Look here Roland System-8 owners! An attempt to reverse engineer unknown SysEx communication

[Foksadure]

Looks like the canonical SysEx checksum algorithm from Roland.

http://midi.teragonaudio.com/tutr/rolsysx.htm

When calculating the Checksum for a “Data Set 1”, you must add up the 4 address bytes and the data bytes. Then you divide by 128 and take the remainder. Finally, you subtract the remainder from 128. You should end up with a value of 128 or less if you did it correctly. This is the Checksum. If the Checksum is 128, then substitute a value of 0.

How to add Roland Checksum for a sendSysEx [Solved]

To actually calculate it, the standard is something like sum all the bytes in the array and truncate to 7 bits, or sum all the bytes and subtract from 256, or … The Roland manuals are usually pretty good about telling you somewhere how it’s done. Alternatively, if you have an editor like HexEdit, you can take a dump with a checksum and calculate various ways across the data bytes until you match what is there

It seems checksum value is ignored in more recent products (Jupiter-X/Xm Juno-X at least).