INTRO

Acoustics of Music, Semester 2 Week1: Physics, Perception, Art •Aims –To outline how the physics of sound relates to its perception and the art of making music. •Learning Outcomes –Appropriate definitions of sound and music. –Understanding of the mechanisms of perception. –Classification of musical instruments. 1.1 Introduction Questions to ask What makes musical sounds an appealing means of expression? How do instruments make musical sounds? How can we make instruments sound better? How can we imitate musical instruments and make new musical sounds? Definitions of sound:   a wave motion in air or other elastic media the excitation of the hearing mechanism that results in the perception of sound A little about sound… Figure 1: Compression and rarefaction. Sound consists of compression waves in air. Energy can pass through air by virtue of the fact that it is an elastic media with inertia and stiffness. Inertia carries particles away from equilibrium and stiffness from atmospheric pressure forces them back. The relative changes in pressure (compressions and rarefactions) can be very small, 20 Pa for the faintest audible sound (5000,000,000 times smaller then atmospheric). All media with inertia and stiffness can carry energy waves and oscillate. The oscillation of air and other media will be an important aspect of this module. A little about hearing Ours ears are incredibly sensitive detectors of energy waves passing through air. After some time in an anechoic chamber subjects can detect ear drum motions of the order of 1/100 millionth of a centimetre. (1/10 the diameter of a hydrogen atom). Key features of the ear are…  Outer ear amplifies sound and helps accentuate spectral and temporal differences in sounds arriving at respective ears. This helps us localise sounds without visual clues. C.S.E., University of Salford Page 1 Acoustics of Music, Semester 2   The Middle ear works as a lever and valve to improve the poor air to fluid impedance match (4000:1) by amplifying forces 35 -85 times. The Inner Ear detects amplitude peaks of induced standing waves. The location of theses peaks depends on frequency. Hairs along the inner ear detect peaks sending corresponding nerve signals to the brain (Place theory). Figure 2: Representation of the anatomy of the ear. Definition of music:  the art of combining sounds so as to express thought or feeling to effect the emotions All types of sound potentially musical (catholic definition). He are some examples… Classical Music (melodic, ordered, refined sounds) Rock (loud with discordant feedback for added expression) C.S.E., University of Salford Page 2 Acoustics of Music, Semester 2 Japanese Taiko Drums (percussive, rhythmic sounds) Electronic (synthesised sounds) Experimental (e.g. Stockhausen) 1.2 Classifying Instruments Examples of instruments A stringed instrument - guitar, bass, violin, cello, sitar, etc receives energy from say a pluck or bow that causes the string to vibrate, this vibration is tonally sculptured and amplified by a sound box. The pitch depends on the length, mass and tension in the string. Figure 3: Sound generation of a stringed instrument A wind instrument - clarinet, oboe, trumpet, flute, etc receives energy from a moving air stream, which is then modulated by the vibration of a read or lips. These act as a valve creating oscillating pressure waves that induce resonance in a pipe. The pitch depends on the length of the pipe and which holes are open. C.S.E., University of Salford Page 3 Acoustics of Music, Semester 2 Figure 4: Sound generation of reed instrument We can see from the above two cases common elements, notably    Excitation source – i.e. a means of inputting energy into the system Wave-guide - i.e. a main oscillator that defines the pitch of the note played Resonator - i.e. a second oscillating system that amplifies and modifies the final sound Musical Instrument Classification - Preferred classification loosely according to wave-guide, resonator and excitation source. Class Examples Excitation Source Main Oscillator / Waveguide String Resonator Stringed violin, guitar, bass, harp, sitar, koto clarinet, oboe, flute, whistle, pan pipes, saxophone trumpet, trombone, tuba, French horn drum, cymbals, gong, triangle, xylophone, rhodes piano, piano singer, choir synthesisers, samplers bow, pluck sound box or a wide thin board Wood Wind blowing, reed air column pipe and bell Brass blowing, lips air column pipe and bell Percussion stick, hammer membrane, wood or metal block cavity, tube or solid material Vocal Electronic larynx muscle electric current air column, tissue analogue or digital electronic oscillators tissues and mouth effects, amplification and speakers C.S.E., University of Salford Page 4 Acoustics of Music, Semester 2 1.3 Physical Parameters and Perception Musical sounds individually or in combination are amenable to an engineering description. We will relate directly measurable objective parameters (physics) to subjective parameters (perception). Physics Frequency Sound pressure level Waveform Perception Pitch Loudness Timbre 1.4 Pitch Defined by the American Standards Association (1960) as "That attribute of auditory sensation in terms of which sounds may be ordered on musical scales" compare this with a definition of frequency “The number of complete cycles of a periodic process (e.g. waveform) occurring per unit time.” Pitch / frequency dependence strongly correlated. The higher fundamental waveform frequency the higher pitch (and vice versa). However the relationship between the two depends on a range of physical and neurological factors. A pure tone at 1000 Hz is defined as having a pitch of 1000 mels at 60dB, hence the relationship between mels and Hertz can ascertained subjectively. Two important characteristics of pitch perception are the ability to   Identify the pitch of a tone – i.e. being able to resolve the harmonic components that form a complex sound Discriminate between different frequencies – i.e. distinguish one pitch from another one a little bit higher or a little bit lower Most music is a sequence or combination of acoustic events called notes. To each note listeners will associate pitch. Notes are discrete entities that C.S.E., University of Salford Page 5 Acoustics of Music, Semester 2   help us remember musical phrases facilitate sharing of musical enjoyment Pitch Perception at the Limits Perceptible frequency range 20 - 20000Hz    <20Hz we cease to hear an uninterrupted tone. (may hear pulses if loud enough). 27hz-5kHz pitch differences easily discernible and musically useful >10kHz our ability to distinguish pitches declines (hear whistle) These are the general limits - individuals vary according to age, health, listening history, etc. Just Noticeable Difference (JND) for frequency Is a measure of our ability to distinguish frequencies, hence pitches. It depends on frequency, intensity and duration and varies greatly from person to person. With Just Noticeable Difference we consider tones presented one after the other or at separate ears. For pure tones of constant intensity (80 dB) at 2kHz can detect change of 10Hz (i.e. only 0.5%) - very small fraction of semitone. Interestingly when two tones are present simultaneously to the same ear the noticeable frequency difference is much greater (>26%) due to the anatomy of our inner ear. Figure 5: The diagram shows frequencies f1 and f2 presented separately and simultaneously. Place Theory "Place theory" - receptors (hairs) at different places in inner ear are sensitive to different frequencies. Tones create standing waves in the inner ear that in turn displace hairs long the Basilar membrane of inner ear. The diagram shows displacement of Basilar membrane as it reacts to different frequencies. Critical Bands C.S.E., University of Salford Page 6 Acoustics of Music, Semester 2 When two tones sounded simultaneously, i.e. presented to the same ears simultaneously, there is a linear superposition of vibrations in the inner ear. Notes of similar frequency interfere along Basilar membrane. At 2 KHz tones must be at least 200 Hz apart to be discriminated, and more than 300 Hz apart to sound "smoothly". This is the critical bandwidth. There are resonance regions in the inner ear which act like a band-pass filters determining the frequency content reaching the auditory nerve. The critical bandwidth corresponds to 1.2mm along Basilar membrane, 1,300 (out of 30,000) receptor cells. Critical Bandwidth is a function of frequency. Moore and Glasburg defined 'Equivalent Rectangular Bandwidth'. It's about two and a half semi-tones around middle C though is a function of frequency. It becomes relatively larger for very low and very high frequencies (ever wondered why bass chords don't sound so nice). Combining tones has some fascinating results both mechanical, i.e. in terms of vibrations set up in the ears, and perceptual, i.e. how our brain evaluates the information via neural processing If you can, try downloading a software synthesiser from http://www.hitsquad.com/smm (e.g. Sync) or try to generate tones with Cool Edit or Matlab. Start with two sine wave tones of the same frequency (440Hz) and then gradually increase one to eventually it’s twice the other (880Hz). As well as beats, can you here other frequencies, higher and lower that shouldn’t be there? What do you think is going on? Some of this can partly be explained by non-linear distortion of the acoustic signal in the ear canal, though there are also some other perceptual effects. The importance of all this to making music will be discussed later as we explore consonance and scales. The Musical Frequency Range Collectively musical instruments exploit entire pitch range C.S.E., University of Salford Page 7 Acoustics of Music, Semester 2 A0 to C8 gives 27.5 Hz to 4,186 Hz (Piano) Middle C is at C4 (261.63Hz) Double Bass (41.2Hz) Piccolo (4725Hz) Musical notes generally used from discrete set of pitches (scales). Frequency increases exponentially with pitch Notes C1 C2 C3 C4 C5 C6 C7 C8 Frequency 32.703 65.406 130.81 261.63 523.25 1046.5 2093 4186 C.S.E., University of Salford Page 8 Acoustics of Music, Semester 2 1.5 Loudness Loudness is the subjective interpretation of a sound intensity. Loudness / sound pressure level dependence strongly correlated though this depends on frequency, duration and spectral balance Given level is represented in decibels, as given by  P SPL  20 log  P  ref   , where Pref =20Pa, the   following levels of sound sources can be measured directly. Common sound sources dB 125 110 100 90 80 70 60 50 35 15 0 Sound Source Jet aircraft taking off Pneumatic Drill Discos Symphony Orchestra, Vacuum Cleaner Inside Coach General Office Whisper (1m) Quiet Living Room Quiet Country Side Threshold of Hearing This fits in well with our loudness perception of such sound sources. However things are not quite so simple. Given the unit of loudness is the phon (in Nm2) - where1 phon equals 1 dB SPL at 1000Hz. Plotting sound pressure level for equal perceived loudness across the audible frequency range one can see C.S.E., University of Salford Page 9 Acoustics of Music, Semester 2 considerable variation. Loudness increases in the mid frequency range - 1 to 4.5 kHz, where hearing is most sensitive. Figure 6: Equal Loudness Curves Also perceived loudness increases with    Bandwidth (sounds >1/3 octave bandwidth) Duration (sounds <100ms) Distorted sounds Interestingly pitch   goes down with increased level at low frequencies goes up with increased level at high frequencies The Musical Dynamic Range Typically music varies considerably in levels of loudness, e.g. an orchestra the range is between 60 and 70dB. CD players cope with this, 16bit signals represent a dynamic range of 96dB (92dB on my sound card). Though there is some debate as to whether this accurately represents all the perceived sound, hence super audio. (Fieldler showed dynamic range of 118dB required for noise free sound reproduction). The graph below illustrates the musically useful range with respect to frequency and sound pressure level. C.S.E., University of Salford Page 10 Acoustics of Music, Semester 2 Figure 7: Musically useful ranges 1.6 Timbre Musical notes are quasi-periodic bursts of acoustic pressure. Periodic complex waveforms can be mathematically deconstructed into simple sinusoidal frequency components (see Fourier analysis later), these components making overall contributions to a frequency spectrum. This to some extent defines timbre, e.g.    Weak harmonics - smooth, pure, flute-like Strong harmonics – brash, full and brassy In-harmonic frequencies – metallic, noisy and percussive. The graphs below represent the quasi-period waveform of a guitar with respect to time and frequency. Figure 8: Time and frequency domain representations of a complex timbre One can see from the frequency spectrum on the right a fundamental frequency (the first spike) and regularly spaced harmonic components. The components also have individual levels that each may vary dynamically with respect to time (sometimes represented by characteristic envelopes). Given we have already seen some of the difficulties in relating subjective pitch and loudness to measurable frequency and sound pressure level; the analysis of timbre with respect to waveform becomes extremely complicated bearing in mind complex waveforms are made up of numerous components each with their own frequency, pitch and C.S.E., University of Salford Page 11 Acoustics of Music, Semester 2 duration. We will also see anatomical, neurological and cultural aspects also influence timbre perception. Hence any descriptor for timbre would be highly subjective. C.S.E., University of Salford Page 12