2017 FFTROCC “MUSIC OF THE FUTURE” SUMMER YOUTH MUSIC-SCIENCE PROGRAM DATE: July 10-August 11, 2017 TIME: 10am to 3pm LOCATION: 1157 Lexington Avenue (at 80th street), New York, NY PROGRAM: 10:00am-12:00am Chorus focusing on polyphony (in the chapel) 12noon-1:00pm lunch break 1:00pm-3:00pm Classical science, geometric and astronomical construction (in All Soul’s School classrooms) AGE REQUIREMENT: Grades 6-12 (ages 13 and above) The 2017 Foundation summer program will focus on the principle of discovery, and the unity between Classical music and science, in an intensive five-week course of study and experiment. Every student in the program is required to join the two-hour morning chorus, learning choral masterworks spanning four centuries with a focus on understanding polyphonic textures. The students will have the goal of performing in a concert at the end of the summer program. (No singing experience required to join the program. All levels welcomed. Enthusiasm a must!) The afternoon program of science and music theory will encourage and equip the students to determine whether and how there exists a pre-established harmony between the thought processes underlying what are popularly called "science" and "art". The topical outline of the five weeks is as follows: WEEK ONE, July 10: The first week will introduce the students to the works of Plato, such as his “Meno” dialogue on the doubling of square and the “Platonic Solids”. Students will be challenged to make the same discovery made by Plato’s original character, as well as construct geometry and nested solids.

WEEK TWO, July 17: Week two will continue to take students through the world of Pythagoras onto the exploration of Astronomical navigation, first investigated by Constructing nested Platonic Johannes Kepler. The students will be solids challenged to reconstruct the fundamental methods of astronomical navigation through polyhedrons, stellations of polyhedra, and even such ancient navigational devices as the Pentagramma Mirifium.

Constructions of stellations of polyhedra


WEEK THREE, July 24: Week three will introduce students to constructive astronomy, we will build simple astronomical instruments that allow us to know who we are, where we are, and how to measure distance to another place without actually going there: things such a quadrant, which measure the height of any celestial body above you; sundial, to measure time and latitude; theodolite, which is to measure distance from object. We will also introduce the building of an astrolabe.

Sundial from Beijing's Forbidden Palace

WEEK FOUR, July 31: Students will be introduced to the musical and scientific discoveries made by Johannes Kepler, the discoverer of the geometry of our solar system, who demonstrated that the planets of our Solar System were arranged according to principles of reason and beauty(1). The students will be challenged to reconstruct the model of the solar system as imagined by Kepler, and will be encouraged to discover the principles behind Kepler's "musical intervals" which defined his idea of the orbits of the planets. This week will focus on a new approach to musical method, not "musical theory". The instructors will utilize an interactive pedagogy, including singing, through which the students will become acquainted with the device of irony in music, and musical ironies for themselves, as ideas (2). Students will also be encouraged to engage in elementary musical composition.


mapping the intervals of our solar system's planetary motion onto a monochord

Platonic solids in relations to the solar system

WEEK FIVE, August 7: This week will continue elements of the work of the first four weeks, and also add on advanced geometry, introducing students to concepts such as the non-Euclidian geometry of Bernard Riemann. Students will also participate in some hands on experimentation on electricity.

Figure 1. Riemann surface for the square-root


1. (In 1601, Kepler proved that the planets were moved around the Sun by the Sun, by the newly discovered (by Kepler) principle of gravitation. In 1618, he made another exciting discovery. Kepler found the reason the planets move at their respective speeds (which nobody before him had known), and that the relationships among these orbital speeds corresponds precisely to the notes of a major and minor musical scale! The planets of the Solar System, in a sense, form a polyphonic chorus, conducted by the Sun! 2. Instead of a series of names and dates, or mere "music appreciation" musical method will be presented as one expression of the way art and science have combined to uplift and advance humanity over centuries. Classical music, and Classical culture will be discovered to be, not a "genre"; It is, rather the history of, and the future of, civilization's progress, documented through musical discoveries and inventions.

COMMITMENT: $500 for the 5-week program (for any students with financial needs, financial aid available for partial or full scholarship. Please contact Ms. Yen 203.441.7488)



NAME OF THE STUDENT: _________________________________________ AGE: _________ SCHOOL: ____________________________________________________

GRADE: _________


What draws you to our summer music-science program? (Please give answer no longer than 2 paragraphs)

2. Your talents. Are you a singer? If so, do you know your voice type? Are you an amateur astronomer? Let us know what interests you!

3. What do you hope to get out of this program?


NAME OF PARENT OR GUARDIAN: ________________________________________________ ADDRESS:________________________________________________________________________ HOME PHONE: __________________________ CELL PHONE: _________________________ EMAIL: __________________________________________________________________________ TWITTER: ___________________________ FACEBOOK: ________________________________

EMERGENCY CONTACT NAME:___________________________________ RELATIONSHIP:_______________________

ADDRESS: ___________________________ ____________Telephone: ______________________ I give permission for my child’s to participate in the 2017 FFTROCC summer program activities.

Signature____________________________________________________ date __________________

FOR MORE INFORMATION ABOUT OUR FOUNDATION, Go to: www.fftrocc.org email: [email protected] call: 203.441.7488 Please mail application for and commitment check to: Mailing address: FFTROCC, 15 East Putnam Avenue, #400, Greenwich CT 06830 Fax: 917.591.7399


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