----- Experience in your own room the magical nature of stereo sound -----

... but you want to design your own loudspeaker?

My conversations with Fitz

... your own loudspeaker?

... come into my parlor ...

2 - An introduction to Acoustics and Hearing

2.1 - Hearing - Part 1
2.2 - The Association Model of Perception
2.3 - Perception of the world around us
2.4 - Perception and the perceiver
2.5 - Hearing - Part 2
2.6 - In summary

SL:  So now let's talk about acoustics and how acoustic phenomena relate to hearing phenomena. Both occur in time and space.

Fitz:  You mean space like my living room or backyard?

SL:  Yes, any volume of air that has objects in it and hard boundaries and where people are.

Fitz:  I hope you focus on my living room, because that's where my new loudspeakers will go.

SL:  Correct, but not exclusively so. Rooms have different sizes and that matters acoustically. You describe the floor area in square-meters and the length, width and ceiling height in meter or use feet and square feet for it here in California. But for acoustics those room measurements carry no meaning unless they are translated into wavelength of sound.

Fitz:  My room is 12 feet by 18 feet with 8 foot ceiling and I have been told that it may be acoustically too small for my speakers with all the stuff that we have in the room. Also, SWMBO is not too happy and the speakers must be small or there is no chance to set them up.

SL:  Oh well, everyone has their problems. Acoustic dimensions can tell you at least where the acoustic problems of your room and your speaker design are likely to occur. 

SL: Sound travels at a speed of 344 meters per second. If the sound is caused by a periodic vibration that repeats itself every "t" seconds, then the vibration has a frequency of F = 1/t Hertz. 

Say it repeats every millisecond, then the frequency is 1 kHz.

Since this vibration travels through the air at a speed of 344 m/s it repeats at distances of 344 mm, which is called its wavelength.

I show you these relationships in spreadsheet format:

Fitz:  Wow, from 20000 Hz to 15 Hz the wavelength changes by a ratio of 1333 to 1.

SL:  Yes. But what matters for the acoustic design of your speaker cabinet and baffle size or for your living room dimensions is not the wavelength, but the quarter-wavelength.

Fitz:  Why is that?

SL:  We will get to that. But basically, when you have a sinewave it has phase-shifted 90 degrees in 1/4th of its period or a quarter-wavelength. Significant acoustical phenomena and interactions occur when two waves are separated by a quarter wavelength or multiples of a quarter-wavelength.

If some object is much smaller in physical size than 1/4th of the sound's wavelength, which hits it, then it is called acoustically small. The sound just travels around the object pretty much unimpeded. If it is 1/16th of a wavelength in size you can forget about it. 

For example, take your 4" x  4" tweeter baffle. At 3.5 kHz a quarter-wavelength measures 1". So the baffle is acoustically large and gets even larger as frequency goes up. The quarter-wave boundary between large and becoming small is in this case at 13.5 mm/s divided by 4 times 4 inch, which equals 0.84 kHz or 840 Hz.

Fitz:  Are you saying that "acoustically large" is a prescription for trouble?

SL:  No, not at all. All I am trying to say is that you better understand what the effect of "acoustically large" is for your speaker design and how directionally your speaker will radiate sound into your living room.

Fitz:  But then we should really look at the ribbon, which makes the sound. It is much smaller.

SL:  Yes. I estimate the ribbon to be 10 mm wide and 50 mm long. That would give for the width:
Fquarter = 344 mm/ms / 4x10 mm = 8.6 kHz and for the length:
Fquarter = 344 / 4x50 = 1.7 kHz

Fitz:  And that means?

SL:  That you can expect vertical directivity effects, like narrowing of the vertical beam and more than one beam in the vertical plane of radiation.

Fitz:  And is that undesirable?

SL:  It depends upon what you had in mind for the radiation pattern of your speaker. But be aware that the polarity between beams changes. At the same time when the air particle density of the main beam aimed at you increases, the air particle density decreases in the next beam, aiming towards the ceiling or floor of your room.

Fitz:  I fail to see the significance of that sort of beaming and in any case the ribbon is narrow in the horizontal plane and that is where sound dispersion really matters. At 10 mm width Fquarter is 5-times higher and at 8.6 kHz.

SL:  We will get into the audible significance of radiation pattern later. At this point I just need to tell you that you are not alone. I look at commercial at consumer and professional loudspeakers and without hearing them I can pretty much tell you how they will sound in a room. By visual inspection I can tell how much attention has been paid to their acoustical design, which determines with what strength they radiate sound in directions different from "on-axis".

I think it is essential to remember some numbers from the spreadsheet and to form a mental image of them. 
The speed of sound is c = 344 mm/ms, thus a quarter wave at 1 kHz is 86 mm long. 

A 100 mm physical dimension corresponds to a quarter-wavelength of
QW = 344 / 4x100 = 0.86 kHz = 860 Hz

You can mark up a ruler with the numbers from A to B, or a yardstick with the numbers from A to C to get a feel for the bottom boundary of acoustically large expressed in kHz and mm. You will need a tape measure to cover A to D.

Fitz:  I will have to digest "acoustic size" and try to see it.

SL:  Use your Design #3 for that. And also look at your room. Above which frequency is it acoustically large?

And note that if some object is acoustically small, then the wave travels around it unimpeded. 
If it is an acoustically small source, then the wave propagates outwards from it like the surface of an expanding sphere. A point source radiates omni-directionally. 

Think of the point source as a pulsating sphere. 
But a back and fore moving sphere, like a ball at the end of an infinitely long pendulum string, is called an oscillating sphere. If it is acoustically small, then it radiates sound in dipole fashion. It does not radiate in the plane that is at right angle to the axis of movement.

A few days later:

Fitz:  Glad that I run into you. I calculated QW for my room and for the length I get 17 Hz. That does not seem right because I know that my lowest room mode is at 34 Hz and below that frequency I supposedly get pressure buildup in the room.  

SL:  34 Hz is correct and that is the result of 2 quarter-wavelength sections or a half-wavelength equaling the length of your room. Nasty and sometimes desirable acoustic phenomena occur at distances that are multiples of a quarter-wavelength. QW is a useful unit of measurement.

For example, if you remove the back wall from your room so the sound can travel right to your neighbors, then you would hear at 17 Hz a loud quarter-wave resonance when you stand in the opening.

If instead of removing the wall you think of extending your side walls to infinity then the sound wave never encounters a discontinuity and no sound reflects back to the source. QW goes to zero and no standing wave can exist in that direction. A structure like this is called a wave-guide. The structure with the opening is called a quarter-wave resonator. And your room structure is called a closed-cavity when it comes to acoustic fields and waves.

SL:  But I am getting way ahead of what I want to talk about. 
But we will get back to this later and to more cases, like when the side walls recede and only the front wall remains. 
And then what happens to the wave when that last boundary shrinks to zero and only the point source of output strength "1" remains?  By the way that is the same strength source in all the pictures. Because the source is directly in front of a wall it generates twice the sound pressure as it does in free-space. But only as long as the wave has a sufficiently large guiding wall. It has that for frequencies above 46 Hz in our example.

SL:  Think about all this before I continue and talk about hearing. Look at your Design #3. Think about the baffle size and the room behind the 8" driver. What are their QW frequencies? And what does that mean?

2.1 - Hearing - Part 1

SL:  The Zen master asks the student: "When a tree falls in the forest, does it make a sound?"

And the student thinks: "That must be one of his trick questions again, I must think before I answer. I know when the tree falls that it makes noise when its branches hit other trees and branches and that it makes a loud crash when it hits bottom. so why is he asking?" 

Fitz:  I get it! Somebody has to be there to hear it. Otherwise it's just air vibration. Sound is what I hear. What I perceive and then associate with branches moving against other branches. 

SL:  The Zen master also asks: "What is the sound of one hand clapping?"

Fitz:  That does not make any sound. But I can hear clapping in my mind. So the sound of one hand clapping is referring to a memory. 

SL:  Sounds reasonable to me, but then I am not a Zen master to know why he asked the questions. I suspect he is inquiring about the student's Self with a capital S, about the person who is hearing or not hearing, and what their state of enlightenment is at this moment. That would jibe with another master's response to a student's question: "What is the essence of Buddhism?" And he answers: "No Self, no problem!"

Fitz:  That gets heavy. Let's talk about hearing.

SL:  Yes, read first what Bregman had to say. His book was published 1990, not that long ago. He explores the amazingly complex processes, which the brain is capable of in order to make useful sense of what pressure variations in the air communicate about the world around us. It's a thick book and I did not make it much beyond the introduction, but it influenced tremendously my thinking about sound. Ultimately, and in combination with Guenther Theile's Association Model and my own experimentation, I learned that a loudspeaker must be friendly with natural hearing processes in order to render sound convincingly.

From:  Albert S. Bregman and Pierre A. Ahad, Demonstrations of Auditory Scene Analysis - 
The perceptual organization of sound, Audio CD

SL:  And now another of Bregman's illustrations of the ear-brain system's capability. I like to call that system our BSP, our biological signal processor. Imagine writing the software for a DSP box that must  function like the BSP. If the software does not work, you will be eaten by a saber toothed tiger.

Fitz:  It would seem that 'room correction' could start a fight with the BSP.

SL:  That is possible. I judge any sound system by how tiring it is to listen to. When after a while you feel like you had enough, then your brain is telling you subconsciously: I have worked enough to compensate for the unnatural cues that I receive. I am tired. 

From:  Albert S. Bregman, Auditory Scene Analysis - The perceptual organization of sound, MIT Press, 1990

Fitz:  That is truly amazing. 
... and what is this Theile Model all about?

SL:  Well, I have to first generate some visuals to illustrate and explain the Association Model of auditory perception. We will talk about the philosophical concept of Gestalt and how we experience it. And then we talk about the ear and upper body as an encoding and decoding device for the world around us in order that the brain can extract meaning and learning in conjunction with its memory part.

It is not obvious at this time, but it all relates to loudspeakers and what they must do for a listener to recognize a Gestalt, and how therefore they should be designed and built optimally.

2.2 - The Association Model of Perception

SL:  I am back.

I encountered the association model for the first time in Guenther Theile's AES Journal paper, "On the Standardization of the Frequency Response of High-Quality Studio Headphones", Vol. 34, No. 12, 1986 December.

I noticed the model again, and this time applied as a guide to effective coding of information, in a white Paper by Clemens Par.

You might read the papers, if you want more background material for our conversation about loudspeaker design and about how and what we hear:

From: Clemens Par, Rationalism versus Empirism, in https://www.intercomms.net/issue-25/va-1.html, 2015
or https://www.linkwitzlab.com/Fitz/rationalism-empirism.htm  
[4] G. Theile, On the Localization in the Superimposed Soundfield, PhD Thesis, Technische Universitaet Berlin, 1980

Here is my friend Clemens looking to convince the engineering world to apply sensible perceptual coding

Fitz:  I will skip it for now and maybe get back to reading the papers later.

2.3 - Perception of the world around us

SL:  Alright, but I must tell you that the association model gives not just a wonderful explanation to how we hear. It applies to all our senses, the five senses through which we experience the world on the outside of our skin: Hearing - Seeing - Touching - Smelling - Tasting. 

Fitz:  How is that? 

SL:  I really must step back a long way, because this is about how we interact with and respond to the world around us. It is about the functional patterns that we have acquired by birth from our parents and by generations before us, through the genetic code in our bodies. It is about learning, since the first scream at our birth into this universe, about experiencing love and pain and then learning to get more love and how to avoid pain. It is about the influence of 'nature' and 'nurture' upon our daily activities and longings.

Fitz:  You are going big again.

SL:  It hardly gets bigger than that. So lets start right away with the Universe.

Fitz:  Yes, I know that Planet Earth and our solar system is just one of millions of solar systems in the universe. I read that they found just recently a cluster of planets, which potentially could carry life as we understand it, and the planets are not that far away in terms of light years. 

I know that we are not the center of the universe, not even the center of our milky way galaxy, but some 20,000 light years away from the center and at the outer fringes of our spinning galaxy, which is just one of millions of galaxies. It is just overwhelming to think about it, but also awe inspiring and humbling.

SL:  Yes, and then to think that our planet is just a youngster in the universe, recycled material from extinguished suns, from stars, which shone brightly before the earth was born. We ourselves, the atoms, which make up our bodies were cooked in a sun. We are literally made up of stardust. We are local condensations and manifestations of a parent sun.

Fitz:  Pretty amazing stuff

SL:  And the beauty is that we are, or can become, conscious of this relationship through the extension of our five senses by scientific instruments, and by communication tools that reach beyond the range of our voice or beyond the drum beats, which were in earlier times used to send messages to people at great distance from each other.

Fitz:  OK. The picture above shows Me inside a Local Reality, which is inside the circle called Planet Earth.

SL:  What is being communicated here, is that we live our lives locally. In the past the extend of that region was defined by the horizon on the water, or the next mountain range, or the forest, or basically by how far we could see. Compared to that, the local reality for hearing, what you can perceive in terms of spatial information with closed eyes, is different in its extension and detail. Touch is limited by the reach of your arms or legs.

Fitz:  But today my Local Realty is far greater, because I have a smart-phone and ear-buds and a car and Facebook and Google.

SL:  Yes, very true. But I still call it Local Reality, because you have self imposed boundaries, which determine how far you reach. You have a local world to which you respond. I have another one. Since you are on my website, our worlds have some amount of overlap.

The point of all of this, is that we deal with, that we experience and live in a bounded world. We can transport ourselves by foot, bicycle, car or airplane to different bounded worlds. Taken together, all these add to and form our experience and learning of the world beyond our skin. We carry in our head and body memories, thoughts, emotions, behavior patterns and models as a result of our journey through life. The journey started with birth. We all came into this world pretty much the same way. We go out in our own unique way. Between those two events we live the story of our life.

SL:  How the story is being written depends upon the inputs and messages, which we have received in the past, and what and how we have internalized them. The story depends upon the inputs, which we receive at every moment and how we respond to them. But the story also develops in response to our resistances, expectations and hopes.

The difficulty for our perceptual apparatus, for hearing and seeing for example, is that we are constantly exposed to information from our local reality. 

When I open my eyes in the morning, I see the reflections of the sunlight, which describe the objects in my bedroom and the objects outside the bedroom window. Since I have memory, which I associate with what I see now, I am not so much interested in the scenery and landscape, but I am looking for what has changed since yesterday. For example I like to know what today's weather is going to be. I know from experience that last night's weather report is not a reliable predictor here, on the Pacific coast of Northern California, where the fog drifts in and out, and the weather can change from sunny to foggy within an hour or two. So the weather has my attention.

Now if I stand up to look out the window, I notice whether the long grasses or any tree branches move, and if so, in which direction. Having been an avid, a practically addicted windsurfer, I cannot help but noticing the smallest movements caused by air, and hopefully indicating a windy day. I no longer dare to go out on the water, aging has its consequences, but I still respond to patterns, which I adopted in earlier times. Water, wind and waves are still calling, when my pleasure now is to wade through the cold waters along a sandy beach near our home.

Fitz:  OK, why are you telling me this?

SL:  I am telling you this because our perceptual apparatus has to divide the world we live in into foreground and background. Otherwise we cannot handle the inflow of information. We need to know what is background, what is consistent, what does not require attention, in order to notice changes in the background, which might carry information, to which we better pay attention. It is the movement against a background, whether it is a visual or a sonic background, which draws our attention. 

As a matter of fact, all our senses are primarily change detectors. Come into a room and it smells bad. After a while you no longer notice it. But then go out the door and you will relish the fresh air.

Fitz:  It's the same with hearing. I get really annoyed with clicks and ticks on my old LP's and often wish I could just ignore them.

SL:  That is difficult to do. You can much more easily ignore tape hiss or LP groove noise, because it is continuous, Your brain can move that beyond its acoustic horizon. But is has to constantly work at it and it becomes tiring. Some audiophiles like to talk about new equipment brake-in. I think it is mostly their brain breaking in, because the brain has plasticity, and is eventually adapting to the reality. The longer the break-in time, the more artificial the sound must have been.  

The clicks and ticks though draw your attention, because you are genetically programmed to pay attention to such signals. In evolutionary terms, there could be a saber toothed tiger in the bushes. We still respond to the commands from a large region in our brain, which is programmed for bodily response and motion, like hiding or running.

SL:  Our conversation now brings me to the Association Model of Perception, or AMP. The general model came to mind as I was thinking about the steps and processes in the Association Model of Hearing, which GuentherTheile and then Clemens Par used for their particular lines of investigation.

I also have been fascinated by books like:

Cesar Hidalgo, "Why Information Grows", 2015
Daniel Kahneman, "Thinking, Fast and Slow", 2011
Michael S. Gazzaniga, "Who's in Charge?", 2011
Pierre Teilhard de Chardin, "The Phenomenon of Man", 1955

The model below brings together what I have taken from various inputs, from my own life's story and from recognizing what is hidden behind "The Open Secret" of life and living. 

Fitz:  So you have tested this model against your experiences and understandings?

SL:  Yes. The beauty of this model is that it not only brings to consciousness the patterns in my response to the realities beyond my skin, but also to a dimension beyond, which touches and enters me through Intuition and Recognition.

Association Model of Perception

Attention }-- Movement --{ Perception

SL:  During Intermission it occurred to me that the Association Model of Perception is as important to understanding life and living, as is Einstein's (e = mc²) to understanding physics.

The AMP describes how we take in the outside Reality and deduce from our perspective a Subjective Reality, which has Meaning to us in context of previous observations of Reality. We associate current input data with stored memory data, many of which are hard to access directly, and we respond accordingly: physically, mentally, emotionally and intuitively.

2.4

SL:  I perceive my physical environment via five sensory transducers: eyes, ears, skin, tongue and nose. Electrical signals from the sensors are transmitted to the brain, which then deduces from them a model of the physical environment. The brain takes into account associations with memories, emotions, love, fear, traumas, pain, suffering, death, love, acceptance, laughter, joy, feelings, thought forms, beliefs, knowledge, education, patterns of thought, skills, convictions, experiences, etc, etc.. This can be a time consuming process before perception and cognition occur. 

Survival of the species requires fast processing of incoming data, which is done by sorting the incoming data streams into static data streams and transient data streams. Transient or changing data streams get first attention. The external visual or acoustic scene is divided into background and foreground. The foreground gets attention and a response, which is most appropriate in the context of the present background. Decisions have been made and actions taken before I am even aware of what has happened. This occurs in the part of the brain, which is hard-wired for survival and with which I was born.

Perception and recognition, which occur after the input data has been processed via associations, leads to completely subjective responses. They are often not appropriate in the context of the external reality. They are instead responses, which come out of various forms of resistance to the external reality.

The Story Teller in your head is the commentator on your journey through life, which may take you from Self-consciousness to Consciousness of Relationships and Connectedness, to Enlightenment, and/or through Grace to Recognition. Along the way your story teller is ready to come up with excuses, justifications and explanations for all your actions and inactions.

Regardless of the nature of the actions, and the consciousness with which they are done, they take place in an all encompassing energetic field of LOVE. That is difficult to accept, but becomes apparent when resistance is dropped.

SL:  The song "Celestial Echo" from the Boris Blank and Malia album "Convergence" is about a story teller. Which story do you tell yourself?

Fitz:  I want to go back to the two modes of mental operation. The first mode comes from my instinctive/intuitive side. The second one is from my subjective perception of reality, after the input data have been filtered by associations and maybe some intuition.

SL:  Yes, and the whole journey through life is one of paying attention to inputs and to respond physically, mentally, intuitively and emotionally. What needs to be learned, is that resistance is futile. Battles are fought for Peace, not for Domination. Ours is a planet of Balance. 

Fitz:  And what about AMP and 
   Attention }-- Movement --{ Perception

SL:  AMP is just the acronym for Association Model of Perception.
AMP also has in it the first letters of Attention, Movement and Perception. 
Movement, response, action or inaction are the outcome of attention and perception. 

I have heard neuroscientists say that the prime purpose for the brain is to control movement of the body. Think about it. What would you do and be, if you did not have a brain? If you could not move and program the brain with experiences of your environment? To instigate new movements? To learn from associations? A tree does not need a brain. It is genetically hard programmed to go for the sunlight.

Fitz:  Can you give me an example of how my own mind works when it comes to the two modes of operation? 

SL:  I love to show you this page from Kahneman's book about 'Thinking, Fast and Slow'. In his terminology System 1 is the fast one and System 2 is slow.

Have fun:

Fitz:  Great! What was your answer?

SL:  10 cent

Note that you just had an experience of your inner workings, how your mind processed the bat and ball question. We perceive not only the world outside of the skin but also the world inside of the skin. We perceive our state of being, though it is tainted by the associations, which are dominant at the moment and which give us the context for the present state of being. Observe how you answer the question: "How are you?"

Note also that in general, perception works against a background, a context. Foreground versus background. A perception derives its meaning from the context. If it is pitch dark and you hear a noise that reminds you of a mouse, then you ask yourself: Does that sound make sense here in this fancy hotel room?

When I listen to the playback of a stereo recording and close my eyes, I ask myself: Where am I? 
My enjoyment of the performance is greatly enhanced, when I do not hear left and right loudspeakers and the listening room, and only a phantom acoustic scene. If the perceived scene is 3-dimensional and naturally arranged spatially, and in a plausible environmental context, then I love to immerse myself most fully into experiencing the music. And that can get loud to a disinterested bystander.

"Musik wird oft nicht schön empfunden, weil stets sie mit Geräusch verbunden", said the cartoonist Wilhelm Busch a long time ago.

SL:  OK, let's move on. 
I now I have laid the basis for talking about the specifics of hearing and how we process acoustic vibrations into meaningful perceptions. After my detours into general principles of perception, life and living we are back to how we are programmed to listen to loudspeakers.

SL:  And before I forget I must point you to a book, which illustrates in numerous examples how the AMP is being gamed for financial gain everywhere you look: "Phishing for Phools - The Economics of Manipulation and Deception" by George A. Akerlof and Robert J. Shiller, 2015.

2.5 - Hearing - Part 2

SL:  I have annotated the block diagram for the Association Model of Hearing to help explain it.
Let's assume we are at a cocktail party. There are groups of people and everybody is talking. That is a lot of noise or air vibration, all of which carries information. Since you always wanted to talk to Fred about your speaker project, you seek him out in the crowd of people, and move towards him, to engage him in a conversation. You call out his name, to get his attention.

SL:  By now being close to Fred you are in a different Gestalt of the cocktail party, than you were in, when you looked for him. But it is still terribly noisy and you have to turn your right ear towards Fred to understand him. Fred's voice and words have your attention and you positioned yourself optimally to discriminate against other voices.

By doing so your right ear receives a higher signal level and more high frequencies from Fred's voice than your left ear, because your head blocks sound from reaching the left ear. The electrical signals from your ears have been coded with spatial position of your head and with your spatial position in the room relative to all sources of noise/sound/voice.

By associating the spatially coded information from the ears with stored memories and learning, the air vibration Gestalt is recognized as Fred's voice and many people talking at a cocktail party. The brain also knows how to correct for the unequal signals at the ears from Fred's voice, so that he sounds the same in timbre, whether you look at Fred or turn your head.

Such spectral correction of ear signals is important for tracking the location of a moving source, which has drawn your attention, relative to other sources of sound, which could be real or could be reflections coming to you from the environment of the moving source.

See: A model for rendering stereo signals in the ITD range of hearing

Turning of the head is used to determine the direction from which a sound is coming. The ears are spaced by about 17 cm = 2r, which corresponds to half a wavelength at 1000 Hz. That corresponds to 180 degrees of phase shift between ear signals. A signal, which reaches both ears from an angle a will have a phase shift between the ear signal outputs to the brain. Below 1 kHz the phase shift is unambiguous, but above 1 kHz a polarity reversal will bring back the same phase shift. Nature prefers the path of least resistance and so uses phase shift only below 1 kHz for finding direction. Actually, it is the inter-aural time delay, ITD, the group delay below 800 Hz, which is used.  Above 2 kHz it is the ILD, the inter-aural level difference due to head blockage for higher frequencies, which is used to find sound direction.

The spatial coding that takes place in the outer and inner ear is quite fascinating.

From:  David M Howard & Jamie Angus, "Acoustics and Psychoacoustics", Focal Press, 2006, Chapter 2.1

The pinna of the outer ear collects the N superimposed sound streams and combines them into a single stream in the auditory canal. The air pressure variations in the auditory canal move the eardrum, the tympanic membrane. The middle ear is essentially an impedance transformer, which converts the pressure variations in the air of the ear canal, to pressure variations in the fluid, which fills the Cochlea.

See also:  J. Blauert (Ed.), Communication Acoustics, Springer 2005

Fitz:  So far, so good.

SL:  The drawing above shows four sound stream excerpts and coming from different directions, A, B, C and D versus time markers 1, 2, 3, 4, 5 and 6. 
The dots represent pressure peaks of an acoustic Gestalt G1(t, p, L), which means G1 is a function of time t, of air pressure p, and of location L of the outer ear in space.
In the ear canal location L1 the four streams are converted to pressure variations p1(t, L1) by summation of the four streams. 

The middle ear couples the ear canal to the cochlea by levers, i.e. by a mechanical impedance transformer, which increases the force generated by the eardrum motion to push with greater force on the fluid in the cochlea and to set up a traveling wave.

The wave travels over a basilar membrane, which responds to the spectral content of the wave. The beginning of the membrane generates electrical impulses in response to high frequency components and the far end of the membrane responds to low frequency content.  The auditory nerve strand, which takes the electrical signals from the basilar membrane to the brain now carries both sound pressure information p1(t, L1) and frequency information F1(t, p1). The brain can turn the head and thus get another data set. From all that information and in connection with associations we recognize the Gestalt G1.  

• Gestalt recognition is based on CUES 

• Two ears with fixed separation, and an obstruction between them, sample the sound-field of the original acoustic Gestalt. 

• The sampling points can be turned and moved, thereby encoding the input data with spatial and spectral information cues

• The brain decodes the incoming data streams by association with cues from memory

• The recognized Gestalt is always SUBJECTIVE and is a sampling of the original acoustic Gestalt combined with ASSOCIATIONS

• What you hear is subjective

How do you respond?
Why?

GRACE
=======  to respond without resistance  =======
  BEING  

SL:  Remember, earlier on we talked about the Zen master asking the student about the sound of a falling tree, about one hand clapping, and about the student asking:

"What is the essence of Buddhism?" And the master answered: "No Self, no problem!"

Fitz:  Yes, and I said: "That gets heavy. Let's talk about hearing".

SL:  Hearing is part of life and living. So if you ask me:  "What is the essence of life and living?",  
the answer is: "to respond without resistance".

2.6 - In summary

A cultural aspect to spatial hearing:

From:  Barry Blesser & Linda-Ruth Salter, "Spaces speak, are you listening?", 2007

Reading material and sound examples

Daniel J. Levitin, "This is Your Brain on Music", 2006
David M. Howard & Jamie Angus, "Acoustics and Psychoacoustics", 1996, 2006

Sound examples:
Ripping paper
Guitar
SFO streets  
Symphony exit 
Applause and inverted applause
Audio productions

Information processing

From:  James V Stone, "Information Theory - A tutorial introduction", 2015

From f-input channels via two bitstreams to h-output channels
and with preservation of spatial information

From: Clemens Par, "Rationalism versus Empirism", 2014

SL:  That should be enough for now about Acoustics and Hearing and it becomes time to continue with:

3 - Acoustics and Mechanics

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