhoanna and some listening tests with Vicky on onlinetonegenerator.com It makes sense since multiplying (say the frequency of note C ie Do) by 3 gives the sensation of Sol (ie 5th) and then by 3 again ie x9 in total gives the sensation of 5th of Sol ie RE which is the 9th of Do. Neat! Further reading Bach Bass Rules - Bach, Niedt - PDF