Psychophysics of the basic sound dimensions / Loudness

1. Psychophysics of the basic sound dimensions / Loudness Perfecto Herrera

2. Physical and perceptual features of sounds • Waveform amplitude -> Loudness • (the larger, the louder) • Waveform period -> Pitch • (the longer, the lower) • Waveform shape -> Timbre • (the more “rippled” –far from sinusoidal-, the richer)

3. Psychophysical Laws • Mathematical expressions relating a physical property with a perceptual sensation • Response = f (sensory stimulation) • Is f linear, potential, exponential? • Are sensations totally independent? • Collect “subjective” judgments when presenting different intensities, pitches, along a single dimension • Find the best fit between the physical magnitudes and the perceptual estimations • Be careful with physiological constraints -> Frequency resolution of the ear, Energy integration, Firing rate limitations…

4. Psychophysical Laws • Which is the absolute threshold for a sensation to happen? • Is it interacting with another physical feature? • Which is the relative threshold (just noticeable difference, JND)? • Is it fixed for all the range of physical stimulation values?

5. Differential thresholds • Which is the minimum difference that can be perceived with relation to a given sensation? • “Just noticeable difference” (JND) or “Differential threshold” • Listen one sound, then another, then decide if they are the same or they are different. • The first difference or jump that is noticed by more than 75% of the listeners is considered to be the JND for that sensation

6. Absolute and differential thresholds

7. Psychophysical Laws • Fechner’s Law: R = k log(I) • R is the sensation, I is the physical property, k a constant to be found or adjusted from the data • Weber’s Law: ΔI/I = k • The just-detectable change in stimulus intensity (jnd or DL) is proportional to the intensity • Stevens’ Law R = kIp • P=0.3 for sound

8. Perception of Loudness

9. Intensity (physical magnitude) I = p2/ρ·c p is the pressure of the air in a given point of space and time; ρ is the density of the air; c is the speed of sound in the medium where it is being transmitted; ρ·c = 40 dines per centimeter.

10. Compression and rarefaction

11. loudness amplitude Loudness The subjective sensation generated by the intensity of the air pressure is called Loudness

12. Hearing Loudness thresholds • MAF (minimum audible field) – pressure measured in the free field where a listener’s head would be. The sound source is directly in front of the listener. • MAP (minimum audible pressure) – pressure measured in the ear canal. Thresholds are measured in one ear only. • Differences in the two measures are due to some binaural advantage, outer-ear filtering (mid frequencies), and physiological noise (low frequencies).

13. Absolute thresholds • Minimum audible pressure: • 0.0002 dines/cm2 = • =0.0002 microbars = • = 20 micropascals = 10-16 W/cm2 • 1hPa= 1 x 108 micropascals • The atmospheric presssure is measured in hectopascals • Normal athmospheric pressure = 1013 hPa • 130dB = 63Pa = 0.63 hPa • A sudden drop of 1hPa –storm approaching- may cause our ears hurt (>130dB change) !!! • http://www.sengpielaudio.com/calculator-soundlevel.htm

15. Hearing Level • Threshold of hearing, relative to the average of the normal population. • For example, the average threshold at 1 kHz is about 4 dBSPL (-> 0 dBHL) • HL expresses the amount the threshold has been raised compared to the normal population • It deteriorates with age, drug and food consumption and behaviour patterns

16. The dBSPL • Unit preferred to measure the Sound Pressure Level • It usually ranges from 0 to 130 • Uses the minimum audible pressure as reference value (P0 ) • What does 0dBSPL mean? No pressure? dBSPL = 20 log(P/P0). • dBs are not additive (20dB+20dB<>40dB)

18. Loudness Scaling • Can we order loudness sensations (i.e., this sound has twice the loudness than another one)? • L = k I0.3 (I: Intensity; Stevens’ Law) • So, a 10-dB increase in level gives a doubling in loudness. • This provides the basis for the loudness scale, measured in Sones. • A 1-kHz at 40 dB SPL isdefined as having a loudness of 1 Sone. So, a 1-kHz tone at 50 dB SPL has a loudness of about 2 Sones (twice as loud), @60dB -> 4 Sones, @70db -> 8 Sones

19. Equal Loudness Contours • 1 kHz is used as a reference. By definition, a 1-kHz tone at a level of 40 dB SPL has a loudness level of 40 phons. • Any sound producing the same loudness (no matter what its SPL) as the reference tone also has a loudness level of 40 phons. • Sones versus Phons (?) • Equal-loudness contours are produced using loudness matching experiments

20. Equal Loudness estimation Skovenborg, Quesnel, Nielsen (2004). “Loudness assessment of music and speech”, 116th convention of the AES

21. Equal Loudness Contours 80-100 phon curves are flatter -> consequences for mixing? Low and high frequencies have to be raised in intensity, specially when listening at soft levels -> consequences for home amplifiers? a.k.a “Isophonic curves” or Fletcher & Munson curves

22. Equal Loudness Contours • Interpret / Explain (voluntary homework) • A tone has 64 sones • A tone has 60 phones • A tone has 60 dBSPL • Two tones are isophonic • If 1kHz @ 50 phones gives 2 sones, may 100Hz @ 40 phones give 2 sones? • Which one has a higher intensity, a tone of 40 phones or a tone of 50 phones?

23. Loudness weighting scales Filters are used in loudness meters to compensate for the changes in loudness as a function of frequency: • dB(A) = ‘A’ weighting: 40 phon curve (approx.) • dB(B) = ‘B’ weighting: 70 phon curve (approx.) • dB(C) = ‘C’ weighting: essentially flat -high sound pressure levels with LF presence.

24. Loudness and duration Energy integration time < 200ms The longer the tone, the louder, up to 150ms

25. Differential thresholds Just noticeable differences for a 1kHz tone and for white noise; they have been estimated using the modulation method (modulation rate: 4Hz). For the sinusoidal case, the sensitivity increases with the intensity level of the tone

26. Neural coding of intensity • Schematic illustration of input-output functions on the basilar membrane (response measured as movement of the BM) • The solid line shows a typical function in a normal ear for a sinewave input with frequency close to the characteristic frequency • The dashed line shows the function that would be observed in an ear in which the active mechanism was not operating

27. Neural coding of intensity • Firing rates of single auditory neurons as a function of stimulus level (rate-versus-level functions) • In each case, the stimulus was a sinewave at the characteristic frequency of the neuron. Curves (a), (b), and (c) are typical of what is observed for neurons with high, medium, and low spontaneous firing rates, respectively

28. Neural coding of intensity • It is mainly coded by means of firing rates: the higher the intensity the higher the rate but… • A single neuron dynamic range (@ 35 dB) does not explain dynamic range of auditory system (@ 140 dB) so.. • The outputs of many different types of cells together may determine perception of loudness • Loudness increases as several well-separated neurons fire around the same moment (remember the critical band issue)

29. Are this 2 tones isophonic? 500, 520, 540 Hz 500, 720, 940 Hz Loudness of complex sounds • Does loudness increase adding energy at any place in the spectrum? • We have to consider the frequency resolution of our hearing system

30. Loudness of complex sounds • Peripheral processing (filtering according to the outer and middle ear specificities) • Computation of the excitation pattern considering the masking effects (cochlea + neural firing approximation) • 3. Conversion of the excitation pattern into band-specific loudness computation. • 4. Summation of the specific band-loudness into the final loudness value • Loudness increases (additively) only when there is energy beyond the critical band