Intonation of solo violin performance with reference to equally tempered, Pythagorean, and just intonations

The purpose of this study was to determine which musical scale best models the solo performances of violinists when they play diatonic scales of C major very slowly and without frequency vibrato as accurately as possible. Eight professional violinists played without stopping three adjacent scales in ascending order (from C₄ to C₇), followed immediately by an analogous return to the initial note C₄ in descending order. Results show that when violin performances are analyzed taking into account the context of the scale in which they were played, Pythagorean and equally tempered scales are equally good models for the description of performances. Just intonation fits the data significantly less well. When the data analysis is limited to the intervals between separate pairs of notes, not taking into consideration the context of the scale in which they were played, observed interval sizes are almost identical to the arithmetic means of the corresponding interval sizes as defined in Pythagorean and equally tempered intonations. Octave intervals calculated by summing the sizes of performed adjacent major and minor seconds within octaves, show an average stretching of 3.9 cents. However, the arithmetic mean of computed interval sizes between two C’s, deviates only 0.3 cents from the theoretical tonal extent of 1200 cents. Results suggest that when scales of C major are played, the tonic C is adopted as an absolute cognitive reference point.