432 Hz versus 440 Hz

I've been aware for a while about the the controversy surrounding the standard A note and whether it should be set to $440\text{Hz}$ (as it now is) or changed to $432\text{Hz}.$ I'm trying in this post to look at the mathematical properties of $432$.

• ${432}^2=186624$ is close to the speed of light as measured in miles per second. Wolfram Alpha gives a figure of $186282$ miles per second for the speed of light in a vacuum which is $99.82\text{\%}$ of ${432}^2$.
  
  
• It also turns out that the area of an equilateral triangle whose numerical area is equal to its perimeter is given by $12\sqrt{3}=\sqrt{432}$.
  
  
• $432$ sits between the twin primes $431$ and $433$
  
  
• The factors of $432$ are $1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216\text{ and }432$. The sum of these divisors is $1240$.
  
  
• $432$ is a 3-smooth number, one that is of the form $2^i\ast 3^j\text{ where }i,j>=0$ or to put it less mathematically it is a number that can be written as a power of two times a power of three, specifically $2^4\times 3^3$. Such numbers have been called harmonic numbers. Here are the harmonic numbers up to $1000$:
  
  

• $432$ is the sum of four consecutive primes: $103+107+109+113=432$
  
  
• $432$ is the sum of two positive cubes: $6^3+6^3=432$
  
  
• OEIS lists $2944$ entries for the number $432$