Inventing a musical instrument

When I was a medical student, I had a neighbor named Danny who lived across the street.  He was young and brilliant with computers, and he played the violin.  But he had one ambition that puzzled me: he wanted to invent a musical instrument.

Glass harmonica

In my unmusical way, I tried to imagine what a new instrument might be.  What family would it be in, I asked Danny: wind? string? percussion?  He just shook his head.  I disappointed him by thinking within the grooves of old paradigms. But the only instrument I could think of that really broke out of these categories was the glass harmonica.

The truth is, I don't know if Danny ever invented his instrument, but this evening I heard a story on NPR about John Cage (1912-1992), who played an important role in avant-garde art and music.  His most famous musical piece, perhaps, is 4'33," a piece where the musician sits at the piano not playing for four minutes and thirty-three seconds while the (initially puzzled) audience hears ambient sound.

John Cage

Cage, whose hundredth birthday would have been today, also experimented with "new" instruments, which were essentially variations on old ones.  For example, he used the "prepared piano," which is a piano with various objects stuck between the strings.  This instrument combines piano notes with percussion. Presumably a musician could do the same thing with a guitar or even a harp. People can also strike their fist on the strings of the piano or click on the keys of a woodwind instrument without blowing into the mouthpiece.  According to Wikipedia, some even put a saxophone mouthpiece on a trombone.  But none of these would have satisfied Danny; they're all just variations.

A new way of producing electronic music might have satisfied him, but I think he was looking for something simpler and more concrete, a new way of creating vibrations. In place of a vibrating string, drumhead, or air within a column, why not ball bearings rolling in a pot or balloons of different size rubbing together... or... or... well, you think of something.

Morris dancers - an inspiration for the miners of Lexicon?

In THE ICE CASTLE, a half-crazed hermit sits deep in a cave trying to invent musical instruments.  In fact, he's trying to re-invent them in a society that has banned them.  He ropes Ivan, one of the novel's protagonists, in to help him.  Ivan is frustrated to realize that although he's familiar with lots of musical instruments at home, he hasn't examined any of them closely enough to draw one or fully explain how it works.  Now there's a thought experiment: if you were stranded in a completely alien culture, could you show them how to make the musical instruments that are so familiar to us?


In the end, with the help of an ancient manuscript, some mathematics and some experimentation, Ivan succeeds in helping the hermit.  He figures out the principle behind tuning stringed instrument. Ivan and his friend Fort also find a way to make an entire band of miners, dancing with bangles on their wrists and ankles, into a kind of group musical instrument.  I guess in the end Ivan did invent a new musical instrument--and so did I.  I just haven't tried to play it yet.

How common is perfect pitch?

Perfect pitch, the ability to recognize (and usually name) a musical note heard without reference to any other note, is considered rare and special in the western world.  A common estimate is that perfect pitch in found in only one person in ten thousand in the US and Europe.

Perfect or absolute pitch is more common than that among singers and musicians, including Julie Andrews, Beethoven, Chopin, Mozart, Jimi Hendrix, Bing Crosby, Yo-yo Ma, and many more. (See one list here.) Perhaps half the musicians in a symphony orchestra can identify a note by name when it is played alone.  Is perfect pitch a marker of musical talent?

Chopin at the piano

Probably not.  True, musicians with absolute pitch can tell whether a tune is played in the key of A flat or B flat.  Their ability to distinguish notes by name probably leads a different esperience of music, allowing them, for example, to unconsciously associate colors with particular pitches.  In practice, however, playing music is more about patterns and relationships among notes than it is about the names of the notes.  Skilled musicians can easily transpose from one key to another. 

It turns out that relative pitch - the ability to tell how far one note is from another - shows up later on the evolutionary tree than absolute pitch. Birds and many mammals recognize particular notes.  Songbirds, for example, can recognize a series of notes, but if the researcher transposes the notes up or down by a couple of steps, the birds are completely flummoxed.

Recent research has built on this bird research to demonstrate that many more people have absolute pitch than previously thought.  In the past, researchers asked subjects to name notes they heard.  People untrained in music can't do that - they don't know how to label the notes they hear.  But if a researcher asks people untrained in music to sing a well-known folk song, many will sing it in the correct key.  That is, they retrieve and produce the "right" starting note, even if they can't name that note.

So it's hard to test for absolute pitch among non-musicians, because they can't "name that note." Researchers at the University of Rochester have found a way around this problem.  Elizabeth Marvin and Elissa Newport taught non-musicians a short string of notes and then asked them to identify this sequence when it was embedded in a longer melody. Musicians with absolute pitch and many non-musicians tended to identify the sequence of notes when it was played in the right key but "miss" it when it was transposed into another key.  That is, those with absolute pitch were relying (like birds) on identifying the exact pitches they had learned rather than the pattern of notes.  

Perhaps, then, the fact that absolute pitch is more common identified among musicians than among non-musicans simply means musicians know the names of the notes they hear.  But again, it's not that simple. Researchers in the US and China have studied absolute pitch among music students in the US and China.  Their findings are clear: absolute pitch is more common among students who began their musical studies earlier.  Starting at age four makes absolute pitch much more likely than starting at, say, age eight or nine.  But an even more striking finding was that Chinese students who started learning music at any age were many times more likely than American students to have absolute pitch.

The researchers hypothesize that tonal languages such as Chinese, which require young children to hear and reproduce different pitches for different meanings, help children develop a stronger sense of pitch.  Growing up with a tonal language is like starting musical training at birth.

Perfect pitch and the question of musical nature vs. nurture play important roles in the society of the Land of Winter described in my novel THE ICE CASTLE.  Only students with perfect pitch can graduate from school and enter the highest ranks of society.  Children of the rich and privileged are raised with music all around them. The poor, on the other hand are discouraged from making any kind of music, and musical instruments are banned.  The society strongly believes that musical ability is an inborn marker of virtue and nobility, and the rich and powerful create a self-fulfilling prophecy where the children of the poor are very unlikely to show evidence of such ability.  Kids deprived of music are less likely to develop absolute pitch, and even those with this ability will be unable to demonstrate it without musical training.

Is there any analogy between the way the citizens of the Land of Winter approach the question of musical talent and the way we in our society approach other aspects of intelligence?  Musing on that question is left to the reader.  Meanwhile, to test your own relative pitch, check here, and to learn if tone deafness is real, visit here.

Testing your musical hearing

I just ran across a great game for testing your ability to hear notes and intervals.  Give it a try and tell me what you think.  I'm not very good at it, but I have the feeling that if I played for a while, I'd improve at hearing and remembering intervals.

For an more complicated online version of the old game Simon, which gives light and color cues as well as sounds as it challenges you to reproduce a tonal pattern, visit the Games page on my Lexicon Adventures website and look for Tone Memory.

Are You Tone Deaf?

a broken and fallen note

Are some people truly tone deaf?  Sure, there are plenty of people who can't carry a tune.  I'm one of them.  But what is tone deafness, and is it real?

According to scientists who study tone deafness, about 5% of people have a significant handicap in hearing and learning music.  The root disability appears to be a difficulty in distinguishing different pitches.  The smallest step of the Western scale is the half step, one-twelfth of an octave. (Indian music uses smaller units of pitch change.) People with amusia have difficulty distinguishing differences as small as that half-step, although they may hear much larger pitch differences accurately, sort of like being able to see the largest letters on an eye chart.

Perhaps about half of those with tone deafness also have difficulty hearing rhythm in music.  They're lousy dancers and even falter in tapping along in time to the music.  They also have impaired memory for music.  They are only half as good as other people in naming a familiar tune.  Often they recognize a song by its lyrics instead of its melody.  Even when they try to memorize a stretch of music, they have difficulty recognizing it when an examiner later plays it back to them. Although most tone deaf people can tell if a piece of music is meant to be happy or sad, many don't particularly enjoy music, and some find hearing it actually painful.

Interestingly, the disability in amusia appears limited to music.  Tone deaf people have little difficulty recognizing intonation in speech.  For example, the difference between a question and a statement is often only a difference in pitch at the end of a sentence. (Think of "You're coming," versus "You're coming?") These differences are large enough that most tone deaf people have no difficulty with them.  (However, I'm not aware of any research on how well tone deaf people learn tonal languages such as Chinese.)

In my latest fantasy novel, THE ICE CASTLE: An Adventure in Music, tone deaf people are relegated to the lowest ranks of society.  Ivan, one of the protagonists, difficulty distinguishing musical pitches, but through careful and attentive listening, he gradually improves over the course of the story.  Such improvement may not happen with the most severely tone deaf, who even after growing up in a music-rich environment or taking music lessons in childhood show no improvement.

I'm fascinated by tone deafness because I fall pretty clearly into that range myself.  My elementary school singing teacher urged me to sing softly or only mouth the words in school performances, but it wasn't just a matter of not singing well.  My father told me that when I was young, if he played two notes on the piano and asked me which was higher, I couldn't tell the answer.  I remember lying in bed on Wednesday nights listening to his madrigal group sing, trying to figure out from the beat whether the song might be one I "knew," like "Yankee Doodle" (a song which, I later learned, madrigal groups sing very rarely).

Gradually, as I got older, the condition's severity lessened.  I took piano lessons for a couple of years, and in high school, where I played the clarinet, I finally learned enough to be able to tell when I hit a wrong note.

Around high school I realized that one reason it was difficult for me to appreciate orchestral music is that I couldn't grasp the idea of musical "theme."  I could never remember previous phrases well enough to notice when they returned with variations.  In listening to unfamiliar music, I was condemned to a perpetual present. It was like trying to read a novel when the characters are always someone you just met.

I did learn, however, that with careful listening, I can more or less blend in with other singers.  With lots and lots of repetition, I can even carry a few phrases of a simple tune on my own.  Even as young children, my kids, all of whom grew up to be fine singers, sometimes asked me to stop singing. I still can't hear when a song on the radio changes key, and I often can't identify a familiar song until the lyrics start.  If I lived in a society where musical intelligence mattered as much as verbal and logical intelligence, I'd be classified as subnormal.  Exploring such a world, where tone deafness is an unsurmountable social handicap, furnished a big part of my motivation for writing THE ICE CASTLE.

Boy singers and an earlier voice change

We all know that boys' voices change during adolescence. Now we're learning that the embarrassing tendency to squeak when speaking may be occurring ever earlier. Currently, a boy's voice starts to change around age thirteen, and a boy is likely to speak in his adult male voice by age fifteen.

Franz Hals - Two Boys Singing

But the voice change hasn't always come so early, as the Washington Post reports. Records from Liepzig's St. Thomas Boys Choir, which is 800 years old, suggest that in the first half of the 1700's, when J.S. Bach led the choir, most boys' voice change began at age 17 or 18.  Moreover, during wartime, when hunger was common in the city, the voice change began even later.  So maybe better nutrition accounts for today's falling age of male voice change.

On average, the pitch of a male's speaking voice falls by about one octave as he passes through adolescence. Singing teachers have assured me, however, that a boy's adult singing range cannot be predicted from his childhood range.  You can't assume that an alto will become a bass while a soprano will become a tenor.

Voice change can be a challenge for all chorus directors, not just those in an elite boys' choir like Liepzig's. As boys' voices become less predictable, they also lose some ability to sing on pitch and sing intervals correctly. Their vocal range may also simply contract for a while. Boys may become discouraged and drop out of a choir or school chorus. Directors of a middle school musical may find their male lead suddenly unable to sing the part. Girls may have to fill boys' roles because too few boys are willing to risk singing.

To me it's telling that we talk about boys' voices "breaking," not just changing.  Maybe the term reflects  our unconscious sense that our sons' adolescence is a loss -- loss of innocence, loss of closeness, loss of beauty and loveableness.

In the Land of Winter, the imaginary setting for my middle grade fantasy THE ICE CASTLE: AN ADVENTURE IN MUSIC, singing ability is each person's defining characteristic, determining social class and educational opportunity. Although I don't directly address how this society handles boys' voice change, I doubt that it does so with any great compassion. After all, there is no place in society for the visitor Ivan, who sings badly. And when Fort, a talented singer, finds his voice ruined by a botched throat surgery, his adoptive family throws him out of the house.

In some ways, THE ICE CASTLE is a parable of the passage through adolescence, where voice change is only one of many troublesome changes. Other signs of passage touched on in the book include increasing independence from parental control, learning to see beyond one's own excessive self-regard, and learning to delight in creativity and invention.

In reality, most chorus directors and singing teachers nowadays encourage boys to keep singing through the voice change. They allow boys to change parts or select music with a narrower range and less challenging intervals. Even if they decide to let the boys take a break, they assure them of their place in the chorus and welcome them when they return.

The choir directors of St. Thomas may rush to fill boys' heads and voices with as much musical knowledge as possible between ages 9 and 12, but that doesn't always work even with music.  Most parents and teachers know that adolescence comes upon our kids before we or even they are ready for it. All we can do is hold their place, keep teaching, and work to assure them that adolescence is a continuation of growth, not a sudden break from childhood.

THE ICE CASTLE launches

THE ICE CASTLE: AN ADVENTURE IN MUSIC, second in the Lexicon Adventure series, officially launches this week, and I'm truly excited.  It's a beautifully printed book, and I'm attached to the story and the characters.

The book opens in December. Aunt Adelaide is ill, and the family gathers, including Daphne and Ivan's younger cousin Lila, a gifted singer. Lila stumbles into Ivan and Daphne's secret land of Lexicon, and in an attempt to rescue her, they follow her into the snowy Land of Winter. Kidnapped by nomads, they are delivered to the town of Capella, where they learn that all that matters for social status and opportunity is how well a person sings.

Lila is celebrated and elevated, while Daphne starts off a schoolgirl and becomes a servant, and Ivan, who is tone deaf, is relegated to life as a laborer, until his rebellious nature gets him sent off to work in the silver mines.

I had a lot of fun writing this book, not least in creating the supporting characters.  There's Fort, adopted child of a high-status family who is disinherited after a botched throat operation ruins his voice.  He becomes a charismatic Dissonant leader, a romantic figure who dazzles Daphne.  There's Kanzat, the nomad chief whose love of fancy words leads him into delicious malapropisms.  There's the grubby and irascible Hermit of the Mine, to whom Ivan apprentices himself to forge a path to freedom.  And there's the glorious and exacting Diva, ruler of the Land of Winter, who each year must summon the spring by singing her way free of a castle built of ice.

I tell the three cousins' stories in alternating chapters that weave apart and together as each follows his or her own story arc.  Lila finds independence and courage to escape from under the thumb of a domineering mother. Daphne moves beyond envy and resentment to embrace loyalty and humble open-mindedness while protecting Lila from a hidden enemy. Ivan embarks on a journey of creativity as he invents his way out of captivity. Each plays a role in bringing greater justice to the Land of Winter. Orchestrating their movements and roles was half the fun of writing THE ICE CASTLE.

Now comes the next step, presenting the book. As with Lost in Lexicon, I've developed an Ice Castle activity fair to use in schools or with groups of readers.  Scarletta Press has produced a short movie introducing some of these activities with ice, melting, and music.  I'll run two of these fairs soon at the Discovery Museum in Acton, MA, first for a group of kid readers and then again at the book's launch party September 23, 2012, to which you're all invited.

We've also updated the Lexicon website, adding new characters, new stops on the map, and two new, musical games.

I truly hope some of you will join the fun of THE ICE CASTLE launch by visiting the website and buying the book. Sometimes people ask whether it's better to buy from the website, their local bookstore, or from an online groups like Amazon or Barnes & Noble.  The truth is, any one is great.  When you request the book from your local independent bookseller, you support local business and diversity, and you encourage them to stock the book. If you buy from Amazon or B&N (and even if you don't), you can make a great contribution by writing a short review or even more easily by "tagging" the book with categories that will help other readers searching for good books that, say, combine fantasy with music. And of course if you order from the website, you can get your book autographed.  So please cool off in this hot month of August with a visit to the musical wonders and snowy landscapes of THE ICE CASTLE.  Let us know what you find!

Music and Fractions

Does learning music help students learn fractions?  According to a small new study reported last week in the online journal Educational Studies in Mathematics, the answer is yes.

Sixty-seven third-graders were assigned by class twice a week, for twelve 45-minute sessions in all, either to regular mathematics instruction or to "academic music instruction" taught by regular classroom teachers.  Students in the music class learned the values of quarter notes, half notes, and whole notes.  They clapped, sang, and drummed, and they filled out worksheets using the time values of the notes to add up to a full four beats, or whole note, in every bar.

At the end of the six weeks, students in the academic music section outscored their peers on a fraction test by 50 percent, a significant difference.

Getting a strong "fraction sense" is an important first step in learning to understand fractions, and it makes sense that a tactile and auditory fraction sense can help strengthen a more numerical or logical sense.  Besides, clapping and singing are fun.  On the other hand, it's important to remember that this is a small study. Because students were assigned by class, there were probably only one or two teachers in each experimental group.  The difference in outcome might be because the teachers in the music group were more enthusiastic.  It's hard to say from one small study.

Of course, the connection between music and mathematics is a well-established one.  Euclid and Pythagoras were both great believers in the connections, and even today many top mathematicians are more than competent at playing musical instruments, not to mention understanding musical theory. 

In my upcoming kids' novel  The Ice Castle: An Adventure in Music, I explore the connections through the investigations of one of my characters, Ivan.  Ivan can't sing, and he's never done more with music than listen to his i-Pod, but he does have an interest in math and experiments.  In the Land of Winter, where music matters more than anything, he uses his understanding of fractions and logic to learn about musical scales, intervals, octaves, and even how to build musical instruments.  As with Lost in Lexicon, there's a brainy aspect to the book, though wrestling with it is completely voluntary.  Kids who choose to do so will be able to read the book just for its adventures: bears, kidnapping, slavery, prison, competition, and a castle made of ice.

As for me, I'm working on extension games and activities that will allow kids to experience more fully the connection between math and music.

Tin ear confession

My parents both sang well, and my father conducted a small madrigal group for many years. The summer I was six, my brother and I spent seven weeks with our maternal grandparents, and for our bedtime story my grandfather, who sat down to practice piano every day after work, sang and explained all the parts in The Pirates of Penzance and H.M.S. Pinafore to us. I remember learning from him what "fiftyfold" and "keelhauling" meant. My grandparents even arranged for my brother and me to start piano lessons with Mrs. Curry, who was plump with curly yellow hair and who drew pictures of plump curved fingers at the top of our assignment pages every week.

But I was terrible at music. Back in California, Mrs. Curry was succeeded by the timid and trembling Miss Perkoe, a pale young lady with long, straight, dark hair and large round glasses. Her fingers were long and slim and cool, and I loved the way they felt when she placed my fingers on the keys. I learned to play a gypsy dance for Miss Perkoe, but she couldn't make me musical. I was tone deaf. If I wasn't looking, I couldn't tell which of two notes was higher when my father played them on the piano. The music teacher at school asked me to sing very softly for school assemblies. My school singing career was further complicated by the fact that any time we sang "Puff, the Magic Dragon," no matter how I fought it, I started to cry. ( I couldn't stand how lonely Puff became when his lifelong friend outgrew and abandoned him.)

In high school I tried again. My cousin played the clarinet; during the summer I had blown though it, and I liked the way it sounded. I joined B band, beginner's band, which had seven students and a cute pale young male conductor, Mr. Dnelson. (My schedule said DNELSON, and even after I learned that his name was Don Nelson, I still thought of him as Mr. Dnelson, a variant of Nelson that went along with how special he was to me.) By the second year, I had graduated to last seat among the third clarinets in the A band. I never progressed further, and I never learned to carry a tune.

That's an exaggeration. One long ski trip, I spent every chairlift ride with my sister Polly (who could sing) practicing a two-part rendition of "Michael, Row the Boat Ashore." By the end of the trip, I could hold up my part, and I remember how that impressed everyone in the family.

In college, my friend John Rosenberg let me sing Faure's Requiem as part of his North House chorus. We decided I was a tenor, and he gave me special tutoring sessions by the piano. He told me that if I listened well to the voices around me, I could match their tones. His kindness gave me my first real sense of the joy of singing in a group.

Still, though, I can't sing, and my husband is just as bad. All five of our children have sung successfully in choruses, and singing is especially important to the three boys. They sing a capella or in choirs. Meanwhile, my own voice, affected by years of asthma and inhaled steroids, has grown more limited and unreliable than ever. I envy my children their ability to hear key changes, to pick out songs from memory, and most of all to be part of groups that get such joy from singing together. I listen, knowing it's like listening to a foreign language where I have a fair vocabulary and have studied the rules of grammar but miss the nuances.

Those are some of the reasons that the second adventure in Lexicon, The Ice Castle, is subtitled An Adventure in Music.