For years musicians and critics have made statements about the nature of swing in jazz in general and the playing of Louis Armstrong in particular, based on the evidence of their ears. In order to quantify these issues, precise timing analyses of two mid-tempo solos by Louis Armstrong were analyzed, focusing in particular on stop-time sections. Two key elements of swing were analyzed; placement of the downbeats, and the swing or triplet ratio. For these solos, Armstrong played fairly close to on the beat, with a swing ratio of about 1.6 to 1.
Eight- and sixteen-bar segments of a large number of historical jazz recordings were timed with a stopwatch, and summary statistics were calculated from those measurements. A variety of aspects of the control of tempo were analyzed. Tempo is normally distributed when calculated in terms of metronome markings, but not when calculated in terms of durations. Jazz performance is very stable, even for solo performers. However, systematic patterns in the small variability observed indicate that it can serve expressive purposes, as evidenced by positive intercorrelations among alternative versions of the same tunes, as well as other factors. It was also discovered that when the bands execute a rapid "double time," the ratios among the tempo changes deviate systematically from exact doubling. Many of the effects can be summarized by hypothesizing that there are two (and perhaps more) preferred tempo ranges.