10. The Field of Music

 

Kathleen’s parents are upset about her pregnancy. But Kathleen is more content now about the prospect of giving birth and parenting a child, and her friends are excited for her. Her tummy keeps getting bigger, and she is wondering where to go to have her baby. Her faculty advisor knows what is happening and is not worried. He sees Kathleen maturing, gaining wisdom through her religious studies and peace through her meditations.

Professor Johannes Britten in the Music Department agreed to talk with the class months ago, but his wife had died suddenly and her passing has hit him hard. The Dean has discussed with him more than once about whether, and when, he should go ahead with their plan for Britten to participate in a class.  Professor Britten has at last insisted that they proceed; this participation, he says, will be part of his healing.

He and the Dean have also talked about the fact that Mozart dealt with his emotions through music. Mozart’s final composition, the “Requiem Mass,” was a masterpiece. It was also the piece of music that Britten’s wife, in the last few days of her life, had requested be played at her funeral. “Mozart's piano concertos are special to me,” Professor Britten confided to the Dean at one moment. “They are like an opera without words. These days, I listen to them in my free time at home,” adding:  “Mozart invented new dimensions to music in rich concerto form. It is most evident in his Concerto No. 9 in E-flat major.”

For his part, the Dean has explained to Professor Britten how the concept of invention fits with the evolution of the universe. “Maybe you can help us build on this idea and see how invention fits with the history of music,” he goes on to suggest. “Students should know how music can increase the richness of life. Let’s keep this particular Concerto in mind as we progress with our thinking together in the class. Perhaps we ought to begin with something simple like the question, “What is a fugue?” They have decided to start there, then move to music history, and see where the wind carries them and the students. 

When Professor Britten arrives for the class, however, it is clear that he is still struggling to come back from his loss. His typically wrinkled clothes are more rumpled than ever—are even stained—and strain shows on his face.

 

Dean: Welcome everyone! We have come a long way on our journey into the deep past. Now it is time to learn about the evolution of music. We have with us Professor Johannes Britten who teaches music history on campus. (Smiles.) I keep learning from him, and we are honored to have him.

As you know, one of our students, Bob (points to Bob) has studied with Professor Britten and will add his thoughts to our discussion. We also have Stewart Perry with us; you remember that he is finishing his doctorate in physics and art, with special interest in music. Welcome  (to Perry). And Professor Benedict is back with us. She will give us some archaeological background. (He nods her way.) Thank you all.

(To students) Today, I would like you to participate more. Keep in mind what you have learned in past sessions and apply this to music. Don’t lean on experts entirely for the answers. Be creative. Offer your own thoughts. Think about those ideas that we have already discussed in class and apply them to music. Ask questions. I want to know what you are learning. (Students figure the Dean is giving them an oral test, in effect. They sit up straighter, concentrating harder. )

Professor Britten, let’s start off our talk on the composer Johann Sebastian Bach. (Professor nods Yes. The Dean goes to the black board and writes:)

Bach and the Fugue

Dean: (Looking at students.) Professor Britten and I spent yesterday talking about evolution. I told him about the ideas we have discussed and asked him: “What is a fugue? Does it have anything to do with evolution?” He said that a fugue is a type of music in which several melodies develop independently and soon they each overlap -- and may even play simultaneously. Each section is called a "voice." (He looks toward Professor Britten)

Britten: (Sits up from a slump, brightening with a smile.) Yes, the fugue is like a round, you know, like "Row, Row, Row Your Boat" (in a singsong), except that in a round, each voice repeats the same theme over and over. In a fugue, on the other hand, the theme becomes more varied, and the organization gets more complex. There are many individual variations that play against the main theme -- or what we call the “subject.” The individual themes give the music a greater richness as they stand both with and over against the subject (looking toward the Dean).[1]

Dean: Well! In philosophy we are all subjects in this natural world. We are evolving in nature with new variations. (He knows that Professor Britten also studied philosophy and has read Hegel’s work.)

Britten: (rousing himself to reply) I had not thought of that connection.

Dean: The astrophysicist Carl Sagan has said that the UNIVERSE IS LIKE A FUGUE. Each voice plays variations on a key theme.  So (looking toward the class), I would like to ask Professor Britten a question: Does the fugue duplicate this principle behind evolution:  could we say, for example, that there is one Subject buried in the Big Bang, which kept becoming more complex with quadrillions of variations that play both with and over against the Subject.[2] (The students sit silent, listening. This is a bigger question than they are willing to venture out on.)

Britten: Interesting. But we need to have some objective standard to make that judgment. We would need to stand outside the universe.

Dean: Well, (smiling more broadly this time). Carl Sagan also said that you could not think about the universe as though you were outside of it. You are always inside the universe. So whatever music you compose is done inside it. We, each of us consists of voices with variations.

Britten: Well, for the composer, music does come from inside. The listener is also resonating inwardly with the music of the composer. But you have to have the ears to hear great music. Not everyone can hear the power and the beauty of a Bach fugue. (Kathleen hears a biblical passage echoing in his words: "He who has ears to hear, let him hear!")[3] 

Dean: You have already told me that you consider Bach to be one of the most creative composers you have ever studied.

Britten: Johann Sebastian Bach. Yes. His composition “The Art of Fugue” is magnificent, absolutely wonderful. (The class hears the emphasis.) His genius was for juxtaposing melodies. They complement one another and make great harmony. 

Dean: Students, please help us now; ask questions.

Alice: Professor Britten, could you say again, what is a fugue?

Britten: A fugue begins with a tune called “the subject.” It’s played alone as one “voice” and can be played by any instrument. Then another "voice" strikes up, while the original voice continues in counterpoint to it; this second “voice” may also create a recurring tune called the counter-subject. The fugue keeps going in two to five or more voices, with the subject entering along with new melodies woven freely around it. It’s a fabulous invention.  

Dean: Tell us more about this invention.

 Britten: Bach uses the word inventiones, as the title for 15 pieces of his work. This concept “invention” referred to a stage in composition, but the notion originated with Marcus Cicero's rhetoric… (to the Dean) You know, the Roman orator.[4]

So the subject in Bach’s music alternates with episodes of free counterpoint in which the subject gets a rest. The subject is like a character that keeps turning up in a friendly conversation. Do you follow me?

Ann: (looking toward the Dean) Each lecture we have is a variation on the subject of evolution. And after listening to each voice, we keep coming back more enriched with our big subject. (Britten laughs, and the Dean is impressed by Ann’s imagination.)

Dean: Except that we can’t all talk at once, which is what happens with the subject in a fugue with its variations. The fugue already transcends us.  

Britten: Here's the Art of the Fugue, the beginning of Contrapunctus One. I’ve brought a CD player so that you can hear it. Listen. You'll hear the fugue subject, then three more entries of the subject, and then we get into four-voice counterpoint. (Everyone listens, fascinated. The music boosts Britten’s spirit for a few minutes, Then he slowly a and gently fades out the sound and says:) How about that! (Everyone nods in favor.)

 

Bach transforms his subject many times through a cycle. The subject is varied by slight rhythmic or melodic alterations, which increase and decrease in complexity, so that when the final subject arrives, it is not immediately heard as related to the first. Some 24 of these gradients link the "new" subject to its “ancestor.” (The Dean sees a connection to evolution here in Britten’s reference to “cycle” and “ancestor” but does not speak.)

Dean: Is this too technical? (The class mumbles “No,” even though what Britten is saying is not perfectly clear to some. They are content to hear more of his explanations and more of the music, they are hoping.) 

Britten: Contrapuncti 1 through 4 are straightforward, except that in the second pair, the main theme is inverted, meaning that every “melodic move up” becomes an equivalent one down, and vice versa. In Contrapunctus 5 the subject enters, both upside-down and right-side-up. (The Dean is not sure what he means here but says nothing.)  From these fairly simple inversions, we really get complex. In Contrapunctus 6, the first voice is the original subject but ornamented, the second voice is the subject inverted, the third voice is the subject right-side-up, the fourth voice is the subject inverted again—except that entries two through four present the subject at double speed. By Contrapunctus 7, the main theme is going at three speeds, variously right-side-up and inverted—with great intensity.

Dean: Wait. I think you are going over our heads. (He wants the class understand everything. And he wants to get Britten to begin to speak about the history of music, but Alice’s hand is waving with excitement.)

Alice: That sounds reflectaphoric. (The Dean is amazed that she has remembered this term and idea.) The mind must “compare and contrast” all the way to the end of the composition. It is full of mirrors.

Britten: Well, yes (somewhat uncertain. Hoping to understand “reflectaphoric,” he adds:) By Contrapuncti 12 and 13, we're in new territory: The entirety of both fugues is presented both right-side-up and mirrored—i.e., upside down—and they all sound wonderful. (The Dean remembers the ancient Egyptian saying, “As above so below;” and the famous dictum of the ancient Greek philosopher Herakleitus, “The way up and the way down are one and the same.”)

Kathleen: I think that angels were guiding him. (She beams; Britten smiles back.)

Britten: Ha! Yes. Bach was a mystic. He was playing otherworldly games when fate stepped in, and he lost his sight. He was blind, and composing, when he died. On his deathbed, he dictated a haunting organ prelude called “Before Thy Throne I Stand.”[5]  (The Dean looks to the class for their thoughts.)

Perry: I have looked at that last work of Bach. He had to weave together four different subjects. He only got to the third one, which happened to be based on his own name.[6]  (The Dean does not want to get sidetracked by too much complexity.)

Dean: Stewart, we should move on. The class needs to get the full advantage of Professor Britten’s knowledge. We should ask him to talk on Music History. (Perry nods a congenial “Yes.”) Okay. I have asked Professor Benedict to start this history. She will begin in ancient times. (The Dean goes to the blackboard and writes:)

 

Music History

Professor Benedict: I will be brief. Let’s see.

The human voice is an instrument that we cannot date archaeologically. Voices don’t survive, not in the way that flints and arrowheads do. Pithecanthropus could have been humming, whistling, yawning, and clicking in rhythm, and we will never know. (She clicks her fingers rhythmically, and students laugh. Pause.) The oldest Neanderthal hyoid bone is dated at 60,000 years old. It predates the oldest bone flute by 10,000 years. Musical instruments date back to the Paleolithic.[7] 

Dean: How about written songs?

Benedict: The oldest song was recorded in cuneiform around 4,000 years ago in Ur, a coastal city in ancient Sumer.[8]

Dean: Hmm. What about in other parts of the world?

Benedict: Indian classical music (marga) can be found in the Vedas in the Hindu tradition. Samaveda is one of the four Vedas that describes music. You can also find music in Persia (Iran today) back in the prehistoric era. I think music goes back to the days of the Elamite Empire there between 2,500 and 644 B.C.E. Another early source of music can be found in Africa… maybe 50 to 100,000 years ago.[9]

But our knowledge of music before A.D. 200 is limited. A dig in the Ukraine uncovered musical instruments made from the bones of a wooly mammoth dating back to 18,000 B.C.E.  Music probably developed among hunter-gatherer groups as a way to communicate with one another. I know that they used drums and horns made from shells. Hunter-gatherer groups then developed agrarian cultures, and music began to have a place in religious ceremonies.

Historical records of Chinese music date back to the Shang dynasty around 1600–1000 B.C.E. Confucius  lived between 500 and 400 B.C.E. and said that music was essential to maintain order.

Emperor Han Wudi, reigned around 100 B.C.E.  He was really big on music and created an Imperial Office of Music. The Chinese were the first to develop a science of acoustics and tune their instruments. They tuned chimes, drums, bells, wind instruments, and string instruments. Yes, Hebrew history (glancing at Jerry). Well, look in the Old Testament! Psalms were sung during religious ceremonies in a call-response between a soloist and the congregation. This was also done antiphonally, that is, by one group following on another. Wind, string, and percussion instruments were used. I could go on, but I think that’s enough for now. (She looks to Professor Britten, who looks toward Bob, his student.)

Britten: Bob, why not pick up on the story in the Roman Empire? Would you also give everyone a copy of your summary of music history? We’ve talked about it. It’s good.

Bob: (Bob hands out a sheet of paper with dates indicating episodes in the history of music.)

Table I: History of Music

AD 325

Constantine declares Christianity the official religion of the Roman Empire, which spurs the development of the Church that shaped European music.

600

Pope Gregory the Great codifies and collects the “chant,” which is used in Roman Catholic services and is named the “Gregorian chant” in his honor.

c. AD 850

Western music begins to move from monophony to polyphony, with the vocal parts in church music moving in parallel intervals.

c. 1030

Guido of Arezzo, an Italian monk, develops a system for learning music by ear. Voice students use a system, called SolfŹge, to memorize their vocal exercises. In the 19th century, SolfŹge developed into the tonic Solfa system used today.

c. 1180

Troubadours appear in Germany and call themselves Minnesingers, “singers about love.”

1430

The Renaissance [[Now no longer called the Renaissance, but the “Early Modern.” –ed]]begins. This period of rebirth favors the simplistic virtues of Greek and Roman Classic styles, moves from polyphony to one harmonized melody and sees the increased importance and popularity of secular music. Josquin Desprez, often called the Prince of Music, is a leading composer of the Renaissance. He worked for ducal courts in Italy and France, at the Sistine Chapel and for kings Louis XI and Louis XII of France. [[I assume.—ed]]

1562

During the Counter-Reformation, Pope Pius IV restores church music to its pure vocal form by eliminating all instruments except the organ, any evidence of secularism, harmony, and folk melody. Giovanni Da Palestrina satisfies the pope's rigid requirements and creates a new spiritual style that legend says “saved polyphony” when he writes the Pope Marcellus Mass, his most famous and enchanting piece.

1565

In Italian music, castration emerges as a way of preserving high male singing voices. St. Paul's dictum prohibited women from singing on stage and in churches. The practice of castration becomes commonplace by 1574.

1588

The English Madrigal School is firmly established. The movement, led by Thomas Morley, produces some of the most delightful secular music ever heard. Madrigals often told stories of love or grief.

1590–1604

A group of musicians and intellectuals gather in Count Giovanni de Bardi's camerata (salon) and discuss and experiment with musical drama. It is during this period that opera is born. Jacopo Peri's Dafne, the first Italian opera, is produced in 1598 and Euridice in 1600.

c. 1600

The Baroque period, characterized by strict musical forms and highly ornamental works, begins in Europe. The beginning of this period signals the end of the Renaissance.

1607

Italian master composer Claudio Monteverdi writes the opera Orfeo, Favola in Musica, a work deemed to be a prime example of the early Baroque musical form.

1625

Francesca Caccini, who most historians say is the first female composer, finishes the opera-ballet La Liberazione di Ruggiero, which is performed at a reception for Wladyslaw IV of Poland.

1631

Professional female singers appear for the first time on the English stage in the production of Chloridia, a court masque produced by Ben Jonson and Inigo Jones.

1639

The first comic opera, Chi Soffre Speri by Virgilio Mazzocchi and Marco Marazzoli, premieres in Rome.

1656

Henry Lawes and Matthew Locke add music to William Davenant's libretto The Siege of Rhodes, which is performed at the Rutland House in London. Davenant helps make the opera-masque a form of public entertainment.

1666

The first signed Stradivarius violins emerge from Antonio Stradivari's workshop in Cremona, Italy.

1675

Matthew Locke composes Psyche, the first surviving English opera.

1685

Johann Sebastian Bach and George Frederick Handel are born. They become principal classical composers of the Baroque period. Bach, who fathers 20 children, explores musical forms associated with the church, and Handel works as a dramatic composer.

1689

Henry Purcell's Dido and Aeneas opens in London.

1703

Vivaldi becomes violin master at Venice's La Pietą orphanage. He writes more then 400 concertos for La Pietą in his 35-year service there.

1705

Reinhard Keiser uses French horns for the first time in an opera in his production of Octavia.

1725

Vivaldi writes The Four Seasons.

1733

The comic opera, La Serva Padrona, from Battista Pergolesi's serious opera Il Prigionier Superbo, wows Europe with its humorous story and enchanting music.

1735

Handel produces his last great operatic success, Alcina, which features dancer Marie Sallé.

1742

Handel's Messiah premieres in Dublin to an enthusiastic audience.

1750

Bach dies. The end of the Baroque period is often seen in conjunction with his death. The highly ornate style of the Baroque period gives rise to the simpler, clarified styles of the Classical period, which also sees the emergence of symphonies and string quartets.

1761

Franz Joseph Haydn becomes Vice-Kapellmeister to the Esterhazy family and Kapellmeister in 1766. Though living virtually as a slave to the family, he had at his disposal an impressive orchestra. During his 30-year service to the family, he completes 108 symphonies, 68 string quartets, 47 piano sonatas, 26 operas, 4 oratorios, and hundreds of smaller pieces.

1762

Christoph Willibald von Glück sets out to reform opera with his Orfeo ed Euridice. He wants to restore opera to what the original composers intended it to be—an art form marked by high drama, few recitatives or orchestral set-pieces.

1770

[[Do you want to include a reference to Beethoven’s birth?—ed]]

1786

Mozart's The Marriage of Figaro premieres in Vienna.

1787

Mozart's Don Giovanni debuts in Prague.

1797

Franz Peter Schubert is born in Vienna. Though many musicians make Vienna their home, Schubert is the only one to be born there.

1803

Beethoven produces his third symphony, Eröica. This piece marks the beginning of the Romantic period, in which the formality of the Classical period is replaced by subjectivity.

1807

Beethoven completes his Symphony No. 5, which many consider to be the most popular classical work ever written.

1810

Robert Schumann is born in Germany.

1815

Schubert writes “Der Erlkönig,” his first public success and most famous song.

1816

Gioacchino Rossini's The Barber of Seville, based on Pierre Beaumarchais's play, debuts in Rome. His Otello opens in Naples.

1818

Beethoven's hearing has deteriorated so badly that he no longer can hear the piano and must communicate with conversation books.

1821

Carl Maria von Weber's Der Freischutz debuts in Berlin, and he becomes the master of German opera.

1826

Mendelssohn writes the overture to A Midsummer Night's Dream, which debuts in Stettin in 1827.

1832

Schumann's career as a pianist is over as one of his fingers becomes paralyzed.

1839

The New York Philharmonic is established.

1851

Verdi's Rigoletto debuts in Venice.

1853

Richard Wagner publishes the librettos to Der Ring des Nibelungen (The Ring Cycle): Das Rheingold, Die Walküre, Seigfried and Die Götterdämmerung. The Ring Cycle is considered one of the most ambitious musical projects ever undertaken by a single person.

1854

Liszt conducts the first performance of his symphonic poems in Weimar. The symphonic poem is an orchestral work, often in one movement, and is usually based on a literary idea. Liszt is credited with creating the genre. His symphonic poems include Orpheus, Les Preludes and Mazeppa.

c. 1860

The slave trade introduces West African rhythms, work songs, chants and spirituals to America, which strongly influence blues and jazz.

Gustav Mahler is born in Bohemia.

1871

Verdi's Aēda premieres in Cairo.

1874

Verdi's Requiem, his most respected work, premieres in Milan.

1876

Tchaikovsky completes Swan Lake. It opens in 1877 at Moscow's Bolshoi Theatre.

Wagner's The Ring Cycle is performed in full at the Bayreuth Festival. The opera house was built to accommodate Wagner's works.

Johannes Brahms completes his First Symphony. Twenty years in the making, the symphony received mixed reviews but would become one of the most popular ever written.

1877

Thomas Edison invents sound recording.

Camille Saint-SaĎn's Samson et Dalila debuts in Weimar.

1878

Thomas Edison patents the phonograph.

1880

John Paine's symphony, In Spring, debuts in Cambridge, Massachusetts. It is the first American symphony published in the United States.

Tchaikovsky writes the 1812 Overture, commemorating Russia's defeat of Napoleon.

1881

The Boston Symphony Orchestra is established.

1882

The Berlin Philharmonic is established.

1883

The Metropolitan Opera House opens in New York.

1885

Gilbert and Sullivan finish The Mikado, which premieres in London.

1888

Strauss writes the symphonic poem, Don Juan, which brings him international fame.

1890

Tchaikovsky's The Sleeping Beauty debuts in St. Petersburg.

1891

Carnegie Hall opens in New York.

1893

Dvorák composes his best and most popular work, From the New World.

1896

Ragtime, a combination of West Indian rhythm and European musical form, is born.

1900

Jean Sibelius's Finlandia premieres in Helsinki.

1901

Mahler's Fourth Symphony, his most popular, debuts in Munich.

1902

Claude Debussy introduces impressionism to music in Pelléas et Mélisande at the Opéra Comique in Paris.

1904

The London Symphony Orchestra is established.

1908

A major change in classical-music style comes about with the release of Arnold Schoenberg's Book of Hanging Gardens. The harmony and tonality characteristic of classical music are replaced by dissonance, creating what many listeners consider to be noise.

1910

Igor Stravinsky completes The Firebird for Sergei Diaghilev's Ballets Russes. Stravinsky will become one of the greatest composers of the 20th century.

1911

Strauss's Der Rosenkavalier premieres in Dresden.

1913

Billboard magazine publishes a list of the most popular vaudeville songs. It's the predecessor to their trademark charts.

1916

Charles Ives finishes his Fourth Symphony, his defining piece.

1919

After moving from its southern rural roots, jazz establishes Chicago as its capital. The city will become home to such jazz greats as trumpeter Louis Armstrong and pianist Jelly Roll Morton.

1923

“Queen of the Blues” Bessie Smith records her first song, “Down Hearted Blues,” which becomes an immediate success.

1924

The Juilliard School opens in New York.

Maurice Ravel's Bolero opens in Paris.

George Gershwin's Rhapsody in Blue premieres in New York.

1925

Alban Berg's Wozzeck opens in Berlin.

1932

Jazz composer Duke Ellington writes “It Don't Mean a Thing, If It Ain't Got That Swing,” a song that presaged the Swing Era of the 1930s and 1940s.

1933

Laurens Hammond introduces his Hammond organ.

1936

Electric guitars debut.

1937

Bela Bartok's masterpiece, Music for Strings, Percussion and Celesta, premieres in Basel.

The Glenn Miller Band debuts in New York.

1938

Roy Acuff joins the “Grand Ole Opry” and brings national recognition to the Nashville-based radio program.

1942

Bing Crosby releases "White Christmas," from the film Holiday Inn. The song goes on to be the all-time, top-selling song from a film.

RCA Victor sprays gold over Glenn Miller's million-copy-seller Chattanooga Choo Choo, creating the first "gold record."

1945

Benjamin Britten's Peter Grimes premieres in London, which signals the rebirth of British opera.

1948

Columbia Records introduces the 33 1/3 LP (“long playing”) record at New York's Waldorf-Astoria Hotel. It allows listeners to enjoy an unprecedented 25 minutes of music per side, compared to the four minutes per side of the standard 78 rpm record.

1949

45 rpm records are sold in the United States

1951

In an effort to introduce rhythm and blues to a broader white audience, which was hesitant to embrace “black music,” disc jockey Alan Freed uses the term “rock 'n' roll” to describe R&B.

Elliott Carter composes his String Quartet No. 1 and becomes a leading avant-garde composer of the 20th century.

1954

Bill Haley and the Comets begin writing hit songs. As a white band using black-derived forms, they venture into rock 'n' roll.

Pierre Boulez completes Le Marteau Sans MaĒtre (The Hammer Without a Master).

1956

With many hit singles (including “Heartbreak Hotel”), Elvis Presley emerges as one of the world's first rock stars. The gyrating rocker enjoys fame on the stages of the Milton Berle, Steve Allen and Ed Sullivan television shows, as well as in the first of his many movies, Love Me Tender.

1957

Leonard Bernstein completes West Side Story.

1958

Billboard debuts its “Hot 100” chart. Ricky Nelson's "Poor Little Fool" boasts the first No. 1 record.

Elvis Presley is inducted into the U.S. Army (March 24).

1959

The National Academy of Recording Arts and Sciences sponsors the first Grammy Award ceremony for music recorded in 1958.

Frank Sinatra wins his first Grammy Award -- Best Album for Come Dance with Me.

1960

John Coltrane forms his own quartet and becomes the voice of jazz's New Wave movement.

1961

Patsy Cline releases “I Fall to Pieces” and “Crazy.” The success of the songs help her cross over from country to pop.

1963

A wave of Beatlemania hits the United Kingdom. The Beatles, a British band composed of John Lennon, George Harrison, Ringo Starr and Paul McCartney, take Britain by storm.

The Rolling Stones emerge as the anti-Beatles, with an aggressive, blues-derived style.

1964

Folk musician Bob Dylan becomes increasingly popular during this time of social protest, with songs expressing objection to the condition of American society.

The Beatles appear on The Ed Sullivan Show.

1967

The Beatles release their break-through concept album, Sergeant Pepper's Lonely Hearts Club Band.

Psychedelic bands such as The Grateful Dead and Jefferson Airplane enjoy great success during this period, with songs celebrating the counterculture of the 60s.

1969

In August, more than half a million people attend the Woodstock music festival in Bethel, N.Y. (near Woodstock, N.Y.). Performers include Janis Joplin; Jimi Hendrix; The Who; Joan Baez; Crosby, Stills, Nash and Young; the Jefferson Airplane; and Sly and the Family Stone.

A Rolling Stones fan is killed at the group's Altamont, California, concert by members of the Hell's Angels.

1970

The Beatles break up. By the end of the year, each member has released a solo album.

1971

Jim Morrison dies in Paris at age 27 (July 3).

The Allman Brothers' Duane Allman dies in a motorcycle accident at age 24 (Oct. 29).

1972

Women dominate the 1971 Grammy Awards, taking all four top categories. Carole King wins Record, Album and Song of the Year, while Carly Simon takes the Best New Artist award.

1973

The Jamaican film The Harder They Come, starring Jimmy Cliff, launches the popularity of reggae music in the United States.

1974

Patti Smith releases what is considered to be the first punk rock single, “Hey Joe.” Punk roars out of Britain during the late-70s, with bands such as the Sex Pistols and the Clash expressing nihilistic and anarchistic views in response to a lack of opportunity in Britain, boredom, and antipathy for the bland music of the day.

1976

Philip Glass completes Einstein on the Beach, the first widely known example of minimalist composition.

1977

Saturday Night Fever sparks the disco inferno.

Elvis Presley dies at Graceland, his Memphis, Tennessee home. He was 42.

1978

Sony introduces the Walkman, the first portable stereo.

1979

The Sugar Hill Gang releases the first commercial rap hit, “Rapper's Delight,” bringing rap off the New York streets and into the popular music scene. Rap originated in the mid 1970s as rhyme spoken over an instrumental track provided by snatches of music from records. Over the decades, rap becomes one of the most important commercial and artistic branches of pop music.

1980

John Lennon of the Beatles shot dead in New York City.

1981

MTV goes on the air, running around-the-clock music videos, debuting with “Video Killed the Radio Star.”

1982

Michael Jackson releases Thriller, which sells more than 25 million copies, becoming the biggest-selling album in history.

1983

With the introduction of noise-free compact discs, the vinyl record begins a steep decline.

1984

Led by Bob Geldof, the band Band Aid releases "Do They Know It's Christmas," with proceeds of the single going to feed the starving in Africa.

1985

Madonna launches her first road show, the Virgin Tour.

Dozens of top-name musicians and bands perform at the Live Aid concerts in Philadelphia and London. The shows benefit African famine victims.

1987

Though African, Latin American, and other genres of international music have been around for centuries, a group of small, London-based labels coin the term “world music,” which helps record sellers find rack space for the eclectic music.

1988

CDs outsell vinyl records for the first time.

1990

Euro-dance band Milli Vanilli admits to lip-synching hits such as "Girl You Know Its True," and has its Grammy award revoked.

1991

Seattle band Nirvana releases the song “Smells Like Teen Spirit” on the LP Nevermind and enjoys national success. With Nirvana's hit comes the Grunge Movement, which is characterized by the sound of distorted guitars, dispirited vocals, and lots of flannel.

1992

Compact discs surpass cassette tapes as the preferred medium for recorded music.

1994

Woodstock '94 commemorates the original weekend-long concert. Green Day and Nine Inch Nails join Woodstock veterans including Santana and Joe Cocker.

1995

The Rock and Roll Hall of Fame Museum opens in Cleveland. Renowned architect I. M. Pei designed the ultramodern, 150,000 square-foot building.

Grateful Dead frontman Jerry Garcia dies.

1996

Janet Jackson becomes the highest-paid musician in history when she signs an $80-million deal with Virgin Records.

Jazz great Ella Fitzgerald dies.

1998

Legendary crooner Frank Sinatra dies of a heart attack at age 82.

1999

The merger of two major recording labels, Universal and Polygram, causes upheaval in the recording industry. It is estimated that the new company, Universal Music Group, controls 25 percent of the worldwide music market.

Woodstock '99 kicks off in Rome, N.Y. Concertgoers complain that the spirit of the original Woodstock has been compromised and commercialized.[10]

[[It is already quite long, but is that the reason for ending this history a decade ago?—ed]]

 

Bob: Everyone can look over this list at your leisure. It is too long to discuss, but I studied harmony and I could give you a brief summary of that story. (Bob looks to Professor Britten, who nods to proceed and goes to the blackboard to write.)

A Brief History of Harmony

I started my readings with “vertical harmonic organization,” which began in ancient Greece. Harmony developed there as a succession of tones within an octave. Scales were used as a basis for singing in unison without melody. (Bob is a little nervous speaking before the class and faculty. His voice trembles, but he keeps going.)

From the 6th to 9th centuries A. D., a dozen scale patterns of tones and semi-tones developed. In the 9th century, only the simplest "perfect" harmonic ratios were accepted: the fourth and fifth octave. But this allowed for the addition of one or two voices. Later these voices began to acquire independence, moving contrary to the original melody. Now…from the 12th to the15th centuries, “intervals, thirds and sixths,” were included, and in some cases, seconds and sevenths. This helped enrich the harmony of voices.

In the 15th century, came the introduction of additional notes that began to foreshadow the major/minor mode system. In the 16th century, the tonic (or keynote) triad became the point of departure and the conclusion in a composition. (He’s been glancing at his notes and stops to take a deep breath.)

In the 17th century, a greater emphasis was placed on a melodic line that was harmonically supported by a base line. In the 19th century, there was a more deliberate use of unresolved harmonies and ambiguous chords. (His eyes are skipping through the details.)

In the 20th century, the use of chords began to get resolved in unexpected directions. And there was the appearance of atonality -- which abandoned the traditional duality of consonance and dissonance. There was a break from traditional scales in recognition of a continuum between consonance and dissonance. There was also a new emphasis on performer improvisation and interpretation. [11]

Should I go on? (He looks to Professor Britten, frankly hoping he could stop,.)

Britten: Well, let me take over. I will expand on what you have said. Thank you so much. (Britten goes to the blackboard and writes the “stages” that he teaches. (As he writes, he speaks:)

 

Music History: Periods of European music

Medieval         (500 – 1400)

Renaissance    (1400 – 1600)

Baroque (1600 – 1760)

Classical (1730 – 1820)

Romantic         (1815 – 1910)

Modern and contemporary

20th century    (1900 – 2000)

Contemporary         (1975 – present)

 

Britten: This is how I teach music history to introductory classes. (The Dean interrupts.)

Dean: But our subject is not “history.”  It is “evolution.” (The Dean does not want just a “music history lecture.”)

Britten: Hmm. Let’s see. Well, help me interpret evolution from details of this history. (The Dean nods.) The history of music in the West begins around AD 500. The music that survived in Europe before AD 800 to the present day is liturgical music, which originated from the Roman Catholic Church, as Bob said.

I know you have talked in class about “replication” in evolution. Listen to this Chant: (He presses a button to start a CD that sounds the chant for about 40 seconds. Students listen closely to the sounds of repetition.) 

It could lull you to sleep, maybe. No, but many of you look almost mesmerized, in fact. It is called  “Gregorian Chant after Pope Gregory the First, who gave his name to the repertory. Repetition. Yes. Now (to the class), help me think how this evolves. I will lead you through these stages of history.

We begin in the 9th century, when there were three important developments with this Gregorian chant. (He looks to the Dean.) I see a quest both for “unity” and “diversity” in what transpired here. First, the Church wanted to unify different chant traditions; but they also rejected some of them in favor of the Gregorian. Second, the earliest polyphonic music began as a form of parallel singing known as organum. That was an invention.[12]   

Third, after a lapse of about five hundred years or more, music “notation” developed. That was a still greater invention. Most of us now take notation for granted, but it would be many centuries before a new system of pitch and rhythm notation developed; with precision and flexibility, I mean.[13]

Tom: “Notation,” “greater precision”: these mean more complexity. And that fits the whole story of evolution.

Britten: Yes. Different types of sacred music developed with this notation in the late 13th century: the motet, conductus, discant, and clausulae. We also see the music of wandering bands of flagellants during the middle of the 13th century, and again around 1350, following the Black Death; we have documents of this sort of music with its notation. These singers mixed folk songs with penitential, or apocalyptic, texts. (Pause.)

Tom: So we can assume that music kept developing more complexity -- like the physical world evolving after the Big Bang. (He is connecting with the Dean’s idea. The Dean is thinking about how human evolution deepens and enriches “interiority.”)

Britten: Yes. The complexity of notation and the variety of music increased. Later in the 14th century, we see the development of the ars nova, the “New Art.” This music has a lot of rhythmic complexity. "Resting" intervals are the fifth and octave, with thirds; sixths are considered dissonances. Leaps of more than a sixth were not uncommon in individual voices.

I classify this music with the Medieval Era, but it had much in common with early Renaissance ideals. It “bridges” between these two periods of history.

Ann: Ah. Is the music of each period picking up themes from its past? I mean: does music evolve like molecules? Molecules preceded the cells. (She is thinking of how the Dean has suggested that “continuity” at each new stage picks up “antecedents,” or previous elements, in order to compose the new.)

Britten: Yes, but I would need to do a lot of research in order to make that comparison with molecules with greater confidence. (Smiles.)

Ann: And the orchestra? How does it evolve? Does one instrument become more refined and then those refinements branch off to another instrument?

Britten: Yes. But people had already been refining instruments for thousands of years, improving on each, one after the other. It would take me a long time just to talk about changes in the strings of the varieties of stringed instruments, to say nothing of focusing on the violin, say.

Ann: (nodding). How did the orchestra evolve? Did it start only with a couple of people, and then move to three, four, five, and more?

Britten: That’s pretty much what happened. About 400 years ago, musicians started forming combinations together that turned into what we would now call an orchestra. In the 1500s, for example, the word "consort" was used to mean a group of instrumentalists—and sometimes singers as well—making music together or "in concert." Two or three would gather, and more would join them. In Italy around 1600, the composer Claudio Monteverdi knew exactly what instruments he wanted to accompany his first opera Orfeo. This was a turning point. For the first time, he said exactly what instruments should play his piece: fifteen viols of certain sizes, two violins, four flutes—two large and two medium-sized, two oboes, two cornetts (small wooden trumpets), four trumpets, five trombones, a harp, two harpsichords, and three small organs.

Ann: So, if we think about all of this in terms of biology, for example, Monteverdi's “combination” was like -- the first organic cells. And it must have led to the multi-celled organism, so to speak -- the orchestra.

Britten: So to speak. It started what we call an “orchestra” in our term today. By that I mean: instruments organized into sections. In the next century -- up to about 1700, which was during Johann Sebastian Bach's time  -- the “orchestra” developed extensively. The violin family —violin, viola, cello, and bass—replaced the viols, and this string section became central to the Baroque orchestra. When Bach worked with an “orchestra,” he sat at the organ or harpsichord and gave cues from his bench. This was the beginning of what you might call the “multi-celled organism.” (Smiles at the analogy and pauses pondering, but the dean points to his list of “history stages” on the blackboard and signals him to keep going).

In the Baroque era, a musical director began to conduct the group of musicians. Jean-Baptiste Lully, who was in charge of music at the French court in the 1600s, used to pound out the beat for his musicians using a long pole, which he tapped on the floor.

The orchestra kept developing in the next century, up to the1800s, the era of Haydn and Beethoven. Now you can imagine the orchestral story expanding from there. Think about the big complicated orchestras we have today.

Ann: Do you see a straight-line development of evolution here? (The Dean sits up, suddenly eager.) I mean: is it like biology? Does the evolution of music look more like a tree, would you say? Or, more like a bush, perhaps? (She remembers that Stephen Jay Gould said animals evolved like a bush with many branches, not like a tree with a single trunk. The Dean thinks that she should get a high mark for this question. Britten needs to think about this and pauses.)

Britten: The evolution of music is not like a tree. I think it looks rather more like a bush, with many lines of development growing from each tiny branch.

Ann: Are there sudden breaks in styles of music leading into the Renaissance? Are there leaps into new forms, like in biology?  (She is recalling the debate in biology about whether there were sudden leaps in evolution between species, instead of just a slow gradual movement from one species to the next.)

Britten: Hmm. I have to think about that one too. Let’s see. Renaissance music began in northern Europe—in central and northern France, the Netherlands, and Belgium. The style of the Burgundian composers (the Franco-Flemish school) was a reaction against the excessive complexity and style of the late 14th century ars subtilior. The Burgundian style contained a balanced polyphony in all voices… (Interrupted.)

Barbara: Ars sub-ti-tilior? (Her lips stumble over the word.) What is that?

Britten: Ars subtilior is Latin and means “more subtle art.” It is a musical style that has more rhythmic and notational complexity. It was centered in southern France and northern Spain. It contrasts with ars nova or “New Art,” which applies to the style of the preceding period that lasted from 1310 to about 1370.

Ann: But that’s no “leap.” It’s only a slight change. It looks like one style evolves incrementally through a previous style, carrying some of the old traits. I’m curious about the meaning of linear “straight-line evolution.” (She is wondering how one form evolves into another, in the way that Australopithecus preceded Homo erectus.)

Britten: Maybe. Scholars consider the ars subtilior a subcategory of the earlier style. You can see that the “change” is very slight. (The Dean thinks of the closeness of Homo habilis to Homo sapiens.) You would need special research to answer that question. The primary sources for the ars subtilior are the Chantilly Codex (quizzical faces).  I mean …that’s the name for the medieval manuscript in which you will find this style recorded. But, that’s a detail. Keep asking me questions. I want to stay with your questions.

Jerry: We talked about “diffusion” in the evolution of culture. Do you see diffusion in music across countries? (The Dean is pleased at how students are recalling earlier sessions with Professor Benedict.)

Britten: Yes. By the middle of the 15th century, composers and singers from what is called “the Low Countries”—like the Netherlands—began to overspread Europe. They took their music with them as they moved into Italy, where the papal chapel and patrons of the arts employed them—I mean such patrons as the Medici, the Este family in Ferrara, and the Sforza family in Milan. They brought with them “smooth polyphony,” which could be adapted for either sacred or secular use.

Benedict: Sacred-Secular use. At this point, these modes are evolving together. They are now separate but equal as they are developing. (She smiles at her intuitive thought.) Interesting. Does secular music now break away from the sacred music of the church? (The Dean remembers a discussion about chemical elements separating and recombining, but Professor Benedict is recalling the class discussion on Human History in which they had spoken of the separation of the secular and sacred.)

Britten: Yes. The sacred compositions at the time were the mass, the motet, and the laude. The secular types were the chanson, the frottola, and the madrigal. They were branches on the evolutionary “bush” as it were. (The Dean looks to see if there are any more questions from students. He sees Jerry’s hand go up.)

Jerry: We have talked about “invention” as a key to evolution. Tell us more about invention . . . I mean music technology affecting music as it develops. (The Dean is glad to hear his idea expressed again.)

Britten: The invention of printing had an immense influence on the diffusion of these music styles, along with the migration of the Franco-Flemish musicians throughout Europe.

Printing is a material invention, but I argue that every new style of music is an invention. You should read about composers in the Franco-Flemish school, like Johannes Ockeghem. They wrote in a contrapuntally complex style. They developed a “varied texture,” and added an elaborate use of canonical devices; Jacob Obrecht and Josquin Desprez were innovative. The Dean and I agreed about this yesterday. Invention keeps going all the way down through history.

Ann:  And do we also agree that invention means more complexity all the way?  

Britten: Well, yes, but complexity alternates -- and combines -- with simplicity. (The Dean listens with interest.) Composers -- in the generation after Josquin des Pres -- explored more complexity in counterpoint, but that increase in a single direction could go only so far without simplicity.

 The most extreme expression of the complexity, by the way, is in the work of Nicolas Gombert, with contrapuntal intricacies ending in Baroque fugal forms. And I see a linear progression in complexity in romantic music in the nineteenth century. It began with Beethoven and Schubert and followed with Wagner and Mahler, Strauss and Schoenberg. Music became more and more complicated through this period, up to about the time of the First World War.  (“But what about the simplicity…?” Ann is thinking,)

So it seems like composers went as far as they could with complexity in this form, and after the First World War, the pendulum swings back. Look at the shift in the size and mix of the orchestra at that time. We find the composer Igor Stravinsky, for example, not writing for a hundred players, as he had done in his ballets Petrushka and The Rite of Spring, but for seven players -- as in The Soldier's Tale and his Octet for Winds. Now Stravinsky is writing simple, tonal lines. Neo-Classicism in music is born.

Ann: What about as music developed into the 20th century, say, with  Jazz? Do you see Jazz growing in complexity?

Britten: The Big Band Swing of the 30s and early 40s gave way to a Jazz called Bebop, and that became very complicated. (He puts his hand to the side of his mouth as though to whisper:) The excitement of crowds for Charlie Parker, Dizzy Gillespie, and Max Roach was enormous.

The complexity in Jazz also kept increasing before the pendulum swung back to simplicity. What we got was Rock and Roll -- Chuck Berry and Elvis. We all shook our legs and danced to a simpler tune. (The Dean thinks that a graduate student should study this subject of “simplicity-complexity” in music in more detail.  “We could go in over our heads with music vocabulary and technology unless we curtail this.”)

Dean: Are there any more questions from students—based on what you’ve learned from our past discussions—that link music to evolution?

Alice: The Dean said that antinomies—I mean opposites— are at work here. Is that true in music? 

Britten: Say more.

Alice: The Dean proposed that opposite ideas are always there in evolution. Evolution is not just based in principle on a mix of the simple and the complex, but also on plurality and unity, and other opposites. Opposites are both separate and mutually involved, like Yin and Yang. And they keep developing together. (For the Dean this is an “A plus” question.)

Britten: I mentioned Igor Stravinsky, the composer. He wrote in his book Poetics of Music that, for him – and I can quote this-- “Variety is valued only as a means of attaining similarity.” Now that could get us into the philosophy of music. Stravinsky also believed that music was a revelation of a “higher order.” The performer simply had to execute it right.[14]

Dean: That’s very interesting. I wish we had more time to delve into musical philosophy and composers’ thoughts on the mysteries of composition. But we have to go back to the basics—we might say of music history, and confine our conjectures to the matter of how music relates to evolution. (pointing to Britten’s chart on the blackboard) Are our thoughts on unity-in-diversity born out here, too?

Britten: Okay. Well, my category of “Early Music” refers to the European classical tradition right after the fall of the Roman Empire in 476 C.E., until the end of the Baroque era in the middle of the 18th century. Music within this span developed diversity in a wide geographic area. Bob, you know the history of culture during this period!

Bob: Yes. What unified everything in the Middle Ages was the Roman Catholic Church. Its music was the focal point for the first thousand years of what you are designating as the period of “Early Music.” Very little non-Christian music from this period survived, because the Church suppressed it. 

Britten: By the middle of the 16th century, several highly diverse stylistic trends became evident. There was a trend towards simplicity in sacred music, directed by the Counter-Reformation Council of Trent. For example, there was the simple austere perfection of the music of Giovanni Pierluigi da Palestrina.

Alice: Those principles of simplicity and complexity – again -- were they constant? (The Dean thinks oppositions are augmented together in evolution, but he does not know how this happens in music. But from what he understands Professor Britten to be saying, he extrapolates that these principles also do appear to “alternate.”)

 Britten: Yes, as far as I can see. A trend towards complexity begins chromaticism – a word that refers to the use of many notes and harmonies foreign to the basic key. Here we see the beginning of the madrigal. It reaches its peak in the avant-garde style of the Ferrara School of Luzzaschi, and the madrigalist Carlo Gesualdo. And then there comes the grandiose, sonorous music of the Venetian school. Its members were creating music of antiphonal contrasts. (Some students look puzzled, repeating, “antiphonal?”) Antiphonal. I mean music that is played by two or more groups performing in alternate sections.

Dean: Good. Keep going. (The Dean smiles and nods for him to go ahead. They are making good progress now along his musical chart.)

Britten: The music of the Venetian school starts to flourish all in a span of several decades around 1600, on the cusp of the transition —in music, at any rate—between the Renaissance and the Baroque.[15] Now we see orchestration develop—by which I mean the addition of instrumental parts, and continuo bass parts.

Famous composers in Venice included the Gabrielis, Andrea and Giovanni. Claudio Monteverdi was one of the most significant inventors at the end of the era. Are you with me? (to students) Can you tell me what, if anything, this has to do with evolution?

Tom: (He wants to be part of the Dean’s “test.”) Herbert Spencer says that the evolution of society involves a differentiation of institutions. Do you see this principle in music: a differentiation of styles? 

Britten: Differentiation? Absolutely. Societies in Europe developed different musical traditions. In England, composers like Thomas Tallis and William Byrd wrote sacred music; a group of madrigalists adapted the Italian form for English tastes. Differentiation…Let’s see.

Look at Spain. Spain developed instrumental and vocal styles of its own. Tomás Luis de Victoria and other composers were writing for a new instrument called the guitar.

Look at Germany. Germans cultivated polyphonic forms built on the Protestant chorales that replaced the Roman Catholic Gregorian Chant. And German composers specialized in organ music. This became the basis for the flowering of the Baroque organ style that ended with Bach.

Look at France. The French developed a special style of diction known as musique mesuré. It was used in secular chansons, with composers such as Guillaume Costeley and Claude Le Jeune part of the movement. Yes, constant differentiation.

Derek: The Dean has also talked about cycles in evolution. How do cycles come into music history?

Britten: Well, they appear in different ways. Formally, for example, there is something called the “song cycle.” (More puzzled faces.) The song cycle is a group of songs performed in a sequence; all of the songs are by the same composer, or they may use words from the same poet. The sequence is given some unity by having something in common. 

Derek: But we talked about the cycles that occur through time—like seasons in the year; and in the economy—like prosperity and poverty; or in psychology (my field)—such as cycles of mania and depression. It should have a linear form of “progress” in greater complexity, showing up in greater and lesser degrees—waxing and waning, you could say.

Britten: Your field is psychology? (Derek nods. Britten looks at the Dean who knows Britten is facing his own depression.) Some great composers became very depressed at times in their life -- Beethoven, Tchaikovsky, Elgar, Bruckner, Mussorgsky. Some great composers even ended up in mental hospitals. Gaetano Donizetti died mentally deranged. (Britten looks to the Dean for support, because he is not sure how to answer this question.)

Dean: And Donizetti also created some of opera's greatest scenes. He helped music “progress” in society. But the idea of “progress” is not the same as “evolution.” You have to have an “end-state” and special criteria in mind to define “progress.”

Remember, we talked about progress in the evolution of technology in terms of increases in speed. We went from the wheel and wagon cart to the airplane and missile. We can see progress in the formation of eyes—changing from a light-sensitive eyespot in the earliest species of the Cambrian explosion to human eyes.

But all sorts of things can happen along the way – including reverses and cycles. Remember we talked about a budding democratic society regressing back into a dictatorship? When we talk about “progress,” it is the long-term picture that counts.

Britten: But Derek is asking about the individual who cycles from health into a depression, but not back to health.

Dean: Yes, but we do not know what happens after death. Alfred Russell Wallace, the co-founder of evolution, believed that individuals who have died “live on” in a subtle body after death. They keep continuing  “on the other side.” The Germans have a word for this, by the way: it is jenseits, which refers to whatever is beyond the natural realm. We can come back to this point in religious studies.

You have to have a criterion or a goal to define progress. We do not have that “final goal” in the study of evolution. (The Dean looks to the class for more questions.)

Barbara: Can you say something more about how elements of music are incorporated from the past into new forms? How do composers create a more complex composition?

Britten: One of the most inventive movements in this era took place in Florence in the 1570s and 1580s, with the Florentine Camerata. The Camerata was a group of musicians, poets, and intellectuals under the patronage of a count. They wanted to bring back the music of the ancient Greeks. So they created a melodic singing style known as monody. (The Dean is conscious of the fact that a monody can also refer to a poem mourning someone’s death.)  It became staged and developed into what we know today as “opera.” The first operas were composed around 1600, and they define the end of the Renaissance. So, here is your case. They incorporated old Greek inventions into something brand new.

Barbara: So it pays to go back and pick up elements of the past to produce something lasting and innovative. 

Dean: Great. (glancing down at his watch) I’m watching the time. Professor Britten (pointing to the blackboard), let’s stay on track with your history. Tell us about the next stage of music -- the Classical Period.

Britten: The Classical Period develops a homophonic texture with more accompaniments. But now composers replace the singers with more instrumentation in their work. In the transition from the Baroque to the Classical Period, the sonata undergoes a change in usage, from being applied to many different kinds of small instrumental work to being applied to chamber music genres—with either a solo instrument, or a solo instrument with piano. 

Instrumental music now overpowers the human voice, and the symphony is born. Small changes lead to what you might call a qualitative change. (For Tom, this brings to mind the small changes in the birds on the Galapagos Islands resulting from their environment that brought Darwin to write about evolution. He raises his hand.)

Tom: So the symphony evolved from the sonata. (The Dean beams pleased to hear students putting together pieces of the evolutionary puzzle.)

Britten: Yes, the symphony evolved from the sonata. The “sonata form” developed during the Classical era to become the primary form of instrumental composition.

But the opera and the oratorio were saved, while the “voice” becomes, let us say, instrumental. We see simple patterns, such as arpeggios and the Alberti bass, liven the movement of the piece.

Mary: How does a new form develop from the old? Was it like the way scientists built on their predecessors, their ancestors? 

Britten: You probably don’t know the names of predecessor-composers, like Johann Stamitz, Franz Xaver Richter, Carl Stamitz, and Christian Cannabich. (By that, I mean they preceded the “greats,” whose names you probably are familiar with.) They exerted a profound influence on Joseph Haydn and Wolfgang Amadeus Mozart, who were the central figures of the Classical period.

These great composers built their work on the past, and influenced those other great composers who followed them: Ludwig van Beethoven and Franz Schubert, for example, who in turn became transitional composers for the next period, and so on,. Beethoven and Schubert would then lead us right into the Romantic Period, expanding and enriching earlier forms of music.

Dean: The “Romantic Period” in music. Now that came with a lot of other changes in high culture also – in literature, philosophy, and the arts. Could we say the Romantic Period deepened interiority? (Professor Benedict knows what the Dean is proposing in terms of developments—above all in the West—in the inner life of people. But she also thinks that the Dean is a little romantic himself on this point.)

Britten: Well, yes. In the Romantic era, music became more expressive and emotional, if that’s what you mean. Let’s see who we can name.

Composers here would include Schumann, Chopin, Mendelssohn, Bellini, and Berlioz. In the late 19th century, we see a big expansion in the size of the orchestra and the number of composers: Johann Strauss II, Brahms, Liszt, Tchaikovsky, Verdi, and Wagner. Between 1890 and 1910, a third wave of composers came with Dvořák, Mahler, Richard Strauss, Puccini, and Sibelius. They created more complex and longer works. Students, what are your thoughts and questions at this juncture?

Barbara: I am in political science. What about the politics in this new period of history? How did that influence music? The nation-state was evolving at this point. Were national anthems composed in the 19th century?

Britten: Yes. And thank you for introducing this aspect of the life of those times. Late 19th century music shows a nationalistic fervor in Dvořák, Sibelius, and Grieg. And in also Saint-SaĎns, Fauré, Rachmaninoff, and Franck. But music has its own character apart from the development of national states.

Dean: We have already entered the 20th century, and now we see inventions in mass media and technologies. Correct?

Britten: Radio gained popularity with records that reproduced and distributed music over a wide area. And now, there is diffusion: music goes everywhere.

Barbara: And democracy is evolving.

Britten:  Yes. Now music is no longer listened to just in private concerts and elite clubs. Artists could be heard nationwide. Music performances became portable. Headphones allowed people sitting next to each other to listen to entirely different performances.

Benedict: It’s invention all the way. (She smiles at the Dean who nods with approval.)

Derek: How did musical instruments evolve?

Britten: Well, in the Medieval Period drums were used mostly for military and dance purposes: kettledrums and bells and cymbals. There were also bowed instruments like the vielles (precursors to the violin family); and plucked strings like the lute; different trumpets, and the horn and small organs. During the 1300s large organs started to appear in the churches. Composers and listeners are very dependent upon new technology.

Dean: What happened with instruments in the Renaissance? Keep speaking about new inventions.

Britten: Renaissance viols were fretted with six strings tuned in fourths, with a third in the middle. They were used in ensembles called consorts. Compositions for the lute were written in tablature; that’s a special kind of musical notation. The wind instrument was the recorder. Organs continued to be played in churches. Two types of keyboard instruments were the clavichord and the harpsichord.

Dean: (Interrupts.) Questions? Think of ways to connect what Professor Britten is telling us to some aspect of your major field.

Derek: (Derek, in psychology, is recalling the class lecture on the brain.) How could this story be connected to the brain and its evolution? I’ve read that there are changes in the brain that happen with new music. So, there could be a correlation here between the growth of the brain and the appearance of new instruments. Each new instrument must have opened a different portion of the brain to appreciate the new sounds and rhythms. Listening to music creates new pathways in the brain.[16]

Britten: You could be right. It took time. The human mind – the brain -- had to get accustomed to new instruments. The Baroque organ was more powerful than the Renaissance organ. The harpsichord’s tone was produced with quills that plucked the strings mechanically every time a key was pressed. The tone was stronger than that of the clavichord, but it could not produce dynamics. The harpsichord is one of the most distinctive sounds of the Baroque Era and was the most favored instrument in solo music.

Dean: And the violin? It has such a range of sweetness, depth, and tenderness. Einstein loved it.

Britten: The violin family became the leader, the dominant timbre in late Baroque ensemble music. It blossomed with the symphony.

Dean: Can we return to our discussion on the principles of evolution? Students, what do you think? Questions?

Mary: I’m wondering again about that word “progress.” Professor Britten, do you see an increase in freedom for music in this history? We saw greater freedom happening in chemistry and biology and many areas of civilization. (Britten is taken aback, puzzled and quiet, thinking. Stewart Perry steps in.)

Perry: Professor Britten, let me clarify what she is talking about in terms of science.

“Degrees of freedom” is a term used in explaining dependence on parameters. It involves counting the number of parameters within which something can operate. In mathematical terms, the degrees of freedom are the dimensions of a “phase space.” In quantum theory, for each particle belonging to a system, and for each independent direction in which movement is possible, two degrees of freedom are defined, one describing the particle's momentum in that direction, the other describing the particle's position along an axis defined by that direction.

Mary: And in biology we saw animals evolving with more freedom. They developed more capacity to make choices -- based on the evolution of their senses and the brain.

Britten: Okay, yes. More choices: more instruments, more chords, more styles. And yes, more freedom for people to compose. Twentieth century music saw more freedom for musicians to choose musical instruments, keys, pitches and styles.

At the end of the 20th century, composers broke the rules of classical music. Inventors challenged the rules by making more amplification available, and also new electronic instruments. The synthesizer revolutionized everything. One musician could now have the freedom to play any “voice” immediately on a single instrument -- the synthesizer. A musician playing a synthesizer had the option of composing with the sounds of violins, coronets, clarinets, drums, bassoons, and so on, all right at a his or her fingertips.

Mary: Wow. “Synthesizing with a synthesizer.” I did not think of that. How did the synthesizer develop?

Britten: Slowly, in my lifetime. Over 50 years ago, the first synthesizers were pretty crude. They consisted of an oscillator with sine waves passed through other modules to alter the initial tone. In the 1960s and 70s, rock musicians began to realize what synthesizers could do. In 1964 the Moog Synthesizer was displayed at the Audio Engineering Society Convention. The first album to hit number one with a synthesizer was in 1967. In 1970 Moog designed the first synthesizer keyboard. It became popular across the country because keyboards were movable; they could be used anywhere. In 1978, the first polyphonic units were created, and inventions on synthesizers went forward from there.

Dean: Yes. Good. We are pretty much up to date on music history—considering the short time available to us, of course. Is it time to look at music theory?

Britten: Oh. It would take years for this class to learn music theory – melody, pitch, rhythm, scales and modes, harmony, dynamics, texture, scales, notation. It’s not easy. We should stay close to your realm of ideas.

Dean: Right. Let’s stick with the ideas on evolution. (He goes to the blackboard and writes:)

Music Theory

Okay, class. Ask the Professor anything about music theory that is connected to evolution. (Pause, for the class to think.) How about in the area of biology?

Tom: In biology, evolution is based on chance. Stephen Jay Gould wrote that if we could rewind the "tape" of evolution, and replay history, the result would not be the same. Humans would be almost certain not to “re-evolve.” This is because natural history is based on randomness. (Britten is not sure what Tom wants to ask.)  I mean, if you think of the number of “contingent causes” that could happen along the way—for example, Gould wrote of asteroids hitting the earth, continental drift, cosmic radiation, etc. The contingencies are so high that it is unlikely they would occur again in the same sequence, or even occur at all. So, my question is: What do you think about this? Is the development of music also based on chance?[17]

Britten: Well! (impressed by Tom’s imagination) How about putting chance and purpose together in evolution? (The Dean sits up, eagerly intent on Britten.)

Aleatoric music is a composition in which some part of it is left to chance -- on purpose. John Cage was a pioneer in this field. His guide was a text called the I Ching. (In a joking way, he says, his colloquial Southern roots suddenly coming through:) Y’all read about the “I Ching” in your assignment in Human History, right? (Everybody nods “Yes,” even though some had forgot about reading the section on the I Ching.) 

In 1957 Cage lectured on Experimental Music. In the lecture, he stated that, “Music is a purposeless play.” Cage also believed that music is "an affirmation of life.” Music is a way to get us to pay attention to the wonderful sounds around us. For example, we don’t usually notice the rhythm of street traffic in the background of our lives. A child picks up a stone and looks at with amazement, enthralled; but we adults don’t normally notice its aesthetic quality. Music, according to Cage, has everything to do with “waking up.” We are pushed by it into enlightenment. (He is speaking lightly—with humor but not facetiously—about enlightenment; but Professor Benedict, a Buddhist, likes this reference to “waking up.”)

Tom: Hmm. (puzzled, since Professor Britten’s words are countering what he has been learning in biology.) So music is based on both chance and purpose? I wonder if maybe that could also be true of Nature. (His forehead tightens: No, this cannot be. Everyone waits for more insight.)

Tell me—all of us—more about the purpose of music.  I’ve studied Natural Selection in biology, and I cannot immediately think of a reason why music would evolve. Why should it? Music is not caused by Natural Selection. There is no struggle for survival going on related to it.

Britten: Well. Music is based on emotions. (Tom’s eyebrows pucker.) If you studied music theory, you would know what I mean.

You would learn all the expression marks on a music sheet—listen as I name some and see if you can tell what they mean—like “Amoroso” (he sounds the word tenderly), “Animato” (he speaks with liveliness), “Doloroso” (sorrowfully); “Furioso” (angrily) “Grazioso” (his voice has a tripping grace now). We all live by our feelings. You grow by them, through them, and past them. You appreciate feelings and transcend them through music. That’s the purpose: transformation and transcendence.

Tom: (Puzzled.) I don’t get it.

Britten: You have grown beyond the emotions of childhood, hopefully; that is, you’ve transcended the way in which you experienced emotions when you were a child. (Tom looks baffled, confused.) I assume you don’t cry for your milk anymore. (He grins, half mischievously, and students laugh.) You had a feeling of self-importance when you were a child. When you had a birthday party, people sang “Happy Birthday,” and you felt proud. (Smile and pause). But now when you sing other songs, your feelings expand. You all have sung the national anthem at some point. It represents a more expansive feeling that you have as American citizens.  So there is some music that brings us beyond our selves and our egos. Now think about this: you may listen to music for its own sake,  simply for enjoying the feeling it evokes. Music says what you cannot say with words. (Britten suddenly feels his grief. The class does not notice, but the Dean does and wonders how he can be brought back.)

Tom: (insisting) But, there is no struggle for survival here. There is no Natural Selection. So, I still don’t get why music would evolve or how there could be a purpose for it.

Britten: Well. There are many reasons. (Looking out the window to move past his sorrow, unable to speak.)

Dean: (picking up Tom’s chain of thought) I’m curious about this, too, like Tom. Hmmmm, let me see. Why would music evolve? (pauses)  Well, at one time, there was no such thing as a concerto. Not Australopithecus, not even Neanderthals could have understood them. Classical music must have evolved as “we” humans matured in civilization. But it must have started from something as basic as the body’s vibrations. (Britten is brought back.)

Britten: Well, yes, rhythm in the body. In ancient times, the body’s rhythms brought people to share their feelings with one another. People wanted to celebrate a birth or mourn a death. (Pauses, halting again to fight his sadness, then rallying once more.) Music evolved to deepen our lives. It evolved to create a greater sense of who we are. Who are we? (This is a sudden, spontaneous question. Whereupon, Mary brightens. This is her signature question.)

(to Tom) Can you tell us, Why are we here?  (Tom is taken back by the energy directed right to him personally. The Dean knows that the professor is asking himself that question. )

Dean: Professor Britten. We talked about the fact that Mozart was an inventor. He brought together deep emotions in his music. He enriched our lives. You referred Mozart’s Concerto No. 9 in E-flat major to me. Could you describe for us something of the way that piece develops musically?

Britten: (Readying himself.) Well. We first hear, Allegro, then second, Andantino, and third the Rondo. And in each of these three concerto movements, Mozart combines different musical elements to create something new. He was working with a soloist to create a sense of her feeling and presence to the audience. (The Dean nods to go ahead, showing his interest.)

The first movement gives the listener—well, for me— the impression of joyful audacity. Yes, there is an eagerness to move ahead, almost unpredictably. And then in the second movement, a key change takes place to relative “C-minor,” and this shifts everything into a dark place. It is infused with a terrible sense of mourning and anguish. (The Dean nods empathically, “yes.”) Finally, the third movement combines both of these feelings into a single intricate and beautiful, almost terrifyingly emotionally complex, whole.

 Dean: Oh. I have to listen to it. How does Mozart put together such different moods…from joy to agony and then to a new power that integrates such different moods? (The Dean is hoping this discussion will help everyone understand that feelings are also part of evolution.)

Britten: Mozart develops each of two emotional sides in the person of the solo pianist. He wants to dramatize the tension between the first and second movements. Then he integrates them by using repeated contrasts in instrumental texture, harmony, melody and theme. (Pause.) Frankly, I am moved when I hear it. (His eyes water.)

Dean: I see: Mozart is bringing together those contrasts to produce a higher, maybe deeper mood. Well, I would say he is synthesizing these movements.

Britten: The first movement is about the audacity of the soloist; it is joyful. The second movement in C-minor takes the concerto's drama in an entirely new direction. In it Mozart introduces a vivid emotional dimension to the soloist  – raw, mournful, soul-wrenching anguish. The musical contrast of the second movement is harmonic in nature; but once again there are additional, less prominent contrasting elements that advance the same thematic ends. (The Dean senses that Professor Britten is returning to normal and, insensibly, relaxes.)

Tom: Does Mozart have a purpose in putting all this together?

Britten: Well. These contrasts serve two purposes. First, Mozart uses harsh dissonances to set the stage; I mean he creates a harmonic conflict between voices in the orchestration. This deepens the listener's sense of spiritual anguish. Then, he intertwines C-minor passages (the main body of the movement) with – I would say -- wistful harmonic forays back to E-flat major. This serves as a signpost for reminiscence of the "happier days" of the first movement. So Mozart uses harmonic contrast to highlight the comparison between the two moods of the soloist, who I mentioned, developed in the first and second movements.

Dean: Interesting. But how does Mozart make the transition between the two moods? (Tom, on the other hand, is thinking: How do the blooming times of ornithophilous flowers, for instance, come to join with the hummingbird’s breeding seasons?)

Britten: To emphasize the new (mournful) aspect of the soloist in the second movement, Mozart uses musical contrasts, carefully chosen. I can tell those of you who know music.

Some of these “contrasts” are anything but subtle: for example, the Andantino tempo of the second movement is markedly less lively than the Allegro of the first, which sends a signal to the listener that an emotional shift is to take place. Composers would understand why Mozart decided to write this movement in the relative minor (C) of E-flat. (Realizing that students may not understand what he is talking about, Britten focuses on them now.) I should explain to members of the class, that minor keys sound sad – the minor key is the mode of the dirge, the marché funerale – and, like tempo, it will specify the emotional tenor of the movement.

Dean: Why does the minor scale convey this mood, would you say?

Britten:  The harmonic minor scale contains a dissonant augmented second interval between the sixth and seventh degrees. Mozart uses it to good effect.

Dean: How? (happy to see that Professor Britten appears to have fully recovered.)

Britten:  In measure 4, he uses a neighboring non-chord tone on the downbeat to introduce the augmented second dissonance between the first and second violins; and then he accents this harsh sound -- laden with associations of mourning -- with a decisive fortepiano. This forces the movement's modality into the listener's consciousness. A similar device occurs in measure 12, where Mozart once again adds non-chord leading tones into an “iv chord,” where they make the same augmented second with “A flats.”

Dean: Goodness! (looking at the class) I think, professor, that you are far beyond us. I do not know music theory that well. (Looking at the class.) Students, do you have questions? As always, think of your major field.

Barbara: In my field of political science we have also talked about transformation. We said the terms of science are the same as the terms of music. In this class, we have talked about how atoms “transform” into molecules, molecules transform into cells, and so on. That led me back to thinking, in terms of political science, about how nations transform. What does “transformation” mean in music?

Britten: Well, “transformation” in music is any process that a composer may apply to some basic element in the composition. An element might be a melody or a chord that changes its progression. It may involve rotation, permutation, inversion, retrogression, indeed, all sorts of reversals and combinations can transform the sound. If the change is big, it becomes a metamorphosis.

Tom: In biology we looked at evolution as both slow and sudden, with occasional gaps or leaps. How does music change its course?

Britten: Well, change in the course of music is also both slow and sudden. Look at the music of Arnold Schoenberg. Schoenberg's atonal music made a revolutionary break with the past, particularly in terms of harmonic structure. This quick kind of change does happen. But some music scholars now challenge just how sudden even this change was. They argue that Schoenberg's “atonal” music does not constitute a sudden break, that is, a qualitatively different type of music. Much of his music is “atonal,” but Schoenberg did not make a complete break with prior practices, even in the harmonic realm. Instead, he transformed music by a series of incremental changes. (The Dean looks out to the class for questions, thinking this point may be too complex to pursue.)[18]

Ann: I’m majoring in theater. We don’t hesitate to ask, what is the purpose of theater? Shakespeare has an answer to that question: Theater holds up a mirror to us …we are actors on a world stage. My teachers say, “Theater arouses, enlivens, and enriches.” But your question... What are we here for? That’s a really hard one. (Prof. Britten nods in agreement. It’s a tough one. He looks out the window without answering. Ann looks around her – awkward, a little disconcerted.)

Tom: (filling the gap) I know what we’re here for! Survival! (Britten looks down, almost furtively. Silence. Students wonder if he is upset.)

Benedict: (pausing, looking at Tom). Check your body. Music is life; it’s in your nature. Feelings in the body told Neanderthals what to do in time of danger.

Britten: (slowly returning to the present) Music radiates from the centers of the body, then out and back through our eyes in our sight, our ears in our hearing and by our touch. Everything is organized according to a center or periphery scheme, with radial structures moving outward. (The class is mystified).

Ann: What does that mean?

Britten: It means that music starts with natural needs. Have you ever been on a lake in the woods and heard the call of a loon? (Someone says, “Yes,” emphatically.) Loons are social. They make different sounds…different calls. The hoot call keeps them in contact with mates, and their chicks. The tremolo call, listeners say, sounds like… insane laughter. (Ann whispers an incredulous “What?!”) This call consists of 8 to 10 notes and is voiced with different frequencies and intensity. It’s a sign of agitation or fear: a predator is too close.

The wail occurs at night; you can hear it for miles. It is haunting. (Ann nods Yes.) It keeps these creatures in contact with each other. They have a community to maintain: they support each other; they need each other. (Tom raises his hand but gets no response. Britten is concentrating.) Then there is the yodel. It is made by male loons to advertise their territory. If you hear it, you are too close. Give them some space.

Tom: You mean: the body and the mind work together like birds of a feather? (Big joke, “haha!”  Tom is booed.) No, I am serious. The body and mind must work together to create music. 

Britten: Yes. The body and the mind are permeable. I mean: they interpenetrate one another. But the mind has a higher purpose than the body. Leonard Bernstein said, “Music... can name the unnamable and communicate the unknowable.” (Anne says to herself “Am I unknowable?” ) Leonard da Vinci said: “Do you know that our soul is composed of harmony!” (And Kathleen thinks,  “But what is the soul?”)

Kathleen: What is causing music to evolve? It is not just social relations. 

Britten: I think the “cause” is concealed.

Kathleen: Concealed in our souls? (She has been reading about the soul in theology.) What do you mean by “soul”?

Britten: I’m not exactly sure. I mean some power deep inside us and beyond the mind… Something that is pushing us to stay alive and find our purpose here on earth. (He stands upright, and deftly straightening his tie, moves the topic back to his own expertise.)

Music theorists look for a scheme, a schemata, in music. (Quizzical looks from the class.) That is the general plan that theorists get from listening to a work of music. A scheme integrates the whole piece.

Alice: The Dean told us that everything we know is based on experience. There is no one scheme.

Britten: He’s right. Music is… a “richly grained experience.” It cannot be explained by a scheme, alone. It’s… well, it’s beyond thought. (Thinks, his hands lifting slowly, palms up in front of him: this is beyond his cognitive comprehension.) It is the cause for thought! (Smiles).

Alice: But my professor in philosophy has said that everything is based on thought. Philosophy teaches you how to think.

Britten: Yes, but music also goes beyond thought. It starts with your body, like I said, from your pulse… and impulse. Then, as you see how music evolves, classical music began to call on very complex emotions. But it does not ignore the bodily impulses. (Derek has read about “cognitive perception,” and he is aware that the body is part of any scheme of thought, So he is curious about where the professor will go with this.)

When we talk about music, we say, the sound is going “up” or “down.” That’s a perception we learn from our ears in relationship to our whole body. We learn that concept from our bodily experience of space. (Alice wonders “Where in the body?”)

In music we talk about a composition being either in “contraction” or “expansion.” We get that concept from bodily perception, from feeling tightening and relaxation in our own bodies and from seeing something’s external to ourselves contract and expand. We talk about music as being “warm” or “cool.” We get that from the body feeling a temperature external to itself. But then from those bodily experiences we abstract from perception to conception. But the body is the source of the idea:  music goes—usually—from pulse and impulse to rhythm and thought.[19]   (split-second pause) Music is cool, wouldn’t ya say?

Alice: So the evolution of music was built up from the body preserving what it knew from our perceptions of Up and Down, Contraction and Expansion. The “body” comes first in evolution and then thought comes later – abstracting from it.

Britten: Yes, and so do emotions… come later. (He thinks for a moment about the unimaginable.)

But…what if your whole body was composed of music? (He speaks directly to Alice, whose eyebrows lift in surprise. He then turns to the Dean.) We don’t know. The body has feelings, like the sensation of pleasure. Then, as we mature physically and emotionally, “pleasure” builds into “joy.” We grow. And music evolves along with deeper emotions. We synthesize conflicting emotions and build new music to express them, and this synthesizing process.

Alice: But how does that happen?

Tom: You heard the professor tell us about Mozart’s concerto. (He sounds rather impertinent. Alice does not like his instructive tone. But he turns to the professor.) Would you tell us more about the basics of musical composition? How do composers create chords? Do they hear them inside the mind? Where do harmonies come from? Where do composers get their ideas? (Big questions, the Dean thinks, not “basics,” but where else but from students?)

Britten: When Beethoven was asked about his compositional process, he said: “The elaboration begins in my head: expanding, compressing, raising, and deepening…It rises, it grows tall, I hear and see the image in its entire extent, as if cast in a single mould.”[20] 

What do you think?

Derek: I’m in psychology. So I would say: music starts in the unconscious. The unconscious carries collective images with emotions that accompany those images.

Britten: Okay, for starters. But it also demands learning the intricacies of musical form in order to be able to contain the expression of those emotions. You need to get the feelings and thoughts—which can be awash in the body and mind—down on paper in a communicable form. (Derek is concentrating fiercely.)

It’s a synthesis of nature, nurture, and education. Skills are learned. Mozart heard symphonies in his head. And Mozart’s father had taught him as a child. So with the training he had received, Mozart could translate the sounds he heard onto paper. He was a genius[21] (Pause.) Questions?

Derek: Do you suppose that we are learning to produce the sound of our own evolution? (The Dean is shocked. Hearing Derek’s question, he recognizes that this is what he has been thinking all along but could not articulate it. He starts to respond but is interrupted:)

Alice: Would you say that music has a philosophy? 

Britten: Yes... and no. The philosopher Schelling said, “Art documents what philosophy cannot represent externally.” The “aesthetic”—music, in this instance—“is the culmination of a philosophical system.” Music is the end of philosophy. So for him, music is not philosophy, but is emblematic of something more.

Alice: More what? What did Schelling say?

Britten: More freedom. Freedom is evolving through music, he said. Music helps us to arrive at a greater sense of freedom...more choices (smiles sadly) perhaps in some heavenly place.[22]

Dean: (noticing his sadness) Class, if you have any more questions, you can ask me, too. Also remember: think for your selves.

Harry: I believe math and music are closely related, but I don’t know exactly how. (politely) Perhaps the professor could help me.

Britten:  The two fields are intertwined. But no math formula can define a melody. A melody is too self-contained, too unique. The successive notes refer to each other in an imprecise chain; they cannot be extracted from the context in which it is building parts within a whole. Dean: (trying more firmly to direct the conversation away from Professor Britten) Class, what do you think? Give your own opinions. I have spoken about binaries in evolution – such as unity and plurality. Nature seems to look for “unity in diversity.” Can you think of how that might also apply in music? (No hands go up.)

Perry: (into the breach) Well, of course if you put it that way, yes. There is unity in harmony. But unity (that is, “unison”) needs dissonance to give the music emotional depth. We need to be shocked emotionally by discord. It is with dissonance that we wake up. Unison by itself could lead to monotony.

Dean: Ah! Harmony is the basis for creating the diversity in a concerto, with all its moving parts. Harmony is what pulls together all those parts, even with their variety. (Britten nods in agreement, but remains silent]. The Dean looks to the class.) Ask me any question that you can’t figure out. Let’s see if all of us can answer without our resident expert.

Tom: Professor Britten said that music involves the body, the emotions, the mind, and the soul. That’s everything that we are…and maybe more than we are. So, I’m stuck. What is the purpose of evolution?

We debated whether evolution was based on Mind or Matter. Our bodies are material; our minds are non-material, but touched with the rhythm of our bodies. Is music simultaneously both music and matter,  like a particle and a wave? Does music answer our debate? (The Dean is taken back by Tom’s thought. Britten is hesitant to speak. Stewart Perry comes forth.)

Perry: Yes! (Then looking around for Britten, raises his hand. Britten nods.) The universe is composed of vibration. Nature is all vibratory, outside and inside our bodies. Music is the “sound” of nature. And we are learning to hear and produce that sound. (The Dean again is pleased and surprised. “Yes. Yes!” he says to himself. “Yes! Music is the ‘sound’ of nature. We are composing the sounds of nature, inventing at this higher level of consciousness. Vibrations in the universe go through our whole body -- atoms, molecules, cells, the organism, and consciousness! Oh! Ah! His excitement would force him speak, but Tom beats him to the draw.)

Tom: We talked earlier about how primitive emotions exist in animals as a precursor to human feelings. We concluded that music begins in animals. Right? (The Dean decides to bring up the subject of vibrations later.)

Perry: (returning to Tom some of his medicine of impertinence). Do you remember what Professor Britten said a little while ago about loons?

Tom: How do you know that music goes back to atoms and molecules? Professor Britten says that music begins in the body. Toddlers dance before they speak.

Perry: But where does that rhythm in the body come from? The body is nature. The body is social. All animals – like loons and babies – are “singing” in common. 

Dean: We talked about the universe being social. Remember? Social relations begin with molecules and keep developing with amoebas and ants, cats and cows, and now with human beings. There must be some sort of capacity for an “identity” with others -- right from the beginning. There must be some—could we call it?— primitive “empathy” right from the get go. There is some sort of communication in nature itself.

So who are we? Where are we headed? What is the future of music?

Perry: You tell us, Professor Britten, where are we going? Will composers in the future write a different harmony with different chords, new instruments, novel sounds. (Perry is thinking: “What are the chords of constellations?!” Kathleen is thinking: “What are the sounds of angels?” The Dean is thinking: “What are the sounds of humanity?”)

 Britten: Our bodies could be playing symphonies right now, and we wouldn’t be aware of the fact.

Perry: Remember what Carl Sagan said? The human body is made of star stuff. We have been the atoms that are also built into constellations. Could each of us have our own song?

Kathleen: We may be more important than we think. (She thinks to herself:  Not even a single sparrow is forgotten by God the Bible says.  And every one of the very hairs on your head have been counted.   Fear not.   You are worth more than a flock of sparrows.)[23] But how could you prove that the body carries music?

Perry: I have looked into this. A resonance operates throughout all the body’s organs. The motion of the liver chimes with the movement of the heart at the interval of an octave. What I mean is this vibration is literal. It’s real, not just in our imagination.[24]

Dean: (more excited) Thanks, Perry; this is a knockout! This resonance should be measurable, and so scientists should be able to prove or disprove this hypothesis. I know about homeostasis in the body, but not about the body’s harmony.

Britten: Yes. Music is like poetry with its alliteration and rhyme – it starts by conserving the past, and giving us the pleasure of recognition. The pleasure builds toward joy: that’s a leap beyond pleasure. By rhythm, it moves us into our soul.

Dean: Yes, and we are participant observers following the creative powers of nature. I hope we’ll be able to expand on this notion. But in the meantime, Professor Benedict, what do you think about all of this? 

Prof. Benedict: I agree. I think composers abstract their emotions into rhythms, and on into chords and songs. In society, emotions become patterned in music. (The Dean looks puzzled as she looks at him). You know, take the Blues, for example. Harmonies bring together disjointed feelings – discordant emotions -- into unity.

We all have had moods. We have lost friends and relatives who die… We get the blues, and so we put those feelings into sound and rhythm. We share the “blues mood” and in doing so create a community.

Britten: Well. We share feelings -- like the loons — but our moods get more complex. We preserve the wail of loons, but we move beyond them. (Students chuckle.)

Perry: How do we move beyond them? By melody, harmony, or rhythm? (The Dean was hoping to see some conclusion to this point, but now Perry has raised a related question.)

Britten: Richard Wagner says that melody is the primary element of music. Harmony and rhythm are “shaping organs.” Melody is a constant digression from the “tonic.”[25]

Dean: The tonic. We should mention to students – those who do not have music training – that the “tonic” is the first note in a scale. Harmony is built from this tonic sound. The tonic starts everything off, and at some point a composer returns to it. Do you understand? (All heads nod yes. Alice raises her hand.) 

Alice: Can I ask you a question, Professor Britten? (He nods and mouths quietly, “Of course.”): Could the Big Bang be the “tonic” of the universe? (A nervous laugh at this question.) Could the universal “tonic” be a tiny representation of the Big Bang? (“Out of the mouths of babes!” the Dean thinks,) 

Britten: Ha! Mmmm. Are you in philosophy? (Alice nods Yes.) Then I can tell you that, if Hegel were alive today, he might think so. Hegel saw music as rising by steps: from rhythm to harmony, and melody. For him, melody represents an Aufhebung by which rhythm and harmony are at once negated, assimilated, and lifted up.[26]  (The Dean worries that students -- except for Alice -- will not understand the German word.)

Kathleen: (Raises her hand.) I’m not sure what that word means. (She tries to pronounce it: “Auf-hay-boong”?)

Britten: Well. It’s hard to translate. It can mean different things, like abolish, repeal, and reverse… And it can mean opposite things, like “cancel-and-keep,” or “out-and-up.” The English term for Aufhebung is “sublation,” which means that something is preserved and changed through aninterplay of opposing forces. Yes, come to think of it: I think that this—I mean this concept encompassed by the complex word Aufhebung— is what the Dean believes explains evolution. [27]

Dean: Well. It’s only an Idea. (The Dean is being sardonic, modestly self-critical. He is close to Hegelian philosophy in his perspective, but he is not a romantic idealist like Hegel and those other philosophers. Never. No one catches his self-critical humor; so he nods to Britten to proceed.)

Britten: This would mean that music is what’s going on in the universe: Harmony with a trillion pitches, clashes, and dissonances. Music – like the universe -- is anchored in a kind of motion/rest dynamic.

Dean: Hmm, are you saying that this interplay of forces —this Aufhebung—is what music is all about?

Britten: In a sense: it’s like poetry. William Wordsworth said “the rhythm of respiration and the beating heart” is just as “organic” as a melody. Check it out.[28]  (The Dean notices that Britten is buoyed by this statement.)

Dean: Check it out? Wordsworth’s claim sounds like idealism again – the German variety. Does music transform what is “real” into what is “ideal”!

Britten: Schopenhauer saw melody as “the highest level in the objectification of the Will.”[29]  He could be right. I remember these lines from Lord Byron’s poem Don Juan:

There’s music in the sighing of the reed;

There’s music in the gushing of the rill;

There’s music in all things, if men had ears:

The earth is but an echo of spheres.[30]

 

(Everybody is silent, absorbing as much as they can of Britten’s words and allusions. This is a little beyond them. The Dean looks out the window, pondering. He is not an idealist, and he has more sympathy with science than with poetry. The class wonders: has some new thought struck him? Finally, he looks at Britten.)

Dean: We talked last night about physics. Pythagoras and Kepler. Perhaps this is the time to break new thought. (The Dean goes to the blackboard writes:)

Vibrations

What about vibrations? Stewart Perry studies them. You heard him say that they could be the “key” to evolution. This goes beyond the Mind vs. Matter debate. (to Perry) Mr. Perry, you may be able help us as we explore this topic. But for now, Professor Britten, maybe you could start us off with Pythagoras.

 

Britten: Pythagoras discovered that the pitch of a musical note depends upon the length of the string that produces it. He correlated the intervals of the musical scale with simple numerical ratios. Look. An octave is produced when a musician plays a string that is stopped exactly halfway along its length.

(Prof. Britten picks up a portable keyboard he has brought to class and illustrates his point by playing octaves.)  The octave has the same quality of sound as the note produced by the unstopped string; but since it vibrates at twice the frequency, it is heard at a higher pitch.

Dean: Anything more? (Smiles because they had both hoped to get to this idea.)

Britten: The mathematical relationship between the keynote and its octave is a frequency ratio of 1:2. In every type of musical scale, the notes “progress” in a series of intervals from a keynote to the octave above or below. (Professor Britten plays chords, fifths and fourths on the keyboard.) Notes separated by intervals of a perfect fifth (ratio 2:3) and a perfect fourth (3:4) have always been the most important “consonances” in Western music. Pythagoras discovered the basis of musical harmony.

Alice: (Eager to stay in the conversation.) Did he see a connection to the universe?

Britten: Ah, yes! For him—as for Lord Byron, in the lines I quoted above—music on earth was a faint echo of the “harmony of the spheres.” In ancient cosmology, the planetary spheres ascended from Earth to Heaven like the rungs of a ladder. Each sphere was said to correspond to a different note of a grand musical scale. Each tone sent out by the planets depended upon the ratios of their respective orbits, just as the tone of a lyre-string depended upon its length.

Perry: (seizing the moment) Kepler was an ardent Pythagorean. Pythagoras and Plato had idealized the circle but Kepler found that “nature” in this case preferred the ellipse. He had to wrench his mind free of the dogma of the circle and said he was almost “driven to madness” on the matter. The astronomer Fred Hoyle said that Kepler’s description of the correspondence between musical ratios and planetary velocities is "frighteningly good." Pythagoreans used music to heal the body and to elevate the soul. [31]

If I remember correctly, the musicologist Joscelyn Godwin says, "...the celestial harmony of the solar system... is of a scope and harmonic complexity that no single approach can exhaust. The nearest one can come to understanding the system as a whole is to consider some great musical work and think of the variety of analytical approaches that could be made to understand it. None of them embraces anything like the whole."[32]

Dean: Professor Britten, Stewart Perry has been studying physics and forms of art as part of his thesis. So be prepared! He has informed us on more than one previous occasion. (Smiles in deference.) Yes, Stewart. What more?

Perry:  Physicists know that vibrations began right after the Big Bang, and that they kept going. We live in a universe of vibrations. (The Dean nods for him to continue.)  They began by opening up those subatomic particles with a spin.  Physicists see a progressive evolution in vibrations that step up in size. Atoms are made of a nucleus and electron shells. The electrons orbit the nucleus and rotate about their own axes. These are vibrations in the category of a million billion times a second (1015 Hertz).[33] 


Dean: Could you say that the frequency of these vibrations changes at each stage of evolution, from atoms to molecules…to humans?

Perry: Yes. Atoms are in groups with a much lower vibration due to their larger mass, but still in the category of Gigahertz (109 Hertz). 
If we look at any aggregate of atoms in a crystal, we find two kinds of motion: a circular spin-like motion and a reciprocating, to-and-fro motion, at relatively fixed points. (Looks to Britten, wondering: Is he being too technical for the class? No answer.) Pythagoras was the first string theorist. (Laughs. And Britten smiles.) [34]

Dean: Is it possible to trace the different atomic and molecular levels of vibrations all the way from the Big Bang to organisms, and Homo sapiens? 

Perry: I would say that vibrations are “turtles all the way down.” In theory, it is “music all the way down” – dissonance, harmony, pitches, and melodies.[35]

At the molecular level, vibrations could go from monatomic to ionic compounds, and to polymers—chains that are 100,000 units long—to the DNA. (The Dean wonders if this assertion can be researched empirically.) The vibrations are measurable in stages, even though we cannot hear them with our ears. (The Dean smiles happily, his question answered. Perry goes on.) A vibration occurs when atoms in a molecule are in periodic motion, while the molecule as a whole has constant rotational motion.[36]

Dean: Can we really document the change? What about the cells in an organism?

Perry: The organic cell has its own vibration level. The vibration is slower because of all those molecules being tied together in a complex order. In the movements of organic life—such as those of plankton—you can find on the outside only the reciprocating—or to-and-fro—motion, like the swing of a pendulum. (The Dean and Professor Britten both look interested; they nod and he continues.)

Our sensory system operates by means of electrochemical substances creating a pulse. Action comes when the neuron fires a spike. “Rest” comes as the cell is regenerating. So out of this action-and-rest code, our brain translates the sensory input into a perception of reality. These reciprocating motions are prevalent throughout the whole animal kingdom. The heartbeat and the pulsing blood-flow are like a pendulum, oscillating. [37] (The Dean is not sure of how science could document it.)

Dean: Have any scientists studied the music of molecules?

Perry: Douglas Hofstadter was the first to propose the idea, I think. He said that music is a medium for expressing the patterns of proteins and their DNAs.[38]

Dean: Wow! So it is being researched! (Perry nods Yes.)

Tom: Can I hear the music of molecules?

Perry: Sure. Google “Gene2music” and look for “samples.” You can hear “protein music” there. Check out the websites of biologists. You can listen to compositions and even submit your own genetic sequence and have it translated to music. The browser allows you to send in a sequence coding for a protein, which will then be converted into music and returned as a MIDI audio file.

Tom: I’ll check it out…Darwin thought music might have its “origin" in animals. These rhythms of molecules -- like bird songs in courtship – may have some sort of meaning for them. Monkeys beat on hollow logs to mark territory.[39]

Kathleen: We know that. But why is classical music capable of making people cry? Birds and monkeys don’t cry, yet my mother cries when she hears Beethoven’s Ninth Symphony. She sobs and sobs. Why?

Dean: What does she say about it?

Kathleen: She says it’s so beautiful. It’s the chords, she says. But, those chords don’t make me cry.

Britten: It’s her experience of listening and learning. She has the chord-sound resonating within her. Otherwise, it would not move her. (Looking at Derek) Derek would say: The sounds of those chords are in the unconscious, waiting to be heard. Beethoven’s chords must speak of sounds that he heard himself, while composing. They are already there, potentially. You just have to learn how to hear and experience them.

Dean: Jerry, you are in linguistics. What do you think?

Jerry: It would be like learning to speak. You speak one word at a time, noun, a verb, and adjective, and pretty soon you know the meaning of a whole sentence.

Britten: Ah! So that capacity to “hear beauty” builds up inside as you grow and learn to feel more deeply -- beyond the capacity and need even for food or sex.

Perry: (Still eager) Music began in those internal vibrations, I am sure. (The Dean nods support for his idea.) Each "particle" became like the string of an instrument, vibrating in frequencies. Each particle, that is, vibrates like a violin with different pitches. These particle “strings” can even split and combine. 

Dean: Tell us more.

Perry: I’m not alone in suggesting this. Dmitri Tymoczko studied at Harvard and now teaches at Princeton. He borrowed some of the mathematics that string theorists invented to test “the secrets of the universe.” (His fingers sign a quotation).

He found a way to represent the universe of all musical chords in graphic form. (By the way, he wrote the first paper on music theory ever published in the journal Science.) He says the cosmos is filled with chords of weird, multidimensional spaces, known as orbifolds; they turn back on themselves with a twist. They are like the Möbius strips that math teachers use to prove that a two-dimensional figure can have only one side.

Dean: Orbifolds?

Perry: A musical chord can be represented as a point in a geometrical space called an “orbifold.” Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have used the non-Euclidean geometry of these spaces. They use short line segments between structurally similar chords. These line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Consonant and dissonant chords possess different near-symmetries and suggest different musical uses.[40]

Dean: What? I’m not sure I understood what you just said.

Perry: Well, the simplest chords, which consist of just two notes, can be represented on a Möbius strip”? Three-note chords reside in spaces that look like prisms--except that opposing faces connect to each other. And still more complex chords inhabit spaces that are as hard to visualize as the multidimensional universes of string theory.[41]

Dean: But... can you prove it? (The whole class laughs.) Perry: Well… soon. Hopefully! String theory points to these higher vibrational dimensions -- D-branes and NS-branes. And all string theories predict “degrees of freedom.” These are extra dimensions of space. String theory may include 10, 11, or 26 dimensions!

Dean: “Twenty-six dimensions”! “Degrees of freedom”! We have talked about freedom before, about whether evolution is increasing freedom. (Smiles.) Is this the purpose of evolution? (Long silence. Barbara has spoken about freedom before and wants to participate; she raises her hand.)  

Barbara: We talked in an earlier class about political freedom. The history of humankind shows increasing degrees of freedom in society. The lower class has gone from being slaves in empires to serfs in feudalism to the employee – the free-wage earner -- in capitalism. Now I think this would fit with the idea of increasing freedom in music.

Mary: (to Professor Britten). You’re right. Look at the possibilities for greater freedom of choice in all these musical instruments. Thousands of instruments are now available from all over the world. A hundred types of drums alone – from snares, bass and kettle drums to bongo congas, Djembes… And look at the strings that have evolved:  the harp, dulcimer, lute…And at all the woodwinds and trumpet and music styles that keep developing, merging and emerging around the world. It is all about increasing possibilities. What better purpose could there be for evolution but freedom!

Tom: Well. Evolution reveals its purpose as it goes along. For Darwin, that purpose was survival.

Kathleen: I think the purpose is to advance more life – in all fullness. I think we are becoming more conscious that everything—even the molecules of stones—is “full of life.”

Dean: (excited by the way students are integrating the information on evolution, from past classes and the present.) My! You are all somethin’ else! But music!

Professor Britten what do you think is the purpose of evolution? Is it about developing a greater life? Is it about the enrichment of experience? Are we ready to go to heaven? (The Dean is joking, while Professor Britten is still resolving his feeling of loss. There is a long silence broken by the Dean.) That was a poor attempt at a joke, I admit. But do students have any final questions?

Barbara: I know you’ve already told us, but I need to hear it again. Would you mind to repeat: how did Bach compose fugues? (She is learning to play the piano in the music department. Professor Britten knows her from one of his classes and brightens.)

Britten:  Ah yes. Remember? Bach states a subject, a single voice. A second voice begins, a fifth above or a fourth below. The original voice plays some new material in counterpoint to the second. This means the two melodies are in a rhythmic profile, each separate and then together. A third voice might enter, and finally a fourth voice, and all the while, the earlier voices accompany the additional ones, all of them combining into a very complex texture.

Barbara: Someday I will play a fugue. (Everybody laughs, but she is serious.)

Dean: But there are also double fugues. And if a fugue has a subject, then a double fugue must have two subjects!  

Britten: Right. One example of a double fugue is the Kyrie from Mozart's Requiem. Bach’s Art of the Fugue also has double fugues with a lot of complexity. The composer of a double fugue must combine the two subjects simultaneously. And a triple fugue is even more complex. Wait till you hear Bach’s Contrapunctus VIII. Just listen to that. We can hear a brief segment of it now, if you’d like. I brought it with me – if there’s time, that is. (The Dean nods his “go ahead.” Britten selects a CD from his briefcase and plays a couple of minutes of the fugue. Harry’s eyes light up.)

Harry: I’m majoring in mathematics, and I’ve studied music a bit. I bet my field connects with the fugue somehow. 

Britten: Yes, you’re right. Bach is writing four to six formulas at the same time, using both the hands and the feet of the playing musician. He starts with a simple premise (like in math), and then escalates the complexity.

Harry: So the composition ends up being both simple (one premise) and complex – with many additions and inversions?

Britten: Yes. We have already talked a bit about Kepler. But we can leap ahead to the Baroque period and find theorists – with names like Johannes Tinctoris and Johann Fux, who said that a fugue represented the harmonia mundi  -- the music of the spheres. According to them, the revolutions of the heavenly bodies produce divine music. (Kathleen is eager to learn more about this for religious reasons.)

Let me tell you a secret: in ancient times, Plato, Pliny, Cicero and Ptolemy had also talked about “the music of the spheres.” Bach belonged to the Society for Musical Sciences. He learned a lot in this Society. The Society upheld the older arts of counterpoint and polyphony, for example, and Bach learned a great deal about them. The idea of counterpoint had developed in medieval Europe during the construction of the great abbeys and cathedrals. Cathedrals were designed to conform to the proportions of musical harmony. [42]

Benedict: Yes. In the Hindu Vedas you can read about Nada Brahma – “sound,” being the Creator. In the works of mystics in ancient India, you will read: “First song, then Vedas or wisdom.” When we come to the Qur'an, we read that “the word” was pronounced, and all creation was manifest. The Sufis held that the whole universe is composed of music.[43]

Dean: Hmm. We saw how science grew out of esoteric societies: Astronomy evolved from astrology; chemistry from alchemy. These ancient beliefs inspired renowned scientists—like Newtown—as well as secret societies!  

Britten: Right. And Nicholas Copernicus …in the 1500s …spent his life talking about cosmic harmonies.[44]

Harry: (Barely audible, almost whispering) I read that a mathematician worked on the problem of harmony -- Leonardo of Pisa in the 1200s, called “Fibonacci.” He discovered the Golden Ratio.[45]

Britten: Ah! Fibonacci numbers apply to Bach’s Art of the Fugue! The Fugue starts simple, before it becomes complex. Listen to the beginning… -- it’s just pure. Then it begins to get complicated; soon it’s elaborate – turning and twisting around its central theme, a spiral dance up a staircase, ascending in circles, like the inside of a seashell. Listen. (He plays 20 measures of the music, so students can understand what he is saying.)  

Dean: Great! Harry… and Stewart, what do you know about the Fibonacci numbers?  (He figures he will be in for a treat, goes to the blackboard and writes:)

Math and Music

Harry: Fibonacci numbers advance in this way:  1,2,3,5,8, 13. You add the last two numbers together to get the next number.

Dean: Fascinating. But what do they tell us? And what about the Golden Ratio? That’s mysterious.

Harry: The Golden Ratio. Yes. It’s a number. Hmmm. Two quantities are in the Golden Ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The Golden Ratio is a number equal to about 1.61…or, something like that. The digits go on forever without repeating.

Alice: The Golden Ratio may explain evolution. Plato said our senses conceal pure thought. There is a hidden truth beyond everything. Stewart, you are ahead of us. What do you think?

Perry: The Golden Ratio exists in molecules. The DNA is based on the Golden Ratio. The length of the curve in each of these helixes is 34 angstroms and the width 21 angstroms. (One angstrom is one hundred millionth of a centimeter.) The numbers 21 and 34 are two consecutive Fibonacci numbers. (Everyone is shocked by Perry’s show of knowledge, but the data is all in his dissertation.) You can also find the Golden Ratio in crystal structures and snowflakes. I am looking into the question of how spiral galaxies carry the Golden Ratio in their structures.[46]

Britten: Well. You are not alone. The violinmaker Stradivarius was aware of the Golden Ratio and used it to place the f-holes in his violin. [47]

Dean: Could symphonies be created around this Ratio?

Britten: The opening motif of Ludwig van Beethoven's Symphony No. 5 in C minor, Op. 67, probably the most famous composition in classical music, occurs exactly at the Golden Mean point of 0.618 in bar 372 of 601, and again at bar 228, which is the other golden section point—0.618034 from the end of the piece, but Beethoven had to use 601 bars to get these figures.[48]

Dean: I wonder whether there is a connection between what people feel in this music – like Kathleen says, her mother has sobbed at its beauty -- and this Golden Mean. Is the brain structured to experience, and recognize, beauty?

Perry: That would be a new research question for me. I will think of it in the future as a hypothesis.

Britten: Interesting. You will find a lot of information about this topic on the Internet. A British composer named Tim Benjamin points to a lot of the details. (to one of his students) Bob, you looked at this. Please hand out that information we talked about. (Bob passes out a sheet of paper with data on the subject.)

Bob: Here are some articles and books that explain how composers use the Golden Mean in their music.

“Some striking Proportions in the Music of Bela Bartókin Fibonacci Quarterly Vol 9, part 5, 1971, pages 527–528 and 536–537.

Erno Lendvai, “Bela Bartók: an analysis of his music,” published by Kahn & Averill, 1971. Lendvai takes a detailed look at Bartók's use of the olden Mean.

Roy Howat, Debussy in Proportion - a musical analysis, Cambridge University Press, 1983.

Courtney S. Adams, “Erik Satie ‘Golden Section Analysis,’” in Music and Letters, Oxford University Press, Volume 77, Number 2 (May 1996), pages 242–252.

Schubert Studies, Brian Newbould (ed.). London: Ashgate Press, 1998. Roy Howat has a chapter Architecture about Schubert's golden sections in his late A major sonata.

Tushaar Power, “The Proportional Design of J.S. Bach's Two Italian Cantatas.” Musical Praxis, Vol.1, No.2. Autumn 1994, pp. 35–46. This is part of the author's Ph.D. Thesis, “J.S. Bach and the Divine Proportion.”

Hugo Norden, “Proportions in Music” in Fibonacci Quarterly vol. 2 (1964), pages 219–222. These are talks about the first fugue in J. S. Bach's The Art of Fugue and shows how both the Fibonacci and Lucas numbers appear in its organization.

Britten: The Golden Ratio is in sections of Claude Debussy's Image, Reflections in Water. The sequence of keys is marked out by the intervals 34, 21, 13 and 8; and the main climax is at the phi position. It is also in La Mer, but I’m not sure that Debussy sought purposely to do it. [49]

Perry: I think the Golden Ratio goes through the whole process of evolution. You find it from sunflowers to classical music.

Dean: Oh! Then this should definitely be studied in all departments!

Perry: Right. The Ratio should be found in every subject -- from architecture to aesthetics, from music to zoology.

Dean: I am amazed. What do you make of this?

Britten: You can see the Fibonacci pattern on the piano: there are thirteen notes in the span of any note through its octave. A scale is comprised of eight notes. The 5th and 3rd notes create the basic foundation of chords and are based on the whole tone, which is two steps from the root tone, by that I mean the first note of the scale. The piano keyboard scale of C to the C above, a span as I said of thirteen keys, consists of eight white keys and five black keys split into groups of three and two. In a scale, the dominant note is the 5th note of major scale. The sequence of keys is marked out by the reverse intervals 34, 21, 13 and 8. And so it keeps going with the Ratio. It would require a lot of time to discuss. [50]

Dean: Stewart Perry! (Looking over to him.) You are doing your thesis on this stuff. Do you find these same proportions and ratios applying in chemistry?

Perry: It’s in the law of constant proportions of chemical compounds. This is a fundamental chemical law.

Dean: What does this law mean?

Perry: Joseph Proust discovered it in 1799 while looking at the law of definite proportions. He found that copper carbonate must always be made from the same fixed proportions of copper, carbon, and oxygen. All compounds contain elements in definite proportions. I mean: chemical compounds have a constant structure, which is not dependent on the conditions of their formation.

Dean: That’s amazing! But it could be over our heads, mine as much as students’. Can you explain that better for us?

Perry: (walking quickly to the blackboard) In physical chemistry we see that the atom ratios in compounds are equal to the ratios of the Fibonacci numbers taken through one: 2/5, 3/8, 5/13, 8/21, 13/34. (As he writes on the board, he says out loud “2 slash 5,” etc.) We know that such ratios strive in the limit to the square of the golden proportion.[51]

Dean: (The Dean is thunderstruck.) My God, Stewart! And this also shows up in plants and vegetation?

Perry: In plant morphogenesis there is a field called phyllotaxis. It is the study of symmetrical constructions in organs of plants. It’s about their origins and functions in the environment. And… 

Dean: And this is connected to Fibonacci numbers?

Perry: Yes. The Fibonacci patterns are in the organization of vegetative shoots and reproductive structures in plants.[52]

Dean: So this is how we evolved from the Big Bang! This Ratio is huge, and not a little frightening. (He turns away.) Mysterious. It comes up in too many places. If we go back to the Big Bang and look for the common principles… (The Dean is quiet for a moment.)

The significance of this Ratio to evolution must be (pauses again fleetingly, then shouts his surprise.) GREATER THAN THE PRINCIPLE OF NATURAL SELECTION. The principle of Natural Selection cannot be found constantly from the beginning of the Big Bang to Beethoven.

Perry: Some call the Golden Ratio mystical, but it is rooted in science. I know it is in galaxy formations. The spiral inside M51 -- the Whirlpool Galaxy -- is close to this golden section. The ratio of the lengths of the thorax and abdomen in most bees is connected to the Golden Ratio. A cross section of the DNA fits nicely into a golden decagon.

Dean: (to Britten) Could “music” be a basis for research in physics?

Britten: (himself astounded) Who knows? (then jokingly) Think about these concepts in music theory: harmony, discord, minor, major, accelerando, andante, pacato, perfect interval, pitch, roll, rubato, diatonic, meter signature, triplet, theme, and the list goes on. Could we be composing the musical “processes” of evolution? Could we be re-composing our own history? 

Derek: Stravinsky’s The Rite of Spring shocked people out of their seats -- when it was first played in 1913. It was explosive, like earthquakes and storms; masterful, like the birth of a never-before-heard musical season. So, I’m wondering what’s next? What’s next in music? (Perry smiles at Britten, Benedict smiles at the Dean, the Dean smiles at the class, and they all laugh.)

Dean: Class, what do you think? Do particles, atoms and molecules have rhythm? Do they rock-and-roll? (Everyone howls.)

Jerry: The sounds of atomic vibrations are outside our ear’s capacity to hear.

Dean: Well. (joking again) When helium and hydrogen came together, how did that sound?

Perry: Like water. (Everybody laughs. They are joking, but everyone, no matter what their special field of study, is wondering if they might be on to something. Does this view fit with most—or all—that has been said in previous classes?) Well. Helium and hydrogen synthesized into water. Right? It’s the same principle when harmony in musical patterns integrates separate “elements”—notes, that is—into a whole. No matter how independent the elements may be, we hear a full sound that’s new, not the individual particulars. We do not just hear a group of independent elements. When we see water, we do not see hydrogen and helium, we see water, a new event, a different whole. The two parts have sacrificed their independence for this event and created a harmony that goes in a new direction.

Dean: Oh. My! (Looking at his watch.) I do not want to stop this conversation—it’s too good! But our time is up. We are making so much – pardon the expression – progress. Quick: we have only two seconds left. Does any student have a fast final question for Professor Britten? 

Kathleen: Professor, you said that Mozart integrated those different moods in his Concerto number 9. I am interested in how music helps us go through bad times and mature.

Britten: Oh, I listen to Mozart in the evening when I am alone. Mozart speaks to my condition… (Pause) I mean, our human condition.

Dean: Time is up. Thank you. We must stop now. We will see you all here next time, same place. Have a great weekend!

 

Kathleen has learned that music can transform human emotions. It can advance her into a new place, maybe lead past her difficult moods and into a new living experience. The Dean and the professor go off for lunch and talk about the transforming power of music. They talk about how, in the Art of the Fugue, Bach transforms his subject several times.

While at lunch, Professor Britten recalls how the principle of freedom entered into the class discussion. He is amazed at how Stewart Perry can take the idea of freedom back into chemistry and physics. The Dean has asked whether “increasing freedom” could be a principle of evolution. Professor Britten tells him he agrees that this is true for music history. For his part, the Dean expatiates on their newly raised topic of vibrations as the basis for explaining and expressing the story of evolution. It could be the basis for studies across the whole university! The Dean’s excitement about the matter knows no bounds…

They leave the campus-dining hall both highly pleased at how the class has gone today, and wave goodbye. The Dean has a feeling that his colleague will be alone this evening, listening once again to Mozart’s Concerto Number 9.

 

 

 

 

 

 

 



[1] Since the 17th century, the term fugue has referred to an imitative counterpoint. The first use of the word cited in the Oxford English Dictionary occurred in 1597, and was recorded in MORLEY Introd. Mus. 76. The word comes from the same root as the word "fugitive,” suggesting rapid flight. By the early 18th century, musicians began to use “fugue” to refer to a genre of music. For centuries it has been used to designate music based on canonic imitation, one voice chasing another. Alfred Mann, The Study of Fugue (Dover Publications, 1987). See also Ebenezer Prout, Fugue (Bartlett Press, 2008)

 

[2] Carl Sagan made this statement about the “universe as a fugue” in a television series called Cosmos: A Personal Voyage, first broadcast by the Public Broadcasting Service in 1980.

[3] Matthew 11:12;  Mark 4:9

 

[4] In his De Inventione, Cicero listed five stages in creating an oration, namely invention (inventio), arrangement (dispositio), style (elocutio), memory (memoria), and delivery (pronuntiatio). Cicero says, “One must first hit upon what to say; then manage and marshal his discoveries, not merely in orderly fashion, but with a discriminating eye for the exact weight, as it were, of each argument; next go on to array them in the adornments of style; after that keep them guarded in his memory; and in the end deliver them with effect and charm.”  Anthony Everitt, Cicero: the life and times of Rome's greatest politician, (New York: Random House, 2001).

 

[5] Malcolm Boyd, J. S. Bach (New York: Oxford University Press, 1999). Klaus Eidam, The True Life of Johann Sebastian Bach (New York: Basic Books, 2001).

[6] David Peat, J.S. Bach’s The Art of Fugue. www.fdavidpeat.com/bibliography/essays/dentler.htm

Peat says that the music has absolute purity and genius of design and that Bach was conversant with Pythagorean philosophy. Bach refers to his fugal pieces with this special term—“counterpoint”—that evokes the notion of opposites, as in Aristotle’s puntus contra puntum. Kepler used the term contrapuntal in his chapter on Universal Harmony. David Peat says you can see opposites as a “Mirror Principle” in the work of Pythagoras. The perfect triangle created by arranging the numbers 1, 2, 3, 4 is central to Pythagorean thought and is present in the pattern of voices of The Art of Fugue. The so-called Music of the Spheres is reflected in the first seven contrapuncti. The seventh, which would be Earth, is a Canon in the Octave. Peat reminds us that the fugue “also means the flight of the soul towards God.”  See also Joseph Kerman, The Art of Fugue: Bach Fugues for Keyboard, 1715–1750 (University of California Press, 2005)

[7] Flutes were carved from the wing bone of the red-crowned crane, with five to eight holes capable of producing varied sounds in a nearly accurate octave. The use of the flutes for the Neolithic musician is unknown, but they were probably played in special ceremonies. Chinese stories tell of the importance of music. The sound of the flutes lured cranes to a waiting hunter. See

http://www.metmuseum.org/toah/hd/jiah/hd_jiah.htm

[8] At the University of California at Berkeley, Anne Draffkorn Kilmer deciphered the music of this song. It was composed in harmonies of thirds, written using a Pythagorean tuning of the diatonic scale. Kilmer, Crocker, and Brown, Sounds from Silence, Berkeley, CA: Bit Enki, 1976), LCC 76-16729.

[9] Steven Brown, Bjorn Merker, & L. Nils, “An Introduction to Evolutionary Musicology,” in: Wallin, Merker, Björn & Brown (eds.) The Origins of Music (Cambridge: The MIT Press, 2000).

[10]  Table I is drawn from Information Please® Database, © 2007 Pearson Education, Inc.

 

[11] This summary is drawn from Anthony Judge http://www.laetusinpraesens.org/docs/conftran/xspmus.php

 

[12] Various articles—including "Organum," "Musica enchiriadis," "Hucbald," "St Martial"—are found in The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie. 20 vol. (London: Macmillan Publishers Ltd., 1980).

[13] The earliest form of musical notation can be found in a cuneiform tablet that was created at Nippur in about 2000 B.C.E. The tablet has fragmentary instructions for performing music in harmonies of thirds, and using a diatonic scale. A tablet from about 1250 B.C.E. shows a more developed form of notation. Anne Draffkorn Kilmer (1965). The Strings of Musical Instruments: their Names, Numbers, and Significance, Studies in Honor of Benno Landsberger = Assyriological Studies, xvi, 261–8. Also Anne Draffkorn Kilmer (1986). Journal of Cuneiform Studies, xxxviii, 94–98.

 

[14] Igor Stravinsky, Poetics of Music in the Form of Six Lessons (The Charles Eliot Norton Lectures, Harvard University Press, 1993.)

[15]  ”Basso continuo”—also "thoroughbass," "figured bass," "basse cifrée" (French), "Generalbass" (German) or "continuo"—is the practice of creating an accompaniment from a composed bass part by playing the bass notes and improvising harmony above them. The term also refers to the composed part itself. Continuo was standard practice in art music roughly from A.D. 1600 to the later 1700s.

 

[16] Barbara Minton, “Music Shown to Facilitate the Development of Neurons in the Brain. Natural Health News, September, 23, 2008. Minton notes how neuronal connections in the brain of an infant and a young child are formed through personal experiences. They are strengthened through repetitions in experience until predictable pathways of “cognitive processing” are established. Once these pathways are formed, they are hardwired and cannot be changed without a lot of effort. So music and rhythm help to create and strengthen more neural connections that allow for auditory processing. Studies find that the brain responds to harmony, and the brain grows in response to musical training in the way a muscle responds to exercise.

Researchers at Beth Israel Deaconess Medical Center in Boston discovered that male musicians have larger brains than men who have not had extensive musical training. The cerebellums, that part of the brain containing 70 percent of the brain's total neurons, were 5 percent larger in expert male musicians. Harmony, melody, and rhythm invoke distinct patterns of brain activity.

 

[17] Richard Dawkins, Climbing Mount Improbable (Viking Press, 1996). Stephen Jay Gould, Wonderful Life: The Burgess Shale and the nature of history (Penguin Books, 1989).

[18] Ethan Haimo describes Schoenberg’s music as divided into three periods: tonal, atonal, and serial. Ethan Haimo, Schoenberg's Transformation of Musical Language (Cambridge University Press, 2006).

 

[19] Robert Walser, “The Body in the Music: Epistemology and Musical Semiotics,” in College Music Symposium 31: 116-26.

 

[20] Reported by Johann Aloys Schlösser and recorded in Carl Dalhaus, Ludwig van Beethoven (Oxford: Clarendon Press, 1991), p. 142.

 

[21] There are many unresolved questions about Mozart's natural ability. At the age of three, he already sat in front of the harpsichord, attempting to find harmonic successions of thirds; whenever he succeeded, his voice sounded joyful. When Wolfgang was four, his father began to teach him the elements of the harpsichord and the rules of composition. For some music historians, it seems as though Mozart did not need to learn. Right away, he began producing minuets and other small pieces for harpsichord, and several sonatas for harpsichord and violin. By his sixth year he had produced a large number of minuets, sonatas, and even a concerto. His ear could recognize that the violin was usually tuned an eighth of a note lower than his father tuned the instrument. Mozart had composed full-length operas and 28 symphonies by the age of 18, mastering virtually every technique.

 

[22] Britten is referring to Friedrich Wilhelm Joseph Schelling. See Andrew Bowie, Aesthetics and Subjectivity: From Kant to Nietzsche (Worcester: Billing and Sons, 1990).

 

[23] Luke 12:6 and Matthew 10:29, 31–35

 

[24]  See Athanasius Kircher, Philosophische Extract und Auszug. As quoted by Michael Spitzer, Metaphor and Musical Thought (Chicago: University of Chicago Press, 2004), p. 157.

[25] Richard Wagner, Richard Wagner’s Prose Works, trans. William Ashton Ellis (Lincoln: University of Nebraska Press, 1993–95.

 

[26] G.W.F. Hegel, Aesthetics: Lectures on Fine Art, trans. T.M. Knox (Oxford: Clarendon Press, 1998 [1842]).

 

[27] In German, the word Aufhebung can have many meanings, such as: abrogation, rescission, suspension, nullification, raising, lifting, removal, abolition, abolishment, repeal, dissolution, closing, reversal, quashing, annulment, revocation, resolving, resolution, breaking off, canceling out, neutralization. On Hegel’s view, see Maurice Blanchot, The Infinite Conversation, trans. Susan Hanson (Minneapolis: University of Minnesota Press, 1993), 15. Also see: John D. Caputo, More Radical Hermeneutics (Bloomington: Indiana University Press, 2000), Chapter 2.

[28] The quote is from Wordsworth’s Prelude, in M.H. Abrams, The Mirror and the Lamp (Oxford: Oxford University Press, 1971).

 

[29] Arthur Schopenhauer, The World as Will and Idea, trans. R.B. Haldane and John Kemp. 9 London: Routledge and Kegan Paul [o.d. 1819].

 

[30] Lord Byron, Don Juan (canto XV, stanza 5).

 

[31] The reference to healing is found in Kepler's Belief in Astrology by Nick Kollerstrom. History and Astrology, edited by A. Kitson (Unwin, 1989), p. 167. Kepler proposed that the dynamics of the solar system are directly analogous to the laws of musical harmony. See Max Caspar, Kepler, translated by C. Doris Hellman (Collier-Mac, 1962). Kepler's laws state that planets move in elliptical orbits at varying speeds, faster when at the perihelion and slower at the aphelion. When the angular velocity of Saturn was measured, for instance, Saturn moved 106" per day at the aphelion and 135" per day at the perihelion. When Kepler computed the ratio 135 / 106, he found it to be within two seconds of a major third musical interval. The ratio between Jupiter's maximum, and Mars' minimum speed corresponded closely to a minor third, and the interval between the Earth and Venus to a minor sixth. These relationships have continued to exist for planets that were discovered after Kepler's death. The Kepler scholar Francis Warrain extended Kepler's researches and found that the angular velocities of Uranus, Neptune and Pluto, unknown during Kepler's lifetime, also correspond to harmonic ratios.

 

[32] Joscelyn Godwin: Harmonies of Heaven and Earth (Thames and Hudson, 1987), p. 130.

 

[33]  Cornell News, “A way to measure the bonds that hold together a single molecule is developed by Cornell physicists,” Friday, June 12, 1998. Bryan T. Marshall, Krishna K. Sarangapani, Jianhua Wu, Michael B. Lawrence, Rodger P. McEver,and Cheng Zhu. “Measuring Molecular Elasticity by Atomic Force Microscope Cantilever Fluctuations,” Biophysical Journal, Vol. 90, 2006.“Vibrational spectroscopy” is the study of the energy and frequency of vibration of molecular bonds. “Atoms are held together in molecules because the negatively charged electrons in one atom are pulled toward the positively charged nucleus of another” and vice versa. But at the same time, the electrons in one atom repel those in the other, and the protons in the nuclei do the same. This constant push-pull creates a vibration, as if the atoms were connected by tiny springs in constant motion. The vibration is unique for each arrangement of atoms in a molecule, and in the language of quantum mechanics, “each vibration has a characteristic energy level.” An electron whose energy matches or exceeds that of a vibration energy level in a molecule can pass through the molecule more easily. By measuring current flow through molecules over a wide range of energies, scientists can create a “vibrational spectrum” that provides a fingerprint of the bonds in a molecule and thus is a powerful analytical method for identification of unknown chemicals.

[34] To see molecular vibrations animated, go to http://www2.ess.ucla.edu/~schauble/molecular_vibrations.htm

 

[35]  “Turtles all the way down” refers to an infinite regression about the origins of the universe. It refers to an ancient belief that the world is borne on the back of an enormous turtle. Jay Miller, Man, Royal Anthropological Institute of Great Britain and Ireland, New Series, Vol. 9, No. 2 (Jun., 1974), pp. 306–308. Also see Stephen Hawking, A Brief History of Time (Bantam Books, 1988).

 

[36] E.B. Wilson, J.C. Decius, and P.C. Cross, Molecular Vibrations (McGraw-Hill, 1955. Reprinted by Dover 1980). A vibration is excited when the molecule in its ground state absorbs one quantum of energy. Different texts suggest that when two quanta are absorbed the first overtone is excited, and so on to higher overtones. The motion in a normal vibration can be described as a kind of simple harmonic motion. The vibration energy is a quadratic function (parabola) with respect to the atomic displacements, and the first overtone has twice the frequency of the fundamental. In reality, vibrations are enharmonic, and the first overtone has a frequency that is slightly lower than twice that of the fundamental. Excitation of the higher overtones involves progressively less and less additional energy and eventually leads to dissociation of the molecule. The vibration states of a molecule can be probed in a variety of ways, including infrared spectroscopy. See also: S. Califano, Vibrational States (Wiley, 1976). P. Gans, Vibrating molecules (Chapman and Hall, 1971.)

[37] D.R. Bloch, Organic Chemistry Demystified (McGraw-Hill Professional, 2006). Foods with high vibrations can harmonize with the body's own unique vibration. For instance, the human body operates optimally at an electrical vibration of between 60–80 MHz, with emphasis on the higher side. Here are some food vibration examples, based on Tainio Technology (the most accurate instrument for measuring food frequencies): Fresh fruits (organic and picked when ripe) 80 MHz; raw green vegetables (organic) 65–72 MHz; Wild fish 50–55 MHz; farmed fish 40–45 MHz.

[38] Douglas Hofstadter, Godel, Escher, Bach (Vintage Books Edition, 1980, p. 519). Hofstadter discusses the similarities between genes and music. Also see Kenshi Hayashi and Nobuo Munakata. "Basically musical," Nature 310 (12 July 1984): 96. Ross King and Colin Angus, Immunogenetics 24: 71–78. 1986. C. Miner and P. Della Villa, (1997). “DNA Music.” The Science Teacher. 64 (5), 19-21. For more see: http://www.whozoo.org/mac/Music/Sources.htm.

 

[39]  No author listed, “Biologists are addressing one of humanity’s strangest attributes, its all-singing, all-dancing culture,” in The Economist December 18, 2008.

 

[40] Dmitri Tymoczko, “The Geometry of Musical Chords,” Science 7 July 2006:
 Vol. 313. no. 5783, pp. 72–74. 
DOI: 10.1126/science.

 

[41] Tymoczko, ibid.  See also: “Scale Networks in Debussy,” Journal of Music Theory, 48.1 2004.

 

[42] Consult the discussions in Karl Stumpf, “Tonpsychologie,” in Carl Emil Seashore, The Psychology of Musical Talent, chap. VII.  Thomas Amory Coffin

http://www.art.net/~coffin

 

[43] Hazrat Inayat Khan, The Mysticism of Sound and Music (Rockport, MA and Shaftesbury, Dorset, UK, in association with the International Headquarters of the Sufi Movement, Geneva, 1991).

 

[44] Copernicus realized that a sun-centered planetary system gave better predictions of celestial motion and could also be expressed through harmony and elegant geometry. Harmony produces an aesthetic feeling not identical with consonance, which is a sensory relation between tones. But in order to understand harmony, we must start with consonance. There is even harmony in which tones of paint are concordantly related to the leading chords of a musical key.  David Plant, Kepler and the Music of the Spheres.

[45] Mitz DeWhitt goes beyond the secular worldview of physicists and introduces a “sacred metaphysical soul principle,” viewed as a holographic “membrane” whose only function is “to gather and store information and serve as the anti-entropic force within the universe.” The properties of the soul are seen as associated with a figure called the lambdoma, and with the diatonic scale that forms within it, known as “The Scale of the Soul of the World and Nature." This esoteric outlook links with the work of Gurdjieff. See: Mitz DeWhitt, Gurdjieff, String Theory, Music (Xlibris Corporation, February 8, 2006).

 

[46] A. Klug, "Molecules on Grand Scale," New Scientist, 1561:46, 1987.

 

[47] The New Oxford Companion to Music, Volume 2. See “Violins.”

[48] Derek Heylock Mathematics Teaching, Volume 84, pp. 56–57. 1978.

[49] Roy Howat, Debussy in Proportion: A Musical Analysis, Cambridge University Press (1986). Peter Smith, The Dynamics of Delight: Architecture and Aesthetics (New York: Routledge, 2003), pp. 83. David Vassall Cox, Debussy Orchestral Music. (Seattle: University of Washington Press, 1975).  Marcel Dietschy, A Portrait of Claude Debussy (New York: Oxford University Press, 1990).

[50] See Peter F. Smith, The Dynamics of Delight: Architecture and Aesthetics (New York: Routledge, 2003), p. 83.

 

[51] Roger Jean describes a concept of phyllotaxis with a mathematical model of plant growth based on experimental anatomical, cellular, physiological, and paleontological observations. The model provides a framework for formal analyses of botanical data and shows the relevance of phyllotaxis to other structures, such as crystals, and proteins. Roger V. Jean, Phyllotaxis: A Systemic Study of Plant Pattern Morphogenesis (Cambridge University Press, 1994).

 

[52]  Ibid. The Greeks were fascinated by the Golden Ratio, because of the aesthetic proportions it generated in geometry, art, and architecture. Tests have shown that among all the possible rectangles, the one for which the ratio of the base to the height is the Golden Ratio is most pleasant to the eye. The ratios also have a foundation in biological reality. See S. Douady and Y. Couder, "Phyllotaxis as a physical self-organized growth process." Physical Review Letters 68(13): (1992), 2098–2101.