This 5 by 7 symmetric magic tour using six move types was composed by me this evening (12 Jun 2016 - our Queen's official 90th birthday) and is the best so far found on this board. The magic constants are 90 and 126 (i.e. 5×18 and 7×18). It uses six different types of move (my previous best was eight). {0,1}{0,2}{1,1}{12}{1,3}{1,4}
This was derived in part from the "arithmic" king tour on this board, but also used the "method of complementary differences" by Charles Planck, as described in Andrews (
Magic Squares and Cubes 1917) p.257-262. The example by Planck shown there uses ten move types.
