The Lower Limit of melodic pitch

The Lower Limit of melodic pitch

Pressnitzer, D., Patterson, R. D., and Krumbholz, K. (2001). "The lower limit of melodic pitch," J. Acoust. Soc. Am. 109, 2074-2084.

Krumbholz, K., Patterson, R.D. and Pressnitzer, D. (2000). "The lower limit of pitch as determined by rate discrimination," J Acoust Soc Am 108, 1170-1180.

Motivation

To measure the lower limit of pitch for multiharmonic sounds and to investigate its dependence on frequency region using

1) a rate discrimination procedure (Krumbholz et al, 2000) or

2) a melody memory task (Pressnitzer et al, 2001).

Stimuli


FIG. 3. Upper and middle panels: temporal waveforms (solid lines) and
envelopes (dashed lines) of a typical pair of CPH and APH
harmonic tones from the current experiments. In this example, the repetition
rate of the stimuli is 128 Hz and the lower cutoff frequency, Fc , is 0.8 kHz
( filter condition 3). The stimuli were filtered into frequency bands (dashed
line in lower panel) with a lower cutoff frequency, Fc , between 0.2 and 6.4 kHz. The lower spectral ramp, dF1 , was 0.2 kHz wide, the flat portion, bw,
was 0.6 kHz wide, and the upper ramp, dF2 , was 1 kHz wide. The solid
lines show the magnitudes of the Fourier components of both the CPH and
APH tones in arbitrary, linear units.

Results

This slide illustrates the theory behind the sounds used above.

Krumbholz et al (2000):


Figure 7. Transition rates for the RDT functions from the current and previous studies expressed in terms of the harmonic number, N, associated with the frequency, Fc , which specifies the filter condition. The results are from Ritsma and Hoekstra (1974, open diamonds), Cullen and Long (1986, open circles), Houtsma and Smurzynski (1990, open, inverted triangle), Shackleton and Carlyon (1994, open star) and the CPH data from the current study (filled triangles). The criterion and the range were 2.5% and 1% for all but Ritsma and Hoekstra’s data, for which they were 1% and 0.5%, respectively. The solid line shows Ritsma’s (1962) lower limit of pitch for AM tones [reproduced from Fig. 1(b)]. The dotted line shows the harmonic number corresponding to a constant repetition rate of 30 Hz. The dash-dotted and the dash-dot-dotted lines show the two definitions of the limit of spectral resolution proposed by Shackleton and Carlyon (1994) and by Moore and Ohgushi (1993), respectively.

Pressnitzer et al (2001)


Figure 5. Results and simulations for experiments I, II, and III. The mean experimental data are represented as unconnected symbols, the model simulation as curves without symbols. The star and cross symbols on the lefthand side of the figure are, respectively, the results and the simulation for the broadband condition.

Conclusion

PPK01 - A melody-change task was used to measure the lower limit of melodic pitch which was found to be around 30 Hz, provided there was energy in the stimulus below 800 Hz. The value of 30 Hz corresponds roughly to the lowest note on the piano keyboard (27.5 Hz), but it is an octave above the 16-Hz pipe on large organs.

When the stimuli were bandpass filtered, the LLMP was found to increase rapidly with frequency in the region above 800 Hz. This effect is consistent with the results of Ritsma (1962) and Moore (1973) despite the differences in stimuli and experimental task. Above 30 Hz and below the LLMP, listeners still experience a weak pitch sensation but it is not sufficiently well defined to convey melodies with semitone accuracy.

The LLMP does not correspond to the loss of spectral resolution for individual harmonics, as usually defined; un-resolved harmonics can support melodic pitch. The data can be simulated by a modified autocorrelation model where a limit of about 33 ms is imposed on the time intervals that the pitch mechanism can accommodate.

References

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Paper Abstract

This paper is concerned with the lower limit of pitch for complex, harmonic sounds, like the notes produced by low-pitched musical instruments. The lower limit of pitch is investigated by measuring rate discrimination thresholds for harmonic tones filtered into 1.2-kHz-wide bands with a lower cutoff frequency, Fc , ranging from 0.2 to 6.4 kHz. When Fc is below 1 kHz and the harmonics are in cosine phase, rate discrimination threshold exhibits a rapid, tenfold decrease as the repetition rate is increased from 16 to 64 Hz, and over this range, the perceptual quality of the stimuli changes from flutter to pitch. When Fc is increased above 1 kHz, the slope of the transition from high to low thresholds becomes shallower and occurs at progressively higher rates. A quantitative comparison of the cosine-phase thresholds with subjective estimates of the existence region of pitch from the literature shows that the transition in rate discrimination occurs at approximately the same rate as the lower limit of pitch. The rate discrimination experiment was then repeated with alternating-phase harmonic tones whose envelopes repeat at twice the repetition rate of the waveform. In this case, when Fc is below 1 kHz, the transition in rate discrimination is shifted downward by almost an octave relative to the transition in the cosine-phase thresholds. The results support the hypothesis that in the low-frequency region, the pitch limit is determined by a temporal mechanism, which analyzes time intervals between peaks in the neural activity pattern. It seems that temporal processing of pitch is limited to time intervals less than 33 ms, corresponding to a pitch limit of about 30 Hz.