2. 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

3. 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

4. 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.

5. 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

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

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

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

9. 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.

10. 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) focus on cochlear

11. 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.

12. 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 f 1 and f 2, the following can be noted as the frequency of the two start to separate further:

13. Perception of close frequencies separating f 2 - f 1 (Hz) As f 2 is increased in frequency:Critical Band 0 Sound in-tune ~0.5-3 Beating heard. Pitch of f 1 and f 2 cannot be distinguished. Frequency perceived as the average of the two. ~4-10 Vibrato like effect. ~20-300 (~ minor 3rd) Perceived as rough (dissonant). The effect is starting frequency dependent. The region of roughness encompasses a larger musical interval for two low frequency tones, than it does for two high frequency tones. Difference (tartini) tones may be heard. Most salient at 0.25- 0.33 >~m3 Separate pitches, perceived as consonant>1 Increasing Difference in Frequency

14. 1kHz Sweep Demonstration f 1 = 1000Hz (constant) Play f 2 = 1-2kHz (sweep) 51015202530354045

15. 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.

17. 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, 210Hz2000, 2005, 2000, 2010Hz

18. 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

19. 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?)

20. 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.

21. 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 Cantins La Grande Messe de Saint-Hubert Performed by Münchner Parforcehorn-Bläser (on original hunting horns)

22. Concluding remarks: Future research on microtonal music/perception Perception of microtonal music Effect of computer-contolled tuning deviations on composers and listeners 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? …

23. 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