NICANOR ABELARDO

VIOLIN SONATA

by

JOSEPH B. ORTIGUERA

JOANNA BIERMANN, COMMITTEE CHAIR

STEVEN B. BUNKER SUSAN C. FLEMING JENNY GREGOIRE MARVIN JOHNSON DANIEL SWEANEY

A DOCUMENT

Submitted in partial fulfillment of the requirements for the degree of Doctor of Musical Arts in the School of Music in the Graduate School of The University of Alabama

TUSCALOOSA, ALABAMA

2014 Copyright Joseph B. Ortiguera 2014 ALL RIGHTS RESERVED ABSTRACT

Nicanor Abelardo (1893 – 1934) was a composer who emerged from post-colonial

Philippines to create a national musical identity. A composer of over 140 works that included sonatas, concerti and chamber music, Abelardo is best known for elevating the Philippine genre of the Kundiman into a western art-song form. He is credited as being the most prominent and most influential of composers during the height of classism in Filipino music, a period which lasted from the 1860s until the end of World War II.

The Violin Sonata (1931) by Abelardo is a composition for violin and piano that does not fit the characteristics most associated with Philippine music, particularly the Kundiman that

Abelardo is best known for during that time period. Abelardo composed the Sonata as a student at the Chicago Musical College. It is a work that allowed the composer to explore unfamiliar musical languages influenced by Debussy, Schoenberg, Ravel, Hindemith and Bartok. The

Sonata embodied a modern and western sound by a composer who exemplified Philippine music, nationalism and identity. There is no published copy of the Violin Sonata: only the original manuscript and a few hand-copied scores are in existence.

This is a critical edition of Abelardo’s Violin Sonata. It is a work that adheres to the tonal and structural paradigm of sonata form but is chromatically enriched by Abelardo’s integration of the whole-tone scale to create a work that is both diatonic and atonal.

ii DEDICATION

I am a product of the African proverb, “It takes an entire village to raise a child.” This document is a result of the time, energy, patience and belief many have invested in this kid from

Milwaukee. I would like to thank in particular: Dr. Patricia Jones Whyte, for always reminding me to “keep the eye on the prize;” Professor Terry Collins, for always looking out for my best interests and for the many opportunities that led me down a better path in my education and personal growth; Mr. J. Patrick Rafferty, for bringing me down to the South and empowering me to pursue my musical dreams and aspirations; Dr. Joanna Biermann, you are an incredible mentor, there are not enough words to express my gratitude for all that you have bestowed upon me; Dr. Linda Cummins, thanks you for your advocacy, care and incredible compassion in your guidance and teaching; and to my wife Ciana who took a chance to go on this adventure with me in 2004, what a ride it has been and I could not have done it without your endless love and support. Finally, I dedicate this work to my mother who has always given her very best to provide me with every opportunity in life. For all the tutoring, music lessons, trips abroad, miles driven and prayers, I am who I am because of you.

iii ACKNOWLEDGMENTS

Thank you to those who have been instrumental in making this project possible. At the

University of the Phlippines – Diliman: Dean Jose S. Buenconsejo, Professor Sergio Z. Esmillia,

Professor Leticia Del Valle, Ms. Florinda Santos and the College of Music Library staff. At The

University of Alabama: Dr. Joanna Cobb Biermann, for imparting your expertise from the

Beethoven Archives; and Dr. Marvin Johnson, for your extensive time and energy in the analysis chapter. The members of the Abelardo family: Mrs. Cecilia Abelardo Quizon, Mr. Ermin

Quizon, Mrs. Menchie Abelardo, Mr. Leslie J. Abelardo and Sister Maria Anunciata Santa Ana.

Finally to my dear Ate Chona Capulong who always made Teacher’s Village home for me.

Maraming na maraming salamat po sa inyong lahat.

iv CONTENTS

ABSTRACT...... ii

DEDICATION...... iii

ACKNOWLEDGMENTS ...... iv

TABLE OF CONTENTS...... v

1. BIOGRAPHY ...... 1

2. ANALYSIS...... 20

3. CRITICAL REPORT...... 34

4. VIOLIN SONATA – FIRST MOVEMENT...... 38

5. VIOLIN SONATA – SECOND MOVEMENT ...... 65

6. VIOLIN SONATA – THIRD MOVEMENT ...... 79

7. CATALOGUE OF VARIANTS...... 105

REFERENCE LIST ...... 106

PERMISSION TO PUBLISH...... 108

v BIOGRAPHY

From the first landing of Miguel Lopez de Legazpi in 1565 until the revolution in 1898, the Philippines had been a colony of Spain. Augustinian, Dominican and Franciscan missionaries brought Western music along with Catholicism to the Philippines. The Spanish used genres of

Western music to evangelize and acculturate the indigenous populations throughout the colonial era. By the 1800s a Filipino national awareness had evolved. Native Filipinos who had, “direct contact with Europe brought ideas of the French Revolution and the Enlightenment to the colony.”1 By the 1860s demonstrations against Spain were rampant in Manila and by the late

1880s the relationship between Filipinos and Spain had deteriorated. The return of Dr. Jose

Rizal, considered the national hero of the Philippines, to Manila in 1892 was the start of many events that led to the revolution against the Spanish colonial government. General Emilio

Aguinaldo, who led the Revolutionary Government, declared the First Philippine Republic on

June 12, 1898. However, the Treaty of Paris, signed on December 10, 1898, by the United States and Spain, turned the Philippines into a U.S. Territory until the end of World War II. Philippine independence from the United States finally came on July 4, 1946.

Nicanor Abelardo was born on February 7, 1893, in the town of San Miguel de Mayumo,

Philippines, five years before the Philippines declared independence from Spain. San Miguel is a town in the province of Bulacan, one of the Tagalog speaking regions on the main island of

1 The Life Works of Marcelo Adonay, ed. Elena Rivera Mirano, vol. 1, Music and History in the Manila of Marcelo Adonay (Quezon City: University of the Philippines Press, 2009), 56. 1 Luzon.2 Valentin Abelardo and Placida Santa Ana, raised a total of eight children, of which

Nicanor was the oldest. His mother, who came from a family of painters, wood carvers and sculptors, sang in the church choir and worked as a dressmaker. His father was a self-taught musician who learned how to play the violin and banduria.3 Valentin eventually became the primary music teacher in San Miguel, teaching all string instruments and leading the town

Rondalla band.4 With the banduria, he would play haranas with the local group of Haranistas.5

Despite being the town maestro, he needed to sustain his family by additionally working as a photographer, goldsmith and tailor. He even tried his hand at politics.

At just seven months of age, Nicanor Abelardo ostensibly demonstrated signs of innate musical sensitivity. It is reported that he remained alert rather than fall asleep when Tagalog lullabies were sung to him. It was the steady rhythm of the marches by the town’s band that lulled him to sleep. He made up melodies as a young child and even played with self-made instruments of bamboo. According to Epistola, Abelardo was described as being “good natured and endearing,” despite receiving harsh discipline from his father.6 At age five, his father gave him his first banduria and later instructed him in the rudiments of solfeggio along with lessons on the piccolo-banduria, laud and guitar.7 At six, he had mastered the guitar and people considered

2 The majority of biographical information and quotations in this section come from Ernesto Epistola, the author of one of two published books about Nicanor Abelardo: Ernesto V. Epistola, Nicanor Abelardo: The Man and the Artist: a Biography (Quezon City: Rex Printing Company, 1996). Most scholarship on Abelardo’s life and music cites Epistola. The other main source is Alfredo M. German, Ang Buhay at Musika ni Maestro Abelardo (Bulacan: Bulacan Cultural Arts and Historical Foundation, 1993). It can be found in the Philippine National Library and is written entirely in Tagalog. 3 The banduria is a chordophone that looks similar to the mandolin and has six pairs of strings. 4 The rondalla is an ensemble of string instruments that are played with a plectrum. The standard Filipino rondalla ensemble consisted of a banduria, the laud, octavina, guitar and double bass. 5 Haranas were courtship serenades sung by men wishing to court a woman outside her window. The haranas were songs in either duple or triple meter, in either major or minor keys, with simple harmonic accompaniment on the guitar or rondalla. 6 Epistola, 9. 7 The laud is similar to the rondalla but with a longer neck and with a range one octave lower. 2 him a child prodigy.8 He played in a popular rondalla group led by his father, who unfortunately would discipline Nicanor quite openly and harshly when he made mistakes. Nicanor therefore practiced his part constantly out of self-defense.

Nicanor reportedly loved the haranas so much that he would rather play his instrument than sleep. He particularly loved the kundimans and kumintangs that the Rondalla group played.9

He quickly memorized all the old kundimans sung in the town and accurately played what he had just heard. When he was seven, his father taught him how to play the violin. Epistola described the instruction as “play-your-notes-as you-can technique,” because Valentin was also a self- taught violinist.10 Nicanor also continued to receive lessons from his father in solfeggio and mastered melodic and harmonic dictation.

His renown as a child prodigy attracted the attention of the local Spanish gentry, who retained their land holdings and wealth even though the Philippines was no longer a Spanish colony. They wanted to send him to Spain for formal instruction in music but his mother would not allow it, although she later regretted that decision.

School was difficult for the young Nicanor. It took him three years to complete the second grade. He was not good at academics and had a difficult time socially. He was a sickly child and began wearing thick glasses at age eight due to a bout with the smallpox virus. Perhaps because of his difficulties in school, his parents sent him to Manila when he was nine where his uncle, Juan Abelardo, resided. Nicanor attended the Primera Enseñaza (primary grade school, still based on the Spanish colonial education system). Juan was a painter who exposed Nicanor to

8 Epistola, 10. 9 The Kudiman and Kumintang are closely related popular love songs of the 1800s accompanied by a guitar. 10 Epistola, 12. 3 the visual arts and provided his own children with piano lessons from a teacher who would come to the house. Nicanor, who did not receive instruction, would listen to the lessons and try to teach himself how to play. Eventually he played the piano better than his cousins. Nicanor apparently was no more successful in the Manila school, as his classmates constantly mocked him for his unkempt appearance; but he supposedly laughed along with the mockery. When his father learned that Nicanor was playing piano rather than studying, he brought him back home and enrolled Nicanor in the San Miguel Primary School. This meant a further change in education systems since the school was organized after an American model. At the same time he returned to playing with his father’s Haranista group, also learning how to play the harp. He played music with his early childhood friend, Francisco Tecson, better known as “Pakong” until the latter departed for the United States to study dentistry. Epistola writes that the inspiration behind the famous Kundiman, “Nasaan Ka Irog?” (Where art thou, my love?) is about Pakong and a girl named Segunda, who were not allowed to be together because they came from rival families.

“Nasaan Ka Irog?” is dedicated to Dr. Francisco Tecson.11

By the time he was sixteen, Nicanor had completed the sixth grade. Despite his academic difficulties, Nicanor found a job as a primary school teacher in Sibul Springs, Bulacan due to a shortage of teachers. Since Sibul was far from San Miguel, Nicanor went to live with another uncle who resided nearby. Every weekend Nicanor would return to San Miguel. Eventually he was posted even further out in the province to teach in San Ildefonso, significantly further from his home in San Miguel. No longer able to go home on the weekends, Nicanor spent his time making music: singing, playing guitar and composing on his own. There he composed a march titled “Banaag at Lakas” (Glimmer of Strength), reportedly for a local constabulary band.

11 Epistola, 22-26. 4 Nicanor returned to Manila at age eighteen to attend the Segunda Enseñaza (high school) at the Liceo de Manila. He returned to live with his uncle Juan but was still behind academically, so the entire family pitched in to help him catch up in school. At this time, Nicanor taught himself how to paint by observing his uncle and other family members, who at that time painted for Manila theatres. He also learned about literature, particularly poetry, through his cousin

Mariano who shared poems in both Spanish and Tagalog, languages in which Nicanor was proficient. He attended zarzuelas with his uncle’s family, who were regular patrons, and eagerly studied their structure and presentation.12

Music was constantly played and sung in Juan’s house. Nicanor spent many hours at the piano by himself and became an excellent improviser. When his uncle saw how well his nephew now played, he sought an experienced pianist who could provide advanced training. This led

Nicanor to work as an apprentice under the best cinema pianist in Manila: Francisco

Buencamino, who was also from San Miguel.13 Providing music at the cinema did not satisfy

Nicanor’s musical appetite so he found more work as a guitarist accompanying singers. This led him to meet Florentino Ballacer, an important figure in the zarzuela scene at that time.

Ballacer was quite impressed with the nineteen-year-old Abelardo’s guitar playing and improvisation skills, and in 1912 he asked him to collaborate on composing a zarzuela, a new challenge for Nicanor. With Ballacer serving as librettist and Abelardo composing the score, they produced their first collaboration: “Lucila,” a zarzuela in three acts. It was presented at the

12 Zarzuelas are Spanish comic operettas. They have spoken dialogue along with singing in the traditional operatic forms of arias, recitatives and choruses. 13 Francisco Buencamino Sr. (1883–1952). A composer from San Miguel de Mayumo, Bulacan. Buencamino was a student of the eminent Philippine composer and conductor of the late 19th century, Marcelo Adonay. He composed many Tagalog operettas and zarzuelas. Buencamino taught at the Ateneo de Manila in the early 1900s. He also taught at the Centro Escolar de Señoritas and headed its Music Department for 30 years. He founded the Buencamino Music Academy in 1930, and had Abelardo as one of his students. N. Tiongson, ed., CCP encyclopedia of Philippine Art, Vol. 6: Philippine music (Manila: Cultural Center of the Philippines, 1994). 5 old Opera House in Manila but failed commercially, with critics panning it as a “first-class flop.”14 A few months later they completed “Akibat,” an operetta in one act. Unlike “Lucila,” it was an immediate success. According to Epistola, “Akibat is a zarzuela on nationalism. It tells the story of a character named Akibat who betrayed his own people to Magellan.”15 In other words, it is a Spanish language piece telling the story of a native Filipino whose actions lead his native country to become a colony of Spain for 333 years. After this first success, Abelardo started writing more zarzuelas. Companies regularly approached Abelardo for whatever he composed, but he also wanted to continue playing for Buencamino and so began playing jazz in the saloon in Calle Aceiteros.

On February 4, 1916, the Philippine Legislature established a conservatory of music in

Manila. According to Banas, this was a result of musicians, music lovers and members of the first Philippine Assembly during the American regime wanting a “concrete manifestation of the government’s concern for the country’s culture and arts.”16 Seven months later, the University of the Philippines Conservatory of Music opened with Wallace W. George, a voice professor from the New England Conservatory, as its first director.17 Abelardo was one of the first students to enroll. Although he had only seven years of primary school and two years of secondary school, he was still admitted to the program leading to the Teacher’s Certificate in Science and

Composition.18

14 Epistola, 30. 15 Ibid., 30. 16 Raymundo C. Banas, Pilipino Music and Theater (Quezon City: Manlapaz Publishing Co., 1969), 120. 17 “The Directors and Deans of the College,” College of Music University of the Philippines Diliman, accessed February 27, 2013, http://music.upd.edu.ph/Administration%20of%20the%20College%202.html. According to Epistola, the opening date was October 4, 1916, but the UP College of Music website lists the opening date as September 4, 1916. 18 The modern equivalent to the Teacher’s Certificate in Science and Composition is a degree in music theory and composition. 6 In 1917, the twenty-four year old student and musician began to seriously court a young

Sixta Naguiat, whom he had met three years earlier. Epistola describes the romance as follows: at one of the movie houses at which he had worked, Abelardo had befriended a ticket girl,

Pacing. When there was no need for mood music or when it was intermission, the two would talk and help keep each other company. On one afternoon, Abelardo saw Sixta resting next to her elder sister, Pacing. He did not know that his friend had such a beautiful sister. Eventually he would send letters to her, “morning, noon and night; night letters were especially delivered.”19

Abelardo would also try to see Sixta whenever he could, sometimes coming straight from his job at the saloon to see her at mass. When he told his mother that he wanted to marry her, she was against the idea knowing that her son would marry a girl who was socially beneath him: Sixta only had a fifth grade education and came from a “family of taquilleras and refreshment parlor cashiers.”20 Abelardo convinced his mother that he loved her and she finally agreed, although his father was entirely against the union. The parents of Sixta were strict and expected a formal courtship, where both parents of the man would come to the house and ask the woman’s parents for their daughter’s hand in marriage. Abelardo’s father refused to go, so his mother went alone.

Since both parents were not present, Sixta’s family refused the marriage proposal. Later that day,

Abelardo explained to Sixta that their only option was to elope. According to Epistola, “they went to a Methodist minister who married them at the Knox Memorial Church on June 16, 1917.

After the ceremony they returned to their respective homes. When Nicanor told his parents what they had done, his father was furious and whipped the twenty-four year old Nicanor like a little boy. But on July 1, 1917, a second ceremony (this time, a Catholic one) was held at the Santa

19 Epistola, 35. 20 Ibid., 35. Taquillera: box office clerk or ticket clerk. “Taquillera” WordReference.com, accessed February 27, 2013, http://www.wordreference.com/es/en/translation.asp?spen=taquillera. 7 Cruz Church in Manila at four o’clock in the morning. Nicanor Abelardo and Sixta Naguiat were officially married.”21

Abelardo was now a married man, a student at the UP Conservatory and an active saloon musician. He and his new wife moved to a house close to the Conservatory where he was studying. He did well in his music-related coursework and composed more zarzuelas. He was a serious student; what he had learned by doing as a child was now being explained on a theoretical or scientific basis. However, Epistola reports that Abelardo wrote many exercises for compositional practice which puzzled his professors, who could not say whether they were right or wrong. Epistola claims further that Abelardo did not believe in hard and fast rules to composing, and he found no clear rules for or against his harmonization in his textbooks.

Abelardo’s ears and his perfect pitch guided him.

As a conservatory student, Abelardo was required to study one or two secondary instruments aside from the piano, which was his primary instrument. He studied piano under pianist Jose Estrella, violin with Bonifacio Abdon and the banduria with Jose Silos, all of whom would later be recognized as significant Filipino composers. He also studied voice with

Victoriano Carreon, who had been a pupil of the Italian Maestro Enrico Capozzi. Abelardo studied other instruments as well, but his ultimate goal was to compose.

In addition to his intense musical subjects, Epistola writes:

“he had realized how important foreign languages were to him. Spanish was not much of a problem; he spoke it fluently. It was English he sought. He felt he could still improve his English by reading. What he read, he supplemented by talking

21 Ibid., 36. 8 with his many American friends. Soon, he was using English with ease and fluency that many thought he talked like an American.”22

As a result of this fluency, he received numerous invitations to play for American parties and organizations.

Abelardo still worked in the saloon in the Lerma district of Manila. He was the pianist/leader of a dance band where most of the members were heavy drinkers. They used gin as an important tool of their trade: the gin would help them play better and stay awake longer.

Abelardo, too, began drinking heavily. Despite being the butt of many jokes due to his drinking,

Abelardo was respected by the musicians who collaborated with him. Band members considered him a great musician who knew everyone’s part by memory after a first reading. All the requests for dances to be played were always directed to him, according to Epistola: “The band had a very large repertoire: about twelve hundred pieces of one-steps, fox trots, waltzes and ragtimes.”23

On July 15, 1918, Abelardo was appointed to teach in the Conservatory as an assistant instructor in solfeggio and harmony. He was twenty-five and a junior there. No one questioned this appointment, for everyone knew that Abelardo always received perfect grades in those subjects. One year later, he was promoted to full instructor.

On April 4, 1921, Abelardo graduated from the UP Conservatory of Music, receiving the

“Teacher’s Certificate in Science and Composition.” Two years later, he completed his postgraduate work in Science and Composition. He composed his Op. 12 Concerto in B-flat minor for piano and orchestra as his major composition that year. It was a standard three- movement concerto, but the first piano concerto to incorporate Philippine melodies.

22 Ibid., 41. 23 Ibid., 44. 9 Abelardo established himself as a composer, teacher and orchestra leader. Many prominent families sent their children to study piano and solfeggio with him. On November 20,

1924, he was appointed head of the Department of Science and Composition of the UP

Conservatory. Though proud of this honor, the corresponding salary that came with the promotion was not enough to support his family of five. Abelardo therefore continued to work his evening job as leader of the dance orchestra at the Santa Ana Cabaret. “Like any other cabaret orchestra, Abelardo’s group played anything that would satisfy the customers who came to dance. They played ragtime, fox trots, one-steps, waltzes and all the music that their generation could dance.”24 Abelardo’s Conservatory superiors did not appreciate the fact that their colleague was a “cabaret musician.” As a result, Alexander Lippay, the director of the

Conservatory, created a rule stating, “no professor should engage in an occupation that would be derogatory to the prestige of the conservatory.” 25 Abelardo tried many times to resign from his position, as there was no way he could support his growing family without his evening job.

Lippay never accepted the resignation letters because there was no one who could replace

Abelardo.

Abelardo disliked his cabaret job, but the work supplemented his monthly income and allowed him a higher standard of living in addition to ensuring that his children would not suffer the same poverty that he had experienced as a child. The demands and hours were long and he now slept fewer and fewer hours. He believed that gin would help him combat the fatigue.

“It did sustain him for a time, or so he thought. And he drank it like [an] ordinary soft drink. Abelardo drank gin for breakfast, after using the first few mouthfuls as mouthwash. Eventually he could no longer control his body’s constant craving for

24 Ibid., 53. 25 Ibid., 53. Alexander Lippay headed the UP Conservatory 1927 – 1930. The Directors and Deans of the College,” College of Music University of the Philippines Diliman, accessed February 27, 2013, http://music.upd.edu.ph/Administration%20of%20the%20College%202.html. 10 gin, so he stopped at every sarisari [convenience store] store where gin was sold. But he was one of the very few who knew how to drink…Before he knew it, his drinking made him a very sick man and for a month he was in a hospital. When he came out, everything seemed right again.”26

Epistola describes Abelardo’s family life in colorful terms. It was anything but ideal. The author describes Abelardo as being a devoted and loving husband who “spoiled” his wife. He did not want her to do any kind of laborious tasks like washing clothes. He wanted to provide his wife with the very best and she happily obliged by spending his month’s salary on clothes for herself. He would often have to cook for himself after working long hours. She did not seem to care that her husband of social and professional standing would wear shabby clothes. Sixta was a jealous woman and secretly spied on her husband. She was described as being a very capricious wife and perhaps that was one of the reasons why Abelardo drank so much. 27

Abelardo composed numerous sacred works, most of which are no longer extant.

Although not a religious man, he had many clergy friends who often asked him to compose hymns, songs and masses for the church. He was very happy to do this and gave away his compositions without payment. As Epistola observes, “Most of the time, he would give out the original manuscript even without his signature. This is why we do not have many of his sacred works today.”28 Abelardo was most fond of the town fiestas.29 Despite his demanding schedule, he made time to conduct, sing and play in the High Mass. He was quite popular among the priests because he spoke Spanish fluently and used it with wit. Abelardo was the life of the after-

26 Ibid., 55. 27 Ibid., 61. 28 Ibid.,61. 29 The Philippine Fiesta was an annual celebration where the town would celebrate its patron saint or pay homage to the life events of Jesus Christ and the Virgin Mary. 11 mass celebrations and parties at the homes of those he visited during the fiesta. He enjoyed eating and drinking well.

As a composer at this time, Abelardo possessed a remarkable gift of concentration.

Regardless of his environment or circumstance, he had the ability to work under any condition and to complete compositions quickly. Not only was he expeditious with his compositions, he was also a disciplined and neat composer. His manuscripts are legible and easy to read. He was able to notate anything he heard. When the latest 78 rpm records of popular songs in America would arrive in the Philippines, Abelardo would immediately transcribe what he heard and then quickly arrange the songs for his cabaret orchestra, thereby creating the largest repertoire among the local Manila dance bands. This made his band the most popular in the city. In my interview with Abelardo’s niece, she remembered her uncle composing constantly on napkins, street car tickets, whatever was available at that time. And when he was surrounded by his children, who were climbing and jumping on their father, he would still stay engaged in whatever he was working on at that time.30 Epistola writes,

“There was nothing really that could dampen Abelardo’s will and power to create. His alcoholism, his kidney trouble, and other barriers to any creative artist could not destroy his spirit.”31

In 1928, the University of the Philippines granted Abelardo a year’s sabbatical from his teaching duties. He wanted a change of environment and went to Cebu to work as a music director of a large theatre.32 There he befriended Philippine composer Manuel Velez. At the

30 Sister Maria Anunciata Santa Ana, Dean, College of Music and Performing Arts at St. Paul University Manila, interview by author, 17 July 2012. 31 Epistola, 59. 32 Cebu is a province in the Philippines, located in the Visayas or the principal middle region of the Philippine Islands. 12 conclusion of the year’s leave, Abelardo resigned from the Conservatory of Music. He wanted to study abroad and learn new ideas about music, particularly about atonality, according to Epistola.

A diploma from a foreign country would increase his prestige and reputation, but unfortunately financing this desire would prove to be an issue.

The Conservatory of Music could not find a replacement for Abelardo, so he decided to resume his previous position. He was very popular as a teacher and revered by many students for his ability to easily explain the most difficult harmony lessons. Despite being back on the

Conservatory faculty, Abelardo remained intent on studying abroad. The current director of the

Conservatory, Dr. Francisco Santiago, had previously done so and Abelardo believed he should also be afforded this opportunity.33 Although he had received an invitation to study at the Real

Conservatory in Madrid, he preferred to study in America. Santiago had earned his doctorate at the Chicago Musical College, and this institution became Abelardo’s goal.

On February 19, 1931, the University of the Philippines granted Abelardo a year’s leave with pay. He was given several “despedidas” or going-away parties where he received money for his trip. Although still worried about not having enough money to maintain himself in America,

Abelardo departed on May 2, 1931, on the Canadian Pacific Steamship Empress of Russia to

America with his $500 savings, a trunk and a wooden suitcase. The ocean voyage was twenty- three days long. On the passage, Abelardo busied himself with compositions that he could publish once he arrived in Chicago. The ship landed in Vancouver, where Abelardo then boarded a train to Chicago. He arrived in Chicago the morning of May 23, 1931. In a letter written in

33 Dr. Francisco Santiago headed the UP Conservatory from 1930 to 1946. The Directors and Deans of the College,” College of Music University of the Philippines Diliman, accessed February 27, 2013, http://music.upd.edu.ph/Administration%20of%20the%20College%202.html. 13 Tagalog to his wife dated May 29, 1931, Abelardo wrote of his astonishment at depression-era

Chicago:

“After a seemingly endless trip on the train from Vancouver, I reached the land of my dreams at 8:30 in the morning with God’s help and mercy…First thing I did was to rest because of sheer tiredness and second to save myself from people who are taking advantage of others, in Chicago, the state of their economy is very poor, a lot beggars and homeless are everywhere asking for money, for coffee or bread.” 34

Having come to Chicago to study music, he visited the city’s music schools and confirmed his desire to attend Chicago Musical College. The cost of enrollment was $481, but Abelardo only had $400 of his original $500 left. He was informed he could pay the tuition on installment, which would cost more but was the only way he could enroll. He placed his hope in future scholarship opportunities because he was quickly running out of funding, and in the meantime he wrote home for more money.

Abelardo matriculated at Chicago Musical College and found himself more advanced than most of his classmates. To the surprise of his primary teacher, Dr. Wesley LaViolette,

Abelardo demanded to take the final examinations for the undergraduate and graduate coursework he was enrolled in and passed all the exams. However, a one-year residency was required and there was an additional hurdle: Abelardo did not have a high school diploma. His financial problems were mounting. Abelardo tried to join the Musician’s Union but he could not afford the $100 initiation fee and dues from his quickly dwindling money, and therefore he could not find work as a musician in Chicago. Additionally, no one wanted to buy his pieces. Abelardo tried to save money by adhering to a very strict budget. He found the cheapest room he could

34 Nicanor Abelardo, Chicago, to Sixta Abelardo, Manila, 29 May 1931, trans. Chona Capulong. Letter in the hand of Nicanor Abelardo. Private collection of Cecille Abelardo Quizon, Quezon City, Philippnes. 14 that was close to the college and limited himself to two meals per day, believing he could either sleep or study during one of the missed meals. Despite these hardships, Abelardo was remarkably productive; he composed the violin sonata and a fugue for string quartet in a mere three weeks.

The Sonata for Violin and Piano premiered at an 11 a.m. recital on Saturday, July 25,

1931. The performance took place at the Punch and Judy Theatre in Chicago Musical College.35

Fellow students, violinist Alex Peusner of Milwaukee, Wisconsin and a student of Leon

Sametini; and collaborating pianist Ralph Squires of Morgan City, Louisiana and a student of

Rudolph Ganz, the Director of the College, premiered the work.36 After the recital, many came to congratulate Abelardo. According to Epistola, “many were wondering how a Filipino could have written such a sonata. It was too modern for their taste.”37 His teacher, Dr. LaViolette, could not have been more pleased with what his student had accomplished in the span of two short months.

Ganz used Abelardo’s Nocturne for Piano as the subject of his Interpretation-Repertoire class, a tremendous honor.

The fall of 1931 was an auspicious time for Abelardo. He had received more money from home, he was given the Wesley LaViolette Scholarship of $1,000 and he became his teacher’s assistant. He was the first student at the College to have earned top grades in all his graduate courses. He was well on track to obtain his master’s degree if he could pass his high school examinations.

35 The Punch and Judy Theatre was originally the Steinway Hall, which was located in the Chicago Musical College building. 36 German, Ang Buhay at Musika ni Maestro Nicanor Abelardo. Bulacan: Bulacan Cultural Arts and History Foundation, 1993. 37 Epistola, 81. 15 In the fall semester, the Chicago Musical College Symphony Orchestra began to rehearse his Cinderella Overture, which he had also composed during his first few months in Chicago.

The work prompted considerable discussion in the musical community and premiered on

December 12, 1931, in a gala concert. A few days later, a review of the performance appeared in the Musical Leader, a national musical magazine of the 1930s, which called it “a work displaying originality and marked ability in the smooth weaving of intricate materials.”38

Abelardo was then interviewed by the Musical Courier in 1932, one of the most popular music magazines in America at that time. He became one of two graduates to receive a master’s degree one year later. At this time, however, he was becoming homesick. Financial pressures were increasing, and he was fearful of not having enough money to return home. Abelardo had sent his songs to two publishing companies, Sam Fox and Presser Co., but neither of them showed any interest. His many fears led the composer to seek alcohol again in Prohibition-era Chicago.

“There were rumors and gossip that Abelardo was again the alcoholic he had always been. Talks circulated that he did not even care what he drank anymore; he consumed bootleg whiskey and bathtub gin by the bottle. The gossip also said that he left the Lorraine Hotel to move to an apartment adjacent to a ‘still’ and ‘speakeasy’ which was open all day.”39

Abelardo later moved into a house with a professor of Spanish at DePaul University who was also an alcoholic.

Abelardo’s anxiety to get home was mounting, but he did not have the funds to return.

The University of the Philippines could not help him. His wife went to their provincial home capitol of Bulacan to ask the Governor for assistance. The Governor of Bulacan in turn wrote the

President of the University of the Philippines with some suggestions to ease Abelardo’s situation,

38 Ibid., 95. 39 Ibid., 101. 16 but the President ultimately could not do anything. There were collections taken up by friends from home: private organizations, his former pupils and even the Philippine Constabulary Band for whom he wrote one of his first compositions. Unfortunately, the sum total of the money collected could not pay for the ticket home. Abelardo therefore remained in Chicago and continued to drink. “Drinking was his only escape. It brought him solace and relived his consuming sense of impotence by blurring the cruel outlines of his real world. He associated less with ‘respectable friends’ and went with those who drank with him.”40

In July 1932 Abelardo received the long-awaited $500 from home, most of which was a loan from the University of the Philippines. He quickly bought his ticket and boarded the SS

President Taft in Seattle on July 18. He did not have his diploma in hand at the time because the results of the University of Illinois college entrance exam, which served as the high school equivalency exam, had not been released and he did not have the $25 for the diploma.

Abelardo arrived home on August 15. Friends and family welcomed him back but were disturbed by his appearance. “He was much thinner than they expected, and his enormous middle betrayed a bloated stomach. His complexion had the grayish pallor of a person suffering from alcoholism.”41

Upon his return to the Philippines, Abelardo resumed his position as instructor in the

Conservatory of Music. He did little composing but wrote numerous articles on music. Subjects included nationalism, the lack of music appreciation in the Philippines, the psychoanalysis of music, conducting and even a treatise on modern harmony.

40 Ibid., 108. 41 Ibid., 110. 17 On June 21, 1933, Abelardo finally received his Master of Music diploma. He had passed the high school examinations he took at the University of Illinois and paid the $25 diploma fee.

Abelardo had finally accomplished his goal. However, the University had hired another music professor to take his place and it seemed that his University of the Philippines Conservatory colleagues no longer took him seriously, apparently because of his drinking. Despite the advanced degree, Abelardo did not get the raise he had been expecting or the promotion he felt he deserved. He remained at the rank of an instructor.

Abelardo resigned from the Conservatory on February 27, 1934. His health was failing and he had difficulty coping with his disappointment at not having received what he thought he deserved after having worked so hard in Chicago.

On March 19, 1934, Abelardo suffered an intestinal hemorrhage in the morning and was hospitalized later that evening in a weakened condition. On March 20, 1934, his entire family gathered in his room at the hospital to celebrate two happy events: his eldest daughter’s birthday and his youngest sister’s graduation from the University of the Philippines. Abelardo was very happy to see his family and friends gathered together. “But it was the last time he would see his beloved ones gather together. Maybe he sensed that. The family had the same feeling.”42 Later that evening, with his immediate family and mother and sisters around him, Nicanor Abelardo died at the age of forty-one as a result of an intestinal hemorrhage.

Abelardo’s March 24, 1934 funeral was well attended. Epistola describes it as follows:

“the rich and the ‘important’ people came with big wreaths of expensive flowers and the funeral parlor overflowed with them. Friends came to hold necrological services and to extol him in their speeches. Musicians came in bands from far- away provinces to play their sad funeral music. The ‘little’ people and the dirty

42 Ibid., 118 18 beggars who had learned to love him because of his understanding for them came with nothing save the silent prayers in their hearts. They remembered that this was their friend who invited them into his home to hear them sing and accompany their songs.”43

Epistola described the funeral procession as “a thick line of silent people about two miles long and headed by the Philippine Constabulary Band.”44 Because it was the Lenten season, music was not allowed at the funeral mass. But his sister Victoria pleaded with the priests who eventually allowed the singing of hymns for the dead for Abelardo’s benediction. Nicanor

Abelardo was finally laid to rest that afternoon at the La Loma Cemetary in Manila. “It was a hero’s farewell and many people would later compare it to the funeral of the first President of the

Commonwealth of the Philippines, Manuel Quezon.”45

43 Ibid., 119. 44 Ibid., 121. 45 Ibid., 121. 19 ANALYSIS

The Violin Sonata by Nicanor Abelardo is a three movement work which adheres in broadest outline to patterns inherited from traditional tonal literature. Movements I and III exhibit design features of Classical sonata form, or “first movement form.” Movement II follows a ternary design. Movements I and III may be understood in A minor while Movement II is in E- flat, notably a tritone's distance from A. In his article Nicanor Abelardo: Filipino Classicism in the Art of Music, Ramon Santos quotes Abelardo as saying:

“I have written a ‘sonata’ for violin, … on the atonal basis. I have been released at last from the Classical Bond, I have been sent to wander in the new horizon taking for a guide Hindemith, Schoenberg, Bartok, - and the ultra modern style.”46

Santos continues his discussion of basic characteristics of the tonal language of the Sonata:

“The tonal language of the Violin Sonata is not atonal in the sense of the pre-serial and serial works of Schoenberg and his school from Op. 11 (Drei Klavierstücke), cast more according to the tonal explorations of the Second String Quartet and the Chamber Symphony, in which reference to tonality is intended to dramatize its deconstruction by entering into a field of tonal ambiguities. While Abelardo wrote his Sonata in the domain of ‘A’ as the tonal center, the entire music was written as though challenging the overall influence of ‘A’ as a place of rest. The overall scheme of the three movements is in fact based on a tritone relationship: A-minor/major (1st Movement); E-flat major (2nd Movement); A-minor (3rd Movement).”47

In his discussion of the first movement of the Sonata, Santos continues by observing that . . .

“In his attempt to depart from the syntactic framework of the harmonic language, Abelardo utilized the tonal regions as merely baseline structures to hold together larger formal units, rather than as interrelated events in a linear continuum. . . . in the ‘Violin

46Ramon Pagayon Santos, Tunugan: Four Essays on Filipino Music (Quezon City: The University of the Philippines Press, 2005), 53. 47Ibid., 55. 20 Sonata,’ Abelardo's lines have been completely liberated from the conventional rules of chromatic harmony, using semi-independent intervals of fourths, fifths, and displaced octaves, or diminished and augmented triads. In the first fifteen bars, [of the First Movement] the entire passage is braced by two tonal-regions – A and D on its way to E- flat (ms 18), the tritone of A. Within the A-D frame is a vigorous dramatic unfolding of Abelardo's thematic material.”48

The following diagrams chart the overall design of each movement and the bass motions

(described here by a succession of letter names) as they are aligned with formal divisions. In addition, Roman numerals have been attached to each letter name to indicate possible tonal harmonic functions; however, as Santos has pointed out, “upper voices do not necessarily follow tonal harmonic implications of the bass voice.”49 With this important qualifying and limiting constraint firmly acknowledged, I propose the following diagrams of the formal design and basic tonal structures of each of the three movements:

Movement I

Movement II

Movement III

48Ibid., 55. 49Ibid., 55. 21 These classic models are elaborated and extended to a considerable degree by many features which depart from expected tonal norms. The third movement in particular follows the classical paradigm of sonata form in broadest outline only in that while there is a clear introduction (mm.1 – 20) and a first theme area (mm.21 – 56) and a transition (mm.57 – 81) which leads to a second theme on E-flat, the motion to that secondary tonal area is not punctuated by a decisive cadence nor is the secondary tonal area reinforced by a closing theme or codetta with authentic cadences which establish E-flat firmly as a concluding secondary tonal area at the end of an exposition. Instead, an abbreviated second theme (mm.82 – 101) is followed by an extended development section (mm.102 – 165) directed toward a strong dominant E- natural (mm.146 – 165), preparing a long concluding section or recapitulation (mm.166 – 321) clearly reasserting a tonic A.

The third Movement then resembles classical sonata form in that there is a clear first theme and tonic tonal area on A and a clear return of that material at the beginning of a recapitulation, also on A. However, while the exposition does have a transition leading to an identifiable secondary tonal area on E-flat, that plateau is insufficiently well established and the associated thematic material truncated to initiate the beginning of an extended development section leading eventually to a structural dominant on E (m.146) and a decisive recapitulation which follows. In addition, while the recapitulation does incorporate familiar alterations, such as a redirection of the transition to F (upper neighbor to the dominant E?) instead of the E-flat of the exposition, it is the exposition in this special case which is abbreviated, not the development, as might have been the case in a traditional “sonatina form.”

22 In Movement I opening thematic material in measures 1-10 unfolds over a predominant

A minor tonality, although chromatic elaborations of the scale degrees of A minor permeate the texture from the very beginning. The passage proceeds in four measure phrases with the thematic material introduced in the violin in measures 1-4 imitated in measures 5-8 where rhythm and melodic contour are preserved for the most part but where the specific intervals of transposition vary from note to note.

As Santos has demonstrated, important ascending skips of a perfect fifth in measures 3 and 4 (F-natural to C-natural, A-natural to E-Natural, and F natural to C-natural) are answered by diminished 5ths or “tritones” (G-sharp to D-natural, B-natural to F-natural, and E-natural to B- flat respectively) in measures 7 and 8.50 In spite of the irregularity of these intervals of imitation, adjustments in the second phrase (mm. 5-8) can still be understood to a considerable degree as elaborations of A minor (F-natural upper neighbor to the Dominant note E in measure

5, G-sharp, lower neighbor to the tonic note A in measure 6, B-flat as an upper neighbor to the

50Ibid., 55. 23 tonic note A in measure 7, etc.). An adjusted version of the thematic material in measures 1-8, this time in the piano, is redirected in measures 9-16 to a climactic E-flat in measure 16 (both piano and violin) and is particularly notable as that point of arrival initiates a decisive descending whole-tone scale (E-flat, C-sharp, B, A, G, F, E-flat), continued for an additional octave in the left hand of the piano which leads to a low E-flat on the downbeat of measure 18 and the initiation of transitional materials. The transition concludes in measure 28 with an additional whole tone segment in the violin (F, E-flat, D-flat, B, (A), G). Segments from this succession answer in the piano in measures 30-34.

As Santos has pointed out in his discussion, Abelardo has deliberately tried to extend inherited tonal norms to embrace atonal practices and chromaticism. “Abelardo, upon being exposed to the musical revolution unfolding in the West, saw his past creative experience as one of confinement and circumscription, a life cloistered by the dogmas of form and the harmonic language.”51 The frequent juxtaposition of diatonic, chromatic, and whole-tone collections recurs throughout and can be understood as accounting for important characterizing features of all three movements.

Santos has discussed this mixture of elements as deriving from the practice of other composers and from various stylistic trends of the early part of the Twentieth Century

(Impressionism, early departures from nineteenth century chromaticism by Schoenberg, the

“mystic chord” of Scriabin, etc.)52 While these observations are useful as ways of understanding the various influences affecting Abelardo at the time he composed this work, and an awareness of these influences is useful in establishing the historical context from which this music emerges

51Ibid., 54. 52Ibid., 55. 24 as well as some basis for understanding and appreciating the diversity of influences affecting compositional decisions from moment to moment, section to section, and movement to movement; they do not result in analytic paradigms which reveal an integrated pitch structure underpinning and linking thematic materials, phrase structure, and form.

Construction of such a paradigm or paradigms is particularly challenging in this work where at least two different referential pitch collections (diatonic minor-major scale, and the whole-tone scale) are juxtaposed throughout and where varying degrees of their simultaneous appearance summarize to produce an over-riding chromatic texture, frequently atonal in character. If such an insight is possible, the extensive in-depth investigation and analytic techniques required to reveal such a model lie outside the intended scope of this paper. Even so,

I would like to propose a way of understanding interrelationships among these pitch collections which may help set the stage for a more intensive study, should such an investigation be attempted in another context.

The following examples diagram the way each of these collections divides the octave and how the interrelationship of those collections suggests ways of understanding important aspects of pitch organization. Notice: 1) that the diatonic scale (minor mode, ascending form) and the whole-tone scale are mutually exclusive in pitch class content except for the first two scale degrees, A and B in the collection starting and ending on A and E-flat and F for the scale transposed to E-flat; 2) that the first three pitches of the descending form of the minor mode (A,

G, F-natural) and the last three pitches of the ascending whole-tone scale (F, G, A) are composed of the same pitch classes; 3) that the last tetrachord of the descending form of the minor mode

(D, C, B, A or A-flat, G-flat, F, E-flat) may engage the “Phrygian 2,” the chromatically lowered

25 second scale degree (becoming D, C, B-flat, A or A-flat, G-flat, F-flat, E-flat); and 4) that the summation of these two collections (including the lowered second degree of the descending minor mode) results in a complete chromatic collection.

The whole-tone scale does not provide perfect fifths, the boundary interval of major and minor triads. In particular, it is important to recognize that the fifth scale degree does not nor does not form a perfect fifth with the first or a possible “tonic.” In fact, the fourth and fifth scale degrees form intervals of an augmented fourth and a minor sixth respectively with a possible

“tonic,” such as might be inferred from the opening of Movement I. Sudden shifts from a diatonic collection in A minor, to a whole tone collection on E-flat, such as that which occurs in measures 16-17 in the first movement, result in an harmonic goal far outside any normally expected for a secondary tonal plateau in A minor. This kind of motion disrupts “tonality” and introduces a strong “atonal” element at the deepest structural levels of pitch organization. This motion is not the result of “modulation” in the traditional sense, as common triads are not

26 available between A and E-flat. However, it does seem important to recognize that the juxtaposition of the whole- tone scale on E-flat and the E-flat collection which produces the major-minor implications in measures 18-21 (see violin part in particular), though mutually exclusive in pitch content for the most part (E-flat and F are common tones) are related to one another, scale degree by scale degree, by half step, the characterizing interval from diatonic collections which determines modality and the interval which imparts the strongest voice leading tendencies (leading tone to tonic, minor 6th down to the dominant, fourth scale degree down to the third, etc.).

The juxtaposition of these two collections then, sometimes successively and sometimes simultaneously, not only results in a fully chromatic texture but at the same time results in a texture predominated by step motions much of the time, most notably by half-step motions. For example, notice the very opening of Movement I (D-sharp to E, G to F-sharp, etc.) or the principal theme in Movement II (E-natural to F, G to A-flat etc.). These half steps facilitate greatly the establishment of tonal regions as such step motions, particularly when they are formed by dyads separated by larger intervals, have a strong tendency to subordinate one note of the dyad to the other. The emphasized pitch then may become part of a deeper structure

(ascending or descending diatonic fragment, major or minor triad, etc.) which helps establish, if only temporarily, a sense of “tonic.”

It is particularly interesting to notice how this juxtaposition or association of diatonic elements and whole-tone elements may happen simultaneously in the structure of a single thematic idea, and on occasion at deeper levels, to support decisive motions to important cadence points.

27 The example above charts the contour of the opening thematic materials in Movement II. See how the boundary interval of the principal theme in the violin, C to E-Natural, is followed by two half-step motions, E-natural to F and G to A-flat, imparting a strong feeling of F minor. At the same time however, that skip from C down to E-natural, a minor sixth, and the terminal note of the ascending scale, A-flat, are all elements in a whole-tone scale on C: C, D, E, F-sharp G- sharp (eharmonically equivalent to A-Flat), A-sharp / B-flat, C. The intervening notes, F and G are not parts of the whole-tone scale; however, the two notes forming the opening skip and boundary interval of the line, along with the note of termination, A-Flat, are all members of a whole-tone scale coexistent with the foreground in F minor. Notice as well that the notes C, E- natural, and A-flat all receive agogic accents.

This theme, illustrated above, is then transposed up a minor third to E-flat in measure 15 where

28 the same duality of diatonic scale on E-flat minor and whole-tone scale on E-flat coexist once more. In the example below, a second transposition to G in measure 21 does not continue with a third literal statement of the theme but does preserve the duality of juxtaposing diatonic scale segments (G, F, E-flat, D, etc.) with skips of a minor sixth in a series of successive segments in measures 21-30, all of which associate that interval with diatonic scale segments: G to B-natural in mm. 21-23, D to F-sharp in mm. 23-24, B-natural up to G in mm. 26-27, C up to A-flat in mm.

28-29, and E-natural up to C in mm. 29-30.

It is very interesting to notice that, whereas this duality in Movement II features a diatonic foreground in service of whole-tone middle-ground collections, themselves “atonal” in implication, just the opposite is true in the beginning of Movement III where foreground elements delineate whole-tone collections in service of middle-ground and back-ground diatonic, tonal structures.

The opening octaves of E - natural in the piano in measures 1-3, repeated dramatically in measures 6-8, 11-13, and in measures 17-20, are interpreted finally in measure 21 as having a strong dominant function, where, subject to local voice leading constraints (G-sharp to A-natural in the violin and B-flat to A in the bass), they lead to an A minor triad in measure 21. This more background motion of V (E) to I (A) in A minor is juxtaposed however with interjecting and accompanying whole-tone segments in measures 3-5 and 8-10 (piano), 13-16 and 20 (in violin), and 17-20 in the piano. The simultaneous statements of ascending and descending whole-tone 29 scales in the piano in measures 16-19 and the accelerated repetition (diminution) in the violin in measure 20 of that same scale (C, D, E, F-sharp, G-sharp) bring together B-flat in the bass and

G-sharp in the top voice, an augmented sixth in a traditional tonal context, which, is this case, is resolved accordingly by expanding to the octave on A.

All notes in measures 17-20 are derived directly from the whole-tone scale on C, with the exception of the B-natural in the piano on beat one of measure 17 and that same pitch (three octaves higher) on beat one of measure 20. The appearance of this one single pitch class from outside the collection which controls all other elements in this passage may seem out of place on first encounter; however, some understanding of its significance in this passage can be gained by thinking of these notes, particularly the B-natural in measure 17, as a resolution of the augmented sixth (C-natural to A-sharp) in measure 16. In fact, every adjacent pitch class in any whole-tone collection may, under enharmonic reinterpretation, be “resolved” as an augmented sixth (a major second is enharmonically equivalent to a diminished third or, by inversion, an augmented sixth). The basic principle of enharmonic reinterpretation and this particular example in measures 16-21 (C, D, E, F-sharp, G-sharp, A-sharp reinterpreted as B-flat, C) not only provides a way of understanding the decisive resolution to A minor in measure 21 but other relationships as well, such as the succession in measures 100 to 102 where the pedal E-flat, sustained from measure 76 through measure 99, is reinterpreted as D-sharp and resolved to an

E-natural in the bass in measure 102. D-sharp and F-natural in measures 100 and 101 form a diminished third which collapses to the E-natural in measure 102, D-sharp up to E, and F-natural down to E (implicitly here as the E-natural resolving the F does not appear in that same register).

As is typically the case in this composition, the “E-major triad” in measure 102 is accompanied by additional elements: in this case C-sharp and D-sharp. Interestingly, the sixth in the right

30 hand, E to C-sharp, expands to an octave D-sharp to D- sharp.

As represented in the examples above, the material from the third movement in measures

3-5 and 8-10 (examples a and b) interrupts the emphatic E-natural which prepares the decisive motion to A in measure 21. These passages are transpositionally related (the second is a tritone higher than the first) and attract special attention analytically, both because of their strategic location in Movement III and the fact that measures 8-10 have appeared literally in Movement II in measures 60 and 61 and later in measures 135 and 136 where they are transposed up a major ninth. These passages and their relationship to the repeated E preceding and following incorporate many of the characterizing voice leading features of the work as it assumes at the same time a major structural role in the opening of Movement III. Notice as well in example c, that these passages incorporate some of the same basic pitch class relationships (at the same pitch level in measures 3-5) as the opening material in the violin in Movement II. This recurring presence in different guises necessarily draws our attention to the particulars of this passage and

31 to a consideration of the extent to which it incorporates many of the basic structural and voice leading tenants of the composition.

As examples a and b show, open notes at both transpositional levels derive from the same whole-tone collection (C, D, E, F-sharp, G-sharp, A-sharp). Closed notes derive from the second or “complimentary” whole-tone collection (D-flat, E-flat, F, G, A, B). While this hexachordal division neatly partitions the total chromatic scale into two distinct whole-tone collections, and while one of these collections has a strong representation in Movement II and in Movement III

(C, D, E, F-sharp, G-sharp, A-sharp), it does not, in and of itself, reveal generative processes which account for the frequent juxtaposition of this whole tone-material with elements from the complimentary hexachord or elements from parallel diatonic collections.53

For example, in this case the bass line of measures 3-5 starts on B-flat and terminates on

E while its counterpart in measures 8-10 starts on E and terminates on B-flat (both notes from the whole-tone collection on C). This tritone division of the octave on E is familiar as it reflects other such tritone divisions, especially large scale relationships from A to E-Flat in Movements I and II, as illustrated in the first example of this chapter. The upper voices, in similar fashion, span intervals of a minor sixth from this same whole-tone collection, E to C and A-sharp to F- sharp respectively. Furthermore, the first chord and the third chord in each passage as well as the boundary notes in melody and bass (E and C and B-flat and F-sharp respectively) in the fourth chord, all drive from that same collection. All other notes in these passages, with the exception of the G-sharp and the D-natural in the fifth chord of measure 5, derive from the complimentary

53 Hexachords are said to be complimentary if their combined pitch class content sums to the total chromatic collection.. 32 hexachord (B, C-sharp, D-sharp, F, G, A) and, more importantly perhaps, are related to elements in the first by semitone (E to F, C to D-flat, B-flat to A in measures 3-4 and A-sharp to B, F-sharp to G, and E to E-flat or D-sharp in measures 8 and 9). As result, and in spite of the fact that the second chord in each group forms an augment triad consistent with that complimentary whole- tone collection, the introduction of the half step relationships between the first and second chords organizes this collection so that the second chord is emphasized or “tonicized” as a result of these semitone “resolutions” and a sense of tonality, if ever so temporary and transitory, is imposed on the configuration (F minor in the first case: E, F, A-flat, C and perhaps B-minor in the second: A-sharp, B, D, F-sharp in the second). The incorporation of other semitone relationships, most notably in measure 5 (C to B, G, to G-sharp, and D-flat to D-natural) results in an unmitigated dominant seventh chord on E, predicting perhaps the eventual arrival of A minor in measure 21.

The pervading juxtaposition of tritone relationships, augmented triads, whole-tone scales, with latent tonal forces such as structural fifth relationships in the bass and semitone motions at critical cadence points accounts for the mixture of elements which characterize the surface of this music. While this brief discussion leaves open questions about the possibility of a more integrated way of understanding these rich and varied musical textures, it does I hope, set the stage for further rewarding investigation along those lines.

33 CRITICAL REPORT

I was first introduced to Abelardo’s Violin Sonata by Professor Sergio Z. Esmilla when I was an exchange student at the University of the Philippines College of Music in 1995. Professor

Esmilla had given me a photocopy of a hand-copied violin part and piano score which I was supposed to learn under his tutelage that semester. Years later, I asked him where he had obtained his copy of the Violin Sonata. He was not sure from what source or when he first obtained this copy, but he knew it was not copied from the item housed at the University of the

Philippines College of Music Library, which I could corroborate in the summer of 2012. At that time I visited the library and was given access to the collection of works by well-known Filipino composers. The reserved area has drawers and vertical file boxes of music and scores by

Philippine composers in alphabetical order.

The Sonata was found in a vertical file box with no shelf number but with a label indicating it contained Abelardo’s music; there are also two drawers that hold his music. The piece was housed in an expanding legal-sized folder. The folder contained the full score and a violin part. The score at that time did not have any kind of protective binder and appeared to be an item in general circulation that was accessible to all.

When determining whether the worn score is in Nicanor Abelardo’s hand, I compared the notation and writing of dynamics against the autograph score of Abelardo’s Sinfonietta for String

Orchestra and found them to be the same. The pages of the Sinfonietta score are also on the same “Parchment Brand” as the Violin Sonata. At the end of each movement of the Sonata and

34 the Sinfonietta the composer notated the location and date of completion. All three movements of the Sonata indicated Chicago, Illinois as the location and the date in which it was completed. The location and date of composition of these works by Abelardo are consistent with what was described by both biographers, German and Epistola. Abelardo’s handwriting shows some defining characteristics: the “S” in both titles are similar in that they both have extra curves on the top and bottom of the letter. The capital “C” is also very characteristic, having an almost complete circle decorating the top of the letter. Dynamic markings are also written in Abelardo’s hand, particularly clear in the abbreviated crescendo and allegro indications.

The score is bound in a 27.5 cm x 33 cm faded and worn brown cover. It bears a UP

College of Music Library stamp on the top right corner. In the middle of the front cover was apparently a title in red pencil and a faded ink symbol with a treble clef in the center of the cover. The cover appears to have been subject to water damage. The top and bottom right corners are dog-eared, worn and extremely fragile. The back of the cover is torn with the bottom half missing, exposing an unused back page of the bound score. The pages of the score are 11” x 17” and are bound by 25 saddle stitched gatherings. The bound score is made up of one type of paper, with “Parchment Brand” printing at the bottom of the left corner. To the right of that, “No.

6 – 12 lines” is printed. On the bottom center of the page, “Made in U.S.A.” is printed and to the very right corner, “Belwin Inc. New York. U.S.A.” There are four systems printed on each page, each system made up of three staffs, with a treble clef printed for the solo instrument on the top staff and with the bottom two staffs bracketed together for the piano accompaniment.

There is a separate violin part kept with the score, but it is a newer copy written on white manuscript paper that originated from the Blessing Music Store in Santa Cruz, Manila, as printed

35 at the bottom of one side of each page. The violin part is notated in a different hand with a different calligraphy pen than the score. It is not known who produced this particular violin part.

The first page of the score bears the title in the center and the tempo marking of Allegro on the top left corner of the page. On the top right corner, where composers usually write their names, is a name in quotations: “Hiram.” This is written in the same ink as the rest of the work but with red ink on top of it to cross it out. When investigating the name “Hiram,” I was reminded that the literal translation of “Hiram” in Tagalog is “to borrow.” Perhaps Abelardo used the pseudonym “Hiram” to show that he felt the work was to some degree composed in a musical idiom still unfamiliar to him and that he had borrowed musical ideas from composers whom his teacher, Wesley LaViolette, had recommended he study. In a letter written to his friend Antonio J. Molina, Abelardo wrote “I have written a ‘sonata’ for violin, and a fugue for string quartette on the ATONAL basis.[…] I have been sent to wander in the new horizon taking for guide Hindemith, Schoenberg, Stravinsky, Bartok – and the ultra modern style.”

The score is written entirely in black ink which has faded, particularly in the dynamics, articulations, accidental markings and the measure numbers. There are many pages where the ink had bled through to the other side of the page or where the ink had transferred to the adjacent page. There are pencil markings throughout the score which are not autograph, particularly in the piano accompaniment. Presumably these were added by a pianist using the score. Whether they were suggested by Ableardo cannot be established. There are a few additional markings in the violin part of the score. These are not corrections for the violin, but are markings to aid the accompanist in seeing cadential points or dynamics. There is a penciled marking in measure 150 of the first movement indicating that the violin part is to be played up one octave, but the writing is not Abelardo’s.

36 There are definite corrections by the composer in the score. In the first movement in measures 102 – 104 the composer pasted a correction using the same paper as the rest of the score. In the second movement in measures 87 – 95 a slur and several notes seem to have been whited out and corrections inserted in black ink. These appear to be autograph. In the third movement, measure 296 was originally notated with many ledger lines. Abelardo crossed this out and rewrote the measure using octave notation.

37 V S S N A I E J.O

1 2 3 V œ β Œ Œ œ œ− œ − ∀œ % ∀œ œ œ− œ œ ∀œ ∀œ− œ œ− ∀œ µœ− 1 2 3

% β Œ Œ Œ ˙ œ ˙ œ ∀˙˙ œœ ˙. œ P ˙ œ ο ˙ œ ϖœ œ œ > β ˙ œ Œ ˙ œ Œ œ œ−− œ œ−− œ Θ ˙ Θ ˙ 4 5 6 7 œ− V. œ− − − œ œ − ∀œ µœ œ ∀œ œ − − œ− œ− œ œ % 3 œ Œ œ ∀œ Œ αœ œ ∀œ− œ 3 œ œ œ− œ œ− œ 4 5 6 7 œ œ ϖ % œ ∀œ œ œ αϖ Œ Œ ∀ ˙ αœ œ ∀œ œ œ ˙ œ . ˙ œ P. œ α∀˙˙ ϖ œ œ œ α˙ œ Œ œ αœ > œϖ œ θ ˙ œ œ œ œ œ œ œ−− œ œ−− œ ˙ Θ ˙ 8 œ 9 10 3 V. αœ œ œ ∀œ œ œ œ œ œ œ œ œ− αœ œ œ 3 3 3 ‰− œ − œ œ− œ − œ œ œ œ % Θ 8 9 10 œ œ ∀ œ ∀œ œ − αœ œ œ œ ∀œ œ Œ % ∀ œ µœœ ∀œœ ∀œ ∀ œ œ œ œ œ ∀œ ∀œ œ P. œ œ Œ œ− œ œ − − œ − œ œœ œ Œ − œ ˙˙ > ˙œ œ œ œ ∀œ œ œ− ∀œ œ αœ˙ œ œ−− œ œ−− œ ˙ Θ ˙ Θ ˙ 38 11 12 − 13 œ œ ∀œ− œ V. œ œ œ œ − œ œ œ œ œ œ œ− − % œ œ œ œ 3 αœ 3 5 ∀˙ 11 12 3 13 œ αœ œ− ∀œ œ− ∀œ µœ− œ œ œ œ % œ− œ œ− œ œ− ∀ œ µ œ− œ αœ œ œ œ Œ ∀œ µœ− ˙ œ− ∀œ ∀œ µœ− 3 œ œ œ œ− œ P. ˙ œ− œ ∀œ ∀œ œ α œ œ Œ œ− > ˙ œ œ œ œ ∀œ µœ œ œ œ œ œ œ˙ ∀œ − œ œ œ ∀œ ˙ œ− Ι ˙

14 3 15 16 ˙ œ α˙ V. ∀œ % œαœ œ œ α˙ ˙ 14 15 16 αœ œ αœ− αœ œ œ œ αœ œ− αœ − ∀œαœ œ œ % αœ− αœ œ Œ œ− œ αœ− αœ œ− œ œ œ− ∀œ œ œ αœ P. α œ−α œαœ œ− œ α ˙ 3 Œ ˙ œ œ αœ ∀œ− œ > αœ µœ ∀œ œ œ αœ αœ œ œ− œ œ− œ ∀œ− œ œ œ− œ− Ι ˙ œ

17 18 19 3 3 ˙ 3 V. œ œ αœ œ œ œ œ αœ œ œ % ∀˙ œ ˙ ∀œ œ œ αœ 3 3 œ

17 18 19 œ− œ Œ ˙ ∀œ œ œ αα˙œ % œ− œ− αœ µ˙ αœ œ œ P. . ∀ ˙ ‰ œ œ αœ Œ 3 ˙ 3 3 3 3 œ αœ αœ œ œ αœ > αœ αœ œ œ œ ˙ œ αœ ∀œ− œ œ − αœ 3 3 œ αœ œ œ αœ œ œ αœ 3 ˙ œ 3 ∀œ− œ ˙

39

3 20 21 3 3 3 αœ œ V. αœ œ αœ œ œ αœ œ œ % ∀œ ˙ œ œ œ œ 3 3 œ 3 20 21 αœ œ œ % œ αœ µ˙ œ ∀œ αœ µœ α˙ œ P. ‰ œ ‰ œ ‰ œ αœ 3 3 αœ αœ œ 3 3 33 αœ αœ œ œ > αœ œ œ œ œ œ œ αœ 3 3 œ αœ œ αœ αœ 3 œ œ œ

22 23 V. Œ ∀œ œ ∀œ œ % ∀œ ∀œ 3 ∀œ 3 3 3 22 3 23 αœ œ αœ αœ œ αœ αœ ∫œ α œααœœ œ ∫œ œ œ œ œ α˙ œ œ œ 3 α œ % œ 3 œ P. αϖ ‰ αœ œ 3 3 αœ œ αœ αœ 3 > αœ αœ œ œ ˙ αœ αœ αœ 3 3 œ œ œ αœ 3 ˙ αœ

24 3 25 26 αœ− œ− œ V. αœ œ œ ∀œ− µœ % ∀œ ˙ œ œ œ œ α˙ ∀œœ œ− œ

24 25 26 œ, ∀œ, œ, % ∀α˙ œ ∀α˙ ∀œ− œ α˙− œ ∀œ œ αœ œ 3 P. ˙ 3 3 ˙ 3 3 ˙− 3 3 3 3 , ∀œ, œ œ > ∀œ µœ ∀œ œ œ αœ ‰ œ œ ‰ œ œ ‰ œ œ ‰ œ œ ‰ œ, , αœ œ œ œ αœ œ œ œ œ,

40 27 =˙ œ œ 28 29 30 V. œ œαœ ˙ œ œαœαœ œ œ œ % ∀œ œ œαœ œ αœ œ ∀œ ∀œ 27 = = 28 29 30ϖ αœ µœ , , , ααœœ µ∀µœœ Œ αœ ∑ Œ % ˙ œ ˙ α˙ αœ œ ∀œ P. ∀˙ œ ∀œ œ αœ ˙ ˙ ϖ , > ˙ α œ ˙ α˙ ϖ Œ œ αœ, αœ, Œ ∀ϖ

31 3 32 33 34 35 V. % œœ Œ ∑ œ ∀œ ∀œ œ 31 32ϖ 33 ϖ 34 œ 35 Τ , , , , ∀œ % Œ œ ϖ œ ˙ αœ œ œ αœ œ ∀ϖ ∀˙ αœµ œ ∀œœ œ ∀œ œ P. ϖ œ œ œ 3 ϖ ˙ œ , œ, , Τ œ œ > Œ œ αœ αœ ϖ , , , , ∀œ, , œ, αœ œ œ œ œ ∀œ ˙ ϖ œœ œ œ œ œ œ œ

36 37 38 39 40 V. ∑ œ œ œ œ ∑ ∑ % œ ∀œ œ ∀œ ˙ 36 = 37 38 39 , 40 αœ œ œ α œ ∀œ αœ œ αœ α œ % ∀ œ œ ∀œ œ ∀œ œ ∀œ˙ œ ∀ œ œœ ∀œ µœ œ œ œ αœœ œ αα œ œ P. œ œ œ ˙ α œ ∀œ ∀œ ∀œ µ œ œ ∀œ œ ∀œ œ α˙ > œ œ ˙ œ œ œ ∀œ œ œ µœ αœ œ ˙ αœ œ ˙ œ ∀ œ œ ˙ ˙

41 41 42 43 44 V. ∀œ œ œ œ œ œ ∀œ œ ˙ αœ ˙ % œ œ ∀˙ œ œ ∀œ œ, , 41 42 43 œ 44 αœ , , œ , , αœ œ œ αœ , αœ % ∀œ˙ œ œ œ αœ œ œ αœ œ œ œ P. œ ∀œ œ œ œ œ œ ∀œ ∀œ ˙œ œ œœ œœ œ ∀œ œ œœ œœ œ œ œ > œ œ œ αœ œ œ ∀œ ‰ œ œ œ Œ ‰ œ ∀œ œ Œ αœ œ

45 46 47 48 œ œ , α˙ αœ α˙ V. ∀œ, œ, œ œ ˙ œ œ œ œ− % œ αœ αœ, Œ

45 46 47 48 , , , , , , , œ αœ αœ œ ˙ œ ˙ % ∀œœ œ œ œ œœœ ∀œ ααœœœ ‰ œ œœα‰œ œ α˙œœ œ œ œ œ œ œ αœœ œ œœ œ œ œ œ P. œ œ ‰ œ œœ ‰ œ αœ œœœ œ ˙ œ ˙ αœ ˙ . œ ο œ œ ‰ œ αϖ α˙ αœ = = > ˙ ∀œ œ ‰ œ ϖ Œ α˙ Œ α˙ ˙ αϖ αœ αœ α˙ αœ

49 50 51 αœ αœ αœ αœ œ œ ∀œ œ œ œ œ V. œ œ œ αœ œ œ œ œ αœ œ œ ∀œ œ % 3 3 3 3 49 ο 50 51 œ œ œ αœœœ ι ι œ αœ αœœ œ œœ œœ œ œ αœ ‰ ∀œ ‰ œ ‰ œ ‰ œ ‰ œ ‰ œ œ œ œ œ œ œ œ œ ∀ œœ œœ œœœœ œœœœ œœœœ œœœœ œœ %α œ œ œ œ œ œ αœ ∀∀ œ œ œ œ œ P. œ ‰ ‰3 ‰ 3 ‰ ‰3 ‰ 3 ‰ Ι Ι. Ι ο αœ αœ ι ι > αœ œ œ ‰ αœ αœ αœ αœ αœ αœ ι œ œ αœ œ ◊ αœ αœ œ ∀ϖ

42 52 53 ˙ ∀œ œ ∀œ œ œ œ œ œ ∀œ œ V. ∀œ œ ˙ 3 % 3 3 3 3 52 ι ι 53ƒ ι œ= œ= œ= ‰ ∀œ ‰ œ ‰ œ ‰ œ ‰ œ ‰ œ œ ‰ ‰ Œ œ œ œ ∀œœ∀ œœœœ œœœœ œœœœ œœœœ œœœœ œœ œ œœ œœ œ œ ∀œ œ œ œ œ % ∀∀ œ œ œ œ œ œ œ œ œ œ œ œ 3 ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ 3 P. 3 Ι3 3 Ι3 3 3 . ƒ ∀œ] ∀œ] > ˙ ∀œ ∀œ ϖ ˙

54 ∀˙ 55 ∀œ œ œ œ ∀œ œ œ µœ V. ∀œ œ ∀˙ ∀œ œ 3 % 3 3 3 3 54 3 3 œ œ œ 5Ε5 3 œ œ œ ∀œ œ œ œ œ ‰ ‰ ‰ αœœ œœ ‰ œ œ ‰ œ œ 3 œ œ œ œ % α œ œ µœ œ œ œ œ œ œ œ œ œ œ P. œ œ œ œœ ∀œ ∀œ Ε > ˙ ∀œ ∀œ ∑ ˙

56 57 V. ∀œ œ œ œ œ ˙ œ ∀œ œ œ œ œ % œ, , 3 3 3 3 3 3 3 = = = 56 57 œ œ œ œ œ œ œ ∀œ œ œ œ œ % ‰∀αœ ‰ µµœ ‰ œ ‰∀αœ ‰ œ œ ‰ œ œ ‰ œ œ 3 ∀œ œœ œœ œ œ 3 P. œ ∀œ µœ ∀œ œ œ ∀œ > αœ œ œ œ ∀˙œ œ ˙ œ ∀œ ˙

43 58 59 œ œ αœ œ œ αœ α˙ œ œ αœ V. ∀œ œ œ œ % 3 3 3 58 αœ œ œ 59 œ œ œ œ œ œ α œ œ œœ œ ∀œ µœ αœ œ œ œ œ αœ œ œ œ œ œ œ œ œ œ œ % ‰ œ œ ‰ œα œ ‰ œ œ 3 ‰αα œœ œœ œœ œœ œœ œœ œ œ œ œœ œœ 3 3 œ œ œ œ œ œ œ œ P. 3 3 3 α=œ 3 > ˙ αœ ϖ ˙ ϖ

60 61 œ œ œ œ œ αœ œ œ œ ∀œ œ V. œ œ ∀œ œ Ι % 3 ‰ = = = 60 61 ˙ αœ œ œ µœ œ œ ∀œ œ ∀œ œ α œ µœ œ œ œ œ œ œ œ œ œ œ ∀œ œ œ œ ˙ œ œ œ œ œ % ααœœ µœ œ œ œ œ œ µœ œ œ ∀œ œ œ œ œ ∀∀œœ œœ œ œ œ 3 3 3 3 œ œ œ œ œ œ œ œ œ P. ‰ 3 ‰ 3 ‰ 3 3 > α˙ αœ œ ϖ α˙ αœ œ ϖ 62 63 ∀˙ œ œ œ ∀œ œ ∀œ V. Ι ∀œ % ‰ Œ. = = = 62 ∀œ œ ∀˙ 63 œ œ ∀˙ œ œ œ œ œ œ œ ∀œ œ œ œ œ œ ∀∀ œ œ ∀ œ œ œ œ αœ œ œ ∀œ œ % ∀œ œ œ œ œœ œœ œœ œœ œœ αœ œ αœ œ œ ‰ ∀ œ œ ‰ ‰ 3 3 ‰ œ œ œ ∀œ P. 3 3 α œ αœ 3 3 3 œ 3 > ϖ ϖ ϖ ϖ

44 64 œ œ œ 65 œ ∀œ V. œ œ œ α˙ % ∀œ Œ 64 65 œ− œ ∀œ œ ∀œ œ œ− αœ 3 œ % ∀œ œ œ œ ˙ 3 ∀œ 3 œ 3 3 Ι P. ‰ αœ œ 3 3 3 ˙ ‰ αœ ‰ααœ œ ‰ µœœ œœ ‰ œ œ ‰ œœ œœ > œ αœ œ œ œ œ œ αœ œ œ œ ϖ œ ϖ

66 67 68 V. œ ˙ ˙ œ % Œ Œ ∑

66 67 68 œ− œ αœ œ œαœ œ œ œ œ œ œ ∀œ 3 3 œ− Ι œ œ œ % 3 3 ∀œ œ œ ∀œ œ ∀œ œ ‰ Ιαœ œ ααœ œ P. ι œ œ œ œ œ œ œ œ ι ι ‰ αœœ œœ ‰ œ œ ‰ œ œ ‰ œœ œœ ‰ αœœ αœ ‰ œœ œ ‰ œ œ > œ œ œ œ αœ ∀œ αµœ αœ ϖ ˙ α˙ ˙ αœ

69 70 71 72

V. ∑ ∑ ∑ œ œ− œ % ∀œ Ι 69 70 71 72

% œ œ œ œ αœ œ œ œ ∀œ P. ∀œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ∀œ œ αœ µ œ ‰αœ œ αœ œ ∀œ ι Ι ο 3 3 3 ‰ œ ‰ ι ι ι > œ œ œ œ œ œ ∀œ ∀œ œ αœœ œœœ œ œ ∀œ œ œ œ œ ∀ œ œ ‰ ‰ ‰ 3 ‰ œ ∀œ µ˙ α˙ œ œ œ œ œ œ œ œ œ œ

45 73 74 V. œ œ− œ œ œ α˙ % ∀œ Ι 73 74 3 3 3 3 αœœ œœ œœ µ œ œ œ % œ ∀œ αœ µ∀œ αœ œ œ ααœ œ œ α œ œ œ µµ œ œ œ P. αœ µ œ 3 3 3 > ‰ ‰ ‰ œ œ ‰ Œ œ œ œ 3 œ œ ˙ œ œ œ ˙ 75 76 V. − − αœ αœ œ αœ α˙ œ œ œ αœ œ œ œ œ œ œ œ 3 3 3 % 3 75 3 3 3 76 3 ∀œ α œ œ œ % αœ œ œ ααœ œ œαα œ œ œ µµœœ œœ œœ αααœ œ αœœ œœ œ œ œœ œœ P. œ œ.œ œ œ œ œ œ > œ œ œ Œ ˙ œ œ œ œ œ ˙ œ œ 77 78 œ , αœ αœ œ− µœ œ œ αœ µœ œ œ œ œ œ œ αœ V. œ œ αœ αœ µœ œ œ œ % 3 3 3 3 3 3 3 3

77 3 3 78 3 3 ] ] ] ] αœ œ œ œ œ œ αœ œ % αα œ œ œ αœœ œœ œ œ œ œœ œœ αα œ αœœ œœ œœ œ œœ œœ œœ P. œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ 3 3 > œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

46 79 œ ∀œ 80 ϖ œ œ œ œ œ αœ µœ œ ∀œ V. œ œ 3 3 3 3 3 3 % 3 ƒ 79 3 3 80 œ αœ œ αœ µœ œ œ ∀œ ∀œ œ œ œ œ œ œ œ œ œ œ αœ α œ œ œ œ œ œ œ œ œ œ αœ œ œ % αα œ œ œ œ œ œ œ œ ‰ αœ œ œ ‰ œ œ œ P. 3 3 3 3 > œ œ ƒ œ œ œ œ œ œ œ œ ˙ ˙ œ œ œ œ œ œ ˙ 81 œ 82 83 œ œ œ ∀œ œ œ ∀œ œ ∀œ µœ V. ∀œ− œ œ− ∀œ 3 Ι % 3 Ι 3 3 3 81 82 83 œ œ œ œ œ œ œ œ œ αœ œ αœ œ œαœ œ œ œ αœ µœ ˙ ∀œ œ œ œ % 3 œ œ œ œ ∀œ œ œ œ œ œ œ œ œ œ ∀œ œ œ œ œ µ∀œœ œœ ∀œ œ P. ‰ αœ œ œ ‰ œ œ ‰ œ œ ‰ œ œ ‰ œ œ ‰ œ œ œ œ œ∀œ œ œ œ œ 3 3 3 3 3 3 ‰ 3 ‰ 3 αœ œ œ 3 ι ˙ œ > ‰ œ œ œ Œ œ αœ œ ‰ ∀œ ˙ ˙ ϖ ϖ

84 85 86 œ V. œ ∀œ ∀œ œ % œ ∀œ œ œ α˙ œ œ ∀œ µœ œ 84 85 86 3 3 3 3 ‰ ‰ ‰ α˙ œ œ œ œ œ µœœ œ œ œ œ œ œ œ œ œ œ % α˙ œ œ œ œ œ∀µœœ œ œ∀œœ œ œ ˙ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ P. ‰ 3 3 3 œ œ œ ‰œ œ œ œ3 œ œ œ œ ‰ œ œ œ œ∀œ œ œ œ ∀œ 3 ˙ 3 3 3 3 3 ι Œ ˙ Œ œ− > αœ ∀œ œ œ œ α˙˙ œ œ α˙ ˙ ϖ ˙

47

3 87 88 89 V. ∑ ∀œ œ % ˙ 3 87 88 89 = = 3 3 ∀=œ =œ œ− œ œ αœ œ Œ œ ∀œ Œ µœ− ∀œ ∀œ œ % ∀œ ∀œ œ œ− œ œ œ œ œ œ œ œ œ P. œ œ œ œ œ œ œ œ3 œ œ− œ œ− αœ − αœ− œ > αœ− œ œ ∀œ− µœ œ− αœ œ ∀œ µœ αœ− αœ œ œ œ œ− œ œ− œ Ι œ− ∀œ µœ œ αœ œ αœ− œ œ− ∀œ− µœ Ι œ œ

90 91 92 œ œ œ ˙ V. ∀œ œ µœ œœ œ ∀œ œœœ œ % 3 œœ 7 ∑ = = 90 3 3 3 3 91 92 œ œ ∀œ ∀œ µœ− ∀œ ∀œ ∀œ œ Œ œ− œ % œ œ œ œ œ œ œ œ œ œ œ œ œ Œ œ− αœ P. œ œ œ œ œ œ œ œ œ œ œ œ ∀œ œ− αœ Ι αœ− œ − œ− ∀œ œ− αœ œ > œ α˙ αœ− œ œ− ∀œ µœ œ− ∀œ αœ− œ αœ− œ ∀œ− µœ œ− αœ œ Ι α˙ œ œ−

93 94 œ ∀œ œ ∀œ œ µœ ∀œ œ œ V. Ι œ % 3 ‰ 3 3 3 3 3 93 ∀œ œ ∀œ 94 ∀∀œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ αœ αœ Ι ‰ % 3 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ P. αœ− œ œ ο αœ œ œ αœ αœ œ > αœ− œ œ αœ− œ œ Ι Ι αœ œ œ œ Ι αœ ‰ 3

48 95 96 97 œ 3 ∀œ œ œ œ µœ ∀œ V. Ι αœ œ œ ι ι 3 3 ‰ œ % 3 αœ œ ˙ œ œ œ œ œ 3 3 œ 95 96 97 œ œ œ œ œ œ œ ι ‰ Œ % œ œ œ œ œ œ œ αœ œ œ œ ϖ P. œ αœ ϖ . − = ‰ > αœ œ αœ αœαœ œ ˙− œ α˙− Ι œ ϖ œ ˙− œ

98 99 V. ∀œ − − ∀œ ∀œ− œ − % œ ∀˙ ‹œ− œ œ œ œ œ 98 99 Œ αœ αœ ∫œ α˙ œ % œ αœ αœ P. 3 3 3 3 3 3 αœ œ œ > œ αœ œ œ αœ œ αœ 3 3 œ œ œ œ œ αœ αœ µœ œ αœ œ αœ œ œ

100 101 102 œ− V. − œ ∀œ− œ − ∀œ µœ œ % ‹œ ∀˙ œ− œ œ œ œ œ œ Œ ‰

100 101 3 102 ι αœ œ αœ œαœ, ∫œ, œ ˙ % αœ αœ Ι œ αœ œ œ αœœαœ ∀∀œ œ œ œ œ œ œ˙ œ œ œ œ œ P. 3 3 3 3 3 3 œ 3 3 αœ œ ∫œ œ œ > αœœαœ œ œœ αœ αœ œ ˙ αœ 3 3 œ αœœ œ œ∫œœ œ αœ œ 3 3

49 103 104 105 ∀œ œ V. œ œ ∀œ œ œ ∀œ ‹œ ∀œ % œ Œ ‰ Ι 3 œ Œ

103 104 105 ˙ œ ∀œ ∀˙ ∀œ œ µ∀˙ œœ ∀∀œ ∀œ ∀œ œ ∀∀ ˙œ œ œ œ œ œ % ∀ œ œ œ œ œ œ œ œ œ œ œ œ ∀œ œ œ œ œ œ‹œœ œ œ œ œ œ ∀ œ ∀œ œ œœ œ 3 3 P. 3 3 3 3 3 3 3 3 3 3 œ œ œ œ > ˙ œ ∀œ ι 3 ∀œ− ∀œ ‹œ ∀œ œ ∀œ ∀œ ∀˙ ∀œ− ∀œ ‹œ ∀˙ 106 107 ∀œ œ V. ∀œ œ œ ∀œ ‰ Ι ‹œ ∀œ œ œ ‰ œ ∀œ œ∀œ œ % Ι 106 107 œ ∀œ µ˙ ∀∀œœ œ œ œœ œ œµ ˙œ œ œ ∀œ œ œ ∀∀œϖœ œ œ œ œ œ œ œ œ œ œ œ % 3 3 3 3 ∀œ 3 µœ 3 ∀œ 3 P. 3

> ∀œ ∀œ ‹œ ∀œ ∀œ ∀œ ˙

108 109 V. ι ∀œ − œ ∀œ œ ι % ‹œ ∀œ œ− ∀œ 108 109 ∀∀˙œ œ œ ∀œ œ œµαµ˙œαœ œ µœ œ œ œ˙ œ œ œ œ œ ˙ % 3 3 ∀˙ ∀˙ 3 ˙ 3 ˙ 3 3 œ œ œ ∀œ P. 3 œ œ 3 > ∀˙ ∀˙ ∀œ ˙ ∀ ˙ α ˙ ∀ϖœ

50 110 111 112 V. = = œ ∀œ Œ œ œ œ % ∀˙ ˙ ∀œ œ 3 110 111 112 = = = = œ œ ∀œ ∀œ αœ Œ œ− œ œ Œ œ % ∀œœ œ œ ∀ œ œ œ− œ ∀∀œœ µœ ∀œœ−µœ P. œ ∀œ œ œ µœ œ œ αœ œ œ ∀œ œ œ− œ œ œ œ − œ 3 3 œ œ 3 3 > œ ∀œ ˙ θ ϖ ∀œ œ œ−− œ θ ‹œ− œ−− œ ˙

113 114 3 115 3 3 V. % ∑ Œ œ œ ∀œ ∀œ œ Œ œ− œ œ œ œ , , œ œ œ 113 114 115 Œ 3 œ Œ œ œ % œ ∀œ œ− µœ œ œœ œ œ œ P. œ œ œ− œ œ ˙− 3 3 ∀œ ∀˙− 3 3 3 ο 3 > Œ œ œ œ ∀œ œ µœ œ œ œ œ œ œ œ œ œ œ œ ∀œ œ œ œ œ œ ϖ

116 117 118 œ œ V. , − œαœ αœ ∀œ œ Œ œ,− œ œ αœ œ Œ ∀œ− œ œ œ Œ œ œ œ % . 116 117 118 3 3 Œ 3 ∀œ µœ œ ∀œ œ œ % œ − œ Œ œ œ α˙ Œ αœ œ œα˙ . ˙−œ œ œ œ ˙ œ 3 P. ∀˙− 3 αœ 3 αœ Œ ∀œ− µœ œ Œ œ ∀œ Œ œ− αœ œ > œ œ œ œ œ œ αœ œ œ ϖ ϖ ϖ

51 119 = =œ 120 − œ œ− œ œ αœ œ œ œ œ ∀œ− œ œ− œ V. œ œ œ œ % Œ 3 119 3 12ε0 œ− αœ œ Œ œ ∀œ œ ˙ % Œ αœ œ œ ˙ ∀œ 3 ∀˙ P. αœ 3 ˙ œ− αœ œ œ ∀œ œ ˙ > Œ αœ œ œ Œ ∀œ ˙ ϖ ϖ 121 αœ œ œ œ œ 122 123 ∀œ œ œ œ ∀œ œ œ œ œ œ œ œ V. ‹œ ∀œ œ œ ∀œ œ œ ∀œ ∀œ ∀œ œ µœ µœ œ œ % 3 3 3 3

121 122 123 ϖ œ % ϖ œ Œ ∑ P. ϖ œ > ϖ œ Œ ∑

124 125 ∀œ 126œ œ œ œ ∀œ V. œ œ− ∀œ œ œ ∀œ µœ ∀œ− œ œ œ œ œ œ ∀œ ≈ Œ % 3 Ι ˙ œ ∀œ ∀œ œ 5 124 125 126 = = œ œ ∑ ∑ ∀œœ œ Œ œœ−œ % ∀œ œ œ −œ P. ] ƒ ˙ > ∑ ∑ ˙ ˙ ˙

52 127 128 129 130

V. % ∑ ∑ ∑ ∑ 3 127 128 12◊9 130 œ−∀œ œ œ−αœ − œ œ− œ œ− œ− − œ œ œ œ ∀œ Œ ∀œ− œ œ− œ− œ œ− œ−∀œ œ− ∀œ µœ− œ œ œαœ œ αœœ œ Œ œ− œ % œœ ∀œ ∀œ œ−αœ œ− œ œ− ∀œ µœ− œ œαœ œ œ œ œ− œ ∀œ− 3 œ P. ] ] œ œ œ− υ ] œ ] ] ˙ œ ˙ œ œ ] > ˙ > œ œ− œ Œ œ œ % œ œ ˙ ˙ ϖ œ œ ˙ ˙ ˙ ϖ œ ˙ 131 132 133 134 V. ∀=œ =œ œ− œ− % ∑ ∑ ∑ Œ 131 132 œ 13α3œ œ œ ∀œ œ 134 αœ− œ œ− œ œ− œ αœ œ œ œ ε œ ∀œ œ− œ œ− œ ∀œ− œ œ− œ− œ œ ∀œ œ œ αœ œ œ œ Œ αœ− œ − œ− œ 3 αœ αœ Œ % ∀œ œ− œ ∀œ 3 œ œ P. œ αœ ] 3 ε œ œ œ− œ θ = =œ =œ œ − αœ−− œ ∀œ αœ > > œ œ œ œ % αœ αœ ˙ Œ ϖ œ−− œ ∀œ αœ ˙ œ ϖ αœ αœ œ 135 136 137 3 œ œ œ V. œ− œ αœ œ œ αœ œ œ αœ œ œ œ œ Œ ∀œ− œ ∀œ µœ œ œ œ œ œ œ αœ % 3 3 3 3 3 3 3 œ œ

135 136 137 = = =œ Œ Œ Œ Œ αœ œ œ % œœ œœ œœ œ œ œ P. αœ αœ œ > =œ =œ =œ œ Œ Œ œ Œ œ Œ œ œ œ œ œ œ

53 3 138 139 140 3 V. œ Œ αœ− Œ αœαœ αœ αœ œ œ αœ αœ œ % œ œ œ− œ œ œ œ œ œ αœ œ œ 3 3 138 139 140 ααœ Œ Œ Œ Œ Œ αœ % œ αœ αœ αœ œ P. α œ α œ α œ œ > œ Œ Œ Œ Œ Œ œ œ œ œ œ œ œ œ œ 141 142 αœ αœ− œ 3 3 3 3 V. œ αœ αœ œ œ œ œ − − % 3 3 αœ œ œ œ ∀œ ∀œ œ œ ∀œ œ œ œ œ œ 141 = ο 142 = =œ αœ Œ ααœ œ œ Œ % αœ œ œ œ œ P. ∀αœ œ œ = = = ο > œ œ œ Œ œ œ œ ∀œ œ Œ œ

143 3 144 145 3 3 3 V. œ− œ œ− − œ− ∀œ œ œ αœ µœ ∀œ œ œ œ œ αœ œ 3 œ ∀œ œ œ œ œ 3 œ 3 œ % œ ∀œ œ ∀œ œ œ œ œ œ ∀œ 3 œ 3 3 − − ∀œ 3 3 143 − 144 145 2 % Œ Œ œ œ Œ œ œ œ œ ∀œ œ œ œ œ œ P. ∀œ œ œ ∀œ œ œ œ œ œ > ∀œ œ Œ œ ∀œ œ Œ œ αœ œ Œ œ

54 146 147 148 œ− œ ˙ V. œ œ œ ∀œ œ œ œ Ι ∀œ ∀œ œ œ œ ˙ % 3 3 3 3 ∀œ ∀œ 146 3 147 3 148 3 œ ‰ ι œ ‰ ι ‰ ι % ∀œ œ œ œ ∀œœ œ œ œ œ œ ∀œœ œ œ ∀œ œ œ ∀ œ œ P. œ œ œ œ œ œ œ œ œ œ œ œ ∀œ œ œ œ œ œ 3 œ œ œ œ œ œ =˙ > œ œ ‰ œ œ ∀œ œ ∀œ œ ‰ œ œ ‹œ œ ∀œ µœ Ι 3 Ι

149 150 151 152 V. œ ∀œ ∀˙− œ œ œ ∀œ µœ ∀ ∀ ˙ % ∀ ∀œ œ . 149 150 151 152 3 ∀ ∀ œ % ∀œ œ Œ ∑ ∀ Œ Œ ∀œ ∀ ˙ ∀œ ˙ . œ œ œ œ P. ˙ œ ∀˙ 3 œ > ∀ ∀ œ œ ∀œ ˙ Œ αœ µ˙ ∑ ∀ œ Œ œ Œ ˙ α œ µ ˙ œ 3

153 154 155 œ œ V. ∀ ∀ ∀˙ œ œ ∀œ œ % ∀ ∀œ œ ∀œ œ ˙ 153 154 155 3 3 3 3 3 3 3 3 3 ∀ ∀ ∀ Œ Œ ∀œ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ % œ œ ∀∀œ œ œ ∀œ œ œ œ œœ ∀œ œ P. œ ∀ œ œ ∀œ œ ∀œ œ 3 œ œ œ µœ ∀œ œ ∀œ œ œ µœ > ∀ ∀ œ œ ∀œ œ œ œ ∀ œ Œ œ Œ œ œ ∀∀œ œ œ œ œ 3 ˙

55 156 157 158 µ˙ ∀œ œ œ œ V. ∀ ∀ œ ˙ œ œ % ∀ œ œ œ

156 157 158 ο 3 3 3 3 3 3 ∀ ∀∀ Œ Œ œ Œ Œ µœ ‰ ‰ ‰ ‰ % ∀œ œ 3 ∀œ œ α œ ∀œ œ œ œ œ œ œ œ 3 œ œœ œ P. ο 3 œ œ œ œ œ œ œ > ∀ ∀ œ µœ ∀œ œ αœ œ œ ∀ œ Œ œ Œ œ ∀œ Œ αœ Œ œ œ 3 µœ

159 160 œ ∀œ œ V. ∀ ∀ œ ∀˙ % ∀ ∑

159 3 3 3 160 3 µ=œ ∀ ∀ œ œ ∀ ‰ œ ‰ ‰ ‰ µ∀œœ ∀œ µœ œ % αœ œœ µœ µœ œ P. œ œ œ œ œ œ =œ µœ œ > ∀ ∀ µœ œ œ œ ‰ œ œ ‰ œ 3 ∀ œ œ œ ∀œ 3 µœ œ 3 3

161 162 V. ∀ ∀ œ µœ % ∀ ∑ œ µœ 161 œ 162 œ œ ∀ ∀ œ µœ œ œ µœ ∀ µ∀œœ α∀œœ ∀œ µ œ œ œ µœ œ αœ % œ œ ∀œ µœ œ œ œ œ αœ P. 3 3 œ œ œ œ œ µœ µœ œ œ > ∀ ∀ µœ œ œ œ ∀ ‰ œ œ ‰ œ Œ µœ 3 3 œ 3 3 3 µœ 3

56 163 164 V. ∀ αœ αœ ∀∀ µœ αœ Œ αœ % αœ− 163 164 µœ µœ− αœ ∀ ∀ α˙− œ αœ ∀ αœ µœ α˙− œ αœ µœ− αœ % αœ Ι P. 3 αœ . αœ αœ œ œ αœ αœ œ œ > ∀ ∀ αœ αœ œ œ αœ œ œ œ œ œ ∀ αœ 3 3 œ αœ 3 3 3 αœ 3 αœ 3 165 αœ 16α6˙ œ V. ∀ ∀ α˙ œ− œ− % ∀ Œ Œ 165 αœ 166 αœ− µœ ∀ œ αœ− œ− αœ µœ αœ ∀∀ αœ œ− αœ µœ αœ αœ− µœ % œ αœ− Ι Ι P. œ αœ µœ αœ αœ œ αœ µœ œ œ > ∀ ∀ µœ αœ œ œ œ œ œ œ αœ œ œ œ ∀ µœ 3 3 3 αœ 3 3 3 3 3 167 ˙− 168 V. ∀ ∀ ∀œ œ œ µœ œ œ œ œ % ∀ Œ

167 168 œ 3 3 3 3 ∀œ œ− ∀œ− µœ ∀ ∀ œ ∀œ− µœ % ∀ ∀œ œ− Ι µœ œ œ œ œ œ œ œ œ œ œ œ P. µœ œ œ œ œ œ œ œ œ œ œ œ µœ . œ ∀œ œ œ œ œ ο > ∀ ∀ œ œ œ œ ∀ œ 3 3 3 œ αœ Œ œ− œ 3 œ αœ œ− œ

57 169 170 µœ µœ V. ∀ µœ œ αœ œ œ œ µœ œ œ αœ œ œ œ œ ∀∀ œ œ œ œ % 3 3 3 3

169 170 3 3 3 3 3 3 3 3 ∀ ∀ % ∀ µœ œ œ œ œ œ œ œ œ œ œ œ µœ œ œ œ œ œ œ œ œ œ œ œ P. µœœ. œ œ œ œ œ œ œ œ œ œ µœ œ œ œ œ œ œ œ œ œ œ œ ∀ αœ− œ > ∀∀ œ œ Œ αœ− œ œ− œ µœ− œ − œ− αœ αœ− œ µœ− œ αœ œ œ œ œ− αœ œ œ− 171 3 6 172 αœ µœ αœ œ œ αœ œ œ œ αœ œ V. ∀ ∀ œ µœ µœœ œ œ œ ∀ œ œ αœ œ œ œ œ % 3 µœ αœµœœ œ 6 3 3 3 3 171 172 3 3 3 3 3 3 3 ∀ ∀ œ œ œ % ∀ µœ œ œ œ œ œ œ œ œ œ œ œ µαœ œ œ œ œ œ œ œ œ œ œ œ 3 α œ œ œ œ œ œ œ œ œ œ œ œ P. µœ œ œ œ œ œ œ œ œ αœ œ œ œ œ œ œ œ œ œ œ œ ∀œ œ > ∀∀∀ ∀œ œ αœ− µœ αœ− µœ − œ αœ− µœ œ − αœ− µœ αœ− µœ œ− œ αœ µœ 173 174 = µœ αœ œ œ œαœ µ=œ αœ V. ∀ ∀ µœ œ αœ œ œ µœ ∀œ αœ ∀ 3 αœ œ µœ 6 µœ % 3 µœ αœ 6 173 3 3 3 174 = ∀ ∀ µ αœ œ œ ∀ αœ œ œ œ œ œ α œ œ œ œ œ œ α˙ % µ œ œ œ œ œ œ 3 µ ˙ P. α αœ œ œ œ œ œ œ œ œ ƒ ∀ µœ œ αœ œ− œ > ∀∀ œ Œ œ µœ œ αœ œ− œ

58 175 176 177 αœ µœ œ αœ αœ µœ µœ œ αœ µ=œ α=œ =œ =œ V. ∀ ∀ œ œ ∀ Œ œ αœ µœ œ αœ Œ œ αœ µœ µœ œ αœ µœ αœ œ œ % 3 3 175 176 177 = = ∀ ∀ ˙ α˙ αœ œ œ ˙ % ∀ µα˙ µ ˙ Œ µ œ œ œ ˙ ˙ 3 α˙ αœ œ œ ˙ P. 3 > ∀ ∀ œ œ œ œ œ œ œ αœ µœ ∀ Œ œ ∀œ œ Œ œ αœ ∀œ œ Œ œ œ œ œ œ œ œ ∀œ œ œ µœ ∀œ œ œ œ œ

178 179 180 µ=œ α=œ , œ, ∀œ œ ˙ ∀œ œ ∀˙ V. ∀ ∀ ∀œ ∀ µœ αœ œ ˙ 3 œ ∀˙ 3 ∀œ œ ∀œ ∀œ 3 % 3 3 3 3 178 3 179ε œ 180 3 ∀œ ∀ ‰ ‰ œ ‰∀œ ‰ œ œ ‰ ∀ œ œ ∀∀ œ œ œ œ œ œ œ œ œ ‰ ‰ œ œ ∀œ ‰ œ % Œ œ œ œ œ œ ∀œœœœ œœ œœ œ œ µ∀œœœœ ∀œ ∀ œ œ P. œ œ œ œ œ Œ œ œ œ œ œ 3 ∀œ ∀ œ ∀œ œ > ∀∀∀ œ œ œ œ œ ϖ œ œ œ œ œ œ ϖ ϖ œ ϖ 181 √ 182 œ µœ œ 183 œ œ ∀œ œ V. ∀ ∀ œ œ ∀œ µœ œ ˙ ∀ œ œ œ œ 3 3 ∀œ ∀œ œ 3 % . œ œ 3 3 3 181 3 182 3 3 183 3 3 œ œ œ ∀∀∀ œ œ ∀œ œ œ œ œ œ œ œ œ ‰ œ ‰ œ ‰œ ‰ œ % ‰ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ‰ œ œ µœ œ œœ œ∀ œ 3 3 œ œ œ œ œ ∀œ œ œ œ œ œ P. œ ∀ œ œ œ œ œ 3 œ > ∀ ∀ ∀œ œ ∀ ϖ ∀œ œ œ ϖ 3 œ

59 184 185 œ œ µœ µ˙ œ œ œ œ œ V. ∀ ∀ µœ œ œ ∀ œ œ œ3 % ∀œ 3 3 3 3 3 3 3 3 3 3 184 185 ‰ ‰ œ ‰ µœ ‰ ∀ ∀ œ œ µ œ œ œ œ µœ % ∀ œ œ œœ œ µœ œ µœ ‰ µœ µœ ‰ œ œ ‰ œ œ ‰ œ œ œ œ 3 P. œ Œ œ µœ > ∀ ∀ œ œ µœ ∀ ϖ ϖ

186 187 188 œ V. ∀ ∀ œ œ œ œ µœ œ ∀ œ œ ∀œ œ ∑ ∑ % 3 3 = = 186 3 3 187 = = 188 = = 3 ˙ ∀˙ ∀ ∀œ œ ˙ ∀œ œ ˙ ∀∀ œ œ µ œ œ ˙ ∀ œ œ ˙ % ‰ααœœ ‰µœ µœ œ œ ∀œ œ œ ∀œœ œ ∀˙ ∀œœ œœ ∀ ˙ P. µœ ∀ œ œ œ µ œ œ ˙ ∀ œ µ ˙ 3 œ αœ œ œ œ 3 ∀ œ 3 ƒ ] ] ] ] ] ] > ∀∀∀ αœ œ œ œ œ ˙− œ œ œ Œ œ œ œ α œ œ µœ ∀œ œ œ œ œ œ œ œ œ œ œ œ œ œ 3 3 189 3 190 ι œ œ αœ œ V. ∀ ∀ œ ∀œ, œ, µœ− œ œ ∀ œ µœ ∀œ ∀œ % œ 3 œ 189 190 ∀ ∀ Œ µœ µœ œ % ∀ µµœ αœ ‰ µœ œ µœ œ ‰ œ œ ˙ 3 P. œ œ œ αœ œ 3 µœ µœ 3 ˙ 3 3 3 œ 3 3 ‰ µœ > ∀ ∀ ∀ œ αœ œ µϖ ϖ œ µϖ

60 191 192 193 V. ∀ ∀ % ∀ ∑ ∑ µœ ∀œ

191 192 193 ∀ ∀∀ ι œ− ι µ˙ % ∀œ œ œ− œ ‹œ œ œ ∀œ œ œ µœ µα œœ ∀ ∀œœ P. œ œ ∀œ œ ∀œ µœ ∀ œ µœ α œ µ œ ∀ œ œ.αœ µ œ αœ œ ο 3 3 3 3 3 3 3 3 3 ∀ > ∀∀ ‰ ‰ ‰ ‰ ‰ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ˙− œ œ œ

194 195 3 3 V. ∀ ∀ ∀ œ œ œ µœ œ œ œ % ˙ œ œ œ œ 3 œ œ œ 3

194 195 ∀ ∀ ∀ œ αα œαœµ œ˙ % œ αµœ− µ œ ∀∀œœ ∀ µœœ µœœ œœ œœ P. µœ − µ œ œ œ œ 3 > ∀∀∀ œ œ ˙− œ œ œ œ œ

196 197 V. ∀ αœ αœ œ œ œ ∀∀ µœ œ œ αœ œ œ œ œ œ œ αœ µœ œ œ ∀œ œ œ 3 œ œ 3 3 3 3 3 % 3 3 196 197 ε 3 3 ∀∀∀ % µœœ œœ œœ œœ ∀œœ œœ œœ œœ œœ œœ œœ œœ P. µ œ œ œ œ µ œ œ œ œ œ œ œ œ ∀ > ∀∀ œ œ œ œ œ œ œ œ œ œ œ 3 œ 3

61 198 199 ϖ œ œ µœ œ œ ∀œ œ ∀œ œ ∀œ V. ∀ ∀ œ œ œ ∀ 3 3 3 3 % 3 3 3 198 199 3 3 3 αœ œ œ œ œ ∀ α œ œ αµœ œ œ œ œ ∀œ ∀œ œ ∀∀ œ αœ œ œ œ % µ∀œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ ‰ œ œ œ ‰ œ œ œ P. œ œ œ œ œ œ3 œ œ œ3 œ αœ œ œ 3 ƒ 3 ∀ > ∀∀ œ œ œ œ œ œ œ 3 œ œ œ ˙ ˙ ˙ 200 201 œ œ œ œ œ V. ∀ ∀œ œ ∀œ œ ∀∀ ∀œ− œ % 3 Ι

200 3 201 ∀ ∀ œ œ œ ∀ αœ œ µœ œ œ œ œ œ œ œ œ œ % 3 αœ œ3 œ µœ ∀œ 33 3 ∀œ œ œ œ œ œ œ œ œ œ P. ‰ œ œ ‰ œ œ ‰ œ œ ‰ œ œ 3 3 3 3 ‰ αœ œ œ ‰ œ œ œ Œ œ > ∀∀∀ œ œ œ œ œ œ µœ œ ˙ ˙ ϖ

202 203 V. ∀ ∀ ∀œ µœ œ œ ∀ œ− ∀œ ∀œ ∀œ œ œ % Ι ∀œ 202 203 ∀ ∀ ∀ ˙ œ µ˙ ∀œ % ∀œ œ œ œ œ ∀œ µµœ œ ∀∀œ œ œ œ œ œ œ ∀œ œ ∀œ P. ‰ œ œ œ œ œ ∀œ œ µ˙ 3 ∀œ œ œ œ 3 3 ∀œ 3 ι ˙ ∀ œ œ Œ ˙ > ∀∀ ‰ µœ ϖ ˙ ˙

62

3 204 205 206 V. ∀ ∀ = = % ∀ œ œ µ˙ ι œ œ αœ œ− œ 204 205 20œ6 œ 3 3 3 ∀ ∀ ] ] œ− œ ∀ œ œ œ œ œ œ œ Œ œ % ˙− ‰ œ œ ‰ œ œ ‰ œ œ œ œ− P. ‰œœ œœ œ œ3 œ œ œ œ œ œ œ œ œ œ œ œ œ œ 3 3 3 3 ι 3 ∀ Œ œ µœ µœœ > ∀∀ ϖ ∀œ œ œ − µ˙ œ œ µœ Œ ϖ ˙ ˙ µ œ

207 208 αœ αœ µœ V. ∀ ∀ αœαœ µœ µœ % ∀ µœαœαœ µœ Œ Œ œ− œ αœ µœ αœαœ µœ 207 αœ− αœ 208 µœ− αœ − αœ− œ µœ− αœ ∀ ∀ αœ αœ αœ− œ œ % ∀ µœ− αœ œ µœ− αœ œ œ P. α œ ˙ œ αµ œœ ˙˙ œœ µœœ > ∀∀∀ α œ ˙ œ µœ Œ µ œ

209 210 211 3 3 3 αœ− ] œ œ œ œ] V. ∀ ∀ αœ œ, œ, , , œ µœ œ œ œ œ ∀ µœ− αœ œ œ œ œ œ µœ 3 µœ 3 % œ µœ µœ œ œ œ œ 3 œ 209 210 œ 211 ∀ ∀ ] ] ∀ Œ µœ œ % ˙ œ µœ œ œ œ µœ œ αœ œ P. µ˙ œ µ œ œ œ µ œ αœ œ ] > ∀ ∀ µœ œ ] µœ œ ∀ Œ µ˙ œ œ αœ µœ œ µœ µœ œ œ αœ µœ µœ œ œ

63 3 3 3 212 213 214 3 œ œ 3 ∀œ œ œ œ œ ∀œ œ œ œ V. ∀ ∀ ∀ œ œ œ œ œ œ œ ∀ œ œ œ œ œ œ œ % ∀ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ 3 3 3 3 œ œ œ œ œ œ œ œ œ œ œ œ œ œ3 œ 3 œ ======ο œ œ 3 212 ε 213 214 √ ∀ Œ ∀∀ Œ œ Œ Œ œ Œ œ œ œ œ œ œ œ œ % œ œœ œ œœ ϖ œ œ œ œ œ œ œ P. œ µœ œ µœ ϖ ε ο ∀ ϖ ϖ > ∀∀ œ œ ϖ Œ œ Œ œ Œ œ Œ œ ϖ œ œ ϖ 215 = 21œ6 217 = =œ œ V. ∀ ∀ œ œ œ œ œ œ œ œ œ Τ % ∀ œ œ œ œ œ œ œ œ œ œ œ œ œ Œ œ Œ œ 3 œ 3 3 3 œ 3 3 3 215 3 216 œ 21ϖ7 ∀ ∀ œ œ œ œ œ œ œ œ œ Τ % ∀ œ œ œ œ œ œ œ œ œ œ Œ œ Œ ϖ œ œ œ œ œ ϖ P. œ ƒ œ Τ > ∀ ∀ ϖ œ ϖ ∀ œ Œ Œ ϖ ϖ

64 II N A A V α 2 % α α 3 ∑ ∑ ∑ ∑ ∑

α 2 œ % α α 3 µœ ∑ œ ∑ œ P œ µœ œ œ αœ > α 2 µœ ∀œ µ˙− > œ œ ˙− > αœ œ α α 3 µœ % œ % œ

V. α œ ι % α α ∑ ∑ ∑ µœ− œ œ ˙

αα α˙ ι‰ % α œ œ œ œ œ œ œ œ œ œ œ œ œ œ P. œ αœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ > α œ œ œ œ œ œ œ œ œ Œ œ ˙œ œ œ α α œ ˙− α˙− ˙ œ œ ˙− ˙− ˙ 3 V. α œ œ œ ι œ œ œ ι % α α œ µœ œ œ œ Ι µœ œ œ œ µœ œ œ œ œ− œ

αα % α œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ P. œ œ œ œ œ œ œ œ œ œ œ œ œ œ ε ο > α ˙œ œ œ œ œœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ α α −− œ ˙ œ ˙− ˙− œ ˙− ˙− ˙− ε

65 V. αα œ α˙ œ œ œ αœ œ œ œ % α œ œ Ι œ œ Ι α % α α œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ αœ œ αœ œ œ œ œ P. αœ œ œ œ œ œ αœ œ œ œ œ œ αœ œ œ œ œ œ αœ œ œ œ œ œ > ˙ α˙ œ− œ ˙ ααα œ œ α˙−

V. α œ œ œ− œ œ œ œ œ œ œ œ œ œ α α αœ œ œ œ Ι 3 µœ œ− œ µœ % œ 3 Ι 3 ˙ α µœ œ œ œ % α α œ œ œ œ Œ œ ˙ Œ ∀œ œ P. αœ œ œ œ αœ µœ œ œ αœ œ ε œ αœ œ œ œ œ œ œ œ ∀œ œ > α œ œ œ œ œ œ œ œ µœ œ µœ œ œ œ œ α α ˙− αœ α˙− αœ œ œ

V. α œ œ œ œ % α α µœ ∀œ œ œ ∀œ µœ œ ι ∀œ œ− ι µœ− œ œ œ œ ˙ αα œ Œ œ− œ Œ % α ˙ µœ ˙ œ− ι P. œ Ι ˙− µœ œ œ ο œ œ œ > œ œ œ œ œ œ œ œ ∀œ œ œ œ œ œ œ œ œ œ œ αα œ œ œ µœ œ œ œ œ œ œ œ œ α œ µœ œ œ

66

3 3 S G V. α % α α œ œ œ œ œ µœ œ Œ Œ ˙ œ œ œ œ µœ œ œ− œ œ ι œ ˙ α œœ µœ˙− œ œ ˙ % α α ˙ œ œ ι ‰ ˙ œ œ ˙ P. ˙ œ µœ− œ œ ι αœ ι Ε œ œ œ œ œ œ œ œ œ œ œ > α ‰ œ µœ œ œ œ ‰ œ œ œ œ œ œ œ œ œ œ œ œ œ œ α α α˙− ˙ œ µœ œ œ α˙− ˙ œ µœ œ œ

V. α % α α − Œ ˙ œ œ ˙ œ ˙− ˙ œ œ œ œ αœ œ α œ œ µœ œ œ œ µœ œ œ œ œ µœ œ œ œ % α α œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ αœ µœ œ Ι µœ œ µœ œ 3 P. Ι œ = œ œ œ œ œ œ œ œ œ= œ= > α œ œ œ œ œ œ œ œ œ œ œ αµœ œ µœ œ œ œ œ œ œ α α œ œ œ œ œ œ œ œ œ œ œ Ι V. α œ− ι % α α ∑ Œ ∀œ ∀˙ œ− µœ µ˙ ∀œ ∀œ ∀œ ˙ œ ∀œ ∀œ œ œ α µ∀œ ∀œ− œ ˙ ∀µœ œ ∀œ µœ ∀ œ ∀œ œ α α ∀œ˙ µœ ∀œ− ˙ œ ∀œ µœ ∀œ œ % − Ι P. ∀œ ∀œ ∀œ œ ∀œ œ µœ œ œ µœ œ œ œ œ œ œ œ œ∀œ œ > ∀œ œ µ œ œ œ œ œ œ µ œ œ œ œ ∀œ œ µœ œ œ œ ∀œ µœ œ œ œ αα ∀œ α ∀œ œ ∀œ ∀œ

67 V. œ ∀œ αα ∑ Œ % α µœ ˙ œ− œ ∀œ œ ∀œ ∀œ œ œ ∀œ− ∀œ œ œ ∀œ µœ ∀œ µœ œ µœ ∀œ ∀œ œ œ œ ∀ œ− ∀œ œ ∀œ αα œ µœ ∀œ œ µœ ∀œ œ Ι ∀œ % α Ι ∀œ ∀œ 3 3 P. Ι œ ∀œ œ µœ œ œ œ ∀œ œ µœ œ œ ∀œ œ µœ œ > µœ µ œ œ œ œ µœ µ œ ∀ œ ∀œ µ œ œ œ œ ααα µœ µœ œ œ œ µœ Μœ Ι ∀˙ V. αœ ˙ α ∀œ œ µœ œ µœ 3œ % α α µœ ι ∀œ ∀œ ∀œ œ œ œ œ œ œ œ œ œ œ œ ∀∀œ˙ − αœ ˙ µœ αα ∀œ ∀œ œ Œœ ˙œ− œ œ œ œ œ œ œ œ œ % α ∀œ ∀œ œ αœ œ œ œ αœ µœœ P. ∀ œ œ œ œ αœ œ œ œ œ αœ αœ œ > α ι ι œ œ œ ι œ œ αœ µœ œ α α ∀œ œ αœ ∀œ œ αœ

V. œ αα œ œ ∀œ œ œ œ ι µœ œ− ι œ œ % α 3 µœ− œ œ œ œ œ œ œ α α α ‰ ‰ ‰ ι ‰ % œ αœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ P. œ αœ œ œ œ œ œ œ œ œ ‰ αœœ œ ‰ œœ Ι Ι > α αœ µœ œ œ œ α α α˙− ˙− Œ ˙− ˙− ˙− ˙

68

3 V. α œ œ œ œ µœ œ œ α α œ αœ œ µœ œ œ αœ œ œ œ œ ∀œ œ œ % 3 3 3

α œ αœ % α α œ ∀œ œ œ œ µœ αœ œ œ œ œµœ œ œ œ œ œ œ P. ‰ αœ µœ œ ‰ αœ œ œ ‰ µœ µœ œ ‰ œ œ œ œ Ι Ι Ι Ι > α α α µ˙− ˙− ∀˙− ˙− µ˙− ˙− ∀˙− ˙−

V. œ− − œ− αα µœ αœ œ ∀œ œ µœ αœ œ œ œ % α 3 3 3 α α α œ œ αœ− œ αœ œ αœ œ− αœ œ µœ œ % αœ œ αœ P. œ − œ αœ ι œ αœ − œ µœ ιœ ‰ œ œ œ ‰ œ œ œ > α œ œ œ αœ œ œ α α ˙− µ˙− ˙− ˙− œ 6 ι œ œ œ œ œ V. œ œ α œ œ œ œ œ œ œ % α α 6 œ œ œ 6 œ œ œ œ ∀œ œ œ ] ] α œ] œ µ˙˙ œœ % α α œ œ µ ˙ œ ‰ Œ P. Ι ] ] ] ι œ œ > α ˙ œ ‰ Œ œ ∀œ α α œ µœ µœ α œ œ µœ ˙ œ œ

69 V. α µœ œ αœ % α α Œ œ œ œ ∑ ∑ œ α˙

∀œ µ˙ ααα Œ ∀œ µœ œ ∀ ˙− % µ˙− ˙ ∀ œ œ œ ˙− ˙− P. α˙ − µ˙− ˙ µœ ∀œ œ ˙− > α ˙− ∀˙ Œ α α ∀˙− µ ˙ ˙− ∀ ˙− ˙

V. œ α − αœ œ œ ι % α α œ Œ Œ ∑ Œ Œ œ µœ œ ‰ Œ α ι ι ι ι ι ι ι α α ι ‰ ‰ % œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ P. œ αœ œ œ œ œ αœ œ œ µœ œ œ œ œ αœ µœ− œ œ − − > αα œ ‰ Œ ˙ ˙ µ˙ œ α œ ˙− ˙− ∀œ− Ι α˙− ˙− µ˙ αœ œ αœ V. α œ− œ ˙ œ % α α ∑ Œ Œ Œ Œ Œ ∀œ−

αα ι ι ‰ ι ι ι ‰ ι ι ι % α œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ P. œ µœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ∀œ µœ µœ αœ œ µœ > α µ˙ ˙ µœ œ α α − − − œ œ µœ µ˙− ˙ µœ− œ ˙

70 µœ αœ V. α µœ µœ ∀œ µœ % α α ˙ œ− œ ∀œ Ι ‰ µœ− œ Ι ‰ µœ− œ

α ι ˙− − % α α ‰ µµœ œ œ œ œ µµœ œ œ ‰˙ µ∀œ œ œ ‰œ µ∀œµœ œ œ œ P. µœ œ œ œ ˙Ι− Ι ˙− Ι œ µœ œ Ι ˙− > µœ αœ µœ ααα ˙ µœ− œ µœ αœ µœ ˙− ˙− ˙ µœ− œ ˙− µœ V. œ ∀œ µœ αα ∀œ µœ Œ Œ % α 3 ∀œ µœ µœ œ− ∀œ µ˙ α ι ι ˙ι ι ι α α œ µœ œ µœ œ œ œ œ œ µœ œ œ µœ œ œ œ % œ µ∀œ œ œ ∀ œ œ œ œ œ œ œ œ œ ‰ œ œ œ œ P. Ιœ µœ œ Ι µœ ˙− > α œ− œ α α ˙− µ˙− ˙− ˙ % ˙− µ˙− ˙−

V. œ αœ ααα ∑ Œ Œ œ Œ ∑ % œ− œ ˙ ι ι ι ι αα œ µœ œ œ ∀˙− µœ œ œ œ œ˙µ−œ œ œ ‰ œ œ œ ‰ œ œ œ % α œ œ œ œ ‰ œ œ œ œ œ œ œ œ œ œ œ œ œ œ P. ∀˙− Ι˙− Ι œ œ œ œ œ œ µœ µœ œ µœ αœ α œ > ˙ œ œ % α α ˙− ˙− % − œ µœ αœ ˙− ˙− ˙ œ− œ

71 V. α œ αœ œ œ œ œ œ α α Œ Œ µ˙ Œ Œ Œ œ− % œ− œ ι ι ι ι ι α œ œ œ œ œ œ œ œ œ œ œ œ αœ œ œ % α α ‰ αœ œ œ ‰ œ œ œ ‰ αµœœ œœ œœ ‰ αµœœ œœ œœ ‰ œ œ œ P. œ œ œ ˙−œ œ œ ˙− œ œ œ ˙− α ˙− α > œ αœ % α α ˙− ∑ Œ œ αœ œ− œ ˙ œ œ ˙− αœ − ˙ œ ˙ œ ˙− œ − œ − − V. α œ− œ µœ αœ ∀œ− œ µœ αœ ˙ % α α ∀œ α ι ι ι ι ∀œ ∀œ µœ− œ % α α ‰ αœ œ œ ‰ œœ œœ œœ ‰ αœ œ œ ‰ œœ œœ œœ ‰ ∀œ ∀œ ∀œ µœ− œ P. ˙− ˙− α ˙− ˙˙− ι ∀œ œ œ > α œ œ œ α α œ αœ αœ αœ œ αœ µ˙‰− ˙ ∀œ− œ ˙− µ ˙− œ , , ∀œ œ , , V. œ ∀œ ∀œ ∀œ, ααα œ, ∀œ % , ∀œ, ∀œ œ , − ∀œ ∀œ ∀œ ∀œ− µœ ˙− ˙− α ˙− % α α ∀˙− ∑ ∑ ‰ œ œ œ œ P. φ ˙− µœœ αœ œ, , œ, φ ˙− , , , φ , αœ, , œ > œ , αœ αα ˙− ∑ ∑ ‰ œ α ˙−

72 µœ œ µœ œ ˙ V. α αœ œ œ µœ− œ œ % α α œ œ œ µœ œ 3 Ι œ œ ˙− œ ι α α˙ ˙− œ µœ− œ % α α ˙ Œ ∑ ˙− œ− œ P. µœ ˙ œ ˙ œ > α Œ ∑ ‰ œ œ œ œ œ œ œ œ œ α α ˙−œ œ 3 œ œ œ ˙−3 3 ‰ 3 3 ‰ 3 œ œ œ œ œ V. α µœ œ œ Ι µœ œ œ % α α Ι œ œ α œ ˙ œ µœ œ œ œ % α α œ ˙ Œ œ œ œ œ œ œ P. µœ ˙ œ œ œ ˙ œ œ œ µœ αœ > α œ œ œ œ œ œ œ œ œ α α œ œ 3 œ œ œ œ œ œ ‰ 3 3 ‰ 3 3 3 3 3 3

œ µœ œ œ œ α˙ V. α œ µœ œ œ œ œ− œ % α α Ι ι œ α˙ αœ ι α œ µœ œ œ œ œ ˙ α œ µœ−˙ œ % α α œ œ œ œ œ œ α˙ Œ œ−˙ œ P. µœ 3 Ι αœ ˙ ‰ αœ œ œ œ œ αœ œ œ œ > α œ œ α˙ αœ œ αœ œ α α œ œ œ ˙− 3 3 3 œ œ 3 œ œ 3 3 3 œ ˙− ‰ 3 œ 3

73

3 œ œ œ αœ œ œ œ V. α œ œ œ œ % α α Ι Ι œ α˙ αœ œ αœ œ α αœ ˙ α œ µœ œ œ œ œ % α α œ α˙ Œ α œ œ œ αœ P. α˙ αœ œ œ ˙ αœ œ œ αœ œ ααœ > œ œ œ œ œ œ αœ œ œ œ α αœ 3 3 αœ œ 3 αœ œ œ α α 3 3 3 ‰ 3 ‰ 3 ‰ 3 œ œ œ− œ œ œ œ œ œ αœ œ œ œ œ œ œ µœ V. α œ Ι % α α 3 3 œ αœ œ α œ œ œ œ œ µœ œ œ œ µœ œ œ œ % α α Ι αœ œ œ œ œ Œ œ αœ œ µœ œ œ œ µœ 3 µœ œ œ P. Ι ι ι œ œ ‰ œ œ œ œ œ ‰ œ œ œ µœ > α αœ œ œ αœ œ œ œ œ œ œ α α œ œ 3 3 3 3 3 3 3 œ ˙− 3 αœ − 3 α˙ œ− œ œ œ œ œ œ µœ œ µœ œ œ œ V. α Ι ∀œ œ œ ∀œ % α α 3 3 3 œ œ œ αα œ œ œ œ ∀œ œ œ œ ∀œ œ œ α˙ œ œ œ % α ˙− ∀œ œ œ œ œ 3 P. œ αœ > ‰ œ œ œ αœ œ œ ‰ œ αœ œ œ αœ ‰ œ µœ œ œ œ α œ 3 3 œ œ œ œ œ œ α α 3 3 3 3 3 α˙− 3 ˙− µ ˙− 3

74

3 3 œ œ œ µœ œ V. α œ œ œ œ ∀œ œ œ œ œ œ œ ∀œ œ œ µœ œ α α œ− 3 µœ 3 % Ι 3 αœ œ α α˙ µœ œ − œ % α α œ ˙− œ αœ µœ œ œ− œ P. ι ι ι ι œ œ αœ œ œ œ œ > α ‰ œ œ œ œ œ œ ‰ œ µœ œ œ œ œ œ œ ∀œ 3 3 3 3 αœ α α 3 3 3 œ µœ ˙− ˙− 3 3 ˙− œ αœ αœ V. α œ œ µœ œ ∀œ œ œ µœ µœ− œ % α α 3 3 3 Œ Œ Ι ι ι œ− œ ‰ œ ˙ œ ˙ α ˙ œ œ− œ œ ˙ % α α ˙ œ œ P. ˙ œ œ αœ œ µœ αœ œ µœ œ œ œ œ œ œ αœ œ œ œ > α œ œ œ œ œ œ œ α α œ 3 3 œ 3 3 œ 3 3 œ œ œ 3 3 3 αœ œ αœ œ V. α œ ˙ œ œ µœ œ œ− œ œ œ % α α 3 œ− œ œ œ œ œ αœ− œ ˙ œ− œ ˙ α œ œ− œ œ ˙ œ− œ ˙ % α α ‰ œ œ œ œ œ P. Ι 3 œ œ αœ œ αœ µœ > α œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ α α œ 3 3 œ 3 3 œ 3 3 œ œ 3 3 œ

75 ˙− œ œ œ œ− œ αœ œ œ œ αœ œ V. α œ œ œ αœ % α α 3 3 3 œ œ 3 œ− µœ ˙ œ− œ œ œ œ œ− œ ˙ œ− œ œ œ αœ œ œ α œ− µœ ˙ œ− œ œ αœ œ ˙− œœ % α α 3 œ œ œ œ 3 3 œ œ P. Ι œ œ αœ µœ αœ œ œ œ αœ > œ œ œ œ œ ‰ œ œ œ α œ 3 3 αœ 3 3 α α œ ˙− 3 œ ˙−

3 3 V. α % α α ˙− αœ œ œ œ œ œ œ αœ 3 αœ œ œ œ œ, , α α α Œ Œ Œ œ % œœ µœ ∀œ ∀˙− P. αœ œ œ 3 ˙− > α œ µ˙ α α œ Œ Œ Œ œ ∀œ œ ∀œ ˙− αœ µœ œ αœ µ œ −

3 V. α % α α ˙− µœ α˙ ˙− ˙ µœ œ œ µœ œ œ µ ∀˙ α µ œ ∀œ µ αœ œ œ ∀œ œ œ µœ α ˙ % α α ‰ œ ∀ œ α œ ∀œ µœ ‰ œ µœ œ ˙ ˙− Ι 3 ∀œ − P. Ι ∀˙− µœ œ ∀œ œ > α ∀œ Ι α α ‰ Ι 3 ‰ ∑ ∑ µ˙ œ µ˙ œ

76 ˙− œ V. α œ ˙− α α ˙ œ− Œ % œ− œ α % α α œ α˙ ˙− œ Œ Œ ∑ P. µœ ˙œ œ œ ι ι ι ι ι µœ œ œ œ œ œ µœ œ œ ˙ αœ œ œ > α œ œ œ œ œ œœ œ αœ œ œ œ œ− œ œ œ α α œ αœ œ œ µΙ˙− œ αœ œ œ Œ œ− œ

V. α œ αœ œ œ− œ µœ œ ∀œ % α α ˙ Œ ∑ Œ Œ

α œ œ œ œ ι ι ι α α ∑ ‰ ∀œ œ œ œ ‰ ι ι œ µœ œ % ∀œ œ œ œ œ œ œ œ œ œ œ P. ι ι µ œ œ œ œ œ œ œ œ œ µœ œ œ œ œ œ > α œ œ œ œ œ µœ αœ α α µ˙− ˙ œ− œ ˙− ˙− µ˙− ˙ œ œ œ ˙− œ αœ œ µœ œ µœ œ œ αœ œ µ˙ œ œ− V. α Ι % α α ∀˙− ∀˙− ˙− α ∀ ˙− ∀ ˙− ˙− α α ˙− ˙− − ˙− ˙− ˙− % ˙− ˙− ˙− ˙− œ œ P. ˙− ˙− ˙− ˙− ˙− ˙− > α œ α α ˙− ˙− µœ œ ∀œ ˙− ˙− ‰ œ ˙− ˙− ˙− µ˙− ˙− œ

77 √ − − ˙− ˙ ˙ V. α % α α µ˙− ˙− œ α œ œ % α α P. > ααα ∑ ∑ ∑

78 III S

A N A V 5 % 7 ∑ ∑ ∑ ∑ ∑ ∑ œ œ œ œ œ œ œ œ œ œ ˙− œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ˙− œ œ œ œ œ 5 αœ− œ− œ− % 7 Ι Ι Œ ‰ ∀œ− αœ− œ− αœ− µ∀œ− Ι P − ε œ œ œ œ œ œ œ œ œ œ ˙− αœ œ œ œ œ œ > 5 œ œ œ œ œ œ œ œ œ œ ˙− − œ− αœ− ˙− œ œ œ œ œ 7 Ι Ι Ι

V. % ∑ ∑ ∑ ∑ ∑ ∑ œ œ œ œ œ ˙− œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ˙− œ− ∀˙œ− µœ− œ œ œ œ œ œ œ œ œ œ % Ι Œ ‰ ∀∀œ− œ− ∀∀œ− ˙− Ι Ι P. ε − − œ œ œ œ œ ˙− œ αœ œ− α˙− œ œ œ œ œ œ œ œ œ œ > œ œ œ œ œ ˙− œ œ œ œ œ œ œ œ œ œ Ι Ι Ι

œ œ œ œ œ œ œ œ œ V. œ œ ∀œ ∀œ ∀œ œ ∀œ œ œ œ œ ι ∀œ ∀œ œ œ œ Ι Ι % œ ∀œ ∀œ œ Ι. Ι ο˙− ˙− œ− ι ι ι ‰ œ− % Œ œ œ œ œ œœ. œ œ œ œ œ œ œ œ œ œ œ œ œ œ ∀œ− P. Ι ο˙− ι ι ι ι > ∀ ˙− ∀∀ ˙− αœ− ˙− œ œ œ œ α œ˙− œ œ œ œ ˙œ œ œ œ œ ˙˙− œ œ œ œ œ ‰ αœ− − ˙− − œ

79 III ∀œ ∀œ œ− œ ∀œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ− œ œ ∀œ œ œ œ V. œ œ œ œ œ œ œ œ œ œ œ Ι % Ι Ι œƒ− œ œ− œ− œ− œ− œ ∀œ− ∀œ− ∀∀œ− ∀œ− ∀œ− ∀œ− œ− œ ∀œ œ œ ι ∀ œ− œ− ∀œ− œ− œ− − ∀œ œ œ œ % ∀œ− ∀œ ∀œ œ œ ∀œ œ œ P. ƒ œ ∀œ ∀œ > − ∀œ− œ− œ− œ− − œ œ ∀œ œ œ ∀œ− ∀œ− œ− αœ œ− œ Ι œ œ− œ− αœ− œ− œ

V. œ− œ ∀œ œ œ ∀œ œ œ % œ− œ Ι œ œ− œ ∀œ œ œ ι œ œ ∀œ œ œ œ œ œ œ œ− œ œ œ œ

% œ− œ ∀œ œ ι ∑ ∑ ∑ ∑ œ− œ. œ ∀œ œ œ P. œ ο œ− œ ι œ ‰ Œ− œ ‰ Œ− œ ‰ œ ‰ œ ‰ œ ‰ > œ− œ ∀œ œ œ ∀œ œ œ œ œ œ œ œ œ œ− œ ∀œ œ œ œ − œ − œ œ αœ œ ∀œ œ œ œ œ ‰ Œ ‰ Œ œ ‰ œ ‰ œ ‰αœ ‰

V. œ œ œ œ œ œ− œ œ œ œ αœ œ œ œ œ− % œ œ œ œ− αœ œ œ œ œ = œ = ‰ œ ‰ œ ‰ ‰ ‰ ‰ ‰ ‰ œ ‰αœ ‰ % œ œ œ œ œ αœ œ αœ œ P. œ œ œ œ α=œ ‰αœ ‰ Œ− ‰ > œ ‰ œ ‰ œ ‰ ‰ αœ œ ααœ ‰ œ ‰ œ œ αœ œ œ œ œ œ œ œ ‰ ‰ œ ‰α œ ‰

80 III

αœ V. œ αœ œ œ αœ œ œ αœ αœ αœ αœ œ αœ œ œ œ αœ œ œ αœ œ œ αœ % .

αœ =œ αœ œ αœ œ α αœ αœ œ ‰ αœ ‰ œ ‰ αœ ‰ œ ‰ααœ ‰ α œ ‰ααœ ‰ % œ œ œ. œ œ P. œ αœ œ αœ œ αœ αœ > αœ αœ œ ‰ αœ ‰ œ ‰ αœ ‰ œ ‰ αœ ‰ αœ ‰ ‰

αœ œ αœ ∀œ œ œ œ ∀œ œ œ œ œ V. αœ αœ αœ œ ∀œ œ ∀œ œ− œ œ œ % Ι œ œ ∀œ α αœ α αœ ∀œ œ ∀œ œ œ œ− % α œ ‰ α œ ‰ ∀ œ ‰ œ ‰ ∀ œ ‰ ‰ ∀œ ‰ œ− P. αœ ∀œ œ ∀œ œ œ αœ− αœ ∀œ > αœ ‰ αœ ‰ ∀œ ‰ œ ‰ ∀œ ‰ œ ‰ ‰

œ œ œ V. ∀œ ∀œ œ œ œ œ ∀œ‹œ œ œ œ œ ∀œ ‹œ œ œ œ œ œ œ ∀œ ∀œ œ œ œ œ % Ι œ œ œ − œ− ∀œ− œ− ∀œ− œ− − − œ− ∀ ∀œ− œ− œ− ∀œ− ∀ œ− ∀œ− œ œ œ ∀œ− œ− ∀œ− % ∀ œ− œ œ− ∀œ− œ− P. ε œ− αœ− œ− œ− αœ− − αœ− œ− αœ− > œ œ œ œ αœ− œ− αœ− œ œ œ

81 III

œ œ œ V. ∀œ‹œ œ œ œ œ ∀œ ‹œ œ œ ∀œ ∀œ ∀œ œ œ ∀œ œ % ‰ Œ− ‰ Œ− œ œ œ œ œ ∀œ− œ− ∀œ− œ− ι œ− ∀œ− α œ− ∀œ− œ œ œ œ œ œ œ œ œ % ∀œ− œ− ∀œ− Ι ∀˙− ∀œ œ œ œ œ P. ∀ ˙− œ ‰ Œ− ε ∀ ˙− œ œ œ œ œ− œ− αœ− œ− ρεψ > œ− − − œ Ι ∑ Œ œ œ œ œ œ αœ œ− œ Ι

œ œ œ ∀œ ∀œ V. ∀œ ∀œ œ ∀œ ι œ œ œ œ œ ∀œ % ∀œ ∀œ ∀œ œ œ ∀œ œ ∀œ ∀œ ∀œ œ ∀œ Ι Ι ρεψ œ ∀œ ∀œ ∀œ ι ι ι œ ∀œ % ∑ Œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ‰ P. ρεψ ι ‰ Œ− œ− > ∀œ− œ œ ∀œ − − ∀œ− ∀∀ ˙− œ œ ‰ Œ œ ‰ Œ αœ ‰ œ ‰ Œ− œ œ αœ œ− œ V. Ι % ‰ ‰ ∑ ∑ ∑ ∑ ∑ ƒ œ− œ ∀œ œ œ− œ œ ∀œ œ œ œ − ι œ œ ∀œ œ œ œ− œ ∀œ œ œ = % ∀œ œ œ œ œ− œ ∀œ ∀œ œ œ œ œ Ι œ œ ∀œ œ œ œ œ œ œ œ œ P. ƒ œ œ œ œ œ− œ αœ− ∀œ œ œ ∀œ œ = œ− œ œ œ œ− œ ∀œ > œ− œ Ι œ− œ œ œ ∀œ œ œ œ ‰ œ œ œ œ ‰ œ ‰ œ− œ œ− œ ∀œ œ œ Ι œ œ œ œ œ œ αœ

82 III

V. % ∑ ∑ ∑ ∑ = αœ αœ œ αœ αœ % œ œ− αœ œ œ αœ œ αœ œ œ αœ− α αœ œ œ P. œ œ αœ− œ α œ œ− α œ αœ œ αœ = = > αœ ‰ œ œ œ αœ ‰ααœ ‰ αœ ‰ αœ− œ œ œ œ œ αœ αœ œ œ αœ− αœ αœ œ œ αœ− αœ−

V. œ œ αœ αœ αœ αœ αœ αœ αœ αœαœ αœαœ œ αœ αœ œ % œ.αœ œ œ αœ œ œ

αœ % ααœ ‰∫ αœ ‰ ααœ ‰∫ αœ ‰ ααœ ‰ αœ ‰ αœ ‰ œ ‰ P. αœ. α œ αœ α œ αœ αœ α œ αœ > œ αœ ‰ αœ ‰ αœ ‰ αœ ‰ œ ‰ αœ ‰ αœ ‰ αœ ‰

œ œ αœ œ œ αœ œ œ ˙− œ œ αœ αœ ˙− V. αœ œ œ œ œ αœ % ρεψ ρεψ œ − αœ− } œ œ œ œ œ αœ œ− αœ − } ι % αœ ‰ œ− α œ− α œ− } œ ∀œ ∀œ œ α œ µœ− œ− } ˙− αœ œ œ œ ∀œ œ œ P. } ˙ αœ } ˙− α œ

} ρεψ

}

} }

} −

> αœ œ− αœ− œ− α˙− œ − } ∀˙− ‰ ‰ Œ } ˙ αœ œ− αœ− œ− ∀} ˙− ρεψ

83 III œ œ œ αœ œ αœ œ− αœ µœ œ αœ αœ V. œ ∀œ œ αœ % Ι Ι œ αœ œ ∀œ œ œ αœ œ αœ µœ œ œ

‰ Œ− αœ αœ % αœ α˙− αœ− œ− αœ− œ− α˙− P. ˙− α œ− µœ− α œ− µœ− α ˙− > αœ œ œ œ œ α˙− œ− αœ− œ− αœ− œ ‰ Œ− ααœ Ι α˙− œ− αœ− œ− αœ− œ

P M V. αœ ‰ Œ− ∑ ∑ % œαœ µœ œ ∀œ œ − P Mαœ− œ αœ ∑ αœ % αα˙− α˙− œαœ œαœ P. ˙− α ˙− αœ œ αœ œ > αœ αœ αœ αœ ∑ αœαœ αœαœ αœαœ αœαœ αœ αœ

V. œ− œ− αœ αœ œ αœ− αœ αœ αœ % œ− œ− − Ι Ι − œ−

∑ αœ ∑ αœ ∑ % œαœ œαœ P. ο αœ œ αœ œ αœ œ > αœαœ αœαœ αœαœ αœαœ αœαœ αœ αœ αœ αœ αœ Œ− αœ αœ αœ

84 III

V. αœ αœ αœ Œ− αœ αœ œ % œ− Ι − œ− œ− œ− œ− − Ι

αœ α˙− ∑ αœ % αœαœ αœ αœ œαœ P. œ αœ œ αœ α=œ− αœ > αœ αœ > αœ αœ % ‰ αœ αœ αœ αœ αœ αœ αœ αœ

œ− αœ− αœ V. αœ− αœ αœ− ι % Ι œ− œ− œ αœ œ− œ−

∑ αœ αœ ∑ % αœαœ αœ αœ P. αœ œ œ αœ œ ∀œ > αœ αœ αœ œ œ œ αœ αœ αœαœ œαœ αœ œ œ αœ αœ ∀œ

V. % ‰ Œ− ∑ ∑ ∑ ∑ œ œ− ∀œ− ∀ œ− ∀œ− ∀œ− ι œ− ∀œ− α˙œ− ∀ œ− % ˙− ∀ ˙œ−− ∀œ ∀ œ− ‹œ œ ∀ ˙− − P. − − ∀ œ œ− − ∀œ− œ > œ− ∀œ œ ∀œ œ œ œ αœ œ œ ‰ œ ‰ œ œ ‰ œ ∀œ ‰ œ œ œ œ œ ∀œ œ

85 III − αœ− œ V. % ∑ ∑ ∑ ∑ ε αœ− αœ œ− œ− œ− ι − − α œ− œ− αœ˙− œ− ∀œ œ αœ˙− ∀œ α˙− ∑ % œ− αœ− œ œ˙− − ∀œ− P. − αœ αœ œ αœ œ œ œ œ αœ œ αœ œ αœ > œ ‰ œ αœ ‰ œ œ ‰ œ αœαœ αœ œ œ αœ αœ αœ αœ αœ αœ αœ− αœ œ− αœ− œ− œ− œ− œ− αœ− V. œ Ι % Ι

L.H αœ αœ αœ % αœ ∑ αœ œ ∑ P. αœ αœ œ αœ αœ œ > αœαœ œ αœ αœ œ œ αœ αœαœ αœαœ αœαœ αœαœ αœ αœ − αœ αœ αœ αœ− αœ− V. Ι œ− œ− αœ− œ ∀œ % Ι

α œ µ œ − αœ− αœ− αœ− α œ−αœ µ œ− œ ‰ −αœ αœ ‰ − œ œ % αα˙œ− − α‰œ− œ µ‰œ− œ α œ− µ œ− P. α αœ˙− αœ− αœ− αœ œ ∀œ αœ œ αœ αœ − − > αœ αœ αœ αœ αœ αœ œ αœ αœ œ αœ αœ αœ αœ αœ

86 III αœ− αœ− αœ œ αœ− V. αœ œ− œ− Ι % ‰ Œ− αœ αœ− αœ− αœ − œ− αœ− αœ œ − αœ− − αœ œ αœ œ αœ− αœ αœ αœ % œ− œ− αœ− Ι P. Ι ε αœ > αœ αœ > αœ > αœ % αœ αœ αœ % αœ αœ αœ αœ αœ œ œ αœ αœ αœ αœ αœ αœ αœ αœ αœ αœ− αœ αœ αœ− V. αœ− αœ− Ι œ− œ % Ι ‰ ‰ Œ− = − αœ− œ αœ œ− œ− αœ− œ− αœ− αœ− œ % αœ− œ− œ− αœ− œ− αœ− ‰ P. = > œ > αœ œ > αœ αœ % αœ αœ αœ αœ αœ % α˙− αœ αœ αœ αœ αœ αœ αœ αœ α ˙− ∀œ− V. ∀œ œ− % ∑ ∀œ− ∀œ− œ− ∀œ Ι ∀œ √ ∀œ ∀œ− ∀œ− œ− ∀œ − ∀œ− œ œ œ− ∀œ ∀œ œ− ∀œ− ∀œ− œ % ∀œ− ∀œ− Ι œ− œ P. Ι

œ > œ œ > œ > ∀œ ∀œ % ∀œ ∀œ ∀œ ∀œ ∀œ % ∀œ ∀œ ∀œ ∀œ œ ∀œ ∀œ œ ∀œ œ œ œ œ

87 III

∀œ− œ V. ∀œ ∀œ ∀œ− œ œ αœ− ‰ Œ− % Ι œ− œ ∋√( ∀œ − œ − ∀œ− ∀œ ∀œ ‹œ =˙− % ∀œ− œ ∀ œ− ∀œ− ∀œ P. Ι œ œ œ œ α=œ− > ∀œ ∀œ ‰ > ∀œ œ αœ œ ‰ > ∀œ % ∀œ ∀œ ∀œ ∀œ œ ∀œ %

V. αœ− œ− αœ− % ∑ ∑ œ αœ Ι ι αœ− αœ− αœ− αœ− αœ− ˙− % α œ− œ− αœ− œ œ α ˙ α œ− αœ− ˙− α ˙− ˙− P. ο αœ αœ œ αœ αœ αœ αœ œ αœ œαœ œ > αœ αœ œ œ αœ αœ œ αœ αœ œ αœ œ

œ− V. αœ− œ− œ− œ œ œ œ % œ− œ ‰ Œ− ∀œ Ι Ι ‰ ι œ œ− œ− œ− ι αœ− − − œ œ œ œ % αœ− αœ− α˙œ− œ œ α ˙− œ α˙− œ œ œ−∀œ 512 − − P. αœ œ αœ ∀œ œ œ œ œ ∀œ œ ∀œ œ œ œ œ > œαœ αœ œ œαœ αœ œ αœ αœ œ αœ œ œ ∀œ

88 III

∀œ ∀œ− œ− ∀œ œ V. œ œ œ ∀œ œ ∀œ œ Ι ∀œ ∀œ Ι ‰ Œ ‰ Ι Œ ‰ Ι % . ι ι = œ ∀œ œ− = = % œ− œ− Œ ‰ œ− œ− Œ ‰ ∀œ µœ œ− œ œ œ œ− œ−. œ œ œ œ œ− P. αœ− œ− ∀œ− œ œ− ∀œ œ œ œ ρεψ œ− ∀œ− > œ ∀œ Œ ‰ œ œ œ B Œ ‰ œ œ œ Œ− ˙− œ œ œ œ œ ˙− œ œ œ œ œ ˙− œ œ œ œ œ ˙− œ œ œ œ œ œ αœ œ− œ− Ι œ−Ι œ− œ− ∀œ œ œ œ œ œ V. Ι Ι œ œ œ œ % Œ ‰ Œ ‰ ‰ = = = œ− œ− œ− % Œ ‰ œ αœ− ∀œœ− Œ ‰ αœ œ αœ− œ− Œ ‰ αœ œ œ−œ œ œ− ∀œ − œ− œ œ− œ− œ− œ P. αœ− = − œ− œ− = œ− Œ− = œ− Œ− > Œ ‰ œ œ œ Œ ‰ αœ œ œ Œ ‰ αœ œ œ ˙− œ œ œ œ œ ˙− œ œ œ œ œ ˙− ˙− œ œ œ œ œ ˙− œ œ œ œ œ ˙− Ι œ œ Ιœ αœ œ œ œ œ œ œ œ ∀œ œ ∀œ œ ∀œ œ œ V. œ œ œ œ Ι Ι Ι Ι % Œ ‰ ‰ = ι œ =œ œ œ œ œ =œ œ œ œ œ αœ œ− Œ ‰ œ ∀œ œ œ œ œ œ œ œ œ œ œ œ % αœ αœ œ− ∀œ œ œ ∀œœ œœ œœ œœ œœ ∀œœ œœ œœ œœ œœ P. − Ι Ι œ Œ− Œ ‰ œ ∀œ µœ œ− œ− > œ− œ− œ− œ− œ œ œ œ œ ˙− œ− œ œ− œ œ œ œ œ ˙− œ− − Ι

89 III œ œ œ ∀œ œ œ œ œ œ œ œ V. ‹œ ∀œœ ∀œ ∀œ œ ∀œ ∀œ ∀œ œ œ œ ∀œ œ % Ι Ι Ι Ι Ι

œ =œ œ œ œ œ =œ œ œ œ œ] % ∀œœ œœ œœœœœœ ∀œœ œœ œœœœœœ ∀œœ ‰ Œ− ∑ ∑ P. Ι Ι œ− > œ− œ− œ− œ− œ− ‰ Œ− ∑ ∑ œ− œ œ − œ = =œ ∀=œ ∀=œ œ A M ∀œ =œ œ V. œ ∀œ œ ∀œ Ι Ι Ι ‰‰ Œ ‰ ∑ ∑ % . = œ− œ ∀œ œ ] œ− œ− = = œ= œ ∀=œ œ œ œ − ∀œ− œ œ œ œœ∀−œ œ œ ∀œ œ œ = = œ=∀œ œ % ∑ Œ ‰ œ œ œ− œ œ œ−œ œ œœ∀œ . ‰ Ι ‰ œ œ œ− œ P. ε ƒ œ œ œ− √ ι ι ι ] ι > ∑ Œ ‰ œ− ι œ ∀œ œ œ ∀œ ∀œ ι œ ∀œ − œ œ œ ∀œ ∀œ œ œ œ œ œ œ ∀œ œ = = = œ œ œ ∀œ

V. = = ∑ œ œ− œ œ œ œ œ œ % œ œ œ œ œ œ œ œ− œ œ œ œ = ο = œ ι % ∀œ œ œ œ œ ‰ Œ− ∑ œ ‰ œ ‰ œ ‰ αœœ ‰ œ ∀œ œ œ œ œ œ ∀œœ µ œ P. œ = =ι = =ι ο ‰ œ ‰ œ ‰ ι ι > œ ∀œ ∀œ œ œ ∀œœ αœœ œ œ œ œœ œ œ œ œ œ œ αœ œ œ œ œ œ œ œ œ œ αœ œ œ ∀œ ∀œ œ œ œ œ œ œ œ œ Ι œ œ œ Ι œ αœ œ œ œ œ œ αœ

90 III

V. αœ œ œ =œ œ αœ αœ œ œ œ œ− % œ œ œ œ− αœ œ œ œ œ

= œ α œ α=œ % ∑ ‰ ‰ œ ‰ αœ ‰ œœ ‰α œ ‰ αœ αœœ αœ . œ P. œœ α œœ = = œ ‰ αœ ‰ ι ι ι > αœ œ œœαœ œ œ œ αœ αœ œ œ αœ œ œ œ αœ αœ œ œ œ œ œ œ œ œ œ Ι œαœ œ œ œ αœ αœ œ œ αœ œ œ œ αœ αœ αœ = œ αœ αœ = œ αœ V. œ αœ =œ œ αœ œ αœ =œ œ αœ αœ αœ αœ αœ αœ αœ % œ œ

= = αœ α=œ αœ α=œ αœ αœ αœ αœ α œ αα œ α œ αα œ % œ ‰α œ ‰ œ ‰α œ ‰ α œ ‰ αœ ‰ α œ ‰ αœ ‰ P. ι = = = = αœ αœ αœ αœ αœ αœ > œ œ œ αœ αœ αœ œ œ œ αœ αœ αœ αœ αœ αœ αœ œ œ αœ αœ αœ αœ αœ αœ αœ αœ αœ αœ œ αœ αœ αœ Ι œ αœ αœ Ι αœ Ι ∀œ œ œ œ ∀œ œ œ œ œ V. œ ∀œ œ ∀œ œ− œ œ œ ∀œ ∀œ œ œ œ œ ∀œ‹œ œ œ œ œ % Ι ƒ π =œ =œ ∀œ − ∀œ œ ∀œ œ œ ∀œ− ∀œ− œ− ∀œ− œ− % ∀ œ ‰ œ ‰ ∀ œ ‰ œ ‰ ∀œ ‰ œ− ∀ œ− ∀œ− œ− ∀œ− P. π ƒ αœ− œ αœ ∀œ =œ œ œ ∀œ =œ œ œ œ − − œ− œ− > ∀œ ∀œ ∀œ ∀œ ‰ ∀œ Ι œ œ œ ∀œ Ι œ œ œ œ

91 III

œ œ œ œ œ V. ∀œ ‹œ œ œ œ− œ œ œ ∀œ ∀œ œ œ œ œ ∀œ‹œ œ œ œ œ ∀œ ‹œ œ œ % Ι Ρœ œ œ ο ∀œ− œ− − œ− ∀œ− œ− ∀œ− œ− ∀ œ− ∀œ− œ œ œ ∀œ− ∀œ− ∀œ− œ− ∀œ− ∀ œ− ∀œ− % œ− ∀∀œ− œ− ∀œ− œ− ∀œ− œ P. ο Ρ αœ− αœ− œ− œ− αœ− œ− œ− αœ− œ− > œ− αœ− œ− αœ− œ− − − œ− œ αœ œ− œ V. ∀œ ∀œ œ = − ∀œ œ ∀œ œ − ι % ‰ Œ ‰ Œ ∀œ ∀œ ∀œ œ œ ∀œ œ ∀œ ∀œ ∀œ œ εœ œ œ œ œ ρε˙ψ− œ ρεψ œ œ œ œ œ ˙− œ ι ρεψ ι % Ι −

} œ œ œ œ ˙ œ œ œ œ œ

P. }

ε } ρεψ œ œ œ œ ∀œ œ œ ∀œ } −

} ∀˙− ∀œ Ι } − œ − > ∀∀ ˙− œ ‰ Œ = ‰ œ ‰ Œ− œ œ œ œ œ œ ∀˙− œ œ− œ Ι ‰ Œ− ∀ œ˙− œ œ œ œ œ œ− Ι = ∀=œ ∀=œ œ− œ œ œ =œ =œ œ œ œ œ œ œ V. œ œ ∀œ ∀œ ∀œ œ ∀œ ∀œ œ œ œ Ι Ι % Ι . ƒ ι =ι = = = œ œ œ œ œ œ œ œ œ œ œ œ− œ− % ι œ œ œœ− œœ− œ− œ œ œ œ œ œ œ œ œ œ œ . œ œ œ œ œ − − œ− P. œ− œ− ƒœ œ− > œ− œ− œ− œ− αœ− αœ− αœ− ˙− œ− œ− αœ œ− ˙− − αœ− αœ− œ− ˙−

92 III

T œ− œ V. œ œ œ œ œ % Ι œ αœ œ ‰ Œ− ∑ ∑ ∑ ∑ T = = = = œ œ œ œ œ œ ‰ Œ− % œ œ œ œ− œ− ∀œœ− œ− P. œ− − − œ− œ− ˙− ˙− ˙− œ ο ο αœ− œ œ œ = = = ‰ ι > œ œ œ œ− œ− − œ− œ− œ− ˙œ− − œ− ˙œ− − œ− œ œ αœ œ œ œ œ− ˙− ˙− ˙− ˙− αœ = =

V. ∑ ∑ ∑ % − ι ∀œ− œ− œ œ αœ ∀œ− œ−

% ∑ ∑ ∑ Œ ‰ œ− P. œ− ∀œ− œ œ αœ œ− > ∀œ− ∀œœ− αœ ∀œ− œ− ∀œ− œœ− αœ ∀œ− œ− ∀œ− œœ− αœ œ− œ− œ− Ι œ− œ− œ− Ι œ− œ− œ− Ι

2 2 V. % − œ− œ œ − Œ ι αœ œ ˙− œ. œ ∀œ œ œ− ∀œ Ι

% ι ι ι œ œ− œ ∀œ œ œ P. ∀œ œ œ αœ œ− œ αœ αœ− ∀œ− œ− ∀œ > ∀œ− œ− ∀œ− œœ− αœ ∀œ− œ− ∀œ− œœ− αœ ∀œ− œ− − œ− œ− Ι − œ− œ− Ι − œ−

93 III

4 = V. αœ œ− œ− αœ− œ− œ œ œ œ αœ− œ− œ ‰ œ œ œ Ι % ∀œœ∀œ

ι % œ œ œ œ œ− αœ− P. œ αœ− œ− œ− αœ− œ− œ œ œ− œ ∀œ œ ˙− œ−∀œ œ αœ > œ− ∀œ− œ− œ− ∀œ− œ− ι ∀œ− œ αœ œ− œ ∀œ− œ αœ œ− œ œ− œ αœ ∀ œ− Ι − œ− Ι − œ− œ αœ = = α=œ œ αœ œ œ αœ− œ œ œ αœ− V. œ œ œ − ∀œ œ œ œ œ œ αœ Ι Ι % Ι Ι = = ι ι ι ι αœ− œ œ œ œ ααœ− µœ œ œ % αœ œ œ− œ ι œ αœ œ œ œ− œ ∀œ αœ œ œ− α œ P. œ œ œ αœ œ . − ∀œ ε > ι ι ι œ− œ− œ αœ œ− œ− œ œ œ œ œ œ œ œ œ− œ œ œ œ œ œ− œ− œ− αœ œ− œ− œ œ œ œ œ œ œ œ =− œ ∀œ ˙− ˙− œ œ œ œ αœ œ œ œ œ ‰αœ œ œ V. Ι % ? ? ε ∀œ œ œ αœ œ œ ααœ− µœ œ œ ααœ œ ααœ œ œ œ œ œ ααœ œ œ œ ααœ− Œ− % αœ− α œ αœ ∀œ œ œ Ι œ Ι œαœ œ αœ− P. − Ι Ι ε > œ− œ− œ œ œ ι œ œ œ œ− œ− Œ− œ œ œ œ αœ œ− œ− œ− œ− œ œ œ œ œ œ œ œ œ œ αœ œ− œ− œ−

94 III

αœ V. œ œ , , , ι ι ι ι % ∀œ œαœ œ œ œ œ œ œ œ œ αœ αœ œ œ αœ œ œ œ − ∀œ ∀œ αœ αœ Ψ œ− αœ− α˙− ∀œ− αα œ− % ˙− ˙− œ− α α˙− α αœ− P. α˙− ∀˙− ∀œ− α ˙− α œ− Ψ Ψ Ψ ˙ ˙ α˙− ˙− > ∀˙− − − ˙− ˙− ˙− ˙− ˙− ˙− ˙− ˙− P M V. % œ− αœ œ œ− ι αœ αœ œ− œ− œ− œ œ− ∀œ œ œ œ− ο P M œ =œ œ =œ αœ œ œ αœ œ œ œ− % Œ ‰ œ Œ ‰ œαœ Œ ‰ œ Œ ‰ œ αœ αœ αœ− œ œ P. = = α˙− ο ˙ − α˙− ˙ − ι ˙− α ˙˙− ˙− α˙˙− αœ > Ψ − ε − œ œ œ− œ− œ− œ− œ− œ− œ− œ− œ œ œ œ œ œ œ œ œ œ − − − − − − − − Ι V. ‰ Œ− ∑ ∑ ∑ ∑ % œ ι œ œ− œ− α˙œ− œ œ œ αα˙− αα˙œ− œ œ % œαœ αœ œ œαœ œ− − œ− P. αœ ι œ œ œ αœ αœ αœαœ αœ αœ > œ œ œ œ œ œ œ œ œ œ œ œ

95 III

V. % ˙− ι ‰ œ− œ ι œ− œ œ œ− αœ− œ œ œ œ œ ααœ˙− œ− ααœ− αœ ι αœ ι α ˙− œ− œ− œ œ αœ− œ− œ− œ αœ− œ− αœ− œ αœ œ ααœ˙− αœœ− œ ααœ˙− % œαœ œ− œ− œ− P. αœ œ αœ αœ αœ αœ œ αœ œ > œ œ Œ− œ œ œ œ αœ œ œ œ œ œ œ αœαœ αœαœ œ

V. œ œ œ − − ι % ‰ 2 2 ∑ Œ ‰ αœ œ . œ αœ ι √ − − αœ− œ œ αœ− œ− α˙− α˙œ−− œ α ˙− œ ααœ− œ− % œ− α ˙œ−− œ− αœ− œ P. αœ] − ˙− œ αœ > αœ αœ > Œ− œ % œ œ œ œ œ % œ αœ œ œ αœ œ αœ αœ

V. ∀œ αœ œ ι œ œ ι % αœ œ αœ œ œ œ ˙− ‰ 2 2 œ Ι Ι Ι ∀œ− œ . ∋√(− œ− − ] αœ− αœ œ œ− œ− œ œ αœ œ− ˙− = œ− αœ αœ− œ− œ− œ αœ ∀œ− œ− ∀˙− % αœ œ− œ− αœ− P. Ι Ι ∀œ− œ− œ œ œ œ > αœ αœ αœ œ œ > œ œ œ œ œ ‰ œ œ ∀œ % ∑ % αœαœ œ œ αœ

96 III

αœ− αœ− V. αœ œ− αœ − − œ αœ αœ− µœ− ∑ % Ι ο = − œ− œ− − − α˙− ∀˙œ− œ− ˙œ−− − % ααœ˙− œ− ααœ˙− ˙− œ P. œ− α˙− ο αœ µœ œ ∀œ œ œ œ > αœ œ αœαœ œ œ œ œ ∀œ œ œ œ αœ ‰ œ ‰ αœ ‰ œ ‰ αœ œ œ αœ− œ− αœ− œ αœ V. Ι % ∑ ∑ ∑ œ− œ− α˙− œ− ι œ ∀œ α˙œ− œ− α ˙− œ− ∀œ œ ˙− − − − α˙− αœ % αœ ∀ œ− œ˙− − ∀œ− αœαœ αœαœ P. ε œ œ œ œ > αœ œ œ œ > αœαœ αœαœ ∀œ ‰ œ ‰ % αœ œ œ αœ Ι αœ αœ œ œ αœ ∀œ ∀œ œ− œ− ∀=œ− œ− œ− œ− œ− œ− αœ αœ V. Ι Ι % , , ∑ αœ αœ αœ− % αœαœ œ œ αα˙œ− P. ∀œ αœ αœ− αœ− αœ αœ αœ > œ œ αœ œ œ œ œ œ œ αœ œ œ αœ Ι αœ αœ αœ œ œ œ αœ

97 III

œ− . V. αœ− œ− œ− − œ − œ œ % ∀œ− œ− œ− αœ Ι , , , , , , − − ˙− œ− œ− œ− αœ− αœ−œ µœ−œ œ αœœ∀œ œ œ αα˙− % ˙ αœ− œµœ− œ œ− ∀œ− ˙− œ− œ− P. œ− αœ− œ œ œ− ∀œ− αœαœαœ œ œ αœ > αœ > αœ œ œ œ œ % œ œ œ αœ œ œ αœ œ œ αœ

αœ− œ V. αœ− αœ , , αœ αœ− − αœ œ − αœ œ % Ι αœ œ− œ αœ− αœ− αœ− αœ− œ œ αœ− αœ − œ œ αœ− − œ− ααœœ− αœ− % αœ Ι œ− αœ− αœ αœ P. αœ−

αœ > αœ αœ > αœ > œ œ % œ œ œ œ œ % Œ ‰ œ œ œ αœ αœ αœ αœ œ αœ αœ œ− αœ− œ− œ V. αœ− αœ œ αœ− % ‰ Œ− αœ− œ− Ι = = œ− œ− ο α αœ− œ− œ αœ− œ− α œ− œ− ∑ œ− œ− αœ− αœ % œ− αœαœ Ι P. αœ− œ− ε ο αœ αœ αœαœ αœαœ αœ∫œ > œ œ Ι ∑ αœ αœ αœ œ αœ αœ αœαœ αœ αœ αœ αœ

98 III

αœ− αœ V. ∫œ αœ− − Ι œ αœ− œ αœ œ− % Ι œ− œ− − ∫œ− ααœ− αœ œ œ− αœ− œ− αœ− œ− αœ− αœ œ œ− œ− % œ− αœ− œ− Œ− P. αœ œ ∀œ ∀œ ∫œ αœ αœ αœ αœ αœ αœ œ > αœ αœ œ œ αœ œ % αœ αœ αœ αœ αœ αœ

V. œ œ− − œ− œ % ∑ ∑ ∑ œ Ι √=œ− ∀œ− =œ− αœ− œ− αœ− − œ ∀œ− α œ− œ− α œ− œ µœ αα˙œ− œ− ˙− % ∀ œ− α œ œ− . œ− ˙− α˙− P. Ι ο αœ œ œ ∀œ ∀=œ− = αœ œαœ œ αœ œ œ œ œ ∀œ− ∀œ− > αœ αœ œ œ œ αœ % − ∀ œ− αœ αœ œ αœ œ

V. œ− œ− œ− œ αœ− œ− œ ‰ Œ− ∀œ œ ∀œ œ ‰ % . Ι Ι ι œ− œ− œ− ι − œ ∀œ œ œ− œ− œ− ∀œ œ ˙œ− œ− ˙− ∀œ ∀œ œ−∀œ œ % αœ œ− α˙− ˙− α˙−. P. œ αœ ∀œ œ œ ∀œ œ ∀œ œ œ œ œ ∀œ œ ∀œ ∀œ œ œ > œαœ αœ œ αœ œ αœ œ œ ∀œ œ ∀œ

99 III œ œ œ ∀œ ∀œ œ œ αœ œ œ œ αœ œ œ V. Ι ‹œ ∀œ Ι Ι Ι % ‰ ‰ ι ι ι αœ œ œ αœ ι œ œ œ œ œ ∀œ œ− αα œ œ œ œ α œ− œ αœ− œ œ œ ∀œ ∀œ− œ− œ α œ− œ− ∀œ œ % œ− P. αœ œ œ œ ∀œ ∀œ œ œ αœ αœ αœ αœ œ œ > αœ µœ αœ µœ αœ œ œ œ ∀œ αœ ‰

œ œ− œ œ− œ œ− œ− œ œ− V. œ œ œ− œ œ œ− œ œ Ι % Œ ‰ Ι Ι Ι Œ ‰ ι œ œ œ ƒ œ œ œ ∀œ œ œ ∀œ œ œ ∀œœ− œ œ− œ œ œ œ ∀œ œ ∀œ œ œ ∀œ œ ∀œ œ œ ∀œ œ ∀œ œ ∀œ œ− œ ∀œ ∀œ œ Ι ∀œ œ Ι ∀œ œ œ− œ ∀œ œ œ− œ ∀œ œ % œ− œ− P. ƒ œ− œ− œ− œ œ œ œ œ œ œ− œ− > œ ‰ œ ∀œ œ ∀œ œ ∀œ− œ− αœ αœ αœ œ− œ− ∀œ− œ−

− œ− œ œ− V. ∀œ ‹œ ∀œ œ ι ι Œ ‰ Ι Ι ∀œ ∀œ œ œ œ % Ι Ι‹œ ∀œ Ι ‹œ ∀œ =œ− =œ− œ =œ =œ =œ =œ =œ œ− œ ∀œ œ œ− œ ∀œ œ œ œ œ œ œ œ œ œ œ ∀œ œ œ œ œ ∀œœ− œ ∀œ œ œ− œ ∀œ œ ∀œœ œ œ œ œ œ œ œ ∀œœ ∀œ œ œ œ œ % Ι Ι Ι Ι P. . ======> =œ− ∀œ− œ− =œ− ∀œ− œ− œ− œ œ− œ œ− œ− œ− − ∀œ− œ− œ− − ∀œ− œ− œ− œ−

100 III

≥ ≥ ι ≥ ≥ ι V. œ− − œ œ œ œ− œ− Œ ‰ ∀œ œ œ− ∀œ Œ ‰ ∀œ œ % œ Ι ∀œ œ− œ œ− œ Ι œ− œ− œ ∀œ− œ œ− œ = = = ∀=œ ƒœ− œ ∀œ œ Ι ο œ œ œ œ ∀œ œ œ ∀œ œ œ ∀œœ œ œ ∀œ œ œ− œ ∀œ œ œ œ œ− œ ∀œ œ œ ι œ ∀œ œ œ œ œ− œ ∀œ œ œ œ % Ι ∀œ œ œ P. ∀œ œ œ œ ƒ ο = = √ ι ι ι ι ι ∀œ ι ι ι ∀œ > œ œ ∀œ œ œ ∀œ œ ∀œ œ œ ∀œ − αœ− œ œ œ ∀œ ∀œ œ œ œ ∀œ ∀œ œ− αœ− œ œ ∀œ œ œ œ ∀œ œ œ ι œ ι ι œ αœ œ √ι œ œ œ ∀œ œ œ V. œ αœ œ œ œ œ œ− œ Ι œ Ι œ œ œ œ œ œ œ αœ− œ− % − − − − œ− œ− = = œ− œ œ αœ = œ œ œ œ œ− œ % œ œ œ œ− œœ− œ œ− œ αœ œ œ œ œ œ œ œ− œ− œ− œ− P. œ œ œ œ− œ− œ− − œ œ− > œ ‰ œ− œ− œ− œ ‰ œ− œ− œ− ι œ œ− œ− œ− œ œ− œ− œ− αœ ι œ− − œ− − αœ œ œ œ œ ι − αœ œ œ αœ œ V. œ œ œ ∀œ− œ œ œ ∀œ Œ ‰ αœ− αœ− œ− Œ ‰ Ι Ι Ι Ι Ι % œ− œ− œ− ο œ œ œ œ œ − ι % œ œ œ œ œ œ αœ œ œ œ œ œ œαœ œ œ œ− œ œ œ œ œ œ œ− œ− œ œ− P. Ι ο αœ œ ∀œ− αœ− αœ− ι ι ι œ ∀œ œ > ι ι œ œ œ œ œ ‰ œ− œ− − œ œ ∀œ œ αœ œ œ ∀œ œ αœ œ− αœ αœ œ œ œ Ι œ− αœ−

101 III

√αœ œ αœ V. œ ∀œ œ ∀œ œ Ι Ι œ ∀œ œ œ œ ∀œ œ œ œ œ % Ι Ι œ Ι ∀œ œααœ αœ œ œ œ œ œ− ∀œ œ œ œ− ∀œ ∀œ œ % ∀αœ− œ ∀œ− ∀ œ− œ œ œ œ œ œ P. ∀œ œ œ ∀œ œ ο = ∀œ− > ∀œ− ∀œ− œ− œ− ∀œ œ œ− ∀œ− œ− ∀œ− ‹œ ∀œ− œ− œ− ∀œ ‹œ œ œ− ∀œ−

œ œ œ œ αœ œ V. ∀œ œ ∀œ œ œ ∀œ ∀œ ∀œ œ Ι % Ι ∀œ œ œ Ι ∀œ Ι Ι

∀œ ∀œ œ œ œ ∀ œ œ ∀ œ œ œ % ∀œ œ ∀œ ∀∀œœ− ∀œœ− ∀∀œœ− ∀œœ− P. ∀ œ œ œ ∀ œ œ œ − œ − œ − œ − = œ− > œ ∀œ œ œ− œ− œ− œ œ œ œ œ œ œ ∀œ œ œ− œ− œ œ œ œ− œ œ œ œ− œ− œ− ∀˙− œ œ œ œ œ αœ œ ∀œ œ ∀œ œ œ V. ∀œ ∀œ ∀œ œ Ι % Ι ρεψ ∀œ ∀œ œ ∀œ ι œ − − ∀œ œ ∀œ ∀œ % ∀∀œœ œœ œœ œ− ∀∀œœ œœ œœ ∀œœ− œ− œ œ œ œ P. œ œ œ œ − œ œ œ œ − ∀∀œ− ∀∀œ œ œ œ ρεψ > ι > œ œ œ œ œ œ œ % œ œ œ œ œ− œ− œ œ œ œ− œ œ œ œ− œ ∀∀œ œ œ œ ∀∀œ− ∀œ− œ− œ−

102 III 722 ∀˙ ∀œ œ œ œ œ − œ ∀œ œ ∀œ V. ∀œ œ œ œ ∀œ % ι∀œ œ ρεψ ƒ œ . œ ∀œ œ ∀œ œ œ− œ = ∀œ œ œ ∀œ œ ι œ ‰ ∀œ− œ ‰ œ % ∀œ ∀œ œ œ œ œ ∀œ œ œ− P. œœ Ι œœ œœ œœ œœ ∀œ − − ∀œ− ρεψ ε = > > % ι œ− ∀œ ‰ Œ ‰ ∀œ− ∀œ œ œ œ ∀œ − − œ œœ œœ œœ œœ œœ− œ ∀œ ∀œ− αœœ= √ =œ =œ ∀=œ ∀=œ œ ∀œ œ αœ œ œ œ= œ œ ∀œ œ V. œ ∀œ œ ∀œ œ œ ∀œ ∀œ Ι % ι ∀œ αœ œ ‰ . αœ œ Ι = = , œ− ƒ = αœ− œ = = œ− , ∀œ− ∀œ ∀ œ− œ − − ∀œ− œ− œœ− − ∀œ œ− % ∀αœ ‰ ‰ ∀αœ− œ− œ− ∀œ− œ ∀ œ ‰ ∀œœ− − P. œ œ− œ− œ− ∀œ− œ− −. ∀œ ƒ = = > œ− œ œ œ ‰ Œ ‰ œ− − œ ‰ œ œ− œ− œ− œ ∀œ œ ∀œ V. œ ∀œ œ œ œ œ œ œ ∀œ œ œ œ ∀œ œ œ ‰ Œ− œ ‰ Œ− % ∀œ œ ∀œ 4 ∀œ œ œ 4 = = = œ− ∀œ− œ=− œ− = = ∀œ ∀œ− œ− ∀ œ− œ− œ− ∀œ ‰ œ− ∀œ− œ− œ− ∀œ− ∀œ ‰ Œ− ∀œ ‰ % œœ− − œ− œ− œ− œ œ− œ− œ− œ− ∀ œ− ∀ œ P. ∀œ− ∀œ− œ− ∀œ− µ œ− ∀œ = = ] ] œ > œ ‰ œ− œ− œ ‰ Œ− œ ‰ Œ− ˙− œ œ− œ− œ− œ ˙− œ−

103 III

V. % ι ‰ ‰ Œ− − − ˙ ˙ ∀˙œ− ∀œ ˙− œ ∀œ ˙− œ ∀œ % ∀˙− œ P. G˙− ∀œ . > œ œ ∑ ∑ œ œ Pœ.

G

104 CATALOGUE OF VARIANTS

First Movement m50 Vln: B natural a mistake; B-flat correct m84 Pn: F# quarter note stem is not original m93 Vln: There is a bar line mistakenly written after two beats. The measure should have a half-rest with two quarter notes. m102 – 104 Vln & Pn: Pasted on, autograph correction m178 – 179 Pn: Measure repeat not autograph

Second Movement

There are no measure numbers throughout the score notated in the second movement. m76 Pn: There is no stem on the G#/E-natural chord in the right hand m112 Pn: The accidental indicating C-flat on the first beat of the right hand is not autograph

Third Movement

The autograph numbering of measures is erroneously displaced by one measure beginning at measure 195 through the end of the movement. What is indicated by the composer to be measure 195 is actually measure 196. m288 Pn: E-natural to G-flat appear to be crossed out in the left hand m327 – 328 Vln: It is not clear whether the composer intended the A to make double-stops with the above melodic line m331 Vln: It is unclear if the composer intended D to be the bottom note of the chord

105 REFERENCE LIST

Abelardo, Nicanor, Chicago, to Sixta Abelardo, Manila, 29 July 1931. Manuscript in the hand of Nicanor Abelardo. Personal collection of Cecille Abelardo Quizon, Quezon City.

Baes, Jonas. "Composers in the Philippines: Counterstreams in a Post-Colonial Epoch," in Asian Composers in the 20th Century. Tokyo: The Japan Federation of Composers, 2002.

Banas, Reymundo Castillo. The Music and Theatre of the Filipino People. Quezon City: Manlapaz Publishing Co., 1969.

Bernardo, Fernando A. Silent Storms: Inspiring Lives of 101 Great Filipinos. Pasig City: Anvil Publishing, 2000.

Constantino, Renato. A History of the Philippines: From Spanish Colonization to the Second World War. New York: Monthly Review Press, 1975.

Castro, Christi-Anne Salazar. “Music, Politics and the Nation at the Cultural Center of the Philippines.” Ph.D. diss., University of California – Los Angeles, 2001.

Epistola, Ernesto V. Nicanor Abelardo: The Man and the Artist. Philippines: Rex Bookstore, 1996.

Galang, Zoilo, M., ed. Encyclopedia of the Philippines. Vol. 7: Art, National Self-Expression in Music by Antonio Molina. Manila: Exequiel Floro, 1953.

German, Alfredo M. Ang Buhay at Musika ni Maestro Abelardo. Bulacan: Bulacan Cultural Arts and Historical Foundation, 1993.

Guillermo, Artemio R. Historical Dictionary of the Philippines. Lanham, Md.: Scarecrow Press, 1997

Hamilton-Paterson, James. America’s Boy: A Century of Colonialism in the Philippines. New York: Henry Hold and Co., 1998.

Hila, Antonio C. Musika: An Essay on Philippine Ethnic Music. Manila: Sentrong Pangkultura Ng Pilipinas, 1992.

Irving, D.R.M. Colonial Counterpoint : Music in Early Modern Manila. USA: Oxford University Press, 2010

Japan Federation of Composers Inc., ed. Asian Composers in the 20th Century. Tokyo: Nihon Sakkyokuka Kyogikai, 2002.

Mabini, Apolinario. “Apolonario Mabini on the Failure of the Filipino Revolution.” American Historical Review, 11/4 (1906): 843–861.

106 Manuel, E. Arsenio. Francisco Santiago: Composer and Piano Virtuoso. Quezon City: Valerio Publishing House, 1997.

Mirano, Elena Rivera. Musika: An Essay on the Spanish Influence on Philippine Music. Manila: Sentrong Pangkukultura Ng Philipinas, 1992.

Mirano, Elena Rivera, ed. The Life Works of Marcelo Adonay. Quezon City: The University of the Philippines Press, 2009.

Mojares, Resil B. “The Formation of Filipino Nationality Under U.S. Colonial Rule.” Philippine Quarterly of Culture & Society 36 (2006): 11 – 32.

Pfeiffer, William. Music in the Philippines: Indigenous, Folk, Modern. Dumaguete City: Silliman Music Foundation Co., 1975.

Reyes, Pedrito, Mercedes Grau-Santamaria, H. Otley Beyer, and Jamie C. De Veyra. “Nicanor Abelardo,” in Pictorial History of the Philippines. Manila: Capitol Publishing House, 1953.

Santa Ana, Sr. Maria Anunciata, Dean of College of Music and Performing Arts, St. Paul University Manila. Interview by author, 17 July 2012, Manila.

Santa Maria, Felixberto C. The Philippines in Song and Ballad. Manila: Cacho Hermanos, Inc., 1976.

Santiago, Franciso. The Development of Music in the Philippine Islands. Quezon City: UP Press, 1937.

Santos, Ramon. Musika: An Essay on the American Colonial and Contemporary Traditions in Philippine Music. Manila: Sentrong Pangkultura Ng Pilipinas, 1994.

______. Tunugan: Four Essays on Filipino Music. Diliman: The University of the Philippines Press, 2005.

Zaide, Gregorio F. Great Filipinos in History, an epic of Filipino greatness in war and peace. Manila: Verde Bookstore, 1970.

107 108