Perception and Psychoacoustics of Tuning

1. Perception and Psychoacoustics of Tuning Emery Schubert ARC Australian Research Fellow School of Music and Music Education University of New South Wales, Australia E.Schubert@unsw.edu.au Richard Parncutt Professor of Systematic Musicology Department of Musicology University of Graz, Austria Parncutt@uni-graz.at

2. Aim • To describe some psychological and psychophysical issues concerned with the perception of pitch and tuning. • Pitch and Virtual Pitch • Roughness and Critical Band • Just noticeable difference in and categorical perception of pitch • Psychological questions in tuning

3. Vibration -> Pitch Perception • Many sounds (including vowels in speech and musical tones) consist of repeating wave patterns • When the rate of these repeating patterns is less than around 12 repetitions per second (Hertz), they are perceived in the realms of rhythmic pulse, ornaments (trills) or vibrato. • If the rate is increased to above 20 (20 Hertz - Hz) the vibrations fuse into a single percept that is referred to as pitch. • Repetition rates of up to around 15,000Hz can still be perceived as pitch by most people.

4. Frequency -> Pitch Perception • Frequency of vibration can be mapped onto pitch perception. Source: Joe Wolfe, Music Acoustics Group, School of Physics, University of New South Wales: www.phys.unsw.edu.au/~jw/graphics/notes.GIF

5. Dark regions indicate frequencies at which high energy is emitted Lowest harmonic determines pitch Spectograms for 4 tones at D4 (293Hz) and 1 at D5 (587Hz) 1762.02Hz Source: Campbell & Greated, 1987 1468.35Hz 1174.68Hz 881.01Hz 587.34Hz 293.67Hz Square Sawtooth Sine wave French horn Square + 8ve Time ------>

6. Dark regions indicate frequencies at which high energy is emitted Does lowest harmonic determine pitch? Spectograms for 4 tones at D4 (293Hz) and 1 at D5 (587Hz) 1762.02Hz Source: Campbell & Greated, 1987 1468.35Hz 1174.68Hz 881.01Hz 587.34Hz 293.67Hz Square Wave D5 Horn D4 with F0 taken out! Horn D4 Time ------>

7. ~B2 ~B3 ~B4 Missing Fundamental If fundamental is missing, the brain extracts it - ‘virtual pitch’ These are spectral plots, which are like spectograms turned on their side. Fastl, H. & Stoll, G. Scaling of pitch strength, Hearing Research 1(1979): 293-301

8. Summary - Pitch and Virtual Pitch Perception • Most instruments produce harmonically related ‘partials’ or ‘harmonics’. • The lowest of these partials is called the fundamental (F0) and usually determines the perceived pitch. • Other components contribute to the timbre of the tone (whether it sounds like a sine wave, square wave, French horn, human voiced vowel …) • Virtual pitch perceived if fundamental[F0] is missing but some harmonically related partials are present. Suggests higher order processing.

9. focus on cochlear Hearing anatomy & function • Outer Ear: Sound Collection • Middle Ear: Mechanical Transducer • Inner Ear (Cochlea): • Frequency to position (fourier analysis) • Mechanical vibration to nerve impulse • Auditory Nerve, Brain, Mind • Pitch & Timbre Sensation • Right-Left synthesis • Sound Identification (danger, music, speech)

10. Cochlea: Conversion of mechanical vibrations to nerve impulses • Fluid filled tube, divided in half longitudinally by Basilar Membrane. • Sound vibrations in fluid cause the basilar membrane to vibrate. • The Basilar Membrane is tapered in width and in thickness along 3.5 cm length. • Basilar Membrane, Tension and density change with position: • Narrow, stiff near Oval Window. Large and floppy at Helicotrema • Simple sound oscillations produce localized vibration Low Frequencies near Helicotrema. High Frequencies near Oval Window. Hair cells are stimulated in the corresponding frequency region, sending impulses to the brain.

11. What does cochlear do when two nearby frequencies are presented? • When a region of the cochlear is stimulated by a frequency, nearby (topological and, therefore, frequency) areas are inhibited, making the effect of other incoming, nearby frequencies not behave in a simple linear fashion. • For the case of two sine waves (single harmonic) tones f1 and f2, the following can be noted as the frequency of the two start to separate further:

12. Perception of close frequencies separating Increasing Difference in Frequency

13. 1kHz Sweep Demonstration f1 = 1000Hz (constant) 5 10 15 20 25 30 35 40 45 f2 = 1-2kHz (sweep) Play

14. Critical bands • How well can the hearing system discriminate between individual frequency components? • Whether or not two components that are of similar amplitude and close together in frequency can be discriminated depends on the extent to which the basilar membrane displacements due to each of the two components are clearly separated or not.

16. Just noticeable difference (JND) • Just noticeable difference (JND) for pitch as a function of frequency for four different loudness levels • For a considerable portion of the auditory range, humans can discriminate between two tones that differ in frequency by 3 Hz or less. Increments of 1Hz from 200 to 210Hz Increments of 1Hz from 2000 to 2010Hz 200, 205, 200, 210Hz 2000, 2005, 2000, 2010Hz

17. Other Variables affecting JND • The degree of sensitivity to frequency changes, or frequency resolution capability, depends on the frequency, intensity, and duration of the tone in question. • It varies greatly from person to person, is a function of musical training. • It is also dependent on the method of measurement employed (e.g. making a choice between two, versus adjusting). Tervaniemi, M. et al. (2005). Pitch discrimination accuracy in musicians vs nonmusicians: an event-related potetial and behavioral study. Exp Brain Res, 161, 1-10

18. Compare JND with Tuning Systems • Difference between intonation and tuning • Intonation: e.g. singing, string quartet • Tuning: e.g. piano, guitar • Theoretical tuning systems • Pure: M3 = 5:4 = 386 cents • Pythagorean: M3 = 81:64 = 408 cents • Equal tempered: M3 = 400 cents • Perfect pure tuning is impossible! • E.g. M2 + P5 ≠ M6! (9/8 x 3/2 ≠ 5/3) • Tuning of real musical instruments • Piano: stretched equal tempered (M3 = 405 cents?)

19. Intonation and categorical perception When is a tone “in tune”? Two different ranges: • Category width corresponding to scale step: + 50 cents • In-tune (within category) range: + 10-30 cents Role of context: • Both category width and in-tune range are smaller when • slower music (longer tones) • less vibrato • more familiar tuning • more exact tuning • See also categorical colour perception. There are 1200 cents in an octave. An equal-tempered semitone has 100 cents.

20. Higher level cognition • physiological basis for learning •  neural networks (Bharucha) • mental represention (e.g. represention of a tuning system) emerges (learned through exposure) • e.g. 17th century expectation of hunting horn. • Which one (natural or tempered)?Answer: Introduction from Cantin’s La Grande Messe de Saint-Hubert Performed by Münchner Parforcehorn-Bläser (on original hunting horns)

21. Concluding remarks:Future research on microtonal music/perception Perception of microtonal music • Effect of computer-contolled tuning deviations on composer’s and listener’s evaluations • Expressive tuning versus microtonality Tuning feedback by computer interface • Can performers get used to it? (c.f. horn example) • Does their intonation improve faster with feedback? • What is the most accurate performance with/without AP? …

22. Thank you!Perception and Psychoacoustics of Tuning Emery Schubert ARC Australian Research Fellow School of Music and Music Education University of New South Wales, Australia E.Schubert@unsw.edu.au Richard Parncutt Professor of Systematic Musicology Department of Musicology University of Graz, Austria Parncutt@uni-graz.at