s567.py

from research import *
s=begin(567,'Unify full half and quarter Key scales','Do14,7 and3.5 require separate expansion laws?',{'scales':[7,F(7,2),F(7,4)]},['File62 §8.3; File60 §7'])
rows=[[23*u,E*23*u,2*u] for u in [F(7),F(7,2),F(7,4)]]
finish(s,{'input_output_gain':rows,'general_rule':'23u→25u, gain2u'},'The three gains are scaled evaluations of E, not new Keys. They connect the161/175 Covenant unit to80.5/87.5 and40.25/43.75 duration units without making their event placements interchangeable.','Compare the two source routes from483 to490.',{'rule':all(b==a*E and b-a==g for a,b,g in rows),'gains':[r[2] for r in rows]==[14,7,F(7,2)]})