June 21 is the summer solstice. Traditionally, the school kids of 嘉義 would line up in the field just before the noon time. They watch their shadows disappear from there feet. And hooray, this is the way to celebrate the summer solstice.
Historically, one significant event occurred more than two thousand years ago. It was Eratosthenes of Greece who used summer solstice to measure the circumference of the earth.
Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city Syene (located on the Tropic of Cancer), the sun would appear at the zenith, directly overhead. The sun’s ray would shine to the bottom of a well. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation (using a stick to see the shadow & measure the angle) of the Sun was 1/50 of a full circle (7°12') south of the zenith at the same time. Assuming that Alexandria was due north of Syene he concluded that the distance from Alexandria to Syene must be 1/50 of the total circumference of the Earth. The unit he used was different from km. Anyway, after some unit conversion, it turned out to be around 39,690 km. an error of less than 1% (compared with modern data).
Now came the expedition of Columbus in 1492. He started from Cadiz, Spain. He sailed about 7,500 km to reach some place in current Cuba. Since he thought it was India, the distance from Cadiz (lies about 40 degree latitude) to India (go east direction) had to be around 40,000 cos40° – 7,500. This figure turns out to be 27,900 km. Marco Polo’s book should have given him some idea how far from Spain to India (about 9,000 km). The figure of 27,900 km is just too long to accommodate his logic or calculation. Perhaps Columbus & those experts in Spain didn’t believe the data from the measurement of Eratosthenes. Otherwise, Queen Isabella would not have the courage to finance the expedition. Why? 40,000 cos40° – 9,000 = 18,930 km, really too far to sail for Santa Maria (Columbus’ flag ship). To Spain, it was a fortune in disguise. Instead of India, Spain discovered a new continent & history turned a new page. History is interesting & fascinating. Bertrand Russell (罗素) once said “那些有信心的人們都愚昧無知,而那些有理解力的人們都猶疑不决”.
Tuesday, June 23, 2009
Wednesday, June 17, 2009
Class Reunion Photos
Here is the link to the photos from previous class reunions.
http://www.stat.ufl.edu/%7Eyang/NTUEE64/index.html
Enjoy.
http://www.stat.ufl.edu/%7Eyang/NTUEE64/index.html
Enjoy.
Monday, June 15, 2009
Joseph Haydn
Franz Joseph Haydn (1732-1809)
Charles Darwin, Abraham Lincoln & Felix Mendelssohn were born in 1809, a very productive year in history. But nature goes & works its own way---something in something out. 1809 happened to be the year Joseph Haydn passed away. So 2009 is also the bicentennial (兩百週年忌辰) of Haydn, Papa Haydn. Why is he a Papa? There may be several reasons. One of them is that he is the father of symphony & string quartet. Though he was not the inventor of these two musical forms, he worked & improved them to a form that became very significant in the music world. You might think Beethoven is the father of symphony. But in China & Taiwan, Beethoven is called 樂聖, one level above Papa. Interesting enough, we don’t find the same expression as 樂聖 in the western world for Beethoven. Haydn composed 104 symphonies. It is this quantity & sheer productivity that made him the Papa. In the following, let’s explore some of his genius.
The typical symphony of Haydn consists of four movements (樂章):
1st movement: Start with introduction, lasts from 1 to 3 minutes, a very slow pace of intro. Then the main theme follows with brilliant developments.
2nd movement: Andante, slow movement
3rd movement: Minuet (小步舞曲) & Trio
4th movement: Allegro, fast pace of finale.
The most famous symphonies of Haydn are from #93 to #104, so called Salomon Symphonies. The English impresario Johann Peter Salomon commissioned him to compose these symphonies while Haydn visited London from 1791-1792 and 1794-1795.
Symphony #94, Surprise (驚愕交響曲)
http://www.youtube.com/watch?v=0gF-Wzp8Ni8&feature=related
The first movement with introduction, 0- 1:11. Then comes the first main theme.
This symphony got its name from the 2nd movement.
http://www.youtube.com/watch?v=lLjwkamp3lI
It starts like stairway music, someone comes up & someone goes down. Everything goes smoothly and lightly. At 0:34, suddenly a loud chord wakes everybody up, a Surprise! If you are sleepy & dozed around at that moment, you may well be alarmed.
The 3rd movement, the minuet & trio
http://www.youtube.com/watch?v=JrZkH22V6D0&feature=related
Trio is a section sandwiched between two main minuet sections. Here the trio is from 2:34 to 3:43. This is one of the most famous minuets among Haydn’s symphonies. Surprisingly, I haven’t seen any choreographer adapts this in ballet. The melody is so delightful & lovely that you barely can sit still. Trio is usually a contrast theme but sounds harmoniously to the main theme. Minuet is a three-beat (per measure) dance form. It can go from very slow (Beethoven’s Minuet in G) to fast pace (Mozart’s symphony #39 3rd movement).
Beethoven's:
https://www.youtube.com/watch?v=zSXRJwspGU0
Trio is from 1:03-1:53. The whole thing is simple and romantic.
Mozart's:
http://www.youtube.com/watch?v=QnFyS3MflIE
Trio is from 1:50-2:52, played with clarinet (單簧管) & bassoon (低音管) beautifully. Originally trio was played with three instruments, so called Trio (三重奏). In this case, they are clarinet, bassoon & strings. In most cases, there is no such restriction. So trio in minuet is usually called 中段 in Mandarin.
Symphony #45, Farewell (告別交響曲)
This was a good old story. Haydn worked for Esterhazy, a Autro-Humgarian prince, for about 30 years. Haydn and his musician were based in Eszterhaza or Eisenstadt, not in Vienna. When winter came, most musicians were homesick but not allowed to go home. So Haydn composed this symphony to tell his boss how they felt.
Start from 3:54, musician starts leaving the concert hall. Watch the following video, it is self-explainable. This is the 4th movement of the Farewell Symphony.
http://www.youtube.com/watch?v=xmcX8fEIB60
Per history, after this performance, all members of the orchestra were allowed to go home for reunion with their families.
Symphony #101, Clock (時鐘交響曲)
It got the name from the 2nd movement.
http://www.youtube.com/watch?v=B0GCyxO3H9Y
It begins with a realistic tick-tock accompaniment, which runs right along under a charming melody. If you listen to this twice, you will seldom forget the tune.
Another symphony with similar quality is Beethoven's Symphony #8, also the 2nd movement.
http://www.youtube.com/watch?v=V0-UMiiXmO4
Beethoven's clock rate sounds twice as Haydn's. Perhaps Beethoven used a faster microprocessor.
Kaiser Quartet (Emperor quartet, 皇帝四重奏)
Listen to this 2nd movement, hear something you heard before but where? Olympic games? Soccer games?
http://www.youtube.com/watch?v=7tHc9xWhFH4
Haydn composed the melody at the request of the kaiser. It became Austrian national anthem. But during WWII, Hitler swiped it to become Uber Alles, the German national anthem. To a lot of people in the world, Germany & Austria are close enough in culture to be a unified people.
Symphony #100, Military (軍隊交響曲)
The name Military comes from the 2nd movement, Allegretto.
http://www.youtube.com/watch?v=U1UEZUgGTVE
This movement is not Andante, it is a faster Allegretto (rare exception of Haydn). You can hear bass drum, cymbals & triangle played Turkish marching tune, from 2:49. The crescendo is built with trumpet from 3:46 to the end of the movement. The whole movement is really a brilliant military march.
Symphony #103, Drum Roll (鼓聲交響曲)
Introduction starts with ketteldrum (定音鼓) followed with an elaborate cello play. The intro lasts about 3 minutes. This is the time to appreciate the cello’s deep & rich tone.
https://www.youtube.com/watch?v=gT9lgHMGevE
Trumpet concerto (小喇叭協奏曲)
The 2nd movement is often used for trumpet recital. The beginning main theme sounds familiar, sort of like that theme from Kaiser Quartet with a twist. You can appreciate the sound quality of trumpet here.
http://www.youtube.com/watch?v=3Ab9ti35ZTI&feature=related
Serenade (小夜曲)
This is one of the most beautiful serenades. You might think this is from Mozart, but no, it is from Haydn. Haydn’s wife was a tough lady & Haydn was really afraid of her. So when she yelled, he rushed to his study & locked inside. While he found nothing to do in the study, he composed this lovely serenade.
http://www.youtube.com/watch?v=XgbdqXGr1DQ
Haydn visited London & produced 12 Salomon Symphonies. Handel visited London & created fanfare & brilliant water music. Mendelssohn visited London & came up with Scottish Symphony & Fingal’s Cave. It remained to be seen what would come out if Beethoven, Mozart or Brahms have visited London. Interestingly, Haydn’s symphony #92is called Oxford Symphony (牛津交響曲). This symphony was composed before 1791, before the Salomon Symphonies. Then why is it called Oxford? Here is the story. This was like Brahms’ Academic Festival Overture, too late to compose a piece of music for the academic ceremony. Haydn was awarded an honorary doctorate by Oxford University in 1791 (this was during the mess of French Revolution). He had to play something worthwhile in the ceremony. He happened to compose a symphony commissioned by a French (one year earlier) & first played in Paris. It didn’t bother him, he just played it in the graduation ceremony of Oxford. So the symphony got its title "Oxford". Anyway, if Brahms had visited London before, Cambridge would have given him an honorary degree & we would have Cambridge Symphony today.
PS: If you ask me which minuet is the most popular these days, my answer is Boccherini's. You hear it in wedding parties, cruises, radios etc all the time.
http://www.youtube.com/watch?v=kSE15tLBdso
The trio starts from 1:25 and end at 2:48. Boccherini, 生平作曲無數, 僅以此小步舞曲傳世. It is like it in high tech industry. If you hit it once, you get rich & retire.
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