Measurement of overtone frequencies of a toy piano and perception of its pitch

The pitches produced by toy pianos are sometimes perceived to be inaccurate by listeners, some of whom report perceiving the perfect fifth above the nominal note of the pressed key. To investigate these assertions, the overtone frequencies of a toy piano were measured in a frequency range of no more than the eighth harmonic and below 5 kHz, which are considered to be important to the pitch perception of the human auditory system. Time-frequency and time-intensity analyses of the overtones revealed periodic variation in frequency and amplitude, which might be caused by two close vibrational modes. The pitch of a toy piano was found to be tuned to the frequencies of the overtones corresponding the third and fifth harmonics. No fundamental frequency component was observed. The overtone of 1.5 times the missing fundamental frequency appeared above G4. In addition, the overtone of 0.5 times the missing fundamental frequency appeared above G5. The sounds consisting of the prominent overtones corresponding to the 1.5th and 3rd harmonics can be perceived as the perfect fifth above the nominal note. The pitch of the toy piano was perceived as inaccurate in part because the frequencies of the overtones corresponding to the third and fifth harmonics deviated by –4 to +24 cents and +3 to +33 cents from equal temperament, respectively. INTRODUCTION The pitches produced by toy pianos are sometimes perceived to be inaccurate by listeners. In particular, some Internet users have noted that some toy pianos have slightly inaccurate tuning. In addition, some people perceive duplex pitch corresponding to frequencies of the nominal note and a perfect fifth above the nominal note in certain registers. We conducted an informal listening test using a toy piano, the sound source of which consisted of steel bars. Ten listeners with experience playing musical instruments (including six absolute-pitch listeners) evaluated the pitches produced by the toy piano compared to the pitches produced by a grand piano. The nominal pitch was perceived by four listeners including one absolute-pitch listener. The pitch of the perfect fifth above the nominal note was perceived by four listeners including three absolute-pitch listeners. The other two listeners experienced duplex pitch perception, which depends on the listener’s attention. The pitch of the toy piano was formed by the pitch of the missing fundamental, since no fundamental component exists and the frequencies of the overtones are not harmonic. This might cause inaccurate and duplex pitch perception. Although designed primarily for use by children, toy pianos are sometimes played by professional musicians. In this study, the frequencies and amplitude of the overtones of a toy piano below 5 kHz and below the eighth harmonic were measured, which are considered to contribute the pitch of the missing fundamental. In addition, the relationship between theoretical transverse vibration and the frequencies of the overtone and perceived pitch of the toy piano were considered. SOUND MECHANISMS The sound source of the toy piano measured in this study consists of steel bars inserted into a steel beam. The bars are approximately 3 mm in diameter. From precise measurements with an electronic vernier micrometer, the cross section of the bar was found to be not a perfect circle but rather a distorted circle, the diameter of which ranged from 2.85 to 3.01 mm. The base of the bars and the beam are shown in Fig. 1. The base of the bars are scraped to reduce the diameter by approximately 1 mm over a length of 10 to 15 mm, but the the shape and thickness of the scraped sections of the bars are slightly irregular among the bars. Delicate pitch tuning for each tone can be achieved by the degree of scraping. A note is sounded by pressing a key that causes a plastic hammer to strike the bar 30 mm from the clamped end. This mechanism is simple, and often the hammer strikes the bar twice when a key is pressed. Figure 1: Base of bars. ANALYSIS Audio recording An audio recording was made on the floor of a musical instrument store on an IC recorder (Sharp ICR-PS380RM). The recorder was manually held 15 cm above the keyboard, with the microphone directed toward the key that was pressed. The