Equal Temperament and Interval Sizes of Ascending and Descending Intervals

Abstract

Stringed instruments are known to be flexible regarding intonation. This suppleness is arguably at the root of the many discussions concerning tuning and intonation that have taken place in the past. Historical authors have, depending on the era, advocated for the use of just intonation, as well as tempered and Pythagorean, thus deepening the controversy regarding this issue. Similarly, contemporary studies on intonation in the realm of stringed instruments have reached a variety of conclusions, despite observing an apparent adherence to the Pythagorean system and, to a lesser extent, equal temperament. Given this discussion, this paper explored to what extent performances of 53 violin students conform to equal temperament (ET), as well as to what extent alignment or misalignment to ET is a product of chance. In addition, we asked whether the direction of an interval has an impact on its size, as well as whether there is any association between the sizes of different ascending and descending intervals. We also asked whether the academic year of participants had any impact of the size of intervals. Results suggest that the intonation of participants does not match ET, and that differences in interval size regarding ET occur for reasons other than chance; namely, in the case of ascending and descending minor seconds, descending major seconds, descending augmented seconds, ascending and descending minor thirds, descending major thirds, and descending diminished fourths. Furthermore, results not only show that interval direction may have an impact on interval size, but also that there is association between sizes of different intervals. The academic year of participants seemed to have an impact on ascending minor thirds.