This opening lecture introduces themes, concepts, and terminology that will be followed and used throughout the series, including: concert music, classical music, popular music, and Western music. We will see how music is a “mirror” of historical change on various levels. The course will focus on representative works in relation to their historical contexts and will endeavor to build listening skills and a musical vocabulary designed to increase musical knowledge and appreciation. Using Ludwig van Beethoven as an example, the “composer” is discussed, not as idiot savant or Godhead, but as a human being who has chosen music as the conduit for the expression of his or her thoughts, feelings, and worldview.
This lecture introduces the ancient world as a 4,000-year period of extraordinary cultural richness and variety. From this long ancient era, only 40 or so fragments of music have survived. In this lecture, we discuss the cyclical, rather than linear, nature of art and music. The lecture focuses on the role of music in the ancient Greek and Roman world. We will hear a stasimon chorus by Euripides, and we will compare a 1st-century-C.E. drinking song by Seikilos with one written 1,700 years later by Giuseppe Verdi. The lecture concludes with a brief examination of the role of music in the early Christian Church.
This lecture focuses on the changing role of music in the medieval world. Roman Catholic liturgical plainchant dominated the music of the so-called Dark Ages. With the gradual return of civilization to Europe during the High Middle Ages also came the development of composed polyphony, called organum, including a type of organum known as florid organum. Florid organum is exemplified by the music of Leonin, a composer of the Ars Antiqua school. The violent disruptions of the 14th century—the so-called Babylonian Captivity, the Great Schism, the Black Death, and the Hundred Years’ War—led to a rise of secularism, the cultural impact of which could be seen in a new vernacular literature and the beginning of the Humanism movement. The new music, known as Ars Nova, was characterized by isorhythm; Guillaume de Machaut was the most representative composer of this new style.
In the 15th and 16th centuries, the rediscovery of ancient Greek and Roman culture⎯Humanism⎯had a tremendous impact on European cultural, intellectual, and political history. The ancient Greek ideal of music as a power that can change nature and move souls profoundly influenced composers of the Renaissance. We will examine that influence in theory and practice through the ideas of the ancient Greek mathematician Pythagoras, the concepts of musica reservata and word painting, and the evolution of a system of tonal harmony. The music of the mid-Renaissance is represented by the French composer Josquin Desprez.
The musical setting of the High Mass of the Roman Catholic Church became the most important compositional genre of the Renaissance. Composers confined themselves to five parts of the Mass, which itself comprised more than 20 different parts. These five parts are from what is known as the Ordinary, the permanent content of the Mass that is celebrated every day. Three types of Renaissance masses were composed: the cantus firmus mass, the paraphrase mass, and the imitation mass. Josquin Desprez was the master of the paraphrase mass. His Ave maris stella Mass provides an example of Renaissance polyphony. The Protestant Reformation, the Catholic Counter-Reformation, and the Council of Trent had a profound impact on the nature of Catholic liturgical music in general and the Mass specifically. Palestrina’s Pope Marcellus Mass epitomizes the new compositional style that emerged from those developments.
The madrigal was the most important and most experimental musical genre of secular music in the late Renaissance Era. As unaccompanied vocal works, based on “elevated” poetry, madrigals took the Renaissance infatuation with “the word” to the next level. Through the cultivation of word painting, madrigalists illustrated and heightened the meaning of the words of their madrigals, often employing extremely venturesome harmonic progressions. Madrigals by Cipriano de Rore, Carlo Gesualdi, and Thomas Weelkes are examined in order to observe the progressive development of the genre from the mid- 16th century to the very early 17th.
This lecture introduces the brilliant and exuberant Baroque Era. In a series of comparisons between Renaissance and Baroque music, this lecture differentiates between the measured elegance of Renaissance music and the often extravagant emotionalism of Baroque music. Special attention is paid to the scientific and investigative spirit of the Baroque and its impact on the arts of the era. The Baroque artistic duality of emotional extravagance and intellectual control is examined as a manifestation of the scientific and philosophical currents of the time. The lecture concludes with an examination of magnificence in Baroque art, using as a musical example the genre of French overture.
This lecture seeks to build listening skills and a descriptive vocabulary, and it will discuss some essential features of Baroque-era musical style. Music can be defined as “sound in time” or “time defined by sound.” We will acquire a vocabulary for addressing musical sound, defining and discussing discrete sound, frequency, pitch, melody, motive, theme, and tune. We review the musical textures of monophony, polyphony⎯imitative and non-imitative⎯and homophony. The explosion of instrumental technology and design during the Baroque Era gave rise to instrumental music for its own sake, which in turn, resulted in a systematized and codified tuning system, based on 12 different pitches. Thus, both functional harmony and the notation of meter were standardized during the Baroque Era.
In this lecture, we explore some of the essential differences between Italian music and German music, differences that first truly manifested themselves in the music of the Baroque Era. Musical nationalism involves much more than the incorporation of ethnic or ethnic-sounding elements. It evolves from a composer’s native language and his or her social and cultural background. We see that the Italian-based Roman Catholic Church’s emphasis on vocal music led to the cultivation of vocal music that was profoundly influenced by both the Latin and Italian languages. The Baroque Era was dominated by Italian music, although a distinctly national style of music began to evolve in Germany with the advent of the Protestant Reformation. A new emphasis on the German language in worship led to music that followed the idiosyncratic cadences of the German language, while the Lutheran view of all music as a spiritual act had a major impact on the development of German instrumental music.
This lecture examines fugue, arguably the single most representative musical procedure of the Baroque Era. Fugue is defined as a usually monothematic, polyphonic work in which a theme—or, properly, a subject—is examined, broken down, reassembled, and so on in as many different ways as possible. Drawing on fugues by Johann Sebastian Bach and George Frederick Handel, this lecture introduces and examines the three essential parts of a fugue: the exposition, subject restatements, and episodes. The lecture also seeks to define and distinguish the various tuning systems used up to and during the Baroque Era: just intonation, mean tone, and well-tempered tuning.
Opera evolved from the late Renaissance intermezzi/intermedi that developed concurrently with the madrigal. Inserted between the acts of stage plays, these sung interludes, which commented in the same way as Greek choruses on the progress of the play, had, by the late 16th century, become an important genre in their own right. Intermezzi, unlike madrigals, tended to utilize solo rather than group singing. Such solo singing was seen as more expressive and more capable of evoking emotional response than group singing, a view adopted by the members of the Florentine Camerata. Equally inspired by their perception of ancient Greek drama, the members of this group invented opera, rejecting polyphony and word painting in favor of solo singing that attempted to evoke the emotions behind the words rather than merely paint the meaning of the words themselves. Jacopo Peri’s invention of recitative made the invention of opera possible.
Jacopo Peri’s new stile rappresentativo (recitative) was markedly more expressive of emotion than the prevailing madrigal style. Early opera was based on recitative, which moves the dramatic action forward rather than allowing the singer to reflect on the action. Claudio Monteverdi’s recitative is the most dramatically expressive and melodically interesting ever written. His opera Orfeo is a magnificent synthesis of virtually every musical style and technique available during his time. The operatic aria evolved in the 1660s and soon became the focal point of opera, to the eventual debasement of recitative. The aria functions as a passage of reflection, to express feelings, and as a means of character development. The aria “Dido’s Lament” from Henry Purcell’s opera Dido and Aeneas is one of the great examples of operatic expressivity in the Baroque Era.
The two most important new genres to evolve in Baroque sacred music were the oratorio and Lutheran church cantata. The Baroque oratorio, marked by an exuberance not found in the Renaissance mass, incorporated elements of opera. Oratorio evolved in Italy as a substitute for opera, which was banned during Lent. From modest beginnings, as a musical setting of a biblical text, oratorio grew in popularity as an unstaged opera on a religious subject. In England, oratorio became enormously popular thanks to the creative power of George Frederick Handel, whose Messiah was, from the outset, one of the most popular pieces of music ever written.
Unlike oratorio, the Lutheran church cantata was part of a regular religious service (specifically, the Sunday service). It evolved as a musical commentary on a given week’s particular Bible reading, becoming known as the musical “sermon before the sermon.” This lecture examines the evolution of the Lutheran church cantata and its use of operatic elements. It concludes with a discussion of Johann Sebastian Bach’s Cantata no. 140, Wachet auf, ruft uns die Stimme.
This lecture introduces the vital concept of instrumental musical form—preordained processes that organize musical materials into recognizable structures without the presence of (or need for) words. Until the Baroque Era, almost all musical form was determined by the words being set to music. The development of instrumental music during the Baroque Era went hand-in-hand with the creation of musical structures that would render abstract instrumental music intelligible to its audiences. This lecture focuses on Baroque-era musical forms based on the process of variation: passacaglia, ground bass, and chaconne (or ciacona). We will revisit “Dido’s Lament” from Purcell’s Dido and Aeneas as an example of a passacaglia, and we will examine Bach’s magnificent Passacaglia in C Minor for Organ.
The distinction between chamber and orchestral music was not truly recognized until the late 17th century, when composers began to purposely write works for orchestra. Such works included the genre of the concerto, which, like most Baroque genres, grew out of the opera house. Opera was directly responsible for the evolution of overtures and dance suites and indirectly inspired the development of the concerto. This lecture looks at the three types of High Baroque concerti—orchestral or ripieno concerto, solo concerto, and concerto grosso. Also discussed is the terminology surrounding these orchestral genres. Finally, the concerto grosso is examined with special attention paid to the ritornello-form first movement of Johann Sebastian Bach’s concerto grosso, Brandenburg Concerto no. 5.
The dramatic difference between the music of the late Baroque Era and the new Classical Era is brought into high relief when we compare a fugue by J. S. Bach and a piano sonata by Beethoven. The difference is that between the objective and the subjective, between music about process and surface complexity, on the one hand, and vocal lyricism and studied simplicity, on the other. Given that music is a mirror, these dramatic musical differences were a product of societal change. The 18th century saw the evolution of Enlightenment Humanism, cosmopolitanism, the Enlightenment cultural doctrine of accessibility and naturalness, the rise of a new middle class with its Enlightenment-inspired attitude toward music, the growth of musical amateurism, and the emergence of musical Classicism.
The Enlightenment’s influence on musical style resulted in an emphasis on thematic and structural clarity and purity and expressive restraint. This new style became known as the Classical style. In this lecture, we compare the differences between Baroque and Classical music in their treatment of rhythm, thematic material, dynamics, and formal structures. We see how the new Classical focus on narrative (or linear) structure, as opposed to the cyclical structures of the Baroque Era, came to emphasize the function of the cadence, of which there are four basic types. Finally, we examine the geographical and social importance of the city of Vienna in the Classical style’s rise to its zenith.
This lecture initiates a discussion of Classical-era instrumental musical form that will continue through Lecture Twenty-Five. In this lecture, we examine theme and variations form, which represented an adaptation of Baroque-era variations procedure to the expressive and musical needs of the Classical Era. While maintaining much of the compositional rigor of the Baroque models, Classical-era theme and variations form utilizes a “tune” as its theme rather than a bass line. Wolfgang Mozart’s Variations on “Ah, vous dirai-je, maman” is used as an example of Classical-era theme and variations form.
The Baroque-era minuet and trio form is the antecedent of Classical-era minuet and trio form. Baroque French dance suites inspired the composition of an important type of instrumental music, which was almost invariably homophonic in texture and in binary form. Of all the various dances cultivated in this era, the minuet, thanks largely to Louis XIV, enjoyed the most widespread popularity. In pairing a first minuet with a second minuet, called a trio, the form took on a ternary, or three-part, A–B–A structure. Music by Bach, Corelli, and Lully illustrates the nature of Baroque dance form and the minuet and trio in particular.
Using Baroque-era minuet and trio form as a model, Classical-era composers of the 18th century extended the internal formal structure of minuet and trio to create movements appropriate to the multi-movement instrumental genres of the Classical Era. Mozart, in the minuet and trio from his Symphony in G Minor, K. 550, exploited the expressive potential of the minuet as an abstract compositional construct. The trio marks a stunning contrast with the minuet. A quite different example of a Classical-era minuet and trio is found in Joseph Haydn’s Symphony no. 88 in G Major.
Rondo form, based on the process of periodic thematic return, is the least formulaic of any of the Classical- era forms. The antecedent of rondo form is the medieval French rondeau. In a Classical-era rondo-form movement, the rondo theme itself is the central musical element, not the departures from that theme (the contrasting episodes), as is the case in so many Baroque-era ritornello movements. Rondos by Ludwig van Beethoven and Joseph Haydn are analyzed as examples of Classical-era rondo form.
To illustrate our analysis of sonata form in this lecture and the next, we turn to the fourth movement of Wolfgang Mozart’s Symphony in G Minor, K. 550. Mozart composed a prodigious number of masterworks during his short life, despite constant poor health and alongside an astoundingly full and active personal life. The principle of dramatic thematic contrast inherent in sonata form is nowhere more apparent than in the fourth movement of Mozart’s Symphony in G Minor, K. 550. The most complex of the Classical-era forms, sonata form allows for the introduction and development of two or more contrasting principal themes. Although technically a form evolved from Baroque-era binary dance form, spiritually, sonata form was inspired by dramatic procedures inherent in opera.
Sonata form is an instrumental manifestation of operatic procedure, with the character introductions, development, denouement, and curtain calls of the opera house corresponding to the exposition, development, recapitulation, and coda of sonata form. In this lecture, with reference to the uniquely dramatic fourth movement of Mozart’s Symphony in G Minor, K. 550, we will continue our examination of sonata form: the modulating bridge, the development section, and the recapitulation.
This lecture completes our analysis of sonata form. We see how the first movement of Haydn’s Symphony no. 88 in G Major and the sonata-form part of the overture to Mozart’s opera Don Giovanni are more typical of the Classical Era in their degree of thematic contrast than is Mozart’s Symphony in G Minor, K. 550 (discussed in the preceding two lectures). Haydn’s symphony affords us another insight into the humor and ingenuity of that master, while Mozart’s overture to Don Giovanni brilliantly evokes the two principal characters of the opera in its thematic material.
The typical Classical-era symphony has four movements, each with its own distinctive character. The Classical-era symphony grew out of Baroque-era opera and became tremendously popular with the rising middle class of the late 18th century. The accessible, tuneful style of music this middle class audience demanded crystallized in the music produced in Vienna during the last third of the 18th century. More than any other single composer, it was Joseph Haydn who standardized the Classical-era symphony. Haydn’s Symphony no. 92 is a brilliant example of his symphonic model.
The Classical-era solo concerto fit perfectly with the Enlightenment view of the individual (the concerto soloist) in collaboration with, or sometimes pitted against, the collective (the concerto orchestra). During the Baroque Era, the violin family was perfected and the piano was invented. These instruments became the beneficiaries of the concerto repertoire during the Classical Era. In this lecture, we explore double- exposition form, the adaptation of sonata form to the needs of the Classical-era solo concerto. The first movement of Mozart’s Piano Concerto no. 17 in G Major provides an illustration of double-exposition form.
The magnificent opera seria of the Baroque Era was, by the 1730s, increasingly perceived as being elitist and socially irrelevant. In France, Jean-Jacques Rousseau spearheaded the support of a new type of opera (opera buffa), which had emerged in Italy, as the ideal opera for the new Age of Enlightenment. Opera buffa was inspired by the Italian commedia dell’arte, with its more realistic plots, smaller casts, and more tuneful music that focused more on everyday people than on the upper class. Giovanni Battista Pergolesi’s opera La serva padrona of 1733 was embraced by Rousseau in the early 1750s as a model for the opera of the future.
Mozart’s achievements in the genre of opera are unsurpassed, and no composer was better at writing ensembles than Mozart. The operas that Mozart wrote with the librettist Lorenzo Da Ponte are his greatest, and they include Don Giovanni, based on the life of the infamous Casanova, whom Da Ponte knew personally. We look at ensembles from Don Giovanni as illustrations of Mozart’s prodigious ability to sustain dynamic dramatic continuity through the power of his music. We will see, as well, how the introduction to this opera’s overture presages the grim events of the final scene.
Haydn’s music reflects the Classical-era characteristics of balance, accessibility, tunefulness, rhythmic continuity, and artistic restraint. Beethoven’s music, on the other hand, is unrestrained, unpredictable, self- expressive, and self-referential. Beethoven’s music reflects the revolutionary times in which he lived, a time that saw the French Revolution and the rise of the self-made hero Napoleon Bonaparte. Beethoven’s music also manifests his own unique personality and experience, influenced to a large degree by the grimness of his childhood and his devastating hearing disability.
Beethoven’s works are traditionally categorized in four different compositional periods. His Symphony no. 5 falls into his so-called heroic period⎯1803–1815. This symphony exemplifies Beethoven’s artistic creed of self-expression and demonstrates his revolutionary approach to composition. His contextual use of form, his use of pervasive motivic development, his approach to music as an ongoing dramatic narrative, his use of rhythm as a narrative element divorced from pitch, and his continual pursuit of originality are all very much in evidence here.
The second movement of Beethoven’s Symphony no. 5, in double-variations form, allows Beethoven opportunities for thematic contrast in this symphony of contrasts. For his third movement, Beethoven employs a scherzo, a formal procedure abstracted from minuet and trio form. The scherzo, meaning “joke,” provides the turning point in the drama of this work, in which the brilliant mode of C major overcomes the C-minor mode that represents darkness and despair. The dance-like physicality of the scherzo paves the way for the triumphant, life-affirming fourth and final movement.
For many composers working in the 19th century, or the Romantic Era, expressive content came to shape form. Beethoven’s music both anticipated and inspired the self-referential and self-expressive approach to composition that many Romantic-era composers would adopt. Four main trends characterize Romantic-era art: the depiction of extreme emotional states, the cultivation of nationalism, the idealization of the wilder aspects of nature, and a fascination with the macabre and the supernatural. The Enlightenment’s celebration of individualism comes to flower in the Romantic art of the 19th century.
The paradox of the spontaneity and creative freedom of the composer at odds with the concept of preordained musical forms was recognized and dealt with in a variety of ways by Romantic composers. Some Romantic composers continued to use Classical-era forms and some used them contextually. Some abandoned them altogether, replacing them with new forms that included compositional miniatures. Two masters of this idiom were Franz Schubert, one of the greatest composers of lieder, and Frederic Chopin, whose music for solo piano is unique in the repertoire.
Program music allowed many Romantic composers to meet the challenge of creating musical structures that were both compatible with Romanticism’s need for expressive individuality and, at the same, provided a source of compositional cohesion that audiences could understand and follow. One type of program music, the program symphony, is exemplified by Hector Berlioz’s Symphonie fantastique of 1830. The essence of this unique work is the idée fixe (“fixed idea”), which Berlioz uses to provide abstract, structural coherence in this five-movement masterpiece.
Berlioz’s Symphonie fantastique features a unique theme, the so-called idée fixe, that represents the female protagonist of the story and lends thematic unity to the five movements of this sprawling work, even as it changes in character. Berlioz’s musical genius is manifest in his ability to portray psychodrama in the music and in his extraordinarily flexible and creative approach to musical form. The stunning originality and modernity of the Symphonie fantastique made it a model for the Romantic Era.
In contrast to French opera of the 19th century, which constituted a relatively isolated tradition, the Italian and German opera traditions were far more influential and internationally popular. Italian opera was a business venture and conservative in nature. Gioacchino Rossini, one of the great composers of Italian- language opera of the 19th century, was also a master of the bel canto style. This style emphasizes beauty of melody and voice and is exemplified by the aria “Una voce poco fa” from Rossini’s Barber of Seville, one of the greatest opere buffe ever written.
Giuseppe Verdi did not consciously set out to be an innovator, but his creative genius gradually transformed the conventions of the bel canto tradition that served as the basis for his early operatic endeavors. The essence of Verdi’s mature style lay in his focus on dramatic continuity. He deemphasized the traditional divisions of aria, recitative, and ensemble in favor of the ongoing dramatic progress of the storyline, and he made characterization and psychological insight critical components of his operatic conception. His operas brought Italian opera to its greatest height.
German-language opera developed late in comparison with Italian and French opera because it evolved, not by imitating and adapting Italian opera plots and musical style, but by experimentation with uniquely German elements. German Romantic opera uses the spoken dialogue of German singspiel and bases its plots on German legend. Its supernatural element is critical to the development of the drama, and its depiction of a wild and uncontrolled nature is another distinctive factor. German Romantic opera was established with Carl Maria von Weber’s hugely influential Der Freischütz of 1821.
The revolutionary Richard Wagner rejected the traditions of Italian and French opera to create an all- inclusive music drama, characterized by continuous music and continuous drama, and a conception of the role of the orchestra as the “inner voice of truth,” revealing psychological insights through the use of leitmotif. Wagner’s hugely influential music drama, Tristan und Isolde of 1859, illustrates the application of his musical theories and reveals the essence of Romanticism in its aura of mystical and sensuous ecstasy.
During the course of the 19th century, program music was cultivated in various forms and took on increasing specificity, as seen, for example, in the third movement of Mahler’s Symphony no. 1. The 19th century revival of Shakespearean drama resonated with Romantic artists and inspired a great deal of program music, including Tchaikovsky’s Romeo and Juliet. In this lecture and the next, we discuss Tchaikovsky, his compositional style, and his Overture-Fantasy, Romeo and Juliet of 1869.
Many Romantic-Era composers used Classical-Era forms in one way or another. The expressive impact of Romantic-Era music was not antiquated or diluted by the use of Classical-Era forms. Tchaikovsky’s adoption of Classical-Era sonata form for his Overture-Fantasy, Romeo and Juliet, in no way inhibits its powerfully Romantic expressivity. In this work, Tchaikovsky created a piece of music that can be appreciated both as abstract music and as program music.
When the European revolutions of 1848 failed, nationalism came to be expressed in non-political ways. In music, it was manifest in works that incorporated elements of folk music, or folk-like music, and folklore. Frederick Chopin turned to Polish music for inspiration. Johannes Brahms and Franz Liszt were inspired by Hungarian or, at least, gypsy-sounding music. Liszt, one of the greatest pianists (and showmen) who ever lived, was also a composer of such masterpieces as Totentanz. This sensational piece of program music, part theme and variations form and part piano concerto, is an example of Romanticism’s fondness for excess and its fascination with the macabre.
Russian concert music began with Mikhail Glinka, who was rightly revered by the composers of a group known as the Russian Five. These 19th-century composers were musical amateurs, yet they forged a characteristically national style of Russian music that employed Russian folk music and avoided the type of German-style thematic development that dominated western European music. Nicolai Rimsky-Korsakov’s Russian Easter Overture is a brilliant example of the best of Russian nationalist concert music in its seamless integration of old Russian hymn melodies, Western technique, and sonata form.
New music has always been difficult for its contemporary listeners. The self-expressive revolution began with Beethoven and became increasingly extreme as the 19th century progressed. Eventually, composers needed extreme musical means to express extreme states. Mahler, for example, in his Symphony no. 9, depicts his own heart attack and death, pushing traditional tonality to its limits in order to do so. The late 19th century and early 20th century was a time of accelerated change, and some composers, recognizing traditional tonality to be outmoded, responded with momentous changes in terms of the musical language with which they chose to express themselves.
The big break with the tonal tradition came with the French composer Claude Debussy, whose music grew from the French language’s proclivity for color, nuance, and blurred sound. Debussy was a stunningly original composer for whom timbre was as important as melody, rhythm, and harmony. His extraordinary Nuages illustrates his conception of timbre as a thematic element, his rejection of conventional major/minor modes in favor of non-traditional pitch collections, and his studied disregard for conventional harmonic practice in favor of a sense of suspended time.
Debussy was a powerful influence on Igor Stravinsky, who absorbed the French composer’s use of pedals and ostinati and his avoidance of traditional pitch collections. But Stravinsky goes further in his creation of complex webs of interactive thematic lines, and unlike that of Debussy, Stravinsky’s music exudes a powerful sense of kinetic energy and drive through the use of asymmetrical rhythms. Key elements of Stravinsky’s innovative genius are manifest in his groundbreaking The Rite of Spring of 1912.
Arnold Schönberg saw himself not as a revolutionary but as someone who was taking the next inevitable step in the history of German/Austrian music. His musical heritage was that of the German/Austrian tradition, a tradition that he believed was shackled by traditional tonality. His attempt to “emancipate dissonance,” as he put it, led to the creation of works that changed the course of Western musical history. They were written in his so-called freely atonal period and included the seminal and strangely beautiful Pierrot Lunaire of 1912.
Robert Greenberg was born in Brooklyn, New York, in 1954 and has lived in the San Francisco Bay area since 1978. He received a B.A. in music, magna cum laude, from Princeton University in 1976 where his principal teachers were Edward Cone, Daniel Werts, and Carlton Gamer in composition; Claudio Spies and Paul Lansky in analysis; and Jerry Kuderna in piano. In 1984, he received a Ph.D. in music composition, with distinction, from the University of California, Berkeley, where his principal teachers were Andrew Imbrie and Olly Wilson in composition and Richard Felciano in analysis.