Pitch perfect

It's funny, sometimes, what we don't know.  I've played the flute for almost forty years -- started out self-taught (bad experience with elementary school band), then was lucky enough to study with a brilliant classical flutist named Margaret Vitus for five years when I lived in Seattle.  I've since played in three different bands and a community orchestra, and besides the classical repertoire, I've become fairly proficient in Celtic, English country dance, and Balkan music.

But it wasn't until the last band I was in, the trio Crooked Sixpence, that I actually figured out some peculiarities of my own instrument.  I was fortunate enough to play with Kathy Selby, who is not only a brilliant Celtic fiddler but a physicist (then teaching at Cornell University).  Kathy taught a class called "The Physics of Music," which combined her two areas of expertise -- and the class looked at, amongst other things, how specific instruments work.

So it seemed natural for me to ask her something that's always puzzled me; why flutes go sharp once they warm up.  The difference is greater (obviously) when it's cold out -- so the temperature increase the instrument experiences once I start playing it is bigger -- but it is noticeable even on a warm day.  On first glance, it seemed to make no sense.  Objects expand when they warm up, so (I thought) the thermal expansion would make the tube longer, and the pitch should drop, making it go flat.  That they actually go sharp seemed completely opposite to my intuition.

And of course, she immediately knew the answer; it's because sound travels faster in warm air.  Since the frequency of a wave is directly proportional to its velocity, if the sound wave is moving faster, its frequency goes up -- and so does its pitch.  The thermal expansion of the tube is minuscule, so any drop in pitch from the tube becoming longer is negligible.

I also found out from Kathy -- when I attended a free lecture on musical acoustics she gave -- why a bunch of different instruments playing the same note all sound different.  I knew that that the fundamental note (let's say it's A above middle C) has to have a wavelength that is the same length as the tube (or string, or whatever) of the instrument that's playing it.  A sound of that wavelength will set up a standing wave that then sets the air moving and projects outward toward the listener.

But a flute playing an A above middle C and a fiddle playing an A above middle C sound completely different.  The reason, I learned, is because there is more than one wavelength that fits a particular length:

[Image is licensed under the Creative Commons Allowed and forbidden standing waves, File:High School Chemistry.pdf, CK-12 Foundation]

The ones on the left "fit;" the ones on the right don't.  The top one on the left is the fundamental pitch.  The ones further down are called overtones, and that's the key to why instruments sound different.  The greater the number and amplitude of the overtones, the more the sound wave the instrument produces deviates from a simple sine curve.

Sound waveforms, top to bottom -- flute, piano, trumpet.  [Image from Doug Davis, 2002]

As you can see, flute tones are pretty simple, very close to a sine curve.  But look at the trumpet waveform.  Same fundamental pitch -- the peaks and troughs of the waveform line up with the flute's and the piano's -- but the shape is entirely different.  That's because of the number, and intensity, of the overtones.  (Instruments that have forced vibrations from a bow being dragged against the string, like violins and cellos, have a lot more overtones -- and thus more complex waveforms -- than instruments where a string is plucked or struck, like guitars and pianos.  The same comparison holds for double-reed wind instruments like oboes and bassoons, which produce way more complex sound waveforms than flutes do.)

The whole topic comes up because of a paper that was presented recently at the annual meeting of the American Physical Society, which contained the solution to a long-standing question in the physics of music; why do the pipes of an organ play a tone that is considerably lower pitched than the sound wave that should fit the length of the pipe?

Organ builders have known about this for over a hundred years; to get an organ pipe to sound the note you intend, you have to build it a little shorter than you'd expect.  (The "end correction" you have to use to make the pipe's pitch match what physics would predict from its length is equal to 0.6 times the radius of the pipe.)  But why?  Shouldn't a wave of that length be a little too long for the pipe, and be one of the "forbidden standing waves" shown on the right side of the first figure?

The key to the answer was discovered, quite by accident, by a Swiss organ builder named Bernhardt Edskes.  He was working on repairing an organ, and noticed that a tiny piece of gold plating had flaked off one of the pipes.  He only saw it because when he played that pipe, the flake floated above the top of the pipe.  But since there was air blowing up the pipe, why wasn't the flake completely blown away?

Leo van Hemmen, a physicist at the Technological University of Munich, realized that both the "end correction" question and Edskes's mysterious floating piece of gold were the result of the same phenomenon.  When an organ pipe is played, the rising column of air causes the formation of a stable vortex above the top of the pipe.  When van Hemmen used smoke to make the vortex visible, and its height turned out to be exactly 0.6 times the radius of the pipe, he knew he'd solved the puzzle.  The spinning cylinder of air creates a longer tube for the sound to resonate in -- so the wavelength of the lower-pitched note fits perfectly.

Humans have been making music for tens of thousands of years, and I find it fascinating that we are only now understanding the intricacies of what's going on inside the instruments we play.  It may be that we don't need to know the physics of music to enjoy it, but for me, it's fun to find out how complex these things are -- and that all As above middle C are not created equal.

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The fire of the mind

In Umberto Eco's masterful medieval murder mystery The Name of the Rose, we meet a villain who is willing to kill, over and over, to stop his fellow monks...

... from reading a book.

The following is a spoiler, so you can skip the next few paragraphs (scroll down to where it says [end spoiler alert]) if you haven't read Eco's novel.  Which I hope you all will, because it's brilliant.  But the punchline makes a point that needs to be made now, seven centuries after the time in which the novel is set, as strongly as it did then.

Europe of the early 14th century was a grim place, and life was, in Thomas Hobbes's words, "solitary, poor, nasty, brutish, and short."  Religion had an iron grip over people's lives, and the learned men of the time taught that the fear of god was paramount.  This fear was translated downwards into fear of the "hierarchy of heaven," as represented here on Earth by the Pope, Cardinals, Bishops, and the monastic system.  And within that system, questioning and freedom of thought was considered heresy, punishable by death.

In this system we find two opposing characters: the brilliant and curious scholar Brother William of Baskerville, and the stern and unyielding Brother Jorge of Burgos.  William is called in to solve a series of murders that have occurred in an unnamed abbey in the mountains of Italy.  The murders revolve around the abbey's magnificent library, the secrets of which are only accessible to the librarian and his assistants.  And one by one, the monks connected with the library are being picked off by someone who is bound and determined to keep some of its knowledge out of the hands of the monks (or anyone else).

The knowledge in question turns out to be a book by Aristotle that was thought lost; the second volume of his Poetics, in which he describes the proper use of comedy, and argues that laughter is freeing, proper, and purifying for the soul.  When Brother William solves the mystery, and discovers that Brother Jorge is behind the murders and has hidden the book, he confronts the old man, and asks him why it was so important to keep such a seemingly innocent volume out of people's hands.  Brother Jorge responds:

(L)aughter is weakness, corruption, the foolishness of our flesh... (H)ere, the function of laughter is reversed, it is elevated to art, the doors of the world of the learned are opened to it, it becomes the object of philosophy, and of perfidious theology...  You saw yesterday how the simple can conceive and carry out the most lurid heresies, disavowing the laws of God and the laws of nature.  But the church can deal with the heresy of the simple, who condemn themselves on their own, destroyed by their own ignorance...  Laughter frees the villein from fear of the Devil, because in the feast of fools the Devil also appears poor and foolish, and therefore controllable.  But this book could teach that freeing oneself from the fear of the Devil is wisdom.  When he laughs, as the wine gurgles in his throat, the villein feels he is master, because he had overturned his position with respect to his lord; but this book could teach learned men the clever, and from that moment, illustrious artifices that could legitimize the reversal.  

To Brother Jorge, it is worth killing, and dying, for his desperate necessity to keep others from knowing the justification of laughter, mirth, and irreverence.  And in the end, he destroys the book and burns down the library to keep that knowledge from the world.

[end spoiler alert]

Which brings us to what has happened in the Middle East in the last few days.

The depredations of ISIS have been all over the news lately, but none have seemed more bizarre and pointless to the western world as two that have occurred recently.  The Islamic State's arm in Libya four days ago burned a pile of musical instruments, saying that such things are "un-Islamic."  Then, just two days ago, ISIS members in Iraq burned the hundred-year-old library in the city of Mosul, destroying 8,000 rare books that were a treasure-trove of cultural information and history.  "900 years ago, the books of the Arab philosopher Averroes were collected before his eyes...and burned," wrote activist and blogger Rayan al-Hadidi.  "One of his students started crying while witnessing the burning.  Averroes told him... the ideas have wings...but I cry today over our situation."

[image courtesy of photographer Alan Levine and the Wikimedia Commons]

Why, in a situation where ISIS members are fighting daily to maintain ground and to keep control of the people they've conquered, would they stop what they're doing to burn musical instruments and ancient manuscripts?  It seems pointless.  Wouldn't they have better things to do with their time and energy?

No.  What ISIS is doing has its own pervasive, evil logic.

It has to do with exactly the same thing that Venerable Jorge hated the idea of: reading, laughter, and music free people from fear.  If you are going to control people, you must control their thoughts.  The first thing you do, therefore, is to destroy any opportunity for them to experience something outside of that control.

Music lifts our emotions into heights that cannot be measured.  When we read, our spirits are free to think any thought, put ourselves in other people's minds, other places, other times.  Dancing does the same thing, which probably explains why Saudi Arabia's "morality police" arrested some young men four days ago for dancing at a birthday party.

Can't have people experiencing anything outside of the narrowly prescribed range of thoughts, feelings, and actions.  If people go outside that range, anything could happen.  And would.

And then, the sword-bearing horrors who are now running much of the Middle East would not be in control any more.  People would learn that there's more to life than fear and obedience, more than living in terror of a grim, humorless cadre of thugs who are so afraid themselves of intellectual and emotional freedom that they will stop at nothing to prevent it from spreading to others.

I live in hope that in our world of interconnectedness and free flow of information via the internet, such control cannot be maintained for long.  We have seen the difficulty the Saudis are having in keeping the holes in the dam from leaking; bloggers and activists who openly criticize the regime are growing in numbers.  Some, such as Raif Badawi, have paid a horrible price for exercising that freedom.

But the truth that ISIS doesn't want their victims to realize is that the spirit of free thought burns hotter than the flames of destruction.  Even if you set fire to books and musical instruments, you can't really control thoughts, even through threats and terror.  The human mind is stronger and more resilient than that.  So even though I weep for the treasures that were lost in the burning of the Mosul Library, I remain optimistic that the desperate and amoral men of ISIS will one day be trod underfoot and forgotten to all but historians, just as their brothers-in-spirit -- the Inquisition of the 14th century -- have been.