The 128 equal division divides the octave into 128 equal parts of exactly 9.375 cents each. It is the optimal patent val for 7-limit rodan temperament. It tempers out 2109375/2097152 in the 5-limit; 245/243, 1029/1024 and 5120/5103 in the 7-limit; 385/384 and 441/440 in the limit. Being the power of two closest to division of the octave by the Germanic long hundred, it has a unit step which is the binary (fine) relative cent (or relative heptamu in MIDI terms) of 1edo.
128 notes per octave on Alto Saxophon - Philipp Gerschlauer