Construed non-numerically (Rahn 2011, 2012, 2013), the following normal-Forte-order formulations accurately model southeast Asian fixed-frequency tunings: sléndro 11111…, the ‘usual’ pentatonic 22323…, Thai pentatonic ...

According to a widely accepted interpretation, the “unclear” (la-zakû) intervals of Mesopotamian tuning were tritones, which became “clear” (zakû) intervals—in modern terms, perfect 5ths or 4ths—by tightening or loosening ...