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acoustics Bach Prelude Budden chords complex tone corresponding cosine cycle of fifths DATA define diagram discussion equal equation equiangular spiral equivalence relation Figure frequency and log frequency model graph graphic representation harmonic partials harmonious histograms horizontal initial point interval classes interval vectors intonation irregularity factors Joseph Schillinger Lakner log models log2 log2z-log2x logarithm model major triad measure method of graphic minor second inversion musical intervals musical notation musical sound n e Integers nearly regular Note notions number of pitch octave ordered pairs pairs of frequencies phonodeik Physics of Musical pitch classes pitch vectors polar vector position possible PRINT TAB proof Pythagorean scale quadrant quotient radii ratios real numbers regular triads repre representing retrograde-inversion root tone Schillinger model Schillinger's simple tones sinusoidal model spanned subset successive interval vector system of tuning Tektronix 4051 tempered scale transposition triangles vector head vibrations visual wavelength well-tempered scale