African Drums & Ratios Curriculum

Audio from the Chapter

Alignment of Forces/Purposes

by John Belcher

Learn more about this audio file here

Expansions, Combinations, Contractions

by John Belcher | The Sound According to John

The 5th track from the Sound According to John. It follows the Pulse and Meeting Number harmonic rhythms you just listened to, but far more complex. From John, “This piece wouldn’t let me record it until I got the structure right. Equipment kept malfunctioning each time I went to the studio until I got clear about how to organize the composition. I use a “rhythm ruler” structure, which serves as a basis for expanding, combining, and contracting time patterns.” This piece was premiered at the 1985 Rhode Island Composers Forum. Click here to view the original score sheet.

Tin can drums, cardboard tube drum, cowbell, temple block, handclaps: John Belcher

JB Music, 1985

Recorded at Orwig Music Studio, Brown University; Recording Engineer, Maurice Methot

Mali Sound Collage

From the chapter, “We were invited to participate in a teacher and youth leadership conference at the Institut pour l’Éducation Populaire (IEP) (the Institute for Popular Education), an independent primary and secondary school in Kati, Mali, January 13-26, 1999.” This collage is an edited selection of field recordings. “We gave presentations on the Algebra Project’s experiential approach to math education with examples informed by AD&RC lesson and activities. We received valuable feedback on the AD&RC with respect to our use of AAD cultural content and were able to research additional resources for interdisciplinary and multicultural curriculum development. Upon our return home, we initiated a sister school relationship between Ciwarra School in Kati and Young Achievers Mathematics and Science School in Boston. In 2000, Young Achievers hosted a visit from IEP co-founder/director Maria Diarra Keita and co-founder/technical advisor Deborah Fredo, along with a representative from the Mali Ministry of Education. Also, IEP adapted versions of AD&RC lessons that we had provided during our visit, and continued to implement them.”

The Hunter Society (Les Chasseurs)

From the chapter, “After the day of workshops and presentations, we walked back towards our co-host Maria Keita’s home. As we proceeded along the familiar route to Maria’s, we encountered a gathering that took us by surprise. Before us was a crowd of people participating in a ceremony of music and dance. Our hosts guided us to seats of honor that had been reserved for us. We later learned that the event had been organized on our behalf by members of the Hunter Society. We were told that our work had the blessings of this group, which among other functions, is viewed as having a symbolic protector role for the community. The ceremony was very moving, figuratively and literally – literally, in the sense that Hunter Society rituals are accompanied by the firing of rifles, held by members as they perform impressively intricate, fast-paced dance steps. (See link to Hunter Society audio file.) Each time a shot rang out, we would jump out of our seats, bringing delight and laughter to those seated near us. Talk about being moved! And speaking further about being moved (about the e-motion), the singing, the circular processional movement, the sounds of the instruments (donsongoni, a stringed instrument with a gourd resonator and karillan, a grooved metal cylinder, rubbed with a metal rod) combined to make a lasting, deeply placed impression.”

Pulse and Meeting Number (4-cycle, 3-cycle)

by John Belcher & Cassie

A fun recreation with John’s granddaughter, Cassie, to demonstrate a meeting number activity, not an actual classroom sample.

Balanced Forces

by John Belcher | The Sound According to John

The 7th track from the Sound According to John. It also explores harmonic rhythms. From John, “This composition is based upon a 300 beat cycle formed by 26 different pulses (including two opposing “diagonal” pulses played by a bass roto-tom and bell tree). I use spoken syllables for some of the pulses that eventually come together to form the phrase “lovely unified sphere” just before the place in the composition where all of the pulses align – beat # 601, which is also the center of gravity of the composition. This piece was composed for Everett Dance Theatre’s Pandora Restaurant, which premiered at New York’s Dance Theater Workshop in 1990. Click here to view the original score sheet.

Percussion and voices: John Belcher

JB Music, 1990

Recorded at Celebration Sounds Recording Studio; Recording Engineer, Ken Carpenter

Jatibola Dunufola, Anwe

by Students and Youth of L’Institut pour l’Éducation Populaire (IEP)

From the chapter, “During the final day of the IEP conference, as one of the workshops provided by presenters throughout the day, we worked with a group of young people ranging in age from approximately 12 to 19 years old. We shared a few AD&RC activities with the group. At the end of the day, conference participants were asked to gather for a culminating event. Everyone had gathered with the exception of the young people. As we waited, we heard off in the distance, approaching sounds of the young people chanting, accompanied by some of the community drummers. As the procession drew closer, we heard more clearly the chant: “Anwe, anwe, anwe jatibola-dunufola, anwe. Anwe, anwe, anwe dunufola-jatibola, anwe”, “We are, we are mathematician-drummers. We are, we are, we are drummer-mathematicians.”

Photos from Mali

Mali: January 13th – 26th, 1999; “We were invited to participate in a teacher and youth leadership conference at the Institut pour l’Éducation Populaire (IEP) (the Institute for Popular Education), an independent primary and secondary school in Kati, Mali, January 13-26, 1999.”

Photos from Young Achievers

Young Achievers Science and Mathematics Pilot School, 1999 – 2000; “A later noteworthy example of the integrated use of AD&RC lessons and activities occurred at the Boston Public Schools’ Young Achievers Science and Mathematics Pilot School. During the 1999-2000 school year, John co-founded, along with music teacher Atemu Aton, a Rhythm and Mathematics Percussion Ensemble. This provided an opportunity for John to observe how some of the students performed differently in this context in contrast with the formal mathematics classroom setting. Further, John was the Young Achievers fifth grade mathematics teacher at the time. One ensemble exercise involved one student playing a drum pattern, consisting of a motif repeated n (e.g., 5) times with m (e.g., 3) beats appended at the end. The question was posed, “How many times was the drum struck?” To solve the problem, students had to replay the pattern in their minds, determine how many beats were in the motif, account for the number of motif repeats, and the number of beats appended. One of the students in the ensemble, who struggled in the formal math class, could masterfully solve these aural math problems and clearly articulate the steps he followed in solving the problems.”

Listen to the

Sound According to John

Explore a sample

African Drums & Ratios

Lesson Plan