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Goldberg variational problem
Analysis of Goldberg's Change Depth

As a leader in Bach's piano field in our time, Canadian pianist Angela Hewitt recorded a Goldberg variation for Hyperion in 2000. In the following article, she interprets this great work for us from both technical and connotation, hoping that this article can provide updated reference for musicians. The original translation is as follows, slightly abridged.

During his tenure as music director of St. Thomas Church in Leipzig, johann sebastian bach has been struggling with the authorities' indifference to music. But sometimes in order to keep his position, he has to show submission and obedience. The Leipzig Municipal Council does not seem to appreciate Bach's contribution to the music life of the city, and has repeatedly rejected his reasonable request to improve the missionary schools and increase the necessary facilities. 1730, the environment of this city finally made Bach unbearable. He wrote to his childhood friend Geoge Edrmann (then consul of the Russian emperor in Danzig), hoping to find another job outside Leipzig. He wrote in the letter:

"... I find that my present job is far from being as profitable as I described at the beginning; I can't get any other income outside my post; The price here is so high that my superiors are not interested in music at all; My life is full of troubles, harassment and jealousy; I hope God can help me find a satisfactory job outside Leipzig. "

We know nothing about edelman's reply. We only know that Bach stayed in Leipzig until his death (the fact is that edelman soon became the school director of St. Thomas Church School in Leipzig, and Bach's situation was greatly improved, which was the fundamental reason why he stayed in Leipzig-translator). 1733 created a noble mass in b minor for the royal family, hoping to win the title of court composer. Three years later, he was officially named "composer of the Elector of Saxony and the King of Poland", and all this was due to the help of Herman Karl and Baron von Kaiserlink.

Count Catherine is the Russian ambassador to Dresden, and music is his greatest hobby. In his hometown of neustadt, he had a band composed of the best instrumental musicians at that time; Gothenburg is one of those great harpsichord musicians. John Goldberg was born in Danzig on 1727. As a teenager, he studied keyboard music with Bach's eldest son William Friedman in Dresden. Later, he was sent to Leipzig by Count Catherine and studied directly with Bach. His outstanding talent made him famous far and wide. He sometimes seems to be able to express everything he sees with the help of a keyboard. Bach must be very happy to have such a student.

As for the origin of "Variations on Goldberg", it was first put forward by Johann Nicolaus Faucoeur, Bach's first biographer, who wrote in his biography:

Count Catherine is very weak and suffers from severe insomnia. Gothenburg, where he lived at that time, always played some soothing songs for him in the living room at night to help him fall asleep. The count once told Bach that he hoped he could write some soft keyboard sketches with some life-like features for Gothenburg, so that he could get emotional comfort in those sleepless nights. Bach thinks it is best to meet this requirement in the form of variations, and the whole work should have identity in a fixed harmony structure-after all, the count once owed Bach, and he has not done anything ungrateful. Throughout Bach's creative years, the form of this work is unique. From then on, the count called this piece "his" variation, and he was fascinated and carried away; For a long time, whenever sleepless nights came, he would always say, "Dear Gothenburg, please play some of my variations!" " "Bach also got the most incredible reward in his life: the count gave him a golden cup filled with 0000000000 as a gift. Now, however, it seems that even if The Count of Catherine is tens of millions of times more expensive, it is not as valuable as Bach's real masterpiece.

Of course, many musicians are not convinced by this for three reasons: First, this work did not mention any winners when it was published in 1742, and Bach's title was also clear-"keyboard etudes composed of an aria and a series of variations for harpsichord". Second, Gothenburg was only 14 or 15 years old. At that time, the development level of keyboard skills should be comparable to that of now. If he hadn't died young at the age of 29, we might know more. Finally, in all Bach's fixed productions, we didn't find any "golden cup"-although he had a priceless agate cigarette case (according to research, it was given to him by the German emperor Frederick II in his later years). In fact, it doesn't matter what the truth is, just a good story (and a topic that can't be better! )-and there is no doubt that it will always be closely linked with this masterpiece.

In this gorgeous variation, Bach chose an aria as the theme, which originated from a gentle sketch he wrote for his second wife Anna Magdalena in 1725. However, there are still many musicians who have doubts about its origin, which has nothing to do with appreciating the work; What matters is the characteristics and rhythm of this theme-it is a solemn and noble Salabande dance, full of delicate and self-controlled emotions. The French style highly beautifies her-the decorative sound is no longer added at will, but the main part of the melody line. Compared with the superficial melody, the harmony implied by bass is more noticeable, which is the basis of the next 30 variations. This theme consists of four eight-bar sentences with the same harmonic structure: one is based on the tonic in G major; Later, he turned to the dominant chord; After the first iteration, her subordinate tone moved to the relative key (e minor), and more tension was injected into the music before returning to the tonic of the last eight bars (followed by the second iteration). The whole work * * * has three variations in G minor, in which E flat major replaces E minor, and the gloomy mode shows light (except for the particularly special variation No.25, which continues to be shrouded in gloom in E flat minor).

With this foundation, Bach can start to build his magnificent buildings-with exceptionally beautiful proportions and new things emerging constantly. All 30 variations of this work are arranged into a group every three, and the last song of each group is Girl of Snow. They are the most expressive of all variations, and sometimes I even forget to think about their structure because the music here is so exquisite that it brings me endless joy and indescribable excitement. In addition, each group begins with a variation on freedom by the Prime Minister (some are similar to dance music but strictly follow the counterpoint method), and the second song is usually a brilliant Tocata designed for a double-layer keyboard. Gothenburg can have a chance to fully demonstrate his clear and elegant skills.

The first change rippled with a pleasant atmosphere. In the first section, in Bach's music, the jumping and rhythm of the left hand are often used to express the motivation of joy (just like the prelude in A flat major in the first volume of the Law of Average). The technique of crossing hands in these two songs is equally impressive, because this technique is almost equivalent to a feature in later variations. It should be the second variant of Topekata, which gave us the first surprise. She taunted us from the beginning in the form of approaching cannon. This is actually a simple trilogy. Similar to the prelude in D major in BWV936, under the continuous bass background, the two voices started a continuous dialogue-perhaps Bach thought that we should spend some time warming up on the eve of great changes! Then there is the first canon of the whole song-the third variation of homophones. Through a feeling close to dancing, the time value of 12/8 implies a simple and idyllic delicate artistic conception. Because it is necessary to play closely spaced parts with one hand, it will be a challenge for every pianist to convey the complex and staggered structure to the audience completely and clearly (harpsichord is easier to express than modern piano). In the first four bars, the left hand clearly and elegantly explains harmony, and the texture scale develops rapidly.

The fourth variation is a dance music, which sounds a bit wild. The first three sounds jump continuously in the game-like imitation, and syncopation adds a lot of fun at the same time. This is an exciting and brilliant Tokata. The fifth variant uses typical Italian keys, and one hand sometimes jumps dangerously over the other. The music starts with the left hand, and then the right hand plays a very Bach-style inverted counterpoint melody. This piece of music, as Landowska,Wanda said, "She has an irresistible happiness".

Although the original manuscript of Variations on Goldberg has been lost, we still found a copy of Bach's signature at 1974. Compared with the previous international version, this version has added several beat marks, especially in the seventh variation of "Gig Rhythm". It is speculated that Bach may not want the beat of the music to be too slow, so he deliberately made her closer to Sicily or Flanagan, but in fact this French quickstep is very similar to the French overture in BWV83 1. Her scattered and changeable rhythm and keen decorative sound make it one of the most attractive songs in all variations. Due to the steep overlap of hands, the eighth becomes a display of skill and difficulty. French crossed hands need to play the same part of the keyboard at the same time. The biggest problem in piano playing is that you need a high degree of care to avoid sound confusion. But the rhythm of the eighth variation is still puzzling: if you don't look at the score, some listeners will recognize the 3/4 beat at the beginning of the music as 6/8 beat. In order to prevent people from going astray, pianists should emphasize stress a little. When playing this piece of music, the hands are constantly approaching and separating-just like some etudes-and the crossing of arms also provides a visually exciting effect. The next shot, the ninth variation-the end of the third group, is full of charming lyricism, and the music flows in demure. The bass, which is more powerful than the previous gun music, provides a strong support for the beautiful melody.

The tenth variation is the first four fugues-intimate and natural, which reminds me of the March in D major in Anna Magdalena's notebook. The eleventh change is that there are many overlapping hands. This kind of jig dance with the beat of 12/ 16 and some close to Tokata needs to be played gently. She is composed of staggered scales, unpredictable arpeggios and vibrato, and finally disappears into the floating air. Then Bach gave us the first inverted cannon-Variations 12. I noticed that this song has some characteristics with the meaning of king, so I think she should not be rushed to play.

Variations 13 lead us into an extremely lofty world, and I feel that the emotion of the whole work has quietly changed here. If most of the previous variations came from the material world, then the thirteenth variation let us leave there for the first time. Her delicate and restrained melody seems to come from the slow motion of a concerto (but not too slow! ), using the acoustic contour characteristics of some violins and two sighs, rose from the accompaniment to the sky. Near the end, several chromatic scales in the left hand once again enhance the solemnity and mystery of the pure land of bliss. My mind stopped somewhere on the piano, but my fingers were tapping on the keyboard somewhere else-Variations 14 started with sharp and cheerful ridicule, and Bach woke us up from our dreams. In a wide range of falling phrases, irony is the only feature (it becomes rising after repetition). We are often told that in baroque music, decorative notes are played with a strong beat, but here Bach wrote all the notes before the strong beat. So much for the rules! After a period of emotional catharsis, the fifteenth variation shows us the first small variation of the whole song in the form of the fifth gun. The emotional experience of contrast is very suitable, and her downward phrases are still immersed in the sigh of thirteen changes, which is particularly sad; But the corresponding rising melody brings people hope. Bach is not allowed to completely despair of his music, which is due to his firm and profound religious beliefs. The fifteenth variation is a powerful proof of Bach's musical expression. Her rhythm tends to be andante, 2/4 beats, and the music flows in sadness. The bass is full of dramatic attention and imitates the sigh and wide interval of the treble. At the unforgettable end of the music, our hands are separated from each other, and our right hands are still in the air five degrees away from the keyboard-the music fades away, leaving us alone in deep awe, and we are also ready to face more-this is also the end of the first half of Variations on Goldberg.

Goldberg's Variations are often regarded by the music circle as the fourth part of Bach's keyboard etudes, although he has never explained this exactly. This set of etudes is large in scale. The first volume includes all six Partita, the second volume includes "Italian Concerto" and "French Overture", and the third volume is a variation of organ chant. In these works, the characteristics of French overture can be seen everywhere: for example, the opening of the fourth Partita in D major; Needless to say, the works of the same name in the second volume; Then the third volume is the prelude and fugue for organ in E flat major. In Goldberg's Variations, the same is true of the Sixteen Variations. This song opened the second half of Gothenburg with a grand atmosphere of grace and elegance. She is divided into two parts: one is the grand continuous scale, the brilliant vibrato and the intense rhythm-the dominant mode until 16; The repetition is followed by a faster fugue fragment. Although the music texture here is clear and transparent, it is still very orchestral. We have two quick bars in 3/8 time, and each bar adopts the original harmony.

Variations 17 is a high-spirited tokata, and Bach obviously wrote it for the harpsichord with a double keyboard. In the expression of modern piano, hands should be stacked together for a long time to play. Eighteen changes, as the sixth artillery, continued this beautiful feeling. The bass is beautiful, jumping happily under the sound of two guns.

19 Variations is an attractive and exquisite dance. Changing different key-touching techniques can make the three motives play a better role, and retaining repetition can also present more acoustic beauty. This change gives the performer a time to relax-because the steepest top is in front of him!

Variations-Bach is specially made for those brave people who have enough control over their opponents' musical instruments, but she is more than just a skill performance. When the player enters the staccato of 25 to 28 bars, the forest-like notes are only used to express joy and humor. In Bach's music, moments of great joy are often unexpected moments of sadness, and the twenty-first variation pulls us back to the bottomless abyss in G minor. The chromatic scale in the bass part enhances the expressive force of this Canon. In the third section, the rotation motivation starts from the bass. Even if this piece of music is full of pain, it should not be played too slowly-in any case, the true compassion of minors has arrived.

I often feel as if I have been reborn at the dawn of twenty-two variations, and the return of G major is so beautiful. Similar to the imitation of classic songs, dialogue is widely used-it seems that from the beginning of this song, a series of variations will spontaneously form an order and go to the end of the whole work. For those who have a special affinity for this song, the ending of Gothenburg is like the other shore, and we finally know where it will be taken. Bach gave Variations 23 a lot of fun. Here, both hands are playing the game "Catch me if you can". They roll back and forth on top of each other (27 to 30 bars) and come to an abrupt end at the last chord! This technique, which is as fast as lightning in the third and sixth intervals, can be described as the ultimate performance of the piano at that time, and also paved the way for later composers. We get great happiness and excitement not only from the music itself, but also from the personal performance. After demonstrating his exaggerated skills, cannon created a sense of tranquility with 24 variations and an octave. The leading voice of this 9/8 beat pastoral song changes in the middle of the music (between 9 bars and 24 bars). The third degree of the right hand at the end perfectly leads to the third degree of the left hand at the beginning of the next song, and the transformation of these two chords makes the whole atmosphere suddenly change.

Twenty-five variations-undoubtedly the most outstanding variations in the whole work-require not only a high degree of skill, but also a pianist's profound inner experience and expressive force to play her. The rhythm of the song returns to Salabande's original work, the poetic melody interwoven with beauty and pain shows unparalleled emotional depth, and the sad chromatic scale shows the source of romanticism. Landuska's music called Black Pearl is slower than other variations, although they all have the same number of bars. The opening decorative "repetition" is full of singing and expressive force. Bach often used this technique in some works with strong feelings, and later Chopin often used this technique. When the tension is gradually released, the falling melody is accompanied by dissonance and finally ends in the tonic. In some private moments, I will feel another world completely untouched by the world (I intuitively think that Salabande is from the 6th Partita).

If you want to finish the whole performance in Gothenburg at one time, the most difficult thing is to regroup your energy and energy to deal with the dangerous 26 variations after exhausting all your internal forces-we only have a few seconds to rest, and then we are thrown into another highly skilled Tocata. During the performance of this song, the arms need to be crossed for a long time.

The last canon, Variations 27-Bach's only work that abandoned the bass in minor. On the harmony outline of the theme, two guns chattered in a friendly and naughty way, and the ending was sudden and unexpected! Then I rushed into the 28 variations-vibrato practice, and the bell-like strong sound and the big jump vocal cords brought endless joy. The clarity of a piano with superior performance is very necessary for the interpretation of this song. Needless to remind, variant 29 is the last Tokata. Or the beginning of joy, starting with the strong sound like the left hand drum, and then "beating" the chords on the double-layer keyboard. The double octave jump of the left hand adds a lot of extra strength. I think the expression of this song should start from some degree of free improvisation, but the following descending order must be strictly controlled. After that, we were brought into the jubilant thirty changes. We have expected that this will be the tenth cannon, but Bach is often unexpected. This song is a "Quodlibet", which refers to a musical joke that often appeared in popular songs at that time: singers like to add some lyrics with completely different characteristics or emotions to the original song to achieve entertainment effect. People like to play this game at family gatherings very much, especially after eating. At that time, the Bach family held a grand party every year. They usually start with a religious chorus with a festive atmosphere, and finally everyone improvises "quodlibet". The party ended in an atmosphere completely opposite to the beginning, and the lyrics chosen as "quodlibet" are usually very humorous and sometimes even make people laugh. At the end of all the variations, Bach chose two folk songs that he likes to sing at family gatherings. The lyrics are-

The first song:

I haven't seen you for a long time.

Please come closer, closer, closer.

The second song:

I don't like cabbage or beets.

If mom cooks more meat,

I think I will stay for a long time.

By quoting these folk songs, Bach integrated his lofty thoughts into every day and injected warmth and love into our hearts. In the eyes of most people, Bach is a workaholic dominated by strong reason, but he still knows how to enjoy life and expects to share his sadness and happiness with us. Now that all the parties and feasts have passed, the crowd is drifting away; Arias came slowly from other places far away. She is no longer as solemn and clear as at the beginning of the whole song. She was shrouded in a mist and full of beautiful memories-this is one of the most touching moments in all music in the world, and she told us in the most simple tone-that the long journey is over and it is time for us to return to the place where we came.

Landowska once complained: "Nowadays, people are scrambling to buy tickets for the Gothenburg concert, which makes me feel sad and depressed. Are they really out of love for music? No, they don't understand at all-they are just driven by a simple curiosity to see how the most difficult keyboard song since ancient times was conquered by excellent skills. " Of course, the above words were written by 1933, when Landuska had just finished the world's first recording of this work. Today, Gothenburg has become one of the highest symbols of human thought-fortunately, those concert tickets are still selling well! For every interpreter, it is a long-term problem whether to keep repeating when playing, at least depending on whether the length of the work doubles. But no matter what you choose to do, you can't satisfy everyone. Francis Tovey believes that "playing all the time is a sign of being ignorant"; Busoni also opposes repetition, and he even claims that some variations can be completely deleted! Most concert managers don't want to play only an 80-minute piece at a concert; In the past 25 years, I have often played the omitted Goldberg Variations in the second half of concerts. In this new record, my performance has kept all the repetitions-I found that the effect of the work has been infinitely expanded-the architectural beauty of music has never been so shocking-the limited variation has opened up endless changes! I think I will play the non-repetitive version many times in the future, but my inner will will always be interpreted according to Bach's writing.

We should ask ourselves: Why does this work have such strong spiritual penetration? Listening to her often puts me in a moment of deja vu, hiding that feeling inside, as if I had been looking for it all my life. Forget it, maybe this will always be a mystery, a dream! When I decided to write something for Gothenburg, the words became stiff and conservative; Think of 1934 Ralph Kirkpatrick's extraordinary treatise on this masterpiece, and I feel the same way:

There is something more sacred here than what we have heard. It is the most obscure part of the world created by the creator; Just like a melody we hear, only the world itself that has insight into everything can understand its full meaning.

Fortunately, however, the Goldberg variant met this man! He is the famous Canadian pianist glenn gould. Gould was born into a musical family, his father was a violinist and his mother played the piano well. Gould showed great musical talent when he was a child, and he learned to read music when he was still illiterate, especially in playing the piano, which was envied by so many parents who let their children learn piano. When he was a child, he learned the piano quickly and listened well. His mother plays a note at random, and he can immediately say that it is that note across the room. When he was ten years old, he learned to play the first volume of Bach's average speed. At this time, his mother can't teach him. He was sent to the door of Professor Guerrero, a master musician. The professor saw Gould's unusual talent at a glance, and he adopted an unusual educational method: no coercion or coercion. On the specific issues of piano technology, the professor allows Gould to argue with himself or even disobey him, and teachers and students always discuss and communicate with each other. This creative and inspiring way of education produced Gould's unique and even rebellious playing style in the future. Gould, age 19, has completely met all the requirements of a master, and he started his acting career. His extraordinary skills amazed everyone else, and he rose through the ranks and successfully entered the core of classical music. Genius always has some quirks, especially Gould's: when he plays, he hums something while dancing (some people say it's Gould's artistic song), and the chair he sits in is always made by his father, and there is still a piece missing. None of this counts. Later, I began to hate concerts and devoted myself to recording. In his later years, he began to take medicine for no reason, and he didn't get enough sleep for a long time. Sometimes he got up in the middle of the night for no reason to call his friends and play the piano for them. Therefore, he became a "lonely transcendence". If all this has cast a mysterious veil on Gould, then his legendary Variations on Goldberg is even more incredible. Young Gould signed a contract with Columbia Records, and the first record he chose turned out to be a variation of Goldberg, which is the most difficult to play in the world! Goldberg Variations, formerly known as harpsichord keyboard etudes, consist of an aria and a series of variations. It is said that Bach gave it to a nobleman to calm his nerves. This song won Bach a gold cup, which is also the highest reward for his single. The whole variation 1 * * has thirty variations and an aria. The 30 variations of this work are arranged in groups of three, and the last song of each group is Canon. They are the most expressive of all variations, and sometimes I even forget to think about their structure because the music here is so exquisite that it brings me endless joy and indescribable excitement. In addition, each group begins with a variation on freedom by the Prime Minister (some are similar to dance music but strictly follow the counterpoint method), and the second song is usually a brilliant Tocata designed for a double-layer keyboard. Gothenburg can have a chance to fully demonstrate his clear and elegant skills. Maybe you can't understand this, and I can't explain clearly what counterpoint, polyphony, cannon, toccata and fugue are here, but from this long list of complicated terms, you can certainly appreciate the grandeur and superb skills of this masterpiece. Since Gould chose this as his "pioneering work", he must have a unique skill. Sure enough, his style of play is completely different from his predecessors. From the simplest point of view, it takes at least an hour for others to play, and he only needs 35 minutes. Although all repetition is omitted, his playing speed is still stormy. From a technical point of view, it's amazing that he is still at ease in such a high-speed performance. Judging from its popularity, it is undoubtedly well received. Many people who don't love classical music and Bach love classical music just because they have heard his 1955 recording. But no one knows why Gould, 49, suddenly wanted to re-record this work after more than 20 years. You know it's extremely difficult. It's the hardest thing to surpass yourself. Luckily, I downloaded his video at 198 1 In the interview, Gould did not give too many answers about the reasons for the recording. He said it was mainly because of the improvement of recording quality. But many people believe that this is because it is an act of God: Gould died suddenly after his 50th birthday shortly after recording, and this recording became his last work, which happened to be the same as his first recording. So they thought Gould must have felt that he was dying, so he re-recorded Variations on Goldberg. His good friend also said, "When he played the last aria, he seemed to be dead." The first time I listened to this record, I also had a feeling that the piano player seemed to be dying. I found it online. At that time, I didn't know whether to be happy that I could hear the mood of the performer or to feel sorry for the performer of this great work. Because he plays so well, the whole song has a calm smile, happy laughter, crazy laughter, deep thinking, compassionate prayer, and complicated feelings about coming to the end of life. Gould's performance slowed down moderately this time, while maintaining his own style, he also increased the excavation of connotation. From the comparison of the two recordings, we can deeply feel that twenty years ago, he was a young man with high spirits, and twenty years later, he was already a weather-beaten "old man" ... Alas, writing here, I feel as if I can continue to write this legendary story endlessly, but I don't want to write this heavy story. If you are interested, you can check the relevant information and comments from netizens. There are many, many ... I hope you can download these two CDs and the video he recorded at 198 1.