Part One - Concepts, Cities, Humans

Shaping space in a noisy world

In this lecture we ask whether architecture is a visual or a spatial art, how we hear space as part of a total experience of space. We look at sound and bodily responses to sound, and explore the sonic experience - our individual soundtrack from before birth which includes chaos and harmonic sound, and the delicate boundary between them. We acknowledge that we are speakers as well as listeners, that speaking and listening form part of a 'feedback loop' where we adjust our behaviour in response to enclosed sound. We suggest that architecture is shaping space in relation to human activity and relates to the scale of the body, that architecture clothes activity through an intermediate medium of air, which although invisible is material, quivering, full of information. We consider the size of sounds - their wavelengths - and explore reverberation, absorption and focusing of sound. We look at the Sabine equation for calculating reverberation and do a worked example.

Architecture and space

Architecture - so often described as a visual art - might better be described a spatial art. Architecture organizes, divides one space from another, is always political, prevents movement, excludes possibilities, reduces choice. At the same time it creates protected environments: here and there. This is true of the simplest act of enclosure, creating a fence or wall, and the most complex confections of vaults and niches.

We tend to overemphasise the visible in architecture. After all, we convey our ideas through drawings and photographs; and spend a lot of money, time and effort on the solid, visible parts of buildings whereas the air is usually invisible and free. Built fabric conveniently stays put, whereas the air and the people inside buildings move around adding new layers of chaos and complexity. But our buildings shape and enclose the valuable, habitable commodity in buildings: space to live, the theatre in which we live our daily lives.

What is space?

The Cartesian dimensions of space: the x,y and z of our drawing environments are embodied in the inner ear. Our notions of up, along and side-to-side - three mutually independent axes which uniquely describe a point in space - are 'built into' our bodies as organs of balance and hearing. This geometry is inherent to us.

Yet unlike geometric space - which is empty - architectural space is full: full of activity and full of air. We can see walls, but we can hear space.

Sound carries a huge amount of information: through sound we can discover the size of a room, characteristics of its enclosing surfaces, and most importantly who's there and what's going on in the space. We can hear round corners, and learn what we are about to encounter as well as what where we are now.

Cities are noisy places, full of sound. Life is never silent, architectural space - inhabited space unlike a photograph is never silent. When we talk about ambience, mood, atmosphere, we are talking in part about vibrant, aural qualities of space.

Architecture encloses, 'clothes' us and what we do through an intermediate medium of air.

The quivering air

Just because air is invisible doesn't mean it's immaterial. We can feel it as we run or wave our hands. Although of very different densities - air is about one thousand times less dense than water, they are at the same pressure where they meet at the water's surface. We live at the bottom of an ocean of air, under considerable pressure - over ten thousand kilograms per square metre.

This pressurized mixture of gases which we breathe is in dynamic equilibrium - a wonderful phrase which encompasses all aspects of symmetry - that is to say, overall it is static, but if we look at any part of the air it is out of balance - moving to and fro, reverting to a state of balance, a-quiver with vibrations of various kinds.

Vibration & oscillation

All matter is vibrating, as we look closely at apparently 'solid' objects, we see at each level solar systems of vibration: molecules, atoms, sub-atomic particles similar to the structures of vibration we observe in astronomy. At each extreme of scale solidity disappears into quivering space. Only at around our scale -human scale - do things appear solid or unchanging.

The simplest form of vibration is an oscillation: like a pendulum, or an orbit, the matter moves to and fro describing a circle or an ellipse. Vibration is a term to describe many different oscillations happening all at once, a complex of oscillations all taken together.

Sound

Vibration we can hear is called sound. This includes not only the sound we can hear at any particular moment but also rhythms and beats, like the beating of a drum, or a heart beat, or the ticking of a clock that happens over many seconds, minutes and years. It has a time dimension measured in milliseconds up to decades.

Sound informs - gives form to - the air, through waves, which rush out from the event making the sound in all directions unless it is impeded: reflected or absorbed by a material change in the medium.

The speed of sound is fairly constant and stable: about one third of a kilometre say 333 metres/ second. That's fast, but not instantaneous.

Waves transmit energy over space. There is no net movement of matter. But there is a movement of energy and form/shape. We are not talking about a flow of air, but a temporary quivering of air.

Spatial sound

If we imagine a sound event, for example the clapping of hands or snapping of a twig, the sound-event happens at a point, and the sound waves radiate outwards in a rapidly expanding sphere. Close to the sound-event, the energy is contained in a small sphere, further away the energy is spread out across a much larger sphere. So sound has a spatial component: the sound wave not only comes from a particular direction, it tells of distance by the time elapsed and the loss of energy.

The sound here my be quite different to the sound there, even when the locations are only a few centimetres apart.

When we consider that in real life

  • there are many competing sound events happening simultaneously in different places
  • these are reflected by objects in space and are coming at us from many different directions, and
  • we move around

we can see the complexities involved in making sense of the sonic experience.

Bodily reponses to sound

These include:

  • delight
  • ecstasy of dancing
  • a dream-like ecstasy of stillness
  • adjusted heartbeat, breathing, posture
  • irritation
  • nausea
  • vomiting
  • terror
  • fleeing.

Even low levels of background noise impede deep sleep, affect concentration, performance, well-being.

Music on the other hand can increase performance, whether marching songs or work songs, whose rhythms reinforce physical movement, or in the cerbral efects of listening - the so-called Mozart effect.

This is not to say that one is better than the other, life involves a mixture of noise, music and silence, it is in the arrangement of space and activity appropriately, humanely, that we can achieve acoustically successful cities.

So why listen?

We should listen:

  • in order to create habitable space
  • in order to understand space and activity in time
  • to perceive the materiality of space as well as its abstraction as geometry
  • to users, clients and communities, so that our buildings give them what they have asked for rather than what we think is good for them
  • to colleagues and co-constructors, so that we can lead teams effectively
  • in order to avoid elementary acoustic mistakes which spoil otherwise successful spaces and buildings, above all
  • in order to design space acoustically, pro-actively shaping space, surface, materials and textures that positively enhance the acoustics, ambience, feel of space.


Wall and ceiling detail [Marcus Beale Architects 2009]

Cochlea and Labyrinth of the human ear [James Jeans 1937].

Francesco di Giorgio: figure of a man inscribed in an ideal church, c.1470.

Sensations of space

The 'reality' we observe is something which we help to create and in which we participate. We are alive, active participants in the city. Consciousness is not static - there is not 'a state of consciousness', but a dynamic of 'being conscious': observing, feeling, acting. We observe and learn from the result of our actions.

Aristotle [De Anima] said there were five senses: sight, hearing, touch, taste and smell. Other cultures have different numbers of senses, some fewer, some more. Taste and smell are connected. Balance is closely connected with hearing. The perception of radiant heat is closely connected to touch, although the phenomenon is closer to light.

Central to our sensations of space is our sense of our own bodies and body space - I know here my hand is when I extend my arm, whether I am curled up or thrashing around. This sense - too obvious for Aristotle to mention - is now known by the rather ugly Latin-derived word proprioception - from the same root as proprietor. Other body senses include a sense of movement, and a sense of pain.

All these senses, whatever their number - interpreted by experience and coloured by anticipation, add up to a perception of space.

The sense of hearing, listening and speaking is part of an overall sensory experience, to be put together with the others. What a place ‘sounds like’, ‘looks like’ or ‘feels like’, how 'good its proportions are' are parts of a whole. Listening is part of the experience. So whilst space is adubible, and we can and should listen to architecture, architecture is also visual, tactile, and so on. But unless you listen you are missing an important feature of space.

Yet there is something missing from the whole notion of perception - the idea that we receive sensory stimuli which we interpret - this model is essentially passive. In fact we are active: we learn the size of our own bodies by bumping into things, we learn balance by falling off our bicycles and getting on again, we learn to speak or sing by doing it and listening to the results, comparing, judging reactions. There is as much going out as coming in, the active and passive modes: speaking and listening are two sides of the same coin - our participation in ociety and the city as sonic beings.

Synaesthesia

For some, inter-sensory associations are stronger than others, but for all of us associations cross senses. If we consider we are experiencing actual things - for example a lemon, which has a colour, form, taste, smell and sound when you squeeze it, it becomes clear that we are all synaetsthetes - for who cannot taste the sharpness of a lemon just by thinking of it?

We can compare the objective phenomena:

  • electromagnetic radiation: light and radiant heat
  • mechanical vibration: heat and sound
  • volatile chemicals: scents
  • contiguity and proximity: touch and taste.

We can look for organs of sense, touch, sight and so on:

  • eyes
  • ears
  • skin
  • tongue

We can look at the regions of the brain that respond to external stimuli and find clusters.

And we can explore the senses in relation to each other, discerning their different qualities by comparison.

Smelling/scent is good for judging what other organisms are present, close at hand. It connects the smeller to the volatile chemicals circulating in the air around the scent-producer. Like sound, scent is information of the air, but disperses through convection, a flow of air, rather than vibration. It helps us discern who we are dealing with and what mood they are in. It announces food and cooking, warns of fire.

Tasting/food is an intimate connection between the thing being tasted and the tongue of the taster. It relates to smell and touch. It helps us discern what is good to eat from what is poisonous.

Touching/matter is an intimate connection with the body. Think of the sensitive organs of touch: the tongue, feeling for fish bones, or the skin: the largest organ of the body, which forms, almost, the boundary between what is in my body and what is outside it. [Exceptions are the sinuses or inner cavities int he skull, soimportant for singing, which are bone and air with a thin covering of mucus.] Touch helps us discern solidity, texture, warmth, materiality. We can also feel vibrations through touch - hold a cardboard box next to a road to find out - or is this hearing?

Feeling/radiant heat, a radiant connection between the emitter of heat and the person feeling the heat is more like light, or is this seeing with the skin, as the capillaries relax and blood flows into the skin?

Ultimately dissection of the senses into individual components is unsatisfactory because we are considering a continuum of perception: these are themes, groups and categories of experience.

Seeing/light is good for long distances and small detail, is detached, linear, perspectival. Seeing is believing, it has a primary place in our culture of senses, our words for understanding: enlightenment, observing, all evidence the great distinction of light and darkness, of forms taking shape in the dawn, the harsh bright light of day destroying all ambiguity.

We can see a narrow window of electromagnetic radiation through long distances including through empty space. We see one octave of light, vibrations whose wavelengths are just under a thousandth of a millimetre (380 -750 nm). Light travels - for the purposes of architects if not astronomers - instantaneously and at an absolutely constant speed, as far as we know, of about 300,000 kilometres per second. Light gives us a glimpse of great distances, the stars.


The spectrum of visible light - from ultra violet [wavelength >750 nm] to infra-red [< 380 nm].

Hearing/sound is good for medium sized distances: a few centimetres to a few kilometres. We hear round corners. Hearing connects the listener and speaker through vibrations, a wobble of elastic matter. We are physically connected through the air. We cannot hear through discontinuities in the medium. We hear over seven octaves of sound, whose wavelengths are body-sized, room sized (17mm - 17m), larger still if we consider hearing rhythm as hearing.

Sound travels at about 333 m/s (easy to remember: 3 seconds per kilometre), varying slightly with the density and temperature of the air, faster than most things move, but not instantaneous. It helps us judge the size of the sound emitter, distance. By comparing one sound with another, we can perceive very small differences in chronological time.

Hearing

Hearing is a whole body experience. We hear with our ears, but also with our skin, skeleton, diaphragm, the soles of our feet. Whichever parts of our body sense mechanical vibration can be said to hear. Indeed feelings of unease, a haunting nausea, can be experienced with standing waves of the order of the resonant frequency of the diaphragm, around 7-12 Hz. (cycles per second).

Spatial hearing. Physiology of hearing.

We have two ears, left and right, about 12-15 cm apart. That there are two:

  • allows some redundancy - if we damage one ear we are not completely deaf,
  • allows all-round hearing,
  • helps us spatialise: sounds to the right will be picked up directly by the right ear, whilst the left ear has the head in the way, also they will strike the right ear first.

The outer ears or pinnea

  • allow us to discern which part of the hemisphere the sound is coming - they are location finders.

Our sense of balance

  • allows us to keep our ears level, and to know when they are not.

Together this gives us very good location-finding, especially in the most sensitive range.

From pinna to eardrum is called the outer ear.

The middle ear - air-filled - consitsts of the eardrum and little bones - stirrup, hammer and anvil, whose purpose is to collect and mechanically amplify vibration from the ear drum and pass it to the inner ear. The Euastachian tube connects the middle ear to the back of the mouth, so that we can equalise the air pressure either side of the ear drum.

The inner ear: fluid filled tubes, terminating in the round and oval window, the labyrinth ( a deeply resonant architectural word) the sense-organ of balance, and the cochlea, (snail) a tapeing tube curled up into a spiral, within which the basilar membrane, with tiny hairs, acts as a frequency analyser.

This information flows through the auditory nerve to the brain. There are formidable powers of signal processing involved in reducing the complex audible information into something that makes sense.

The diagram opposite shows the range of human ear-hearing. It is shaped like a smiling mouth. The vertical scale shows the pressure range, that is: the variation in pressure between the compressed part of a soundwave where the molecules are pressed together and the rarefied part where the molecules are stretched apart. This is measured in bars, where one bar approximately the atmospheric pressure of air at sea level. At the top of the scale the limit of hearing is defined by the threshold of pain. At the bottom is the threshold of audibility, below this sounds are too quiet to hear at all.

On the left are long-wavelength, slow sounds, on the right short wavelength quick sounds.

A few observations:

As to the pressure variation:

  • Ear hearing is very acute. In our most sensitive range we can hear pressure variations of one ten thousandth of atmospheric pressure, almost at the level of Brownian motion - the random pressure variations of the heat of the air molecules.
  • The range from the loudest to the quietest is enormous, with the loudest sounds in the same sensitive range about a million times the quietest.

As to the wavelength/frequency:

  • The smallest wavelength we can hear is about the size of a thumbnail 17 mm, up to the longest 17 metres.
  • We can hear well sounds between 3 cm and 8 m wavelength
  • We can hear very well from about the size of a eye to the size of a man.
  • The most sensitive range in which we can hear with exquisite accuracy is about the distance between the ears, the size of a mouth or fist, face sized, gesture sized.
  • The average sized sound (the harmonic average) about the size from mouth to belly.
  • Middle C is 4 foot or 1.2 m wavelength.
  • The wavelength of a man singing a comfortable G below middle C is about 6 foot or 1.8m long = the size of a man.

Some conclusions:

  • We hear sounds of appropriate wavelength (size) in relation to our body. Hearing and speaking are anthropocentric. We don't hear what an elephant hears, or what an ant hears. Nor do we sound like them, our centre of attention is different.
  • We hear much more that we can actively listen to. Hearing is so acute that we must block out or consign to the background the vast majority of what we hear.


Di Giorgio man

Ear diagram

Cochlea and labyrinth diagram


The range of human ear-hearing. For a larger pdf version of this image click here.

Making Sound

Before discussing listening, let's look breifly at the other side of the coin, making sound.

Voice, heartbeat, life rhythms. The moving subject movement and dance relate experienced frequency to the human body and movement.

We have first the internal vibrations of the body:

  • heartbeat
  • breathing
  • rhythms of sleep and activity
  • and the resonances of the body: fingers, wrist, lower arm, upper arm, torso and so on, rhtyhms relating to movement and dance.

It is no accident that the names for speed in music relate to natural body rhythms: allegro, andante, adagio.

By moving we make sound:

  • footfall
  • work sounds
  • grunts and groans
  • drumming and banging and so on.

Finally, and especially, the voice. There is no difference between speaking and singing, except that in singing the note has a definite frequency/wavelength and duration.

The voice is a wind instrument, powered by exhaling air from the lungs.

Lung size is increased by lowering the diaphragm, the dome shaped muscle separating ones guts from the chest cavity, and air exhaled through the larynx, where the vocal cords (like the mouthpiece of a wind instrument) makes a rhythic buzz which sets into vibration the cavities of the chest and especially the head. The front part of our upper bodies, the chest and the head have a number of air cavities, the mouth cavity, the nasal cavities, the pharynx, the turbinated bones and nasal passages, and the sinuses: little bony caves, uncovered by skin, the frontal sinuses located in the forehad and sphenal sinus in the centre of the head.

What function do these cavities have? At least two. Since the body has the same density and salinity as sea water, these cavities allow us to float on our backs upwards, with just our face showing above the level of the sea. They also act as fantastic resonators.

We have within us a wind instrument that makes harmonic sound.

Harmonic sound

A tube of air, constrained by enclosure at its sides but open at the ends, when excited into vibration, will oscillate as a whole, and in halves, and thirds and quarters and so on. Within the note are inner notes. This can be illustrated by a tehcnique of chanting with overtones. [Demonstartion MB]

Stretched strings behave in a similar way: the whole string will oscillate as will its halves, thrids, and so on.

These oscillations produce a series of notes and rhythms with a particlar arithmetic relation to each other - the so called 'harmonic series' 1,2,3,4.... (where you compare them as proportions: half, the same, twice, one and a half times, one and a third times and so on). We can hear with great accuracy consonnaces and dissonnaces, this is because the harmonic overtones form one note will coinide or not with the other, and if they are almost but not quite the same, we hear a throbbing wobble, a 'difference tone' between the two.

Harmonic proportion in architecture comes from a speculation that the harmonic series gives an insight into the structure of the universe: that architecture, in adopting one of the mathematical 'secrets of nature' reveled so accurately by the ears, will emulate nature.

We see this in Alberti, Palladio and others.

To what extent harmonic proportions are inherent in structures is in part an issue of intentionality for architect, builder and user. No building is exactly perfect. Walls have thicknesses, frames, cills and beams have thicknesses, we must also allow for tolerance. For example: setting out a building benefits from simple numbers and ratios, for simplicity apart from anything else. We enter such a building and see that it is harmonious: does this mean we understand its simple geometric structure and therefore the building 'makes sense' to us? Or is there some deeper aesthetic resonance at work? To what extent can harmony tolerate imperfection and chaos? How much can we squash a shape until it becomes something else?

The simple relationships between the numbers 1-4 and beyond are inherent to structures of music, harmonically and rhythmically, both harmony and rhtyhm play contrapuntally in time with the early numbers.

The harmonic series has no direct relationship to the Fibonnacci series and the golden section, which is all about growth patterns in nature, and the basis of the modulor of Corbusier, although its early terms 1,1,2,3,5,8 give acceptable harmonics.

Vibrations of a stretched string

Listening

Listening involves a value-system. We listen to what is appropriate and important to us. Our attention is drawn to events that are worth listening to:

  • other humans
  • speech and song - harmonic sound
  • danger
  • water
  • food
  • music

and what is not worth listening to is ignored or suppressed.

Listening requires skill and effort on behalf of the listener even in the quietest moments.

Threat sounds, sound of predators, the screech of polystyrene on glass (a trans-cultural nasty sound). Thunder and earthquakes. Water sounds - Food sounds - Other humans, and particularly those that we love, crying babies, and particularly speech, song, laughter, convivial company and music. Unexpected sounds which might mean something or nothing. And it is place specific, the sound of water, for example are much more noticeable in a desert.

The soundscape, a soundtrack which extends from before birth until death. It is a continuum - there is no point at which one can definitively say this is speech and this is song, this is noise and this is music.

The extremes of this value system are described as: harmony/music/poetry and on the other: noise.

Music

Music is valuable sound. Characteristically music involves inner structures of harmony and rhythm, related to the resonant rhythms of humans. Songs can rouse, strengthen, soothe us, make us amorous, all these though breathing, rhythm sweetness of harshness.

It has a tribal, cultural element: we define ourselves though our music and songs.

Playing classical music at railway stations

Music to shop to to work to.

Function: to make us hear better

Speech

Speech is symbolic sound, sounds which carry a symbolic meaning.

Noise

Noise has two distinct but related meanings:

  • chaotic sound (e.g. white noise) or in the more usual colloquial sense:
  • sound of negative value: (e.g. noisy neighbours) things that worry or annoy us - things wewould rather not hear - a value judgement, very dependent on context.

For example: water sounds have a different significance in a desert.

Here's a text from Luigi Russolo, an Italian Futurist writing in 1913 about Milan, a prosperous industrial city in the plains of northern Italy:

‘Let us wander through a great modern city with our ears more alert than our eyes, and enjoy distinguishing between the sounds of water, air, or gas in metal pipes, the purring of motors which breathe and pulsate with indisputable animalism, the throbbing of valves, pounding of pistons, screeching of gears, clatter of street cars on their rails, cracking of whips, flapping of awnings and flags. We shall enjoy fabricating the mental orchestrations of the banging of store shutters, the slamming of doors, the hustle and bustle of crowds, the din of railroad stations, foundries, spinning mills, printing presses, electric power stations, and underground railways...’ [Luigi Russolo - The Art of Noises 1913.]

The point here is that ambient sound, the din and clatter of modern life, can be made into ‘mental orchestrations’, the 'breathing engines ... indisputable animalism', the 'hustle and bustle of crowds' are being considered, as a whole, as something to be enjoyed. Russolo is pushing back the boundaries of music to include the sounds of modern urban life.

We should consider the sound of our buildings, the whole sound of the city, not only when designing for music or designing out noise, but everywhere: for enjoyment, but also as a means of understanding the city life, to learn to distinguish and hear well and think about what we hear for the whole of our professional lives.

Love noise - the chaos of the city. To love in order to understand, to understand in order to love. A basic technique, discovered by medieval theologians of pure love

Silence

The acuteness of hearing ensures that there is no such thing as absolute silence. Quiet is necessary, as part of a pattern of variable exposure to sound. We need quiet when we sleep. But silence is a rare and profound experience. Here is the composer John Cage talking in 1990 about his experience of silence in the anechoic chamber of Harvard University:

"It was at Harvard not quite forty years ago that I went into an anechoic chamber not expecting in that silent room to hear two sounds: one high, my nervous system in operation, one low, my blood in circulation. The reason I did not expect to hear those two sounds was that they were set into vibration without any intention on my part. That experience gave my life direction, the exploration of nonintention."

His 'silent' piece 4'33" (-273ºC is 0ºK absolute zero) came from this, a reminder that we cannot achieve silence, even in the concert hall, the piece becomes a concerto for audience, or perhaps a concerto for architectural space.

Measuring, describing and quantifying sound:

Acoustic phenomena have been known and exploited since the earliest times. Some examples: cave paintings correlate to places within cave complexes that exhibit marked acoustic properties. The echo-mirror - the acoustic effect win which sound is reflected in smooth stome faces informs the mythology of spirits 'trapped within the mountsin' in a sort of acoustic Looking-glass world. Echo was an ancient Greek deity.

Qulaitative accounts of acoutics include very sensible stuff from Aristotle, including the concept of Potential Sound - a notion which we will explore and rehabilitate in the second lecture - the state of a piano not currently being played or a bell not yet ringing for example.

Quantiative approaches to sound were concerned with the association of wavelength and pitch, which was well understood in ancient times.

Pythagoras, a huge figure in Greek philosophy from the C5 BC is attributed with the knowledge of the relationship of pitch to the harmonic arithmetic of bells, tubes and strings. It is notable that the school of Pythagoras was both mystical and mathematical, they attributed qualities to numbers, so for example the number one (the monad) represented the whole of everything, the universe, and defined a point, the number two (the unlimited dyad) represented all pairs of light dark, night/day and so on, the triad all things that come in threes, defining a tringle and two-dimensional space, the number four a tetrahedron and hence three dimensional space, and so on. (The ancient Greeks did not have zero.)

In the ancient and medieval period, music was part of mathematics: defined as:

  • arithmetic (numbers pure),
  • music (numbers in motion),
  • geometry (bodies at rest) and
  • astronomy (bodies in motion).

Harmony was well understood and the problems of constructing musical scales - combining ratios to create groups interrelated notes on the steps of a scale. (To construct a scale which is both fixed and perfect is impossible, and the modern standard keyboard tuning at equal temperament is an approximation,in which only the octave is perfect, and all the other ratios marred.)

So until the baroque and early modern period, sound science was essentially to do with music and harmony.

From this period, there developed not only the mathematics to deal with change (the calculus) but also an increased interest in experimentation, measurement, calibration of time.

Galileo (1564-1642) gives a concise and clear description of frequency of vibrating strings, resonance and sympathetic vibration.

Mersenne (1588-1648) made an accurate estimation of the velocity of sound, and eplored the concept of frequency.

Athanaseus Kircher (1602 - 1680) explored the transmission of sound through a vaccuum, enquired about the properties of reflection of sound in so-called phonic buildings, the geomtric design of walls and ceilings.

Newton (1642-1747) gives theoretical calculations for the velocity of sound [Principia Bk II Propositisons 47,48,49] as directly proportional to the square root of the elasticity (the more elastic the quicker the sound), and inversely proportional to the square root of the density (the more dense the slower the sound), and measures sound, using Halley and Flamsteed as helpers over a distance of three miles.

Sauveur (1653 -1716) established that the string vibrates as a whole and in parts, the basis for harmonic sound.

Laplace (1749-1827) refines Newtons theory to allow for adiabatic elasticity rather than isothermal elasticity.

Chladni (1756-1827) used sand figures to show the modes of vibration of solid bodies.

Fourier (1768-1830) published a treatise on the Alnalytic Theory of Heat in whcih there is the first formal statement and proof of Fourier's theorem - that any periodic vibration can be expressed as the sum of a (potentially) infinte number of harmonic oscillations.

There is an explosion in the application of differential calculus to questions of sound and vibration, with publicationson acoustics from Euler, D'Alambert, Bernoiulli, Lagrange...

Rayleigh

and Helmholtz

The unit of frequency is expressed as cycles per second or Hertz after the german natural philosphopher puil of Hlemholtz .

Amplitude phonometers and electronic measurement pressure loudness decibels a logarithmic scale comparing one thing to another.

Sabine 1900

Conservation of energy
Reverberation
absorption
Resonance a mechanical (or biological) system which favours a particular frequency /wavelength and so will vibrate in this manner

10 dB = twice the pressure. 20 = 4 times 30 = 8 times and so on. Compare to the threshold of audibility = 0 dB

dB and wieghted dB

Pythagoras

Galileo

Athanasius Kircher - phonic buildings from the Misurgia Universalis 1650

Helmholtz

Sabine

Kircher

Reverberation -

Echoes: greater than 1/20th second. Reverberation, multiple tiny echoes leading to a dying away of sound over several seconds.

Reflecting sound - stone sounds acoustic ‘mirrors’ - absorption - openings

Sabine equation

Rt = 0.16 V/(sum of absorptions + xV air attenuation)

The continuity

M














A fuller chart is available here.

Sound mapping

Marking up a drawing to show the acoustic character of a place

shading from traffic noise

sound that happen intermittently

pictograms and ideograms.