Hi Greg,
thank you for taking time to comment, and for being clear about the toungue level.

Unfortunately there are no fingerings that give less than an octave between the first and second harmonics, and all the second harmonics are so high that a slur to the third is bit too difficult for a beginner trying this exercise.

The instrument is so short that we need to use all of the first and second harmonics, and when we run out of them, you start to need some fingerings I do not even begin to understand, in order to find higher notes.

Of course I could do slurs that involve change of fingering, but this would to some extent defy the purpose of the exercise, would it not?

I am very pleased to know that you are interested in the cornett! I need to be off for work now, but would be very happy to continue this discussion later.

Thanks
Mats