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| French Horn |
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| English Horn |
Horn is a kind of instrument, 中譯 號,角 or 號角. So French Horn is 法國号. Sometime it is also called 法國管. However, 管 usually is reserved for woodwind instruments (木管樂器) such as 單簧管 (clarinet),双簧管 (oboe),低音管 (bassoon) etc. The odd ball is English Horn. This instrument originated from France & something similar to Oboe, 屬木管樂器. So in reality, English Horn is neither English nor Horn. It is double reed, looks like oboe but longer and ends with an ellipsoid opening. You may have been to many concerts and seldom see an English Horn. The reason is that its opening always hides beneath the chair & its opening end is invisible. You might think it is an oboe as they sure look alike. But if you pay attention to the detail, you may discern the curve between the mouse piece & the body of the instrument. It is longer than oboe so its tone is lower and has its unique timber and mood. The best way to get familiar with this instrument is to see and hear it.
In this video clip, William Tell Overture, we don't see the opening of the English Horn as it is too long to show. The time line 0:00-2:44 is the third movement 'Pastoral' (牧歌:寂靜). You can picture a mockingbird (Flute) flying around and playing or communicating with a cow (English Horn).
This is another video clip that displays the performance of the English Horn,11:26 to 12:46. It is also interesting to watch English Horn from 20:06 to 20:34 and then a single violin (concert master) took over. He kept eye contacts with the conductor from time to time until 21:21 when all violins joined in. The story goes like this: Dvorak was very lonely while he composed this movement in a village of Czech in Iowa. He sobbed and chocked during the main theme (Bohemian tune) and had to use a violin to express his feeling and mood. Since violin hesitates, the timing of choke must be precise and so the eye contact required intently.
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| Little Big Horn |
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| Texas Long Horn |
You may ask since there are French Horn and English Horn, do we have German Horn or American Horn? It turns out that there is Little Big Horn in America. But most people don't like or want to mention it, a tragic experience. Fortunately there is Texas Long Horn. It is a long and exciting story if you are a Texan or a UT alumnus. There is German Horn that looks like Alpine Horn, very long. I tried once in Bavaria long time ago and found it hard to blow. Chinese Horn? Yes or no, it is Tibetan Long Horn played by Buddhist monks.
Since a real post horn is hard to find, it is replaced by french horn in most orchestra. In this video clip, we can hear the post horn play from 33.30 to 35:08, second trio. Since the french horn is substituted for the post horn, we can hear the rich tone of the the instrument. The other solo instrument Piccolo can be heard from 32:20 to 33:04, in the first trio.
Let's turn to another type of horn for fun. It is Gabriel's Horn. Most of us are familiar with the picture of Archangel Gabriel blowing a horn. Some mathematicians figure that they can construct this horn better. The way to do is to integrate a curve 1/x around x-axis from 1 to a. But then someone asked a tricky question: what happen if 'a' goes to infinity as Garbiel's Horn can be very long? Here came a painter. He wanted to use Gabriel's Horn as his paint bucket. Since the volume of the horn is finite (integration of 1/x^2 converges) but the area is infinite (integration of 1/x diverges). The painter can't understand why he can't use his finite paint in the bucket to paint the surface of the horn which is infinite. After all, the surface of the bucket is just part of the volume. Here is the inconsistency between the math & the application. While we were Freshmen in 1960, Dr. Kuller never mentioned the story of Gabriel's Horn & its strange phenomenon. The textbook we used by Sherwood & Taylor also fails to mention this. Anyway, there may be many explanations for this paradox. My view is that actually it is not a paradox. Because the painter eventually found a way to paint the whole surface of the horn without running out of his paint in the horn. The trick is to use a special brush that can pick up the paint with any kind of thickness. Using concept of limit, when the thickness of the paint goes to 0, the area it can cover goes to infinity. In other words, x*y*z = A (constant), when z go to 0, x*y goes to infinity. It sounds as if 2-dimensional space can be viewed a special case of 3-dimensional space.
There are some other type of horn such as Cape Horn, Golden Horn (geographical), Hornblower (fictional naval officer) and Chinese Astronomical Horn (角宿). Two bright stars Arcturus (alpha star of Bootes, 牧夫座) & Spica (alpha star of Virgo, 室女座) are called 大角星 and 角星 in China. You can see these two bright stars in the summer night sky. Just extend the tail of the Big Bear (北斗七星), you will find a big yellow star, Arcturus. Extend further with same distance, you will find another bright star, Spica. In this month (August 2012) you can actually see planet Saturn and Mars near Spica within three hours after sunset. The three objects form almost an equilateral triangle. Both planets don't blink usually and the reddish one is Mars.
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When time goes by, the triangle of Spica, Saturn & Mars gets larger in area as the planet Mars moves to east. As of 8/28/2012, the triangle is a right triangle with 60/30 degree approximately. Saturn is at the position of right angle. The triangle can be seen in August & most of the September with Mars shifts to east steadily. There is another triangle in the summer sky. It is truly a triangle year after year since they are formed by three true stars, Vega of Lyra, Altair of Aquila & Deneb of Cygnus. Translated into Mandarin, 織女星, 牛郎星 & 天津四 (天鵝座的 alpha star). Deneb means tail in Arab, ie tail of the swan. In the summer time of North America, you can see them right at zenith (天頂) around 9 pm. This triangle is larger than the one formed by Spica, Saturn & Mars). The Milky Way goes through Cygnus & so Vega & Altair are on opposite side of the Milky Way. From this formation, Chinese came up with a romantic story, 牛郎織女 & 喜鵲橋.
While I wrote Gabriel's Horn, I forgot one other interesting horn, Vuvuzelas Horn. It is a plastic version of Gabriel's Horn and made a lot of news during the World Cup Soccer in 2010. This horn can generate 120 db noise & bury any voice of TV commentator in the stadium. It is a traditional horn used in South Africa. One thing really interesting is that 90% of the horns used during FIFA's World Soccer games are made in 浙江, China. This shows the world is really a village & the marketing coverage is instant.
As we know the volume of the Gabriel's horn is finite but the surface area is infinite when the length of the horn goes infinite. We seem to understand this from the concept of limit. But isn't it weird that the surface (part of the volume) is infinite & the volume is finite. How can this exists in our daily life? If we never learn or contact calculus, we will never believe this phenomena. Although I explained that the Painter's Paradox is not really a paradox with concept of limit, I am not completely satisfied myself. The brain is very complicate & many scholars, scientists & physicians are studying it. So far there are still a lot of unknowns. For example, does this kind of paradox not really exists but we human beings create it? In our life we don't really have infinity. Dividing any number by 0 is meaningless & not defined. To our intuition, the volume of Gabriel's Horn is like its area, keeps increasing when the length goes longer & longer. Since it keeps increasing, why is there a finite value? The subtlety here is even the volume keeps increasing but it will never go larger than certain value. But isn't the surface part of the volume? Why the portion of the whole keeps increasing (no upper limit) while the whole has upper limit? Can this paradox exist due to the concept of limit we create? To our ancestors there are nothing called infinity or concept of limit & so there is no paradox to them. Perhaps we human beings create a lot of things which may not exist at all. They are just in our mind for our curiosity or some other purposes. Gabriel & Gabriel's Horn never really exist and so are those angels, fairies & ghosts. Then how about hell, heaven & god, do they really exist or just something we create? Now we get into the area most people don't want to touch or just don't feel comfortable talking about it.
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