36 bit was popular for scientific computing because 35 gives you a sign bit and 10 decimal digits (yes, that's weird, but that's the argument I read everywhere, including at https://en.m.wikipedia.org/wiki/36-bit. 35 likely was skipped because it its only divisors are 5 and 7, limiting instructions to 7 bits even then was felt to be too restricting. For some architectures, the DoD had a say in this, too. See https://en.m.wikipedia.org/wiki/Unisys_2200_Series_system_ar...)

36 bits got us the 6-bit character (10 digits, 26 letters, and punctuation) with six characters in a word. Because of that, some OSes had six-character file names.

If you want to get upper- and lowercase, you need more than 6 bits. 9 is the smallest divisor larger than 6 of 36, so nine-bit characters made sense.

On such systems, file names could still use 6-bit characters, while applications used 9-bit ones. Also, some instructions could work on words, half words, quarter words, or sixth words.

Someone probably read too much Iain M. Banks and decided to adopt Marain's base-9 system :)

If I'm not mistaken, some old consoles used a 9-bit RGB encoding, so this could theoretically help there. Minecraft also uses a 9-bit system for Redstone, afaik.

The PowerPC based AS/400 systems were technically 65-bit machines, as the extra bit was a privilege flag to separate system code from user code. Hardware enforced security - one reason why it is such a stable machine.

If hex hadn't been invented yet, 9 bits works better with octal. I don't know if that was a factor.