Violin Intonation

Abstract

The purpose of the study was to determine whether violinists, in unaccompanied performance, typically play in either the natural or the equally tempered musical scale, and if not, whether they tend systematically to expand or contract musical intervals as compared with their theoretical magnitudes. Six professional violinists participated in the investigation. Unaccompanied performances of three standard violin selections were recorded by an oscillographic technique. The average fundamental frequency of the main body of each of the tones was measured, and interval extents then were computed. The major part of the study was limited to an analysis of five intervals—major and minor seconds, major and minor thirds and perfect fourths. Tests of reliability of measurement showed that the largest expected error of measurement (±3 SDs) for any given frequency was approximately 0.03 tone, but in at least 78 percent of the cases, measurements were statistically significant to 0.01 tone. The major findings were: (1) The six violinists typically performed in neither the natural nor the equally tempered scale. (2) As compared with both natural and equally tempered intonation, major seconds and major thirds tended to be expanded, minor seconds and minor thirds on the average were contracted, and perfect fourths tended to approximate the theoretical scale values for that interval. (3) The average extent of each of the five intervals approximated its theoretical magnitude in Pythagorean intonation.