Pitch organisation in Western tonal music

1. Pitch organisation in Western tonal music

2. Pitch in two dimensions • Pitch perception in music is often thought of in two dimensions, pitch height and pitch chroma (Shepard, 1964). (asa trk 52) • This is to account for the perceived similarity of pitches that are separated by octaves. • Pitch height is the low / high dimension of pitch. • The relative position of a pitch within a given octave is referred to as its chroma.

3. Pitch in two dimensions • In Western music theory this is indicated by the octave equivalent pitch classes, C, C# etc. • Music notes are identified first by their position within the octave, their chroma, and then by the octave in which they are placed (e.g. G3, F#6).

4. Circularity in pitch • Asa demo 27 - trk 52 • Complex tone with 10 partials spaced at octave intervals • Complex tone shifted up an octave – identical to the original tone – complete octave equivalence • Bell shaped spectral envelope • Chromatic scale • Each tone has clearly defined chroma but absolute pitch height is ambiguous i.e. which octave

5. Circularity in pitch

6. Loudness perception

7. Objective • loudness perception: • the physical properties of sound that contribute to our sensation of loudness • How the loudness of sounds is represented in our auditory system • Hearing impairments

8. Loudness • Formal definition: • “that attribute of auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud.” • Loudness judgments are subjective

9. Measuring loudness • Loudness can be measured in terms of intensity • Intensity – sound energy transmitted per second through a unit area in a sound field • We can hear a large range of intensities (ratio of: 1 000 000 000 000 / 1; level of 120 dB above the faintest sound) • A logarithmic scale that expresses the ratio of two intensities - decibel sound intensity (pressure) level (dB SIL, dB SPL) • dB SPL = 10 log10(I1/I0) = 20 log10(P1/P0)

10. Measuring loudness • Reference intensity, I0 = 10-12W/m2 (watts per square metre), P0=20μPa – gives 0 dB SPL – average absolute threshold for humans at 1 kHz • I1 is x dB in level above the reference intensity I0 • The word level refers to the magnitude of a sound • Absolute threshold (for sound level) – minimum detectable level of a sound in the absence of any other external sounds

11. Thresholds of audibility • Sensitivity of the ear varies with the frequency of a sound • Compare the thresholds of audibility of tones with different frequencies • Demonstration 6: Frequency response of the ear: trk 17-18 • At what frequencies is it highest?

12. Equal-loudness contours • One sound may be perceived as being louder than another even though they are of the same intensity • The perceived loudness of a sound depends on frequency • Indicated in the equal-loudness contours • Equal-loudness contours – dB SPL plotted as a function of frequency for which the listener perceives equal loudness

14. Equal-loudness curves • Listener to adjust the level of a test pure tone (of variable frequency) to match the known level of a 1 kHz pure tone. • The loudness level (in phons) of the 1 kHz tone is equal to its sound pressure level in dB SPL • Repeat for different frequencies of the test tone – we get an equal loudness contour - labelled in units of phons • Q - Max hearing sensitivity at what frequency? Why?

15. Equal-loudness curves • e.g. 40 phon contour - find the level for each frequency to sound as loud as the 1 kHz 40 dB SPL sound. • Audibility threshold curve – indicates the lowest sound level that can be heard as a function of frequency. • Frequency range we are most sensitive to – threshold is lowest – here we are less sensitive to very low and very high frequencies – absolute threshold depends on frequency

16. Equal-loudness curves • Notice about these contours: • flatter at high loudness levels – less of a difference in perceived loudness as a function of frequency • rate of growth of loudness differs for tones of different frequencies • Remember these curves were constructed for pure tones – single frequency sounds

18. Loudness and duration • The absolute threshold for detecting sounds is affected by duration • Up to a few hundred milliseconds the threshold for detecting sounds decreases (more sensitive) with increasing duration. • Effect of duration on loudness – variability in the results • Generally found that for a given intensity, loudness increases with duration up to 100-200ms. • Demonstration 8: temporal integration – trk 21

19. Loudness discrimination • Smallest detectable change in sound level • 0.3-2dB for a wide range of levels and types of sound • a value of 0.5-1dB for wideband noise – holds from about 20dB to 100dB above threshold – JND increases for sounds close to absolute threshold • For pure tones the JND for loudness varies slightly with frequency (best 1-4 kHz) and may improve at higher sound levels.

20. dB scale • Trk 8-11 • Broadband noise reduced in 10 steps of 6dB • Reduced in 15 steps of 3 dB • Reduced in 20 steps of 1 dB

21. Loudness and the auditory system • Mechanisms related to the perception of loudness: • Increase in sound level - increased BM movement – leads to increased firing rates in the neurons of the auditory nerve • spread of activity to adjacent neurons • the summation of neural activity across different frequency channels – critical bands

23. Loudness and the auditory system • Phase locking: more neurons may phase lock to a tone as it is increased in intensity • Pattern of phase locking may be important for coding the relative levels of components in complex sounds (spectral composition) • when the level of a component is increased relative to the other components, the degree of phase locking to that component increases

24. Loudness of complex sounds • The perceived loudness of a sound with a certain amount of energy depends on the frequency bandwidth of the sound – whether narrow or spread over a wide range of frequencies • Related to the critical bandwidth

25. Loudness and the critical bandwidth • The effect of the critical bandwidth on loudness • for a sound with a given amount of energy - louder if its bandwidth exceeds one CB than if its bandwidth is less than one CB. • At low levels (10-20dB) - the loudness of a complex sound is independent of bandwidth • Spread of excitiation and loudness summation across CFs

26. Hearing impairments • Prolonged exposure to excessive sound levels may cause hearing defects • 2 main types of hearing loss: conductive and sensorineural

27. Conductive hearing loss • is where a defect in the outer or middle ear prevents sound from passing efficiently to the cochlea in the inner ear. • Results in attenuation of the incoming sound • some of the causes are wax build up in the ear canal, immobilization of the stapes due to the growth of bone over the oval window (otosclerosis) or an infection in the middle ear due to the build up of a viscous fluid (otitis media). • May be corrected by a hearing aid or surgery

28. Sensorineural hearing loss • generally occurs because of defects in the cochlea, auditory nerve or higher centres in the auditory system. • may be caused by prolonged exposure to loud noise, aging, illness, head trauma, toxic medications or an inherited condition. • Cochlear implants may be used to improve hearing, but most sensorineural hearing losses cannot be treated by surgery • may have difficulty understanding speech, especially in noisy environments

29. Reduced frequency selectivity • Damage to the cochlea structures of the ear can lead to reduced frequency selectivity (a loss in the ability to resolve frequency components) and loudness recruitment • Reduced frequency selectivity may be reversed if the cause (e.g. noise exposure, drugs/asprin) is removed quickly enough. • In an ear with reduced frequency selectivity the auditory filters are broader than those in a healthy ear.

30. Reduced frequency selectivity • A perceptual consequence of reduced frequency selectivity is the greater susceptibility of a signal (e.g. speech or music) to masking by interfering sounds.

31. Loudness recruitment • refers to the condition in which the growth of loudness with increasing level is more rapid than normal. • The absolute threshold of the ear is elevated, but the level at which sounds become uncomfortably loud may be normal. • The effect of loudness recruitment is to reduce the effective range of sound levels normally heard.

32. Loudness recruitment • Loudness recruitment may be due to damage to the active process in the cochlea that enhances sensitivity at low sound levels – outer hair cells • A hearing aid with automatic gain control that amplifies low-level sounds more than high-level sounds may be used to compensate for loudness recruitment (Moore, 2003).

33. Cochlear implant • For people who have a damaged cochlea in particular the hair cells, but a healthy or partially intact auditory nerve, a cochlear implant may be used • The cochlear implant is a system where an array of electrodes is implanted in the cochlea. • This makes it possible to selectively stimulate groups of neurons within the auditory nerve. • The sensation of sound is created by direct electrical stimulation of the auditory nerve.

34. Hearing loss due to aging • presbyacusis • begins at the extremely high frequencies and progresses to the lower frequencies with increasing age. • Yost (2000): a possible reason - sounds of all frequencies cause the stereocilia of the hair cells at the base of the cochlea to bend, while only low frequencies stimulate the stereocilia at the apical end and this may lead to the hair cells at the base “wearing out” before those at the apex