A Dynamical Characterization of Myhill's Property

where +p5 means a stack of a perfect fifth interval, that is, to multiply the frequency of each tone by 3/2. Since two notes an octave apart, i.e., one musical pitch and another with double frequency, sound ‘the same’, this tuning process is emulated by a circle rotation R/Z 3 x 7→ x+ log2(3/2) ∈ R/Z. The continued fractional approximation log2(3/2) ; [1, 1, 2, 2] = 7/12 induces a cyclic sequence of 12 notes