Pitch of Pure Tones Measured by Absolute Magnitude Estimation

Pitch of pure tones was measured by absolute magnitude estimation. Results show that the function relating pitch to frequency in log-log coordinates is much steeper below about 250 Hz than at higher frequencies. me results also show that in part of the scale pitch is proportional to the cochlear frequency coordinates. INTRODUCTION The psychological scale of pitch was investigated by a number of authors with the use of various methods. Stevens’ mel scale was derived from bisection and fractionation (7, 8). Other studies employed equisection (3), eqdappearing intervals (4), haIving and doubling (9), magnitude estimation (5, 6) and magnitude estimation with designated standmd (1). Recently, some criticism has been raised towards the validity and interpretation of the me] scale. In particular, G~enwood (3) argud that the mel scale was biased by a “hysteresis” effect. Rakowski (5) pointed at fundamental controversies in the interpretation of the psychological and musical scales of pitch by leadlng psychologists. The aim of the present study is to re-examine the pitch scale using the method of absolute magnitude estimation (10). PROCEDURE Pitch of 27 pure tones covering a frequency range from 31.5 Hz to 12.5 kHz in l/3-octave steps was measurd by absolute magnitude estimation. The tones were generatd by a Tucker-Davis System ~ and presented monaurally through a Beyer DT 911 earphone at a loudness level of 60 phons. Tone duration was 1500 ms with a 20-ms, squared-cosine rise and fall. Earphone calibration was 103.8 dB SPL for a IV input at 1 kHz. Tone levels corresponding to a 60-phon loudness level at each of the test frequencies were detetined in a preliminary experiment, by a two-interval, two-alternative forced choice, one-dowtione-up, Ioudness-bdance adaptive procedure. Twenty music students with normal hearing, 12 men and 8 women, agd 18–26 years served as listeners in the main experiment. None of them had absolute pitch. The listeners were tested individually in a sound-proof booth, They were required to assign a number to the pitch of the tone so that the subjective magnitudes of the two continua, pitch and number, appeared equal (10). The listener activated a single presentation of the tone by pressing a button on the response box and could listen to the tone at will before reporting the number through an intercom to the experimenter. Each listener completed one series of judgments of 27 frequencies presented in random order. RESULTS AND DISCUSSION The left panel of Fig. 1 shows the geometric means of 20 judgments as a function of tone frequency. The data m plotted in Iog-log coordinates. For comparison, the graph also includes the me] scale (8), and earlier data obtained for pure tones (6) and l/3-octave-band noises (5). The present results show that the pitch function is much steeper below about 250 Hz than at higher frequencies. This finding is in agreement with earlier data reported by Rakowski (5). Similarly, Stevens and Galanter’s pitch function (6) is concave downwards at low frequencies, however, that study did not extend below 100 Hz. In contrast, the mel scale does not exhibit such a pronounced differenm in steepness between the low and higher frequency ranges. The right panel of Fig. 1 presents the pitch estimates as a function of cochlear frequency coordinates proposed by Greenwood (2). The graph shows that the relation of pitch to cochlear distance is close to linear in the greater part of the basilw membrane’s length, except in its basal part, associated with frequencies higher than 5000 Hz,