Killomiter I haven't ever heard of those particular terms. I think I prefer him to say eg. faster or slower hehe
But I think there are various choices - such as initial tempo. And then can speed up the playing, and then go back to initial. Or can slow down the playing, and go back to initial. Or even speed up above initial tempo and then slow down to below initial tempo, and then finally go back to initial tempo. Or slow down to below initial tempo, and then speed up to above initial tempo, and then slow back down to initial tempo. These various cases ... and even other ones ... such as at the end of a bit of music - a slow down to below initial tempo, or speed up above initial tempo - for some sorts of music That's what I was 'trying' to say here.
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And --- also -- good comment you made Killometer! About 'push/pull'. At the moment, the only thing I found online are words like ' pushing and pulling tempo' - associated with rubato. But still looking for their definition of push and pull -- as in exactly what he/they mean by pushing and pulling. And where they start talking about rubato - they then somehow also begin to use the nature sort of words like ebb and flow heheh. It's possible they're just trying to say something like push ahead/forward on the hand-mechanism/device to increase speed, and pull back on a hand-mechanism/device to reduce speed -- or something.