omenti

beyond abracadabra

More than a few in my line of work, particularly those from the generation before me, are amateur musicians.  The first time it became clear to me was in Gale Dick's living room on Friday evenings. He loved to play the violin and had a nice homemade harpsichord as well as a piano.  Friends would come to play, or in my case just listen to, chamber music.  Regulars included a couple of physicists, a mathematician, a chemist, as well as some real musicians who seemed to enjoy themselves anyway.  It was great fun and the beginning of a life-long addiction to live music, even though I'm just a lurker. 

 

Years later I asked Gale if he understood the connection.  He paused and then replied Bach letting it sink in before elaborating.  Bach ... you see, so much of it has beautiful symmetries...   He recalled when he was coming to grips with group theory in grad school.  The year before he'd come across Noether's Theorem and was blown away.¹  Years later, deep into the thicket of a difficult problem,  he found himself playing a Bach violin sonata in his mind.  

Then magic crackled and the work I was doing connected rather profoundly to those other areas. 

Words came easily to him and new ones, or at least ones I couldn't find in the dictionary, would appear.  As he described the violin sonata sequence, one I hadn't heard before appeared:

You see, Bach's music is this abracadaptor that connects two different kinds of magic giving birth to something that is also magic.

 

That was a long time ago.  Years later I found myself giving a talk at Disney Animation.  After lunch I spent the afternoon chatting with a number of people.  Then it happened.  We were talking about the curious physics that often appears in cartoons.  He said that Walt Disney had a set of rules that defined how things moved in his world building.  The rules are good enough that most survive intact. 

They're the abracadaptor that connects the original story with the artwork.  When it's well done the resulting magic is better than what went into it. 

 

Today I found myself using it in a text message to Sarah.  The beach volleyball season that ultimately determines selection for the Paris Olympics begins in Doha tomorrow.  She and her new partner Sophie have only been playing together for a short time and are still working things out.  

You’re armed with some new knowledge and are likely making great progress putting your abracadaptor into regular operation.°

° abracadaptor. n. - A mechanism or technique that connects two different kinds of magic.

 

There are people who do this: that rare skill that allows them to connect the conversation of those with very different backgrounds creating a deep and wonderful communication.  It's a skill I lack and I'm in awe of the few who can do it.  I like to use some engineering terminology to describe these people - impudence matches.  At its highest level two different magics are connected creating something deeper and an abracadaptor is afoot.

 

__________

¹ Don't worry about either of these if they sound foreign.  Both are important tools in the study of symmetry and deeply connected with physics.

 

beyond 88

Yesterday Om pointed out that it was piano day - the 88th day of the year honoring the 88 keys of most pianos.  I read his post a day late, but there's still hope for another celebration with the same name. An obvious choice might involve the Bösendorfer grand where options include 92 and 97 keys in addition to the normal 88.  Music has been written for these beautiful instruments, but why stop there? 

 

Press a key on the piano and a hammer strikes one or more strings which begin to vibrate producing a sound.  The frequency of the vibration depends on the length of the string with longer strings vibrating at lower frequencies.¹  The left most key causes the longest string to oscillate 27 times per second - 27 Hertz (Hz) - while the right most key produces a 4,186 Hz frequency.  In between the keys are divided into 7 octaves, each composed of 12 keys.  Each octave doubles the frequency so the C above middle C has a frequency twice as high. The notes are evenly divided so each key has a frequency 2^1/12 times - just under six percent higher than the preceding key. 

 

Now we're ready.

 

Let's say you wanted a piano with the range of human hearing - usually given as 20 to 20,000 Hz in young children.   Going from 4,186 to 20,000 Hz, after a bit of arithmetic, requires 27 extra keys on the right.  Five keys on the left will get you to 20 Hz..   One hundred and twenty keys and some long arms would be sufficient to entertain young children to the limit of their range.

 

But what about dogs?  Canine hearing goes up to about 40,000 Hz.   All  we need to do is add an octave, or 12 keys, to cover their range.   Other mammals can hear even higher pitches.  Bats top out around 160,000 Hz so we add two more octaves giving us a 156 key instrument.  We don't have to go much higher as the atmosphere strongly attenuates higher frequencies. A bat can produce a very loud noise, but even their sensitive ears are only good for a 20 meter range.²

 

We've left out elephants which go down to about 12 Hz - that works out to 9 keys on the left. We've grown the beastmaster piano to 165 keys.   I won't cover whales because pianos don't work underwater. 

 

The game can go on.  There are any number of natural sounds of lower frequency (infrasound), but we'll leave it at that..  

 

Well - almost.  There are very faint sounds in the universe - ripples that move compress and expand space-time itself.  They come across a wide range of frequencies, but exquisitely sensitive instrumentation is required for some of the loudest - like colliding black holes where the energy that goes into the resulting gravity wave can be the equivalent of several solar masses.   It turns out the frequency of the first one detected was a chirp that went from about 35 Hz up to about 250 Hz (close to middle C).  You can play the signal as audio.

So much information there, but it may not be pleasing so let's end with one of the most demanding pieces for the human voice - in this case a coloratura soprano.  The Queen of the Night in Mozart’s  Die Zauberflöte. 

I'll leave you to find some good piano music today.  Perhaps Om's list is a place to start. 

_________

¹ It also depends on the mass of the string, its diameter and tension.  Additionally a rich set of other frequencies are produced giving the louder central frequency richness and character.  There's a good deal of art in the design and construction of a fine piano and none of the sound the same. 

² It's a feature.  Longer range would confuse them with signals from other bats, plus they tend to work a few meters from their prey.

 

invention

a minipost

I've heard Yasmin Williams a few times  She's an exceptionally inventive guitarist and NPR's Tiny Desk Concert series has featured her a few times.  Here's her latest visit.  

 

(definitely go fullscreen to watch her technique.  Fullscreen doesn't work in some browsers, so go to the NPR link above for their version.)

 

Invention is often a mixture of curiosity and just playing around with things.  The process can seem opaque if it's outside your field, but it's basically playfulness. It's at the heart of art, literature, music, science, technology, sports and much more.  It moves civilization.  

 

 

very light narrative structures

I first heard about Norwegian Slow TV a decade after it began.  I watch a half hour of one of the rail trips. It didn't do anything for me.  Other than hearing about other hits like chopping wood and knitting, I almost forgot about it.  Two months into the pandemic I found my watching a semi-live train trip across Norway.  Much of the  scenery was similar to where I grew up and I found myself watching.   It wasn't long until I found myself daydreaming, creating my own narrative to match the flowing images.  Two hour later I stopped a dream-like story in my head.  

 

About four in the morning the next day I was jolted out of bed with an interesting approach to some physics that I had abandoned months before due to lack of process.    Having your mind work on something when you're not working on it is well known.  I suspect the neural connects I had was making in the narrative I was writing in my imagination had a good deal to do with it.   

 

This morning I caught an episode of Invisibilia that dives into the subject.  Recommended if you have an interest in narrative in any form.  Slow TV is an hours or days long TV show without plot, characters, or tension.  How Norwegians responded as a shared experience is the most fascinating part

I've done a bit of work in remote audio ambiances.   A few created serendipity.  Here's an excerpt from an old post on one:

 

5:25 am - excellent!

 

I brush the last of the snow from my coat and switch on the lights before taking my seat.   few minutes of silence and then a door opens and closes reverberating for about three seconds.  The clicking of shoes echoes through Warner Hall as she makes her way to the bench.  A minute of preparation and then the Praeludium in G by Bach fills her space and mine.  I sit back and shut all but the Bach from my mind.

 

She's doing an excellent job until - rats.  Bach derails and I sit up in my chair looking around.  A female shout fills the space reverberating for about three seconds.

 

sh*tttttttttttttttttttttttttttttttttttttttt!

 

She goes back a few bars and dances through the problem smoothly.  Now a piece I don't recognize, but it is still clearly Bach until about 6:55.   Her shoes and coat go on and steps click to the door in the distance.

 

And a little magic as a female voice is softly singing Bach.

 

A door opens and closes.  The reverberation is about three seconds and then silence. Time to switch off the amplifiers and make some hot chocolate before getting to work.

She was an organ student in Oberlin and I was in a special room in New Jersey where we were working on the reconstruction sound fields.  A special seven microphone array had been installed in the hall with a computer handling compression mixing and compression in realtime.  The bitstream made traveled eastward to our room where a reasonably convincing illusion of the hall's sound space was created.  We had created a virtual acoustic reality.

 

a shot echoed in the dark

   Our guide, the Director of Development for The Cleveland Orchestra, noted how difficult it was to find matching marble for the lavatories.   There were only two of us and we wanted to set up in the main hall, but impressions must be made and little was being spared in the big three year remodeling job. 

 

Cleveland's Severance Hall is a remarkable place.  A odd mash-up of Art Deco and Egyptian Revival architecture, it was finished during the Great Depression and became home to The Cleveland Orchestra.  Like many symphony halls the acoustics were bad boarding on terrible.  Remodeling a few decades later partly fixed the problem, but in addition to rendering the pipe organ unusable,  was architecturally "wrong."  The work underway when we visited would address all of those issues and make the space one of the best concert halls in the world. 

 

Our company was doing quite a bit with digital music at the time.  There was a relationship with the Rock and Roll Hall of Fame and another with the Oberlin Conservatory.  Two of us who were doing much of the Oberlin work developed a relationship with The Cleveland Orchestra and Telarc Records on the side.¹  At the same time work on sound field reproduction was a serious research topic.

 

The idea behind sound field reproduction sounds simple enough. If you've ever been around live music - or even in a recording studio - you've probably noticed your home equipment can't begin to reproduce the acoustic experience.  The problem stems from the fact that the wavelengths of the sounds we hear range over three orders of magnitude and much of it is similar in size to musicians, audience members, seats, curtains, the room itself, etc etc.  These sounds are reflected, refracted and absorbed.  Moving anything causes a change.  It's a difficult problem that the music industry and Hollywood would love to see solved.  Plus it's an interesting problem!

 

The approach we were using had a microphone array on a tripod.  One up, one down and an odd number between them in the same plane as the floor.  Severance was undergoing acoustic tuning and we were going to set up the array to record some music to compare it with other techniques.

 

We were left alone in the open hall. It was very quiet so I did the obvious thing and clapped my hands once.  There was a lovely echo coming from everywhere at slightly different times.   If we recorded an even better "clap" - an impulse function - we could mathematically play with it and create a signature of the room.²  Armed with this we could have some fun.  We needed to create a good enough impulse.

 

Severance Hall is on the grounds of Case Western Reserve University - a lovely area with good restaurants and a lot of art and music.  (if you ever stay in the area get a room in Glidden House - fantastic little hotel).  I figured the school probably had an athletic department and quickly found a track coach.  I was able to talk him into lending me a starter's pistol.

 

Later that night in the darkened hall a shot rang out - only to be captured digitally.  Then a few more just to make sure there was enough.

 

Back at the Labs we had a special acoustically isolated room - an acoustically neutral room (these are rare and not cheap!)   Using the same microphone array that was used in Severance Hall we recorded some live music with musicians in the area.  The music was convolved with Severance Hall's signature and then mixed down to six channels for playback in the room.  

 

It was fairly convincing..  close your eyes and it really felt like the place the shot rang out in the great hall.   Of course you can do better, but it was a great excuse to have a bit of fun.

 

__________

¹ Over the years I’d spent some time worrying about image and sound quality. At one point I thought better was - well - better. My epiphany came in the a perfectly restored 66 red Mustang. It was near Cleveland with the head recording engineer from Telarc Records and a seriously good musician from the Oberlin Conservatory. We were talking about where music reproduction might go with sound field reconstruction and dramatically more information than CDs could provide when a favorite Beatles tune came up on the 8 track (gasp! - it *was* an authentically restoration). The volume came up and the two of them were singing along to the music in pure delight. There is something transcendent about the music - even with awful reproduction in that noisy environment. Portable music players with cheap headphones would be good enough for most. As long as there's a personal touchstone.

²  take its Fourier Transform.

a thread of music

Today is Beethoven's 250^th birthday.  

 

When I was fifteen my big Christmas present was a Norelco cassette tape player.  Pre-recorded tapes were too expensive for me back then so I used its not so great microphone to record music from the family record player.   My Dad had developed a taste for Italian opera along with Tchaikovsky, Rimsky-Korsakov, and a few other late 19^th century composers.  He wasn't  a fan of the classical or earlier periods, but his collection had a smattering from those periods too.  I placed an LP of Beethoven's 6^th Symphony and started recording.  

 

The tape that came with the recorder could record thirty minutes and had to be turned over halfway through, but that didn't matter.  I found myself listening carefully ... much more carefully than usual.  The recorder didn't do a good job on music, so I went back to the LP and listened again.  And again.  Aside from eating M&Ms that's probably all I did that afternoon. 

 

I'm not very good at playing musical instruments but have a history of concert-going.  My first year of college was in Salt Lake City at the University of Utah.   The Utah Symphony had a special offer for college students - the full concert season for fourteen dollars.  The performances were in the Mormon Tabernacle - an acoustically "bright" ellipsoid and perhaps the worst acoustics of any major concert hall.  My regular seat was a focal point for one of the bassoons.  Around the same time I managed to invite myself to a professor friend's Friday evening chamber music evenings.  The hook was set. 

 

The next school was in Pasadena.  Southern California had a lot of great music, but it was impossible without a car and money.  My lifeline was an FM radio.  Grad school turned out to be more interesting.   Stony Brook's  music department was home to The Beaux Arts Trio - one of the world's great piano trios.   Somehow I managed to find my way to more than a few master classes of a good friend who was a cello major.  In my third year things got a bit out of hand. Another grad student and I decided to start a concert series.   In retrospect being naive was a feature.  Somehow we found half of what we needed from the President's office.  It occurred to us the Graduate Student Association could help out, but they had other ideas.  We took matters into our own hands by running for the student senate.  As senators we  pushed for funding again and to our delight managed to get it on a narrow vote.  These things only happen to beginners and fools.    The auditorium we had for the first concert was directly over a bowling alley.   The second concert went more smoothly and by the third it was almost easy.  We even managed to turn a small profit selling out our last eight concerts. Others took over when we left and, excluding this year, the series is still going strong.

 

I need to listen to music carefully and find background music distracting.   The presence of live music is important and, although I'm missing physical presence, live performances during the pandemic manage to give some of it.  My home audio equipment isn't very good, but I've learned performances are deeper than their reproduction.  Books with stained pages are often just fine.

 

In the eight grade we had to take an occupational aptitude test.  My results predicted a poor match for any of the areas, so they had me take it over again.  The results were the same.  Next we had to write an "occupational monograph" on two types of work we were interested in.  The ones I picked weren't on the list, but turned out to predict what I eventually went into.

 

Several of the long journeys I've been on began in my teens. . That tape recorder on a Christmas day set me on one of those journeys What's fascinating is they've turned out to develop in way I couldn't have imagined.   Other threads developed later, but I wonder how many major ones develop then.

 

Today I'll pull out Dad's old LP with  Beethoven 6^th Symphony encoded in its spiral grove.  An RCA Red Seal re-issue of Toscanni and the BBC Symphony Orchestra, it takes me back to that first listen, to it's performance years before and even to Beethoven's writings.    It's amazing how you seem to always find something new every time when you really listen.   Celebrate the day by picking one of your older paths and doing it deeply - Beethoven won't mind if it isn't music. 

 

there were always roads

I had the pleasure of chatting with and, more importantly, listening to Rhinnon Giddens.  She's become well known for tracing the importance of African Americans in music and, at the same time pointing out origins are complex and probably too complex to disentangle.

 

She's a singer, composer, and a fine claw hammer banjo player.¹  These days the banjo is most associated with the white South.  It turns out it came from the Caribbean with slavery and was almost exclusively a black instrument until the 1830s and 40s when white America started to absorb it. From there you can follow it back to Africa and from there to the middle East.  

 

Here she plays an Appalachian piece with Francesco Turrisi accompanying on  a middle Eastern frame drum.

Oddly enough the Irish bodhrán is a very recent instrument based on frame drums from the Middle East - so it fits.  

 

Many - probably most - of our musical styles have has roots elsewhere.  These ancestors also have roots and interconnections.  Trade created a cultural connection machine that made its presence known to people who had no idea where the influences were coming from.  It doesn't take too many people to show up on another shore something new - what can seem like straight-up magic.   Then culture takes and modifies what it finds as it grows.

 

There is no unique source or single direction.  

 

There were always roads...

__________

¹ She's also a MacArthur fellow.  Her music is powerful.  You need to listen.

 

finding the right position for the slider between education and vocation

William Rowan Hamilton had become obsessed with the idea of a three dimensional number system - sort of analogous to complex numbers being a two dimensional system.  The story he later told was every morning his son would say 'papa, can you multiply triples?' to which Hamilton would sadly shake his head and say 'no, I can only add and take away'.   Then, on a walk on the 16^th of October, 1843, he  crossed the Broom Bridge in Dublin and suddenly knew how to do it.  Rather than adding a single dimension to the complex plane, he'd add two giving three imaginary dimensions and one real dimension perpendicular to them.  In his excitement he carved it into the bridge with his knife:  i² =  j² = k² = ijk = -1

 

He called them quaternions.  They had some use in the day, but when people invented linear algebra, the technique fell by the wayside ... that is until quantum mechanics  came along about eighty years later.  And then computer graphics further down the road.

 

It turns out they're a lovely way to think about quantum mechanics and perform real calculations. Erwin Schrödinger knew enough about forgotten math to realize it was a beautiful gem.  Decades later, trying to improve the speed of computer graphics, a physicist realized they could be a key to quickly calculating rotations in space -- and Tomb Raider became the first computer game with smooth graphics on using relatively primitive personal computers.

 

Hamilton had other accomplishments that deeply impacted physics and math, but the quaternion story has a certain romantic element. To this day physicists gather at the Broom Bridge on the 16^th of October to celebrate.

 

The story of physics is that it's extremely important to think broadly and to keep expanding your learning.  It is also is relevant to education and work across many fields today.  That's what I want to get to, but first this wonderful parody of a certain song..  perhaps the best math song ever.

 

What prompted all of this was an email with a link describing the most contrarian college in America.  It's laser focused on a vision of an education seemingly without much a nod to vocation ...  seemingly..   I'd argue that it's too focused on a narrow piece of education, but have no doubt its graduates have learned how to learn..  they have the beginnings of a real education.  Mark Roosevelt, its President, sums it up:

Education should prepare you for all of your life. It should make you a more thoughtful, reflective, self-possessed and authentic citizen, lover, partner, parent and member of the global economy.

It  takes a special kind of student to thrive in a school like that.  I wouldn't have survived - my interests, those that I was motivated to dive into, lay elsewhere.  I'm happy it exists and that there is spectrum of schools for those who look.

 

My belief is a deep education with at least a few focuses creates the second type of person Claude Shannon describes:

“There are some people if you shoot one idea into the brain, you will get a half an idea out. There are other people who are beyond this point at which they produce two ideas for each idea sent in.”

The ability to get multiple ideas is core to serious play and creativity.   I'd claim focusing on education rather than finding the minimally easy path helps create the neural connections that make this possible.

 

A worry is that many, if not most, schools and students tend more towards vocation.  Focus on what is important to get a degree that will get you employed to pay off that mountain of debt.  Many (not all) businesses, on the other hand, would do well to have broader employees who are still learning and growing - those who can think creatively.  There is a disconnect. 

 

I hope this focus on vocation changes.  The rate of real change is great and people will keep up better if they are broader and more adaptable.  When recommending colleges I tend to focus on education ..  often to the consternation of those asking.  Of course I may be a poor example.  My education was far too narrow, but I've been lucky and curious enough to have been able to expand it a bit.  The other note is you can get a wickedly broad experience at many more places than you might imagine.

 

 Finally there's this odd emphasis on over-scheduling many pre-college kids, but I've probably written on how it kills creativity enough.

 

the next step in home audio?

 Still cold from the UPS truck the Apple HomePod woke up when I plugged it in and asked my iPhone for a dance.  They spun about and chatted in their local network for a minute or two before Siri introduced herself.  It was completely unexpected surprise from a great friend who  shares the love of music.  A day into the journey I have a few thoughts.

 

I'm a poor musician, but find it an important part of my life.  Grad school was at Stony Brook.  Besides an excellent physics department one of my reasons for doing grad school at Stony Brook was its proximity to music in  New York City..  That wasn't quite enough, so two of us founded a concert series at the university that thrives to this day.  At Bell Labs it became apparent that music might be a significant driver for Internet use and I found myself walking several paths.  One was sound field reconstruction.

 

Sound field reconstruction is just the fancy way of  recreating the sound where it was recorded or engineered in your home.  In theory you record the acoustic signatures of the recording studio and your living room and create a mathematical operation that makes your living room sound like the recording space.  In practice it's approximately hard.  Sound waves are fairly large and get reflected, absorbed and transmitted by and through everything in your room.  Making matters worse the sound field at different spots in the room is usually very different and things in the room move between and during listening sessions.  We made serious progress, but it took exotic microphone and speaker arrays as well as state of the art (for the time) computing to make it sort of work.,

 

One detail is centrally important.  Imagine sitting before a simple speaker cone.  Most of the sound comes straight at you with the volume falling off as you get away from the speaker's central axis.  Speakers have very characteristic patterns showing how loud they are depending on the angle you're sitting at as well as the frequency of the sound they're producing.  If you have two stereo speakers there is usually a sweet spot where the sound reproduction is optimal.  In this area the sound field can be fairly good and you can close your eyes and visualize where the musicians are.

 

Imagine an array of speakers, each with its own amplifier, all controlled by a computer, you can control the phase and amplitude (loudness) of each speaker.  The waves they send out interfere with each other as they expand outwards.   By controlling the phase and loudness (amplitude) of each speaker you can make them interfere in such a way that they create a new wave that can be aimed.  The little animation shows an array of four speakers in a row, but it can be any number and they don't have to be in a line.  The HomePod uses seven small speakers arranged in a ring.  

(you may have to click on the animation to start it)

 

The HomePod also has a ring shaped array of six microphones.  They listen to the room (sample it) at a fairly high rate and decide what parts of the music, from its stereo signature, need to go where and how it needs be modified to interact with the room and everything in it.  An Apple A8 processor, the same two billion transistor processor used in the iPhone 6 and 6 Plus, handles the computational chores.  This is much more power than we had back in the day.  Although I don't know exactly what they're working on, several people I know who are real experts at this have been at Apple for years.

 

 

The HomePod also has a computer controlled single woofer with its own amplifier mounted vertically to handle the low notes.  

 

I'll leave the specsmanship, mechanical and most of the UX discussion to others and just talk about what it sounded like.  I'm not golden eared, but rather a serious listener.   I focus on the music and let it take me where it pleases. 

 

I listened to works across several genres with the HomePod placed at about ear height in a small acoustically complex room.¹   For very small groups - soloists and piano quartets for example - the sound stage was excellent ..  about as good as my stereo pair of conventional speakers (about $3,000 in speakers).  The HomePod didn't match the reference speakers when I was sitting at the sweet spot, but was better when I moved around the room.  That is astounding. 

 

It was creating stereo -a  term has nothing to do with a pair of anything, but rather three dimensional.  Moving  beams of audio around it was painting a sound field in my living room. 

 

As I listened to larger ensembles I found a less accurate sound field.  That said it was still comparable to my reference pair when I was away from  my very small sweet spot - its effective sweet spot was larger.   Note for some pieces of music a good $500 pair of speakers would do a better job if properly installed, but  would love to see what a pair of HomePods placed about two meters apart would do.  Apple has promised the feature will be available later this year.  I've already earmarked the funds for immediately buying a second unit then.  I suspect a pair of HomePods will blow my reference pair away when it comes to sound stage placement.   That will be even more true for those who haven't carefully adjusted their current speakers with test recordings and a spectrum analyzer. 

 

You can control it from an iPhone, iPad or Mac, but Siri is the intended interface.  I've had poor luck with Siri on my iPhone, but here it works much better.  It's also much more robust to interference.  Microphones beamform too and it's clearly listening to you doing its own cocktail party trick.   That said it, and every other interface I've seen are just wrong when it comes to classical music.

 

Comparing it to the networked speakers from Amazon and Google is silly.  Their speakers are terrible and useful only as acoustic wallpaper you listen to in the background.  They're really microphones in your home listening to you assuming you agree to Google's  or Amazon's value proposition (I don't).  Privacy is vastly different - I'll go with Apple's differential privacy rather than Google's "you are the product" flavor.   But if music is secondary and you want a digital assistant with a speech interface, Google and Amazon are the ticket.  Apple is going after the other audio companies along with making its platform stickier in the process

 

I suspect the speaker will be like the Apple TV - fairly stable hardware with the bulk of improvements coming through software updates.   My list of UI and UX issues is growing, but I suspect this will become part of my life. 

 

And a final caveat - speakers involve personal taste.  YMMV

 __________

¹ I'm very familiar with these pieces.  With one exception  I've heard them live and I've even been involved in the recording process on two. 

Ecstacy  Anonymous 4 and Mike Marshall

Us  Regina Spektor 

Seven Swans Al Petteway

The Heart Asks for Pleasure First  Ahn Trio

Black Horse and the Cherry Tree   K.T. Turnstall

The Littlest Birds  The Be Good Tanyas

Submarines The Lumineers

Pipeline (electric and acoustic versions) The Duo Tones

An Spailpin Fanach Connie Dover

The Heroic Conditions of the Universe Pt 7 After the Storm Alexandre Desplat

Turn it Around Lucius

Jolene Mindy Smith's version

Vespro della Beate Vergine: Domine ad Adiuvandum a 6 Monteverdi

Shchedrik Kitka

Our Town Iris DeMent

Sun Will Set Zöe Keating

Don Giovanni Madamina, IL Catalogo and Questo Mozart  (sort of a sign of politics)

Canon a due Violincelli in D Major Gabrielli

Cello Sonata in D Major Op 69 Beethoven

Suite No 6 in D Major  JS Bach (Yo-Yo Ma)

   

a most remarkable instrument

minipost

Let your spectrum analyzer listen to  middle C on a piano and take a look at what comes out. (guess what?  your smartphone can do it)   Most of the acoustic energy, assuming the piano is tuned to a 440 A is concentrated at a tad below 262 hertz (cycles per second), but other things are going on.  Bursts of energy at multiples of the 262 Hz fundamental  frequency paint the spectrum along with a few other bursts.  The integer multiples of the fundamental frequency are called partial harmonics and the others are inharmonic partials.  Together they form a large part of why a piano sounds like a piano - in fact why a specific piano sounds like that particular instrument - it's timbre.

The time development of a note can be very complex with the distribution of energy in the various harmonics changing as the note decays.   A really nice way to study this is with Fourier analysis.  I gave a crude non-mathematical introduction earlier, but I just came across another beautiful illustration. 

Enter Anna-Maria Hefele .  She's  a remarkable singer who has mastered the art of overtone singing.  Thanks to Richard Feynman's life-long fascination with Tuva you're probably aware of Tuvan throat singing.   Her singing is much richer.  Let's start with her voice as an instrument in this lovely version of H.I.F. Biber's Rosary Sonata 1.

 

and now a graphical look into the flexibility she has ..  simply wonderful!  Such a fine way to show off the overtones.