Here's an oddity: most people have a harder time with double- or triple-tonguing at slower tempos.
With most tricky material, many of us follow that time-honored sequence of "start slow and speed up bit by bit." But, with multiple tonguing, I see lots of people who can (sort of) do it fast but have a hard time slowing it down.
For some reason, this reminds me of reading "The Right Stuff" years ago. I remember Chuck Yeager trying to break the sound barrier in the X-1 and encountering a lot of turbulence right before he broke through. (October 14, 1947). According to the never-wrong Wikipedia, this is because "transonic air movement creates disruptive shock waves and turbulence."
However, once he broke through, the ride became smooth. For some reason, this reminds me of multiple tonguing and also lip trills. We can get into "glide mode" and go really fast but going a bit slower becomes a struggle. I suspect this is because, at faster tempos, we stop thinking of discrete notes and start thinking of a "state" of rapid notes. Perhaps this is like speed-reading words.
There isn't some profound moral to the story except to say that perhaps we should keep this in mind as we practice these faster things. Even with a technical passage, thinking of it as a whole thing, not discrete notes, might help with execution.
It might also help in choosing creative practice strategies. For example: Start multiple-tonguing very fast and gradually slow down (what I like to call the "Wheel of Fortune" exercise.)
[ahem: this very exercise shows up in Trombone Craft, Appendix 2.5 "Speeding up and Slowing Down"].
I also like to use "tempo yo-yo's" in practicing a lick. Start at speed, then slower, then slower, then slower, then really slow, then faster, then faster....
In another way, this reminds me of approaching the speed of light. According to Einstein, the speed of light can't be broken because our mass increases as we go faster. The closer we get, the more our mass approaches infinity (hey, even ice cream can't do that!).
This reminds me of people who gradually speed up but also tense more and more as they go. It seems they can't really get up to tempo with an exponential increase of tension. Sometimes I suggest that they just "fake it" at speed in a very relaxed way and, with each repetition, increase their accuracy.
So, there would be two approaches..
- Keep it 100% accurate and gradually increase the speed.
- Play it at 100% speed [relaxed!] and gradually increase accuracy.