Ok, firstly, the first video doesn't seem to show what you says it shows. He's using the Jamman's track selection to choose a track on the beat buddy and then he's making sure that the tempo of the tracks on both devices match their track number, so that the track number is essentially the same as a tempo display. That's a hack, but it apparently works.
I don't understand what you mean by a MIDI "jack". MIDI plugs/sockets are 180-degree 5-pin DIN plugs/sockets, not "jacks", as far as I know. But doing a search throws up lots of things calling MIDI plugs "jacks", so I'm going with that...not trying to be pedantic, just checking that we're talking about the same thing.
Outputting MIDI from something like the Nano is *dead* simple. The hardware consists of a 220R resistor connected to the output wire. Honestly, that's it. The software involves using the UART peripheral to generate MIDI Clock messages. MIDI
input is worse because you need an optoisolator and whathaveyou. Not huge problems, but not as simple as MIDI output.
Now this is where it *might* get interesting.
MIDI Clock assumes 24 PPQN (Pulses per quarter note). This is the same as the analog pulse output on various bits of analog gear, including the Roland x0x-era boxes, like the TR909, TB303 etc. Converting from 24 PPQN pulses to MIDI Clock is as simple as outputting a single MIDI Clock byte every time a pulse arrives (0xF8 in hex).
The "interesting" part is if the Jamman Sync is *not* at 24PPQN. If that's the case, you'll have to do some "interesting" frequency division. If it's at some useful multiple, then that's no problem. Say it was 48PPQN - Easy, just send a MIDI Clock every second pulse. If it's something worse, like the 4PPQN often used by analog sequencers (basically one clock per sixteenth note - no-one ever played anything utilising 32nd notes back then, apparently) then you've got more work to do. In that case, you have to maintain an internal clock that is sync'd to the incoming pulses, and use the internal clock to guide the output of the MIDI clock bytes. This is a lot more tricky, but not impossible and there are quite a few commercial units that do it.
HTH,
Tom
<edit>Reading around it a little, it looks like the JamSync is just a simple tempo clock (e.g. 1PPQN - one pulse for each beat) so if you want to convert to MIDI clock, you'll have to keep an internal clock synchronised and use that to output MIDI clock bytes.</edit>
<edit again>Nope, sorry. It looks like it's a lot worse than that. Here's a good link:
http://fuzzysynth.blogspot.pt/2015/06/digitech-jam-man.htmlIt's using some proprietary MIDI SysEx messages to control the slaves. Stupid, but there it is. The whole point of standards is so people can make their gear work together, but if DigiTech want to ignore that then...sigh, I guess that's up to them. Although why anyone thinks that helps them sell more pedals in this day and age I have no idea. People tend to react badly to that type of behaviour in my experience.
End result - you'd need to write a full MIDI-parsing engine to separate out and decode JamSync messages
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