Mark Burford
Music history, nineteenth-century music, twentieth-century American popular music. On sabbatical 2014–15.
Virginia Hancock
Music history, music theory, choral conducting.
Morgan James Luker
Ethnomusicology, music of Latin America, cultural politics.
David A. Schiff
Composition, conducting, twentieth-century music including jazz, American musical theater.
Christopher J. Wells
Music history, jazz history, African American music, social and popular dance.
The music department offers a wide range of courses and performance opportunities for majors and nonmajors, as well as private instrumental and vocal lessons. Many courses have no prerequisites.
Pursuit of the music major prepares students for a senior thesis in music history or analysis, ethnomusicological research, or composition. Majors should complete two units of music theory (Music 211 and Music 312), Music History I and II (Music 221 and Music 222), and one unit of ethnomusicology (Music 150) before beginning the second semester of their junior year, and take the junior seminar.
Majors are expected to participate in performance activities; therefore, fees for private instruction in one instrument or voice are waived for junior and senior music majors.
For the junior qualifying examination in music, students will write analytic essays on selections of notated and recorded examples of music and a critical essay on selected music literature.
Independent study courses (Music 481) in subjects not offered in the regular curriculum are available for junior and senior music majors.
Requirements for the Major
- Music theory—Music 211 and 312;
- Music history—Music 221 and 222;
- Ethnomusicology—Music 150;
- One unit of ensemble from among 104 (orchestra), 105 (chorus), 106 (contemporary ensemble), 107 (Collegium), 108 (jazz ensemble), 109 (chamber music);
- One unit of private instruction (vocal or instrumental);
- Junior seminar;
- Three additional one-unit courses in the department at the 200 level or above, one of which must include either Music 343 or an additional ethnomusicology course;
- Thesis (470).
In addition to the requirements for all music majors, the following courses of study are recommended for students writing a senior thesis in ethnomusicology or composition:
- Students planning a thesis in ethnomusicology should take two units of anthropology for either Group B or Group X and three additional units in ethnomusicology.
- Students planning a thesis in composition should take Music 343 and Music 481 (independent study in advanced composition).
Senior Thesis
Before beginning their senior year, students planning to do a thesis in music must demonstrate their competence in the particular area in which they wish to work. That is, they may not use the thesis as an occasion to explore an entirely new area. The thesis may be an extended historical, ethnomusicological, or analytical project, which may include a performance; or a composition thesis, which must include a printed score, a recording of a performance, and an analytical essay. At the beginning of the senior year, students prepare short written proposals describing the nature of their theses for discussion with the entire music department prior to submitting proposals to the Division of the Arts for approval.
Facilities
Music department facilities include Kaul Auditorium, where the orchestra, Collegium, and chorus perform; the Reed chapel, which is used for Friday at Four concerts and other chamber music; the instructional media center (IMC), where students can borrow audio sound media equipment; and the Performing Arts Building which houses the performing arts resource center (PARC), teaching studios, practice rooms, and a large rehearsal hall for Collegium, chorus, jazz, and chamber ensembles. The PARC has a library of scores, recordings, and videos; workrooms; and a computer lab. Practice rooms are available 24 hours a day to students enrolled in music courses. All current members of the Reed community (students, faculty, and staff) are invited to use the facility from 8:30 a.m. until 11:00 p.m. daily.
Performing Opportunities
Many Reed students participate in performance activities sponsored by the department as solo players or singers, in chamber music ensembles, or in the ensembles conducted by faculty and staff members. Registration procedures for lessons and ensembles are explained in the schedule of classes. The Friday at Four series, consisting of 10–15 concerts each year, features performances by students, faculty, and guest artists. The orchestra, chorus, and Collegium perform concerts in Kaul Auditorium each semester.
The department also helps organize and coach chamber and jazz ensembles, which are available by audition for students interested in playing together in small groups. In addition, coaching sessions with members of the music performance staff can sometimes be substituted for private lessons with department approval.
Private Instruction—Denise VanLeuven, director
Reed offers individual instruction in piano, organ, harpsichord, voice, guitar, and all orchestral instruments, as well as jazz and a variety of ethnic instruments. Our teachers, all of whom are accomplished performers, are selected from the best available in the Portland community. Some are members of the Oregon Symphony, the Portland Opera Orchestra, the Portland Baroque Orchestra, and various chamber, jazz, and ethnic ensembles in the area, and have appeared as solo artists with these groups. Instructors are added to the staff as need arises. Please visit the music department website, http://academic.reed.edu/music/, for a detailed listing of private music instructors.
Fees
Fees for private instruction (Music 101) are $477 each semester for twelve 45-minute lessons; some scholarship aid is available. Private instruction fees are waived in one instrument or voice for junior and senior music majors, who are expected to enroll in private instruction for at least two of their final four semesters.
Academic Credit for Music Performance
All students participating in music performance courses (Music 101, 104, 105, 106, 107, 108, and 109) should register; these courses are graded on a credit/no credit basis. The courses carry variable credit: either one-half course or zero credit for one semester. To qualify for credit, students must have taken or be currently enrolled in a one-unit course at level 111 or above at Reed, for which they can receive two half-units of credit for a music performance course, one-half unit per semester (the only exception is Orchestra, Music 104; see the description below). No more than one-half credit may be earned per semester. A second one-unit course at level 111 or above qualifies the student for two additional half-units of credit for music performance. No more than two units may be received for the same music performance course. A third one-unit course at level 111 or above qualifies the student for two more half-units of credit in a different music performance course. These credits in music performance may be used toward the quantity requirement of 30 units for graduation, though not toward the Group A or Group X requirements. If the accompanying classroom course is dropped, credit for music performance must also be relinquished.
Music 101 - Private Instruction
Variable credit: either one-half course or zero credit for one semester of individual instrumental or vocal instruction. Students taking this course for one-half credit are encouraged to participate in at least one student recital. See above for pre- or corequisite for credit.
Music 104 - Reed Orchestra
Variable credit: either one-half course or zero credit for one semester. Availability of credit is dependent on instruments needed for repertoire to be performed in any given semester. Because there are two rehearsals per week, the pre- or corequisite of enrollment in other music courses to earn credit is waived, although the restrictions on the amount of credit that can be earned still apply. The orchestra rehearses and performs works from the eighteenth to the twenty-first century. It presents one or two concerts each semester. Prerequisite: audition required.
Music 105 - Reed Chorus
Variable credit: either one-half course or zero credit for one semester. The chorus rehearses and performs works from all periods of music, often with the orchestra. (No audition required). See above for pre- or corequisite for credit.
Music 106 - Contemporary Ensemble
Variable credit: either one-half course or zero credit for one semester. Offered when there are enough qualified students interested in performing chamber works from the contemporary classical repertory. Performers on any wind, string, percussion, or keyboard instrument are welcome to audition. This course consists of coaching sessions and performances during the semester. Corequisite: participation in the Reed Orchestra (except for keyboard players). Prerequisite: audition required. See above for pre- or corequisite for credit.
Not offered 2014—15.
Music 107 - Collegium Musicum
Variable credit: either one-half course or zero credit for one semester. The Collegium rehearses and performs vocal music from many historic periods suitable for a small group. Prerequisite: audition required. See above for pre- or corequisite for credit.
Music 108 - Jazz Ensemble
Variable credit: either one half-course or zero credit for one semester. Jazz ensembles selected by the instructor rehearse regularly and give several performances each semester. Rehearsals include improvisational techniques, soloing, and accompanying. Prerequisite: audition required. See above for pre- or corequisite for credit.
Music 109 - Chamber Music
Variable credit: either one-half course or zero credit for one semester. Available by audition when there are enough advanced students to form an ensemble of one player per part. This course consists of weekly coaching sessions and several performances during the semester. Prerequisite: audition. Corequisite: participation in the Reed Orchestra (except for keyboard players). Prerequisite: audition required. See above for pre- or corequisite for credit.
Music 111 - Theory I
Full course for one semester. This course examines notation of pitch and rhythm; scales and key signatures; intervals, triads, and diatonic seventh chords; and writing in four parts. It begins with the basic elements of music, but moves swiftly through the contents of a first-semester college-level music theory course. Labs include sight singing, dictation, and keyboard. Lecture and laboratory.
Music 142 - Latin American Popular Music
Full course for one semester. This course examines Latin American popular musics within their social, political, and cultural contexts. Musical genres to be studied include tango, samba, son, nueva canción, tropicália, rock nacional, and funk carioca, among others; themes to be discussed include music and the nation, music and dictatorship, and the crisis of cultural inclusion and exclusion in contemporary Latin America. Understanding how these musics are framed by broader assumptions regarding race, class, gender, and ethnicity will be a key concern of the course. Our focused listening will be complemented with analytical, critical, and contextual readings, including relevant selections from Latin American literature in translation and occasional film screenings. Lecture-conference.
Music 150 - The Cultural Study of Music
Full course for one semester. Music carries a tremendous range of meanings and functions, serving as both a symbol and generator of other forces in social life and history. Taking a comparative approach to a variety of world musical cultures (including selected examples of folkloric, popular, and art musics from Africa, the Middle East, India, Asia, the Americas, and Europe), this course will examine how music communicates and is made meaningful within specific historical and cultural contexts. We will focus on developing the critical vocabulary and listening skills needed to account for music as a cross-cultural phenomenon. Lecture-conference.
Music 211 - Theory II: Intermediate Harmony and Species Counterpoint
Full course for one semester. This course continues the laboratory skills acquired in Music 111. Students are introduced to principles of melodic construction, modal counterpoint, and more advanced tonal harmony, applying them to appropriate musical examples. Prerequisite: Music 111 or equivalent skill, determined by a placement examination given at the beginning of the academic year. Lecture-conference-laboratory.
Music 221 - Music History I
Full course for one semester. This course is an introduction to the study of music history, through focus on repertories of sacred and secular music cultivated in Western Europe from the medieval period to the mid-eighteenth century. The course is not intended to be a comprehensive survey of European art music. Rather, students will develop the listening, analytical, and critical skills necessary to formulate and engage music-historical questions relating to aesthetics, social context, and intellectual history. Rudimentary ability to follow a score or permission of the instructor required. Lecture-conference.
Music 222 - Music History II
Full course for one semester. This course is an introduction to the study of music history through focus on selected examples of art music cultivated in Western Europe, the United States, and globally since the mid-eighteenth century. We will study the features of major genres of concert music and of popular song forms, while also considering manifestations of Enlightenment thought, romanticism, modernism, and avant-gardism in music. Students will develop the listening, analytical, and critical skills necessary to formulate and engage music-historical questions relating to aesthetics, social context, and intellectual history. Rudimentary ability to follow a score or permission of the instructor required. Lecture-conference.
Music 230 - Tango: Music, Culture, History
Full course for one semester. Tango is a rich and diverse cultural practice. Focusing on music and its connections to other expressive forms, especially dance and verbal art, this course will examine tango in its cultural and historical contexts. We will develop a detailed knowledge of the history and stylistic development of tango as a global genre, and explore how musical debates within tango have both reflected and contributed to the broader transformations of twentieth-century society, culture, and politics in Argentina and beyond. Lecture-conference.
Music 235 - The Symphony Between the Revolutions
Full course for one semester. The symphony emerged as a recognizable genre in the early 1700s, but only attained its status as the preeminent form of European orchestral music toward the end of the eighteenth century. Focusing on selected works composed during the first half of the “long” nineteenth century, this course will examine the development of the symphony as a musical genre and as a site of discourse on social, cultural, and aesthetic ideals in Europe from the French Revolution to the continent-wide revolutions of 1848. Prerequisite: sophomore standing. Lecture-conference.
Not offered 2014—15.
Music 242 - Opera
Full course for one semester. Although the orientation of this course is largely historical, its primary focus will be listening to and viewing some of the greatest and most enduring operas in the repertory—works by, among others, Monteverdi, Mozart, Wagner, Verdi, Puccini, and Britten. Students will be required to see the Portland Opera production of Bizet's Carmen during the spring semester and at least one of the Metropolitan Opera's HD videocasts; those who plan to take the course should also, if possible, attend the Metropolitan Opera videocasts of Verdi's Macbeth and Mozart's Le Nozze di Figaro in the fall. Successful completion of writing assignments will not depend on the ability to read music. Lecture-conference.
Music 243 - Music and Globalization
Full course for one semester. Music presents something of a paradox. On the one hand, no expressive form is taken to articulate cultural identity, tradition, and roots more immediately than music. On the other hand, recorded music has circulated widely since the late nineteenth century, when recording technology first enabled sound to be separated from its source. These dual trends have only been exacerbated by developments in digital technology over the last quarter century, such that music is now at the center of claims regarding cultural globalization and its consequences. In this course, we will examine the changing relationship between music, place, and cultural identity at a time when almost any sound can be heard almost anywhere. Discussions and readings will be paired with close analytical listening to significant musical examples from around the world. The goal of the course is to help students develop a critical vocabulary and historical framework for engaging the ethics and aesthetics of music in our global era. Conference.
Not offered 2014—15.
Music 265 - The Musical Geography of New Orleans
Full course for one semester. Bourbon Street, Mardi Gras, jazz funerals…New Orleans holds a special place in American music and culture; musicians from the city have made important contributions to virtually every genre of popular music. However, the city’s history is also steeped in racial injustice and conservative aesthetic politics that polices what “New Orleans music” means. In this course, students explore a diverse range of musicians and musical genres through the lens of New Orleans’ history, socioeconomic and racial politics, and cultural practices. Styles of music to be studied include jazz, blues, R & B, funk, zydeco, metal, and hip-hop. The course emphasizes important local traditions such as the Mardi Gras carnival and recent musical developments in the aftermath of Hurricane Katrina. In exploring musical life in New Orleans, students will engage with critical theories in urban geography, sound studies, and tourism studies to unpack the relationships among sound, race, and place. Conference.
Music 266 - The Music of Duke Ellington
Full course for one semester. As composer, arranger, songwriter, bandleader, and pianist, Duke Ellington (1899–1974) stood at the center of American music. His works mirror the development of jazz from ragtime to hot jazz, swing, bebop, and beyond. We will trace the development of Ellington’s style, the evolution of his orchestra and the influence of its players on his music, and his collaboration with Billy Strayhorn. We will also examine Ellington’s exploration of different genres, including extended jazz compositions, musical theatre, and religious music. Prerequisite: sophomore standing. Lecture-conference.
Not offered 2014—15.
Music 271 - Studying Popular Music
Full course for one semester. This course is an introduction to some of the key aesthetic, theoretical, and methodological concerns in the burgeoning field of popular music studies, which has explored the ways in which meaning is produced through the performance, (re)production, and consumption of popular music. Among the topics the course will address are popular music as creative expression, as recorded sound, and as a field of sociocultural discourse, focusing primarily on popular music in the United States. Prerequisite: sophomore standing. Lecture-conference.
Not offered 2014—15.
Music 277 - Music and Politics
Full course for one semester. This course will examine the relationship between music and politics in a variety of historical and cultural contexts, exploring how and why music has been such a powerful carrier of ideology. Grounded in core readings on the politics of music and the arts, we will address themes of musical nationalism, censorship, cultural policy making, the cultural industries, musical activism and social movements, and the broader expediency of musical culture in the global era. Conference.
Not offered 2014—15.
Music 278 - Classical Music in African American Culture
Full course for one semester. While most discourse on African American music centers on jazz, blues, and other forms of popular music, African Americans have engaged substantively with Western art music for over two hundred years. This course thus investigates the many African American performers, composers, and institutions who have made strong contributions to classical music in the United States. Students will engage critically with the role of classical music in African American churches and historically black colleges and universities (HBCUs), and examine the ideological implications of “high culture” in black political/philosophical movements from racial uplift to Afrocentrism. We will also explore the role of racism in shaping the career trajectories of black composers and classical performers and the especially porous boundary between black classical and popular music. Conference.
Music 305 - Musical Ethnography
Full course for one semester. This course will introduce the theory and practice of musical ethnography, the key mode of ethnomusicological research and representation, to advanced students in ethnomusicology, anthropology, and related disciplines. Combining critical readings on ethnography from music scholarship, anthropology, and a variety of disciplines with hands-on projects (including the production and analysis of field recordings, musical transcriptions, and various forms of qualitative ethnographic data), the course will prepare students to both conduct and critically reflect upon ethnographic research. Conference. Cross-listed as Anthropology 305.
Music 312 - Theory III: Advanced Harmony
Full course for one semester. This course will examine the development of harmonic resources in late nineteenth- and twentieth-century musical idioms through compositional and analytical exercises. In particular we will study contemporary jazz and popular harmony; the impressionist harmonies of Debussy and Ravel; and the early modernist idioms of Stravinsky, Bartók, and Schoenberg. Prerequisite: Music 211. Conference with musicianship lab.
Music 314 - Composition
Full course for one semester. This course is an introduction to contemporary composition. Students will compose and perform short works. The course will deal with problems of instrumentation, notation, and performance, as well as the larger aesthetic issues of coherence and gesture, within a broad range of styles and media. Prerequisite: Music 211 or consent of the instructor. Conference.
Music 343 - Theory IV: Form and Analysis
Full course for one semester. This course prepares students to analyze the fugue as exemplified in the music of J.S. Bach and the sonata forms found in the music of Beethoven; as well as later examples of both genres. Prerequisite: Music 211. Conference.
Music 344 - Ideologies of Improvisation
Full course for one semester. This junior seminar will examine improvisation as a musical practice, analytical object, and subject of critical discourse in a variety of historical and cultural contexts, attending to the musical techniques and artistic ideologies of improvisational performance in equal measure. Case studies will engage a diverse selection of historically significant improvisational practices in world musical culture and reflect the scope and range of critical music scholarship on these issues. Students will also conduct and workshop significant research projects on an improvisatory practice of their choice, together developing the methods and skills needed to undertake substantial independent projects. Prerequisite: Music 150, 221, 222, 312, and junior standing. Conference.
Music 345 - Stravinsky and the Ballets Russes
Full course for one semester. The Ballets Russes, founded by Serge Diaghilev, was a center for the development of modernist ideas about music, dance, theater, and the visual arts from its founding in 1909 to Diaghilev’s death in 1929. We will study the collaboration of composer Igor Stravinsky with the Ballets Russes from the folkloristic Firebird of 1910 to the neoclassical Apollo of 1928. We will trace the evolving aesthetic, cultural and political frameworks for Diaghilev’s dance company, paying attention to the choreographic languages of Fokine, Nijinsky, Massine, Nijinska, and Balanchine as well as the scenic designs. Conference. Cross-listed as Dance 345.
Not offered 2014—15.
Music 346 - Jazz: Music, Dance, and Embodiment
Full course for one semester. This course uses the body as an entry point to exploring jazz as a collaborative, participatory art form. Specific foci in this course will range from social dancing in depression-era Harlem ballrooms and tap dancers’ hybrid dancer/musician identities to collaboration between musicians and choreographers in the black arts movement. Through recent developments in jazz studies and interdisciplinary discourses on embodiment, students will investigate the communicative dynamics between dancers and musicians and will consider the significance of deep corporeal and intercorporeal listening to a range of jazz practices. Applying a critical historiographic approach, students will examine jazz’s complex transition from a “dance music” performed in ballrooms and at parties to an “art music” performed for seated audiences in clubs and concert halls. Prerequisite: sophomore standing and at least one prior course in either music or dance studies. Conference. Cross-listed as Dance 346.
Music 352 - Johann Sebastian Bach
Full course for one semester. We will investigate Bach’s life and music, with attention to works he wrote for the conditions of his employment at different times in his career. The histories of the genres in which he composed—Lutheran church music and other vocal works; and instrumental works, including those for keyboard instruments, other instruments, and orchestra—will also be considered. Prerequisites: sophomore standing and the ability to read music. Conference.
Not offered 2014—15.
Music 360 - Music and the Black Freedom Struggle, 1865–1965
Full course for one semester. The civil rights movement in the U.S., demanding full citizenship for African Americans, is often equated with the momentous sociopolitical developments of the 1950s and 1960s. Increasingly, scholars have situated this “classical” period within a broader historical arc encompassing an ongoing black freedom struggle that dates to Reconstruction. Through close study of historical texts and musical repertory that will include the spiritual, the blues, jazz, and concert music, this course will explore how ideas about musical sound and musical performance played an essential role in articulating the stakes of this struggle and the meanings of freedom. Prerequisite: sophomore standing. Conference.
Not offered 2014—15.
Music 361 - Music in the United States during the 1950s
Full course for one semester. Despite its reputation as a period of American conservatism, the 1950s presented listeners with an array of music exhibiting the widespread fascination with “new sounds,” expressed in jazz (Miles Davis and Ornette Coleman), pop recordings (Sam Cooke, Patsy Cline, and Tito Puente), art music (John Cage and Igor Stravinsky), and musical theater (The King and I and West Side Story). Through study of selected examples from these repertories and relevant literature, this course will examine the performance, composition, and consumption of music in the United States during the 1950s, as well as the contribution of music to broader discourse on the cold war, race and ethnic relations, national identity, and ideologies of modernism and populism. Conference.
Not offered 2014—15.
Music 363 - Mahler and His Influence
Full course for one semester. Although he died in 1911, Gustav Mahler exerted a wide influence on the music of the twentieth century, both as a composer and as a conductor. In this course we will explore how aspects of Mahler’s compositional style were appropriated and developed by composers as different as Arnold Schoenberg, Anton Webern, Alban Berg, Kurt Weill, Aaron Copland, Dmitri Shostakovich, Benjamin Britten, Leonard Bernstein, Luciano Berio, George Crumb, and Uri Caine. We will attempt to discover the historical and political circumstances that favored, or discouraged, a Mahlerian legacy, and also examine how composers negotiated such a powerful precedent in formulating their own styles. Prerequisite: ability to read music. Conference.
Music 364 - The Blues: Forms, Styles, Meanings
Full course for one semester. In this course we will study one of the most important wellsprings for twentieth-century popular music, the blues, proceeding along three lines of inquiry: musical elements that characterize the blues, focusing on formal and harmonic structure, melodic and poetic ideals, and improvisational strategies; stylistic manifestations of the blues, including country blues, “classic” blues, postwar commercial styles, and influences on gospel music, rock, and jazz; and interpretations of the “blues aesthetic” as a cultural signifier, as reflected in music criticism, documentary film, literature, its production and consumption, and international reception. Conference.
Not offered 2014—15.
Music 365 - Avant-Garde Music
Full course for one semester. The term “avant-garde” was applied to music, such as Schoenberg’s "Pierrot Lunaire" or Varèse’s "Ionisation," that broke with techniques of the past, but also to works like Satie’s "Relâche," which challenged and destabilized the very notion of an art work. These tendencies flowered after World War II with the music and ideas of Cage, Boulez, Stockhausen, Xenakis, Berio, and Feldman; this course will primarily study this literature. We will also study composers of the American “maverick” line, such as Ives, Cowell, Harrison, Partch, and Lucier. Conference.
Not offered 2014—15.
Music 368 - The Music of Elliott Carter
Full course for one semester. Elliott Carter (1908–2012) was one of the most important and innovative figures in the music of the second half of the twentieth century and the first decade of the twenty-first. His works for many different instrumental and vocal forces explore new concepts of rhythmic, harmonic and formal organization. We will trace the evolution of his music through analysis of the scores and readings from the large body of critical and theoretical literature devoted to his music. Prerequisite: Music 312 or consent of the instructor. Conference.
Not offered 2014—15.
Music 372 - Junior Seminar: Mozart’s Così fan tutte as Musical Work and Cultural Text
Full course for one semester; junior seminar. The focus of this course is Wolfgang Amadeus Mozart’s Così fan tutte, an opera that, since its premiere in 1790, has received copious scholarly attention. Through close study of Così from a range of interdisciplinary perspectives, the course will explore topics that include late classical style, Mozart’s collaborations with librettist Lorenzo Da Ponte, Enlightenment philosophy, the sexual politics and orientalism of Mozart’s Vienna, approaches to the opera’s production, and, in light of Così’s complex reception history, critical and analytical interpretations of the work. Prerequisites: Music 211, 221, and 222, and junior standing. Conference.
Not offered 2014—15.
Music 373 - Junior Seminar: Brahms and the Symphonic Ideal
Full course for one semester. The focus of this junior seminar will be the four symphonies composed by Johannes Brahms. Premiering between 1876 and 1885, at the height of his career, the symphonies were completed within a relatively concise period in Brahms’ half century as a composer. In differing ways, these works were deeply engaged with challenges posed by the elevated artistic prestige and compositional expectations associated with the post-Beethovenian symphonic ideal. In this course, we will consider Brahms’ orchestral language and analytic approaches to the symphonies, as well as questions pertaining to genre, listening practices, late-Romantic style, and cultural identity following German national unification in 1871. Prerequisites: Music 150, 221, 222, and 312, and junior standing. Conference.
Not offered 2014—15.
Music 470 - Thesis
Full course for one year.
Music 481 - Independent Study
One-half or full course for one semester. Prerequisite: approval of instructor and division.