Fractional tempered stable motion (fTSm) is defined and studied. FTSm has the same covariance structure as fractional Brownian motion, while having tails heavier than Gaussian but lighter than stable. Moreover, in short time it is close to fractional stable Lévy motion, while it is approximately fractional Brownian motion in long time. A series representation of fTSm is derived and used for sim...

In Western music, a musical interval defined by the frequency ratio of two notes is generally considered consonant when the ratio is composed of small integers. Perfect harmony or an "ideal just scale," which has no exact solution, would require the division of an octave into 12 notes, each of which would be used to create six other consonant intervals. The purpose of this study is to analyze f...