My acoustic upright piano is 110 years old, made in 1910. Last time I had it tuned, the tuner used a 440 Hz tuning fork and tuned it by ear, but he broke my B♭7 string. If a piano is not used in an orchestra, but only home use, wouldn't it be better to tune middle A to 432 Hz (Verdi's A) which better resonates with the fundamental 8 Hz Schumann resonance? This lower tuning might sound better and extend string life.
It might extend string life, and it might make the piano sound rather dull since the strings may be designed for the tension at which A is 440 Hz or even higher. Whether it's better is a matter of opinion.
The fact that Verdi used 432 Hz (if that is in fact true; this is the first I've heard of it) has very little bearing on the tuning of a piano unless it is a piano of Verdi's time. It might also be of interest for singers of Verdi's music.
The fact that 432 is differently resonant with 8 Hz than is 440 Hz is not relevant in the least. The number is just an arbitrary standard based on an arbitrary unit of time. The second is hardly a fundamental constant of nature.
As Tim points out in his answer, if an old piano's pitch is low, it might be a good idea to leave it low. Whether 432 is a good frequency for A would really depend on the piano, not on any fanciful numerological ideas.
When playing period music, on period instruments, they are tuned to the standard of that time, if at all possible. Partly to be authentic, mostly to be kind to the instruments. Understandably.
Given that your piano is old, thus the strings probably are too, any Hz lower than 440 will be kinder. There's no good reason to use 432Hz, though. If it was mine, I'd probably go for making B♭ 440Hz. Then at least I could play along with the majority of stuff that's recorded or on the radio - or even along with others that were concert pitch tuned - albeit a semitone out. But that's me.
From your position, any lower tuning would suffice, although there would come a point where the strings were too loose, and sound quality would suffer. I guess that's where tuning experience comes in. An awful lot of older pianos never get back to their original concert pitch, tuners are happier to leave then slightly under, for many good reasons.
Thus - if it's dropped slightly, just get it tuned to itself at that pitch. 440Hz, 432Hz, 428Hz, whatever, it'll still work. Back in the '60s, guitar bands would tune to whoever was best in tune already - that didn't stop things sounding good, even if it was 'in the cracks'!
I tune my own piano and I experimented with tuning to lower frequency because I use A432 when I play ukulele (it makes singing easier for me). A jump to A432 on my piano resulted in the lower frequencies sounding a little dull and "gummy." So I tuned the lower notes as low as I could get them while still maintaining a *nice tone (*which really is in the ear of the beholder and very subjective). For my piano, it ended up at A436. It took some time to do but the experiment was fun amd I do prefer a lower frequency. At A435, it was still pleasant, but it was at the cusp of "gummy" on the lowest A to E which is why I went with A436.
If an acoustic piano is required to play with other instruments tuned to concert pitch then it will be better to tune the piano to 440 Hz. If the piano is not going to play with other musical instruments ( other than voice ) then it can be acceptable to tune it to 432 Hz assuming the piano tuner has a 432Hz tuning fork. Next time I get my piano tuned I may ask for the 432 Hz = middle A just to check out any difference in the harmonies and resonance.
The correct answer is:
If you want to play your piano in an orchestra that plays original-style baroque music (Bach, Händel, Purcel, ...) or even older music, you should tune it in 415 Hz, because this was the standard 300 years ago when this music was composed. Todays baroque orchestras still use this tuning, because some instruments that were built in this era can not be tuned (like the cornett), so the whole orchestra must adopt to these instruments.
If you want to play classic music (Mozart, Haydn, Beethoven) which was composed between 1750 and 1820, you should tune it in 430 Hz. This was the standard 200 years ago.
Romantic music (Wagner, Brahms, Chopin, Schubert) was composed after the era of classic music, up to the 1920ies. It's standard tuning was 438 Hz.
If you live in Italy or Switzerland and play your piano in an Italian or Swiss Orchestra, you would have to tune it in 442 Hz. The Berlin Philharmonic Orchestra had tuned their instruments in 445 Hz during many decades in 20th century, but they lowered their pitch later.
The Vienna Philharmonic Orchestra used 435 Hz in 1858, but 3 years later, in 1861 they switched to 466 Hz and to even higher frequencies in later years, but then moved down again. In 2016 they decided to tune their instruments in 443 Hz which still is in use.
If you want to play popular music, and want to play it in tune, then you should use 440 Hz. In 1938 a conference in London decided that the tone A4 should have a frequency of 440 Hz. And if you buy an electronic keyboard today, you will get an instrument that is tuned in 440 Hz, and all other instruments that are built today to be used in popular music are designed to be tuned in 440 Hz.
But although 440 is standard in popular music since about 80 years, this still does not mean that all songs that have been produces in this era use this tuning. Miles Davis "Kind of Blue" is tuned in 442 Hz. "For Whom the Bell Tolls" by Metallica is in 445 Hz. "Strawberry Fields Forever" by the Beatles starts in 451 Hz and then, after a few bars, jumps down to 443 Hz.
As far as I know 432 Hz never was the standard tuning in any era or in any famous orchestra. Nor do I know any song that originally was recorded in this tuning. The actual hype about this frequency is inspired by some esoteric arguments, that in fact nothing have to do with music.
The Schumann resonance is set a frequencies in which electromagnetic waves in planet earth's atmosphere can resonate. The human body has no sensors to register these waves which are similar to radio waves, but with much much lower frequencies and therefore much much less energy. And there is not just one frequency. The Schumann resonance covers many different frequencies between 7.83 and 33.8 Hz. The frequency of 7.83 Hz (which btw. is not equal to 8) is called "fundamental" just because it is the lowest Schumann frequency. But again: Schumann resonances are an electromagnetic phenomenon that by it's nature can neither influence music instruments nor the human body. To construct an argument pro or contra any tuning frequency for music instruments is humbug.
(Not to forget, that Schumann resonances undergo seasonal fluctuations. In winter you have slightly different frequencies than in summer. Do you really want to tune your piano so frequently?)
So, back to your piano:
If a string breaks, the material of this string was weak. It had to be replaced anyway, and even very old pianos are made to hold the tension of the strings. So, this is not an argument for any tuning. You cannot damage the piano itself by tuning it a little bit higher. Just some old strings can break, but they also can break if you play very loud music.
If you want to accompany any other instrument (like a cheap electronic keyboard that can't be tuned), then you should use the modern standard of 440 Hz. You should also use this tuning if you want to accompany songs that you hear in the radio or on Youtube etc. Because this is the standard tuning and more than 99.9% of all music that comes out of any speaker is tuned in this frequency.
But if you just play your piano alone, and do not accompany any other instruments, it simply doesn't matter. If you're worried about the lifetime of your strings, and still are happy with the sound, use a lower frequency. As mentioned before: Baroque music was composed for 415 Hz, which is a halftone lower than the modern standard (baroque A4 and modern Ab4/G#4 have the same frequency) and even todays baroque orchestras use this tuning, and everybody is happy with it. So, if you feel better with 432 Hz: Do it.
The correct answer is 440hz; this is the accepted 12-tone standard in Western Music. While you are certainly free to choose whatever tuning standard you so desire, the British commission made a decision on 440hz as the best compromise between tuning standards that reached above 450 in some parts of the world.
The reason for a worldwide standardized tuning of A4 is so each note sounded the same whether in Europe or in China. This made things easier for Musicians.
Today, 440hz remains the standard while there is nothing wrong with experimenting and finding what you like.
Since your piano was built in 1910, it was most likely designed to be tuned to either A4= 432hz or 435hz. 435 hz was the widely accepted standard of that time. It was not designed to handle the amount of tension 440hz would bring, which is the reason why the string broke when the tuner tuned it to 440. If you want the higher tuning it is likely the whole frame will have to be reinforced. For that piano, using a tuning it was built to handle is the likely the best choice, either 432hz or 435hz, 432 or even 430 if you want to be safe.