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Steven Brown

Lecture 1a - The "Standard" Model of Music Monday, January 07, 2013 Standard Model of Music  Periodicity of duration values and pitch relations  Isochronous meters (cycles of equal-duration beats)  Rhythmic patters based on simple-ration divisions of the basic beat (2's, 3's, 4's)  Pitches made up of harmonic frequency components (integer multiples of the fundamental frequency)  Pitch intervals based on simple-integer relations among frequencies (2:1→octave, 3:2→P5; 4:3→P4)  Repetitiveness of musical phrases; form  Simple motivic patterns that recur  Melodic motif matches rhythmic patterning  Simple "ostinato" patterns: direct repetition of musical phrases  Making things more complex…  More than one musical line at a time o Parallel lines vs. non-parallel lines  Variable motivic divisions of the beat  Distinct rhythm and melody-bearing parts in an ensemble  Melodic pitches don't align to the principal beat (e.g. syncopation)  Complex melodies and harmonies o Non-motivic melodies o Chords and harmonic progressions  Larger musical forms o Sectional arrangements (e.g. strophes) o Movements in large-scale works  Tune-text alignment o Complex texts o Ornamentations (e.g. melisma)  Complicated rhythms o Complex meters (5, 7, 11, etc.) o Changing rhythms (e.g. 3+3+2)  Additive rhythms rather than divisive rhythms  Complex forms o Changing rhythmic patters o Changing melodic pitch groupings Deviations: Loss of Periodicity   Non-periodic, irregular rhythms  Non-periodic (unpitched) sounds Intervals not based on simple-integer ratios  o Non-consonant intervals o "Atonal" music Cognitive Modules of Music (Two meta-systems of music)  Pitch  Tonality o The organization of musical pitch into scale systems based on fixed intervals  Arousal factors o Emotional expression factors related to register, tempo, and loudness (e.g. happy = high, fast, loud)  Rhythm  Meter o The temporal organization of musical phrases into cycles of equal-duration beats  Entertainment o The synchronization of body movement to an external beat. Lecture 1b - Is Music an Art or a Science? Monday, January 07, 2013 Music as a science  Intervals as simple frequency ratios  Pythagoras studied the properties of strings, and found that common musical intervals were based on simple ratios of the lengths of strings o 2:1→octave, 3:2→fifth; 4:3→fourth  Musical intervals seem to have a strict mathematical basis  Harmonic/harmonicity  Sounds with perceived pitch tend to have periodicity (harmonicity), with harmonics made up of integer-multiples of the fundamental frequency o If the fundamental frequency of a sound is, say, 100 Hz, then the harmonics would have frequencies of 200 Hz, 300 Hz, 400 Hz, 500 Hz, etc.  This was thought to provide a mathematical basis for musical scales and harmony.  Consonance  Helmholtz proposed that dissonance in music is based on “beating” o When the frequencies of two sound-sources are very close to one another, they generate interference in the auditory system, which we perceive as dissonance.  Consonance in music is based on simple physical principles Music as an art  Communication system  Senders and receivers  Musical messages  Intentions and behavioural effects  Musical pragmatics  Uses and control mechanisms  Uses o Ceremonial rituals (religion) o Public places (stores, restaurants, etc.) o Audiovisual media (film, commercials, etc.)  Control mechanisms o Tradition o Governmental control (censorship, propaganda)  Control of re-use (copyright)  Narrative device  Music enhances the emotional meaning of the narrative  The "pragmatics" of music o Musical formulas (in cinema, opera, etc.)  Leitmotifs: short, constantly recurring musical phrase', associated with a particular person, place, or idea  Language  Music's harmonic/tonal language (scales, intervals, harmonic progressions, rhythmic patters, timbres, instrumentation, etc.)  Creating a meaning, a semantic system  Different from natural language but often works in parallel to it (e.g. songs, film scores) Lecture 1c - Music Evolution Wednesday, January 09, 2013 Biological evolution: evolution of the neurocognitive capacity of people to generate and perceive music  Structural: phylogenetic origins; evolutionary history  One trait (or species) gave rise to another trait (or species)  A family tree (phylogeny, pedigree, timeline) with branches "Humans evolved from primitive hominids"   No concern for use of the trait or adaptiveness  Most phylogenetic approaches to music deal with music's relationship to speech o Speech arose from music o Music arose from speech o Speech and music arose from a common precursor  Functional: functional importance; adaptiveness  Darwinian models  Something evolved because of its contribution to survival and/or reproduction o The peacock's tail evolved to increase mating success  No concern for phylogenetic origins  Certain traits, called adaptations, evolve because they contribute to the survival of individuals that bear them  Adaptationist approaches to music consider the potential survival benefits of music o Some theorists have been explicit anti-adaptationists when it comes to music: music is not an adaptation  Natural selection: the trait enhances survival of the individual o Minimal evidence that music making supports individual survival  Sexual selection: the trait enhances the reproductive success but not necessarily survival of the individual o Darwin proposed that music evolved as a device for mate attraction and courtship, similar to the way birdsong is seen  Love songs are not a predominant form in traditional cultures o Music making and dance are costly for the individual; they are good signals of fitness o Sexual selection predicts that music should be "sexually dimorphic" but it is not o Makes music into a purely competitive enterprise  Ex. Male rock musicians have a lot of sexual encounters  Group selection: the trait enhances the differential survival of groups o Something that is good for the group but often at the expense of individuals  Altruism and cooperation  Music is not just made in groups, it is made for groups  Group selection is the only mechanism to explain the within-group cooperativeness of music making  Occurs in part in terms of between-group competition (ethnocentrism) o Territorial device, akin to territorial and long-distance vocalizations in other species  e.g. howling in wolves, duetting in gibbon apes, dueting in tropical bird species all function in the maintenance of year-round territories o Group design features of music: coordination  Beat-based rhythmic entrainment: interpersonal coordination  Pitch blending: polyphonic music textures Cultural evolution: changes to music itself over time and location  Music is universal but its form varies significantly across cultures (cross-cultural diversity)  Within cultures, musics undergo changes over time  Diffusionism  Musical styles originate in certain geographic locations and then diffuse (radiate) to other locations o This is a model of the geographic spread of musical styles o This occurs via migration of individuals away from the "epi-centre" where the style originated  Syncretism  Two musical styles can undergo a blending or fusion process when they come into contact o Hence, much cultural evolution is often based on such stylistic blendings o This is exemplified quite well in "world music" fusions in popular music  Reflectionism Musical performance style is a reflection of the type of culture that produces it   Cultures that have similar subsistence styles tend to have similar musical performance styles, even if they are geographically distant Darwinian culture theories   Memes are "cultural replicators": objects or ideas that get copied/reproduced  Through the process of cultural selection, some memes get transmitted to future generations, while others become extinct  Some examples of musical memes: o Musical systems (scales, rhythms, etc.) o Musical instruments o Song texts o Performance styles o Notation systems o Myths and symbolisms Lecture 1d - Classification of Musics and Instruments Thursday, January 10, 2013 Comparative Musicology  "Ethnomusicology"  Analyze the different musical cultures individually, not comparing between the different cultures Musical genres/forms  Ritual music  Music of (religious) ceremonies  Found virtually in every culture  Classical music  Music of the aristocracy  For the wealthy, governing class people  Folk/popular/secular  Music of the masses for everyday people Musical Classification  Texture: Spatial (separation in pitch space)  Monophony (unison): identical parts o Perfect octave is still considered monophonic  Drone: one part consists of a single pitch while the rest sing in monophony  Homophony: parts are separated in pitch space but are temporally aligned (chords)  Polyphony: different parts, with differing onsets of the parts  Texture: Temporal (Separation in time)  Monophony (unison): identical parts synchronized in time  Heterophony: onsets of parts are slightly desynchronized/misaligned o Sounds messy and unorganized  Echophony: echoing parts  Canon: parts are imitative of each other in a fixed different in time o e.g. Row, Row, Row Your Boat  Polyphony: different parts, with differing onsets of the parts  Rhythm: Meter  Measured (metric) o Simple meters (2, 3, 4) o Compound meters (based on triplets) o Complex meters (5, 7, 11, etc.) o Hemiolas (combinations of 2's and 3's) o Hetermeters (changing meters)  Unmeasured (non-metric) o Parlando-rubato "Spoken"  o irregular  Rhythm: Pattern  Syncopated  Unsyncopated  Scale Type  "Major" type  "Minor" type  "Hijaz" type  "In" type  "Chromatic" type  Vocal Style  Syllabic singing: one pitch is sung per syllable of text  Melismatic singing: multipl pitches are sung per syllable of text  Classify vocal style as being syllabic, mildly melismatic, or highly melismatic  Text Type  Vocables: nonsense syllables o E.g. "lalala"  Words  Classify vocal music as containing: vocables, simple/repetitive texts (like a refrain), or complex (changing) texts  Note: if we don't know the language, it all sounds like vocables  Form  Ostinato: repetition of phrases o Also known as "litany" in Western musicology Strophic forms: successive alternation between sections  o E.g. ABAB, ABACABA  Through-composed: constantly changing, always new material Instrument Classification  Chordophones  String instruments o Bowed Fiddles  o Strummed/plucked  Lutes, zithers, harps, lyres o Struck  Piano, zither  Aerophones  Air columns o Flutes o Reed instruments o Horns, trumpets o Organ pipes  Membranophones  Drums o Cylindrical (tubular), barrel, waisted, frame, goblet, kettle  Idiophones  All the rest; things that are struck  Body percussion, rattles and shakers, metallohphones (metal; gongs, vibraphones), lamellophones (keys; xylophones, vibraphones, thumb pianos), etc. Lecture 2a - Sound Waves Monday, January 14, 2013 Waves  Oscillation: a back and forth motion  Vibration: a back and forth motion that results from the presence of the force of elasticity Wave: a vibration that is propagated through space  A Series of Vibrating Systems Sound source   Generates the basic sound o Various media: air columns, strings, membranes, etc.  Its vibration can be periodic or non-periodic  If periodic, then generates a harmonic series  The pitch of the sound we hear is related to the fundamental frequency of vibration of the sound source  Various media; air columns, strings, membranes, etc.  Resonator  Amplification of the basic sound  Filtering of the basic sound o Certain frequencies of the source are amplified while others are not  The resonator has its own series of vibration modes, or resonant modes o These are know as formants when talking about the vocal tract o These are independent of the vibration frequency of the source o However, when they match source frequencies, those frequencies are amplified  Sound Wave  Transfer of energy of vibration from the resonator to air molecules  Results from the product of the acoustic properties of the source and the resonator  Sound is perceived as the induced vibration of air molecules arriving at our ears  Environmental acoustics o In actuality, the true final step involves a series of interactions with the environment, including the reflection of sound waves off of walls and objects Waves  Rarefaction: area of reduced pressure  Compression: area of increased pressure  The motion of the particles is miniscule compared to movement of the wave itself  Two types of waves  Longitudinal o The particles of the medium are displaced in the same direction as wave propagation through the medium o Sound waves are longitudinal waves But many sound "sources" have vibration modes that involve transverse waves   e.g. plucked string, struck drum-head  However once these sound sources interact with air molecules to generate sound waves, those sound waves are always longitudinal waves  Transverse o Particles of the medium are displaced in a direction perpendicular to the direction of wave propagation through the medium  Traveling vs. standing waves  Traveling wave: a wave that propagates in space o Sound waves are traveling waves o But most sound sources and resonators have vibration modes that involve standing waves  These are called resonant modes  Standing wave: a wave that does not propagate in space o This generally occurs because the wave bounces back and forth between two barriers Velocity   Velocity of sound in a medium is related to: o Stiffness (elasticity) of the medium  Expressed in terms of Young's modulus (E)  This expresses how well the molecules in the medium are coupled to one another  The larger the Young’s modulus for a medium (stiffer), the greater the longitudinal velocity of sound in that medium o Density (which is related to mass) of the medium  The lower the density (mass), the greater the velocity of sound o Why is the speed of sound faster in water than air?  Water has a much larger density than air, which means sound should travel slower in it. However, water has a much greater stiffness than air. Overall, the speed of sound in water is faster than it is in air. o The velocity of sound (c) in air at room temperature is 344 m/s Air is an elastic medium for the propagation of sound   It allows propagation of the vibration of the sound source (or resonator)  Periodic Waves  Frequency (f) = number of cycles per unit time o The unit is the Hertz (Hz), which is one cycle per second Period (T) = time required for the completion of one cycle of periodic motion  o Frequency and period are inversely related  Wavelength (λ) = distance required for the completion of one cycle of periodic motion  Amplitude (A) = the maximum (peak) magnitude of a periodic waveform  Phase = the particular stage in the cycle of motion  v = λf o v is the velocity of sound in a particular medium o Wavelength and frequency are inversely related  Sound pressure level  Because the auditory system is sensitive to the pressure component of sound waves, we measure sound intensity in terms of sound pressure level (SPL)  Psychologically, this corresponds with our perception of loudness  Measured in decibel (dB)  SPL is a relative term, measured to a reference o The reference pressure (p ) is the lowest pressure that can be perceived by the human ear ref  Each 10-fold increase in SPL is a 20 dB increase  Superposition  For sounds that are correlated, the pressures of the sound sources can be added together o Adding pressures together is NOT the same thing as adding decibels together because SPL is a logarithmic relationship o  Sound Propagation  Sound propagates from a source in all directions, and so the propagation occurs in the form of a sphere  As a result, the intensity of the wave decreases with the square of the distance from the sound source o This is called the inverse square law Lecture 2b - Waveforms and Spectra Monday, January 14, 2013 Periodic vs. aperiodic waves  Periodic waves have recurring patters  Sine waves: a single periodic wave  Complex waves: made up of combinations of sine waves  Aperiodic waves do not have recurring patters Time and Frequency domains  Time domain: a representation of a wave as a function of time  Waveform: amplitude vs. time  Spectrogram (sonogram): frequency vs. time  Frequency domain: a representation of a wave as a function of its frequency components  Spectrum: amplitude vs. frequency  The conversion of a waveform to a spectrum (or vice versa) occurs through Fourier transformation It can resolve a complex waveform into a series of sine waves   A spectrum, then, shows the amplitude of each of the constituent sine waves  The process of adding sine waves together to create a complex waveform is called superposition Harmonicity  When the component waves of a complex periodic wave are integer multiples of the lowest frequency component (i.e. the fundamental frequency), than we say hat the wave is made up of a harmonic series  Most pitched sounds are complex periodic waves that are made up of harmonic series Phase  Phase is the particular stage in the cycle of motion, using the angles from a circle as the unit of measure  When adding waves together, they can be in phase or out of phase  Phase will affect the shape of the complex wave that results.  However, it won't affect whether the wave is periodic or not  Adding together harmonically related waves creates a periodic wave o For a periodic wave, the spectrum will have equally-spaced frequencies  The increment between frequencies is the same  Adding together non-harmonically related waves creates an aperiodic wave o For an aperiodic wave, the spectrum will have unequally-spaced frequencies  The increment between frequencies is variable Line vs. continuous spectrum A line spectrum has discrete lines at particular harmonics   A continuous spectrum does not have discrete lines  Has energy at a large variety of frequencies Percussion sounds are often aperiodic and thus un-pitched; the spectrum is continuous  Filtering  Can separate different frequency components  Filters are named by what passes through them, not by what is filtered out  Low-pass filter: allows low frequencies to pass through, and cuts out high frequencies  High-pass filter: allows high frequencies to pass through, and cuts out low frequencies  Band-pass filter: passes a range of frequencies between two cut-off frequencies o That range is called the filter’s bandwidth  The frequency at which the filter operates is called the cut-off frequency  The output spectrum after filtering is the product of the input signal's spectrum and the filter's frequency response Lecture 2c - Africa (Sub-Saharan) Thursday, January 17, 2013 Pitfalls of studying musics of another culture  Terminology: native individuals might not have the same concepts or words to describe their musics as we do  Lack of insider knowledge about the contexts, contents, culture and meaning so musical works and their associated rituals  Lack of insider knowledge about the generative practices and learning processes for musicians Music of Sub-Saharan Africa  Form  Ostinatos are quite common o "Repetition with variation", not just direct repetition  Vocal Style Syllabic   Text type  Mid-range complexity  Repetitiveness  Vocables common in tribal cultures (e.g. pygmies, bushmen)  Scale type  "Major" type common o Generally the major pentatonic scale  Rhythm: Meter  Measured rhythms predominate  Compound meters common (triplets within beats)  Rhythm: Pattern  Mild syncopation common  Polyrhythms o Two simultaneous meters that are NOT related to one another by simple ratio divisions  e.g. 3-against-2 or 4-against-3 o Interlock: avoid aligning onsets with another musician while still maintaining the same overall meter  Texture: Spatial and Temporal  Mostly monophony, homophony, and polyphony  Heterophony is quite rare  Hocket polyphony: a polyphonic technique in which there is alternation of notes between parts (within a musical phrase) Instrument Profile  Chordophones  Not very important  Not many (e.g., kora, harp, zeze)  Aerophones  Not very important  Horns, flutes  Membranophones  Very important  Idiophones  Very important  Lamellophones o mbira: thumb piano  Consists of a wooden board to which staggered metal keys are attached  Played with the thumbs of the two hands Often times people attach pieces of metal to the keys in order to make the sound of the  instrument noisier  Slit drums o Not a drum (membranophone), it is an idiophone! o Consists of a piece of wood or bamboo into which slits have been cut to create “tongues” of different o lengths o Generally sounded by striking the wood pieces with a mallet Other musical features  Drummed languages  Tone languages: the pitch of the voice determines the meaning of the word  Talking drums: pitched drums that can be used to convey linguistic messages by mimicking the high and low tones of the spoken language  Responsorial singing  “Call-and-response” singing, also known as “leader-chorus” singing  Lecture 3a - Acoustics Monday, January 21, 2013 Refraction  The bending of sound waves due to a change in the velocity of sound wave propagation  Caused by  Sound waves entering a different medium o Sound waves get refracted from the medium with the higher velocity toward the medium with the lower velocity o e.g. air to water  Changes in temperature within a medium o Commonly seen with air when there is a temperature gradient  The velocity of sound is greater at higher temperatures than lower temperatures, therefore, sound waves refract from warmer air toward air  Wind affecting the velocity of a medium  Sound shadow (acoustic shadow)  Region where there is not good propagation of sound waves due to refraction Absorption  Sound gets absorbed with it interacts with physical objects  Typically fractional loss  The degree of absorption depends on the surface area of the absorbent  Larger surface area facilitate sound absorption  Anechoic rooms have total absorption and no reflection Diffraction  Diffraction around a barrier  e.g. building, wall, head  Diffraction through openings in boundaries  Sound waves are diffracted away from the edges of an opening  The amount of diffraction increases as the wavelength of the sound wave increases  Longer wavelengths will diffract more  For short wavelengths, a sound shadow will be cast behind the object Note: It’s a relative situation  o When the wavelength is small relative to a large obstacle, diffraction is inefficient o When the wavelength is large relative to a small obstacle, diffraction is efficient Interaural intensity difference  o Low-frequency sounds diffract well around the head, there is no intensity difference between the two ears o High-frequency sounds don’t diffract well, and so there IS an intensity difference between the ears, which the brain uses to localize sound sources.  Sound shadow Reflection  The bouncing of sound waves off a boundary  Between two hard barriers In a tube with two open ends   In a tube with one open end and one closed end  Reflection at hard boundary  There is a build-up of pressure at the reflection point  There is a reversal in direction of the wave, accompanied by a preservation of the phase of the wave  Because all the pressure builds up at the barrier, reinitiating a compression wave in the opposite direction  Reflection a unbounded boundary  The presence of the open end creates a pressure drop  The reflected wave reverses phase compared to the incoming wave  Its as if we started a new wave by stretching the system rather than compressing it  Standing waves (stationary waves)  Occur when the reflected sound waves follow the same path over and over again  For most frequencies, the distance between the two boundaries will not be related to the wavelength of the sound wave  Therefore the compression and rarefaction peaks will occupy all positions between the two boundaries with equal probability  However, when the wavelength is related to the distance between the two boundaries, the wave keeps on retracing the same path as it travels between the two boundaries  This means that the compressions or rarefactions always end up in the same position between the boundaries  Thus the sound wave will appear to be stationary between the reflection boundaries  It is also known as a resonant mode (or formant for voice)  Tube closed at both ends  The pressure components are maximum at the two boundaries  i.e. pressure antinodes at both ends  1/2 wavelength is smallest possible wavelength  e.g. stringed instrument  Node: location where the amplitude is zero  Antinode: location where the amplitude is maximal  Note that pressure nodes and antinodes are reversed positions of velocity nodes and antinodes  Tube open at both ends  Pressure notes exist at both ends  Because open ends can't generate pressure  1/2 wavelength is smallest possible wavelength  e.g. an open tube, like a flute Tube closed at one and ad open at the other   Pressure antinode at closed end and node at open end  1/4 wavelength is smallest possible wavelength  e.g. a stopped tube, like a reed instrument or a stopped organ pipe, or the voice  Resonant Modes  For both an object closed at both ends and open at both ends, the smallest fraction of a wavelength that gives standing waves is one half wavelength  Thus, these configurations can accommodate any integer number of half wavelengths: 1/2, 1, 3/2, 2…  Therefore frequencies are integer multiples of the lowest frequency  Resonant modes are integer multiples of the lowest frequency to give a standing wave  F1 represents the lowest frequency component  Resonant modes are generally labelled F1, F2, F3…  For a tube open at one end only, standing waves occur only at odd integer multiples of the lowest frequency of a quarter wavelength (1/4, 3/4, 5/4…)  Therefore, the frequencies are odd integer multiples of the lowest frequency Lecture 3b - Auditory System Monday, January 21, 2013 Ear Anatomy  Tympanic Membrane A sheet of skin that moves in and out in response to the pressure changes of sound waves   Its vibrations get transmitted to the bones (ossicles) of the middle ear  The area difference between the tympanic membrane and footplate of the stapes acts to amplify the sound pressure by a factor or 34, or about 30 dB increase in SPL  Ossicles  Made up of three bones: Malleus, Incus, Stapes  Cochlea  In the inner ear  A spiral, fluid-filled tube, containing an incompressible fluid  Coils nearly 3 turns from the base to the apex  The oval window is the inlet of pressure to the fluid system of the inner ear, while the round window is the outlet of the pressures  Because the fluid within the system is non-compressible, the two windows bulge in and out as a function of the pressure coming from the middle ear  Two internal membranes create three compartments o The basilar membrane is most important for hearing  Sound input lead to a vibration of the basilar membrane o The auditory organ, called the organ of Corti, sits on top of the basilar membrane "Place" theory of hearing  o Different parts of the basilar membrane are tuned to different frequencies as a result of differences in its internal thickness and stiffness o Because different frequencies activate different locations ("places") on the basilar membrane, this mechanism of coding is called the "place" theory of frequency encoding o The basilar membrane shows the opposite size trend to the cochlea itself; it is 5 times wider at the apex than the base  The base of the cochlea processes high frequencies  The apex processes low frequencies o The frequency axis of the basilar membrane is logarithmic Critical Bandwidth  When two frequencies are very close, we hear only a single frequency, and it occurs in the form of beating (amplitude modulation)  As the frequencies get further apart, we start to hear a separation into two tones, initially with a rough quality, and then with a smooth separation  Critical bandwidth  Is a range of frequencies that is integrated (summed together) by the auditory system  The frequency difference between two simultaneous pure tones at the point at which a listener's perception changes from rough and fused to smooth and separated  Measured in Hz  The basilar membrane can be modeled as a series of band-pass filters, each responding to a certain range of frequencies  The point where the two tones are heard as being separate can be thought of as the point where two peak- displacements on the basilar membrane emerge from what was originally a single maximum displacement on the membrane  The critical band as a different width through the frequency spectrum  Frequency is a linear physical parameter (as measured in Hz) but that pitch is generally perceived logarithmically  After about 1000 Hz, the CB gets larger in absolute terms but this corresponds with a fixed semitone increment  Therefore, absolute bandwidth increases with frequency Sound Localization  Two binaural mechanisms  Interaural TIME differences o The relative time of arrival of a sound wave at the two ears o Sound waves arrive at the near ear before they arrive at the far ear o The brain is able to capitalize on this time difference to compute the location of the sound- source along the horizontal plane o There is no interaural time difference for sound sources that are at the midline (0° azimuth) o The maximal interaural time difference is for sound sources that are directly to one side of the body (90°)  The interaural time difference for objects at 90° is 700 microseconds (=0.7 milliseconds) o Interaural time differences are symmetrical between the left and right sides of the body  Interaural INTENSITY differences o The relative intensity of the sound wave at the two ears o A sound is less intense at the far ear than the near ear o This is due to the fact that the head creates a sound shadow that prevents sound from reaching the far ear at the same intensity as the near ear o The head's sound shadow is most pronounced for higher-frequency sounds  Lower-frequency sounds have longer wavelengths that diffract efficient around the head  High frequency sounds don't diffract well  Interaural intensity differences occur only for high-frequency sounds, therefore they work best for localizing sounds of high frequency  The mechanism doesn't really kick in until about 1 kHz o Because of this frequency dependence for intensity differences, it is thought that interaural time differences are the only significant cues for low-frequency sounds  Both of these cues are used to measure localization of sound in the horizontal plane (right vs. left, front vs. back)  "Azimuth" is used to refer to the location of objects in the horizontal plane o It is expressed in degrees where 0° is the midline, and 90° is to one side  Duplex theory o Interaural time differences are used for low-frequency sounds o Interaural intensity differences are used for high-frequency sounds  Different mechanisms are used to detect vertical elevation Lecture 3c - Aboriginal Australia and Melanesia Thursday, January 24, 2013 Aboriginal Australia  Texture: Spatial and Temporal  Almost exclusively monophonic  Drone comes from the presence of the didgeridoo, which plays a single pitch throughout the music o Didgeridoo is often referred to as a "drone pipe"  Form  Ostinato o Ostinato units tend to be quite a bit longer than those of African music o There are often long breaks between phrases o Note the descending melodic lines  Vocal Style  Syllabic  Text Type  Vocables common Repetitive   More-complex texts present as well  Scale type Minor-type pentatonic scales are most common   Major thirds are not common  Rhythm: Meter  Heterometric o The rhythm sticks give the impression of a definite meter  Referred to as a "one beat rhythm because there is no subdividing of the beats  But the umber of beats per cycle is difficult to discern because it varies quite bit across phrases  Triplet patterns are common  Rhythm: Pattern  Generally lacks syncopation  Other elements are present: o Dotted patterns, triplets…  Instruments  Chordophones o Not very important  Aerophones o Very important o Didgeridoo  Typically about 4 ft long  Made from a hollowed out trunk of a eucalyptus tree  Player vocalizes into it, often includes animal sounds  Generally functions as a "drone pipe", playing a single pitch throughout, often the tonic pitch of the scale being used  Membranophones o Not very important  Idiophones o Very important o Rhythm sticks Melanesia  Form  Ostinatos common  Don't tend hear breaks between parts, unlike Australian aboriginal music  Vocal Style  Syllabic  Text type  Moderate complexity  Vocables used but less than Australian aboriginal music  Scales  Scales tend to be quite complex (don't need to worry about this)  Texture: Spatial  Predominantly monophony and homophony o Homophony not only involves consonant intervals like the 3rd but also dissonant intervals like the 2nd  There seems to be an element of polyphony as well  Texture: Temporal  Echoic polyphony o Note: This form of singing does not really qualify as polyphony since the melodic lines are the same; there is no spatial separation of parts.  "sing-sing" o Members from different tribes or villages come together to demonstrate their cultures o Effect of a "poly-chorus"  Rhythm: Meter  Heterometers  The drum gives the impression of a definite meter o This is a "one beat rhythm" similar to how the rhythm sticks function in Australian aboriginal music  Rhythm: Pattern  Generally lacks syncopation  Instruments  Chordophones o Not very important  Aerophones o Important o Panpipes (pan flutes)  A kind of aerophone instruments made up of rows of individual tubes of gradually increasing length (and thus gradually diminishing pitch) o e.g. flutes (bamboo), reed instruments  Membranophones o Very important o Drums common  Idiophones o Very important o Slit drums, rattles and shakers o Jaw's harp  Consists of a flexible metal or bamboo "tongue" attached to a frame  Tongue is placed in the performer's mouth and plucked with the finger to produce a note  The frae is held firmly against the performer's parted froth teeth, using the jaw and mouth as a resonator  Other features  Responsorial singing  Poly-choruses Lecture 4a - Pitch Perception Monday, January 28, 2013 Harmonics and Overtones  Fundamental frequency (f 0: the lowest frequency component of a complex periodic wave  Fundamental period (T 0: the time for one cycle of a wave at the fundamental frequency  Instruments playing the same fundamental frequency and having the same harmonics differ in the relative intensity of the harmonics  Hence, their spectra and waveforms look different  Harmonic spectrum is the physical correlate of instrumental timbre  Harmonics: frequency components of a complex periodic wave, where the components are integer multiples o the fundamental frequency  Harmonics vs. Octaves o Harmonics increase in additive increments (multiples of the fundamental frequency) o Octaves increase in multiplication increments (doubling)  Overtones: harmonics that are over the fundamental frequency  The first harmonic is the fundamental overtone; the second harmonic is the first overtone  Harmonic = Overtone +1 Partials: frequency components of complex waves that may not necessarily be integer multiples of the  fundamental frequency  The fundamental frequency is the first partial Harmonic = Partial  Perceiving Pitch  Pitch vs. frequency  The psychological correlate of frequency is pitch  Frequency is a physical parameter while pitch is a psychological concept  An increase in fundamental frequency is generally perceived as an increase in pitch  Features of Pitch  Pitch height: pitch I perceived in terms of pitch height, extending from low to high  Octave equivalence: pitches an octave apart are perceived as musically equivalent when played simultaneously (ie as chords)  Relative Pitch: intervals have the same quality no matter where they occur in pitch space  Transposition: changing the pitch height of a intervallic sequence (melody) doesn't change it quality  Two complementary issues related to pitch: Fusion  o A complex periodic sound contains multiple frequencies (ie harmonics), how come we perceive it as a single pitch and not as a chords? Unfusing  o Given our tendency to fuse complex periodic waves into single pitches, how is it that we are able to perceive chords?  "Place" theory  Difference frequency components of the input sound stimulate different positions or "places" on the basilar membrane  Harmonic sounds contain multiple frequencies, yet the brain seems to extract a single pitch-percept from the combination  Method 1: find the lowest frequency component (the fundamental) o The missing fundamental: the prediction of Method 1 is that removal of the fundamental frequency should result in a pitch shift of one octave o Removing the fundamental frequency from a complex periodic wave often results in an unchanged perception of the pitch  "the phenomenon of the missing fundamental" o Therefore, method 1 cannot be the correct explanation for pitch analysis o This demonstrates that the fundamental does not have to be present for pitch perception to occur  This is a phenomenon of "virtual pitch" a pitch is perceive whose frequency is absent  Method 2: find the minimum frequency difference (increment) between adjacent harmonics o Not correct  Method 3: find the largest common (integer) denominator of all the frequencies o The brain extract the highest common factor of the harmonics o Hence, removing the fundamental doesn't change that relationship, leading to the phenomenon of "virtual pitch" Problems with Place theory  o Phenomena like "the missing fundamental", in which the fundamental is perceived even when it is absent o People's discrimination of pitch is much finer that is predicted by the size of the critical bandwidth  Just Noticeable difference (JND)  The minimum difference in frequency between two tones in order for someone to say that there is a difference between them  Is much smaller than the critical bandwidth  Is approximately 1/30 of a CB (ie 1/12 of a semitone, or about 8 cents)  Hence, the JND is much smaller than the resolution of the analysis-filters of the cochlea o Pitch perception below 50 Hz cannot be accounted for by the place mechanism  Harmonic contributions to pitch How many harmonics actually contribute to the brain`s calculation of the common denominator, as  based on the basilar membranes' place mechanism  Successive harmonics can only make (individual) contributions to pitch if they are in separate critical bands  If they are part of the same critical band, they are not resolved from one another by the place mechanism  The ability to resolve harmonic components becomes reduced as we move to higher frequencies o Because CB's increase in size with increasing frequency while harmonic increments are fixed o At a certain point , the CB becomes larger than the harmonic increment, and therefore harmonics cannot be resolved individually from that point on by the cochlear place mechanism o For most periodic sounds, this occurs at around the 6th or 7th harmonic  Problems with the place theory  Phenomena like "the missing fundamental", in which the fundamental is perceived even when it is absent People's discrimination of pitch is much finer than is predicted by the size of the critical bandwidth   Pitch perception below 50 Hz cannot be accounted for by the place mechanism Temporal Theory of Pitch Perception  "volley theory"  Based on the periodicity of musical sounds  Frequency is encoded by the rate of firing of auditory neurons  For example, a 200 Hz sound is encoded by a neuron firing 200 times per second; hence, the neural firing is in phase with the sound  Individual neurons cannot fire more than 1000 times per second  Thus, a one-to-one mechanism cannot encode sounds above 1000 Hz  The solution provided by the nervous system is a volley mechanism: instead of firing in a one-to-one manner with cycles of the sound wave, the neuron fires at some multiple of the frequency o Hence, high frequencies are encoded by a population of auditory neurons rather than by any single neuron Phase locking breaks down above 5000 Hz   Thus above that point, only the `place ` mechanism is operative, but human hearing in that region is quite poor  The temporal theory is an explanation for why we are so sensitive to pitch even though the critical bandwidths posited in the place theory are so wide  (ie. An explanation for why the JND for frequency is so much finer than the CB Pitch vs. Frequency  Fusion: Pitch perception seems to be based on finding the common denominator of the first 6-7) harmonics, rather than perceiving these harmonics individually  Unfused: given our tendency to fuse complex periodic waves into single pitches, how is it that we are bale to perceive chords?  How do we unfuse pitch-percepts? Lecture 4b - Intervals and Tuning Systems Monday, January 28, 2013 Pitch vs. Frequency  There must be mechanisms that permit us to unfuse components Consonance and Dissonance  The psychoacoustic basis for consonance and dissonance relates to the concept of critical bandwidth  When two tones are more than a CB apart, they are judges as consonant  When the tones are between 5% and 50% of a CB, they are judges as dissonant  Maximum dissonance occurs when the frequency differences is 1/4 of a CB  Note that a typical CB is about 2 semitones in width, then the 1/4-CB corresponds with the interval of about a quarter tone Fusion vs. Separation  Situations where there are identical frequencies between the two tones are the most consonant  These are the places where there should be the most perceptual fusion  The extreme case is the octave, where all the harmonics are shared o As a result, octaves can be hard to perceive as chords  Places where dissonance occurs between nearby harmonics from the two tones tend to favour separation of the pitches Implications for choral writing  Because the size of the critical bandwidth varies across the frequency range a given interval can be more dissonant in a lower register than in a higher register  As a result of this psychoacoustic influence of CB on the perceived dissonance of intervals, choral writing tends to space out parts by at least a 4th if not more in the bass parts Unfusing Components  Dissonance among the harmonics of the two tones makes the individual frequencies stand out through beating or roughness  On pianos, octaves are intentionally mistuned so as to allow them to stand out  For many instruments, the temporal onsets of the harmonics of a single pitch are not synchronous Tuning Systems  Musical scales  A musical scale is a set of possible pitches for creating melodies and harmonies  A "diatonic" scale is made up of whole tones and semitones Tuning Systems   Pythagorean tuning o Based on the "circle of fifths"  Start with a pitch and keep on proceeding by an interval of a perfect 5th  Then bring the pitches down into the original octave until you have filled in all the slots for the chromatic scale  This takes 7 octaves o The first C and the C seven octaves about it will be slightly mistuned with regard to simple doublings of frequency  This error is referred to as the "Pythagorean comma" and is roughly 1.5% error (quarter semitone) o The frequency ratios of the Pythagorean major scale are not the simplest ratios you can obtain for these intervals; the "just" scale has those ratios  Just intonation o Any system of tuning in which all of the intervals can be represented by ratios of whole numbers with a strongly implied preference of the smallest numbers compatible with a give musical purpose o The most "natural" tuning since the interval ratios are most consistent with implied intervals of the natural harmonic series o The scale is made by keeping the intervals that make up the major triad pure  The other intervals are made in reference to them o Drawback: this scale can only be used in one key at a time  Hence, ensembles that tune to just intonation have to retune their instruments to play a piece in a different key o With regard to melodic intervals, there is one type of semitone but two types of whole tones: 9/8 and 10/9  Equal temperament o Tuning used today because it allows for the simplest transitions for playing pieces in different keys o All semitones are made to be equal; they are all set to be 1/12 of an octave  Hence, all semitones (and whole tones) are the same o The price we pay for easy transposition is that no interval is perfect vis-a-vis the natural harmonic series  All intervals are slightly out of tune compared to "natural" intervals  The only just-tuned interval is the octave (2:1) o Cents  Each semitone in equal temperament is equal to 100 cents, a whole tone is 200 cents, an octave is 1200 cents  The cents scale allows us to take the logarithmic parameter of frequency and put it onto a linear scale Tonic intervals: the interval between a given note and the tonic of the scale Melodic interval: the interval between any two non-tonic notes Lecture 4c - Timbre Thursday, January 31, 2013  Timbre refers to sound quality (tone quality)  Attribute of an auditory sensation that is left over when pitch and loudness are controlled for Contributions to timbre  Spectral energy distribution  Presence or absence of high-frequency harmonics  Synchronicity in the attacks and decays of the upper harmonics  All harmonics enter in close alignment  The entry of harmonics is sequential (i.e., tapered, staggered) Spectrogram/Sonogram  Frequency vs. time graph  Harmonic components are easy to visualize as horizontal lines  Note and harmonic onset easily visible Phases of a note  Three phases  Onset o Build-up of the sound o "attack" Steady-state  o Longest part of the note o Stable Offset  o Drop-off of the sound o "decay" For some instruments, the onsets of harmonics can be more or less synchronous   They have sharp attacks  For many instruments, the harmonics emerge in a sequential fashion Tone quality and harmonics  Instruments that are harmonic-poor tend to sound dull or flat or simple  Instruments that are harmonic0rich end to sound richer, fuller, sharper, and more complex  Instruments with odd harmonics only tend to sound nasal Amplitude envelope: range of amplitude Lecture 4d - Middle East Thursday, January 31, 2013 A dispersed style-region  Found in Islam/Muslim areas Turkish Classical Music  Rhythm: meter  Simple, binary meters  More complex meters also present  Exceptions ininstrumental solos o Can be in free (i.e., unmeasured) rhythms o "taqsim" is used to describe a s solo piece involving free improvisation  Similar exception in solo vocal forms o Chanting of religious texts (Torah, Koran) and specialized forms like the "call to prayer" (adhan) in Muslim culture  In general in world musics, free rhythms are much more associated with solo forms than group forms  Rhythm: pattern  Syncopation mild or absent  Texture: Spatial  Monophony Homophony and drone are not common in the classical musics of Arab/Muslim cultures   Texture: Temporal  Monophony, but heterophony as well  This is found especially in southern Spain (Andalucía) and Morocco o Hence, this instrumental style is often referred to as the Arabic-Andalucian style  Form  Through-composed and strophic  No simple ostinatos  Larger forms as well: suites composed of movements  Vocal style  Highly melismatic o Most melismatic singing style of any world musical style  Melisma o Text is involved rather than vocables o Melisma appears to be ornamental than then melodic o The melisma notes are in generally faster than the main melodic notes  Neumes o Inflective marks that indicate the general shape, but not necessarily the exact notes or rhythms to be sung o Almost always indicate melismas  Text type  Vocables not common  Complex text, including liturgical text and literary text related to poetry  Scales  Maqam (Arabic "scale") o 10 families of maqam's o Hijaz  Dastgah (Persian "scale") o 12 principal dastgah's Instruments  Chordophones  Very important  Lute o Oud  Principal lute of the Arab world  Short neck, belly-shaped body, no frets,  11 strings: 5 paired, one single; four pairs are tuned in 4ths o Tar Persian lute   Long, thing neck with 28 frets  3 courses of double strings tuned in 4ths  Kemanche o Spiked fiddle  Zithers  Aerophones  Important  Ney (flute)  an end-blown flute found in Persia, the Arab world, and Turkey. It is usually made of bamboo  Played in a very breathy (noisy) manner  Shawm (reed instrument) o Instrument associated with snake charming o Double-reeded instrument, precursor of the Western oboe  Membranophones  Important Idiophones   important Neumes  Inflective marks that indicate the general shape, but no necessarily the exactd notes or rhythms Lecture 5a - Chordophones Monday, February 04, 2013 Stringed Instruments  Thee different ways of activating a string  Plucked (or strummed) o Plucking is a transverse movement -> generates transverse waves in the string o Plucking creates a displacement of the string at the point of plucking  Hence, resonant modes that have a displacement node at the plucking point cannot occur o The fundamental frequency of a string is related to its length, tension, and mass per unit length o Examples:. Guitar, harp, harpsichord, lute  Violin, viola, cello, double-bass in pizzicato mode  Struck o The striking point is a displacement antinode, so all resonant modes with displacement notes at that striking point will be lost from the spectrum o Examples: piano, zither  Bowed o Bowing can create a continuous sound o Bows are made up of strands of hair, usually house hair  Bow hairs need to grip the string; "sticking-and slipping" mechanism o Because of the nature of the string displacements during bowing, the waveform of a bowed string is note a sine wave but rather a sawtooth waveform  A sawtooth waveform has all harmonics present, each one decreasing in proportion to its harmonic number  o Examples: violin, viola, cello, double bass, spike fiddle  The sound source is the string  By itself it provides very little energy for generating sound waves  Typical activation will be transverse; strings conduct transverse waves  Two factors will control pitch: length and tension of the string  Typical resonator is the body of the instrument  Propagation of vibrations occurs from the string to the bridge to the body to air in the form of sound waves  The violin body has many resonant modes of vibration o They are due mainly to the vibration of the top and back plates of the instrument o These modes do not form a simple harmonic series  The spectrum of a violin body is a continuous spectrum The output spectrum of the violin (effect of the string + the body) is the PRODUCT of the line spectrum of the string and the continuous spectrum of the resonator body  Those frequencies from the string that most closely match the resonant frequencies of the body are the ones that are most amplified  In the case of a violin, this corresponds with the frequencies of the second
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