How did they transform the original music to A=432Hz?
If they did it in the naïve way, it would result in a decrease in tempo by almost 2%.
If they did it in the naïve way, it would result in a decrease in tempo by almost 2%.
There seem to be other things the article doesn't tell us, such as how the authors verified that the music they used had been tuned to A=440 in the first place (since it's far from universal) or why, given an infinite number of possible tuning frequencies, a great many of which have been chosen by musicians at some point, and given no obvious physical basis for this specific choice, they went for A=432 instead of any other value below 440.
[edit: removed warranted but uncivil snark]
Even a small shift will introduce some audible artifacts in most music. Will they be more or less apparent to the listener than the difference between recordings tuned to A=440 or 432 would be? I don't know. Depends on the music and the listener, I imagine. That would (be one of the many, many unstated things that would) matter to a paper like this.
(For what it's worth, I wrote and maintain a widely-used timestretcher library. Possibly this means I am more aware of the limitations than the strengths of such technology)
It's not hard to hear the artifacts in DJ tempo stretch algorithms if you listen closely, especially when they are applied to a full mix (as opposed to single instruments). Of course they're small these days, but when you're trying to measure a subtle effect, they're too much of a confounding variable.
More involved would be to re-tune a piano and play the same song twice.
A 432 A makes the math behind music so much nicer to work with (ignoring legacy baggage).
Personally, I prefer a brighter concert-A, 444 or higher.
432 vs 440, independently of any unit, makes the math easier.
432Hz vs 440Hz, obviously, is two pitches that form an audible interval.
But 432 can be a valuable explaining tool. Just don't read it as Hz, but Hz' (prime), cycles per s', such that 432Hz' = 440Hz.
That's about as far as I'm willing to defend 432.
Incidentally, there are 432,000 seconds in 12 hours.
Also fun - while continuing to acknowledge the somewhat arbitrary nature of human units - the diameter of the moon is 2159.1 miles - remarkably close to half of 4,320. The Sun's diameter is 865,370 miles - very close to twice 432,000. That they look the same size from Earth is wild to me, and suggests that Pythagoras may have been onto something with the music of the spheres bit.
Also, just because our units could be otherwise, doesn't mean they are entirely arbitrary. I believe that things like that have a sort of wisdom of the crowds, evolution over time thing going on. Like other aspects of language, there is more to its development than is immediately obvious.