Glad to help. I’m going to try to write some stuff about this for an FAQ, I think.
If you get “Inv” from jdelay only occasionally, it’s just a glitch in your audio signal chain. If you get it for every reading, and everything else seems consistent, it means that either the input or output of your audio hardware inverts the signal. Mine does this, BTW. It shouldn’t make an audible difference unless you’re combining sounds processed through your computer with other sounds that are not being inverted, in which case you may get some (or much!) cancellation unless you invert the polarity again in the computer to compensate.
Actually, setting the latency really low is only necessary if you’re doing real-time interactive things, like using a software synthesizer, that need an immediate response. For multi-track recording, Ardour is supposed to compensate for the latency due to the ALSA buffer settings (i.e. period size and count) and other known latencies (e.g. in certain plugins). The only difference you’d see due to bigger buffers would be some extra milliseconds delay in the transport rolling after you click Play. In the current version, though, the latency compensation is apparently not working.
The jdelay loopback test will report a smaller latency with smaller buffers, but 3 x 64 is probably as small as you’ll be able to go on your hardware. Higher sampling rates mean lower latency when measured in ms, because the frames in the buffer are processed faster.
When Ardour’s latency compensation gets fixed, you would calculate the extra input and output latency as follows, for the settings you mentioned:
2190 frames round-trip latency - 3 x 512 frames software buffering latency = 654 frames hardware buffering latency
The hardware buffer is in your sound card, and JACK doesn’t know how big it is. You can generally assume that the hardware input and output latency would be about equal, so you’d divide 654 frames by 2 and set the input and output latency each to 327 frames. With a loopback test, you can’t really measure just one or the other!
(Come to think of it, 327 frames input and output latency seems a little high to me - perhaps being a USB device there is more latency.)