Verifying the frequency ratios in the musical scale of just intonation with "hear-and-see" learning tools

Abstract

In engineering colleges, Acoustics often includes the musical scale topic, which is not very popular with most engineering students. In order to face this situation, this paper presents two alternative or complementary “hear-and-see” learning tools for the musical scale of just intonation. The first one combines the hearing of musical notes from an electric organ with the display on an oscilloscope from which the frequency ratios are inferred. Alternatively, the frequencies are computed in advance on the basis of the theoretical frequency ratios, and an audio editor allows to hear the resulting notes, while the PC screen can display similar graphs to those on the oscilloscope.