You can start to apply permutation techniques in your compositions without having to learn the entire Schillinger System. In this introduction to the system, we’ll examine permutation, a simple technique that offers the musician infinite options. Schillinger’s mathematical approach addressed many of the exceptions to the rules of traditional music theory. In fact Berk’s initial course offerings were called Schillinger Problems and focused on solving compositional problems. The basic philosophy is that the system can help solve musical problems. Schillinger’s teachings continue to be useful, fresh, and exciting and can aid your music writing. “ constitutes my formal musical education almost in its entirety,” attested the late Bill Leavitt, Berklee’s first Guitar Department chair. Later he renamed it Berklee College of Music. Berklee founder Lawrence Berk was trained by Schillinger and established Schillinger House in Boston. During the 1940s, Schillinger-certified teachers spread throughout the country and developed more than 40 schools under his name. The complete Schillinger System of Musical Composition was written as a four-year course that was taught in private lessons. Because Schillinger’s system is a musical theory based on mathematics, it can be applied to all styles of music past, present, and future. Today, students of the system occupy all genres, from pop to classical to jazz to new age. Avant-garde composer and performer Mikel Rouse composes multimedia rock operas that are based on the system, as are works by experimental pianist and composer Yaron Herman. King, John Cage, and Quincy Jones used facets of the Schillinger technique. Music written by Vic Mizzy for the TV shows The Addams Family and Green Acres and for the film The Ghost and Mr. Film composers Leith Stevens and John Barry both studied the Schillinger System. George Gershwin’s Porgy and Bess and Glenn Miller’s “Moonlight Serenade” were written with the Schillinger System. In turn they composed music that is familiar to millions. The Ukrainian-born theorist lived from 1895 to 1943 and taught professional musicians the system of musical composition he devised. Finally, there are $3!$ possible seating orders for the $3$ men, so there are altogether $3\cdot2\cdot3!=36$ arrangements that have all $3$ women sitting together, and the probability of getting one of them is $\frac$ of getting one of them.The name Joseph Schillinger may strike a chord with some, but Schillinger’s contributions to music have eluded most students and musicians. Thus, there are $3$ pairs of seats in which we can put $W_2$ and $W_3$, and we can seat them in either order. In order to get the $3$ women seated together, we must have one of the arrangment patterns $W_1WWMMM$, $W_1WMMMW$, or $W_1MMMWW$, where $W$ stands for a woman and $M$ for a man. As you say, there are $5!$ ways to fill in the other $5$ people. Since the table is circular, we can list any arrangement by starting with $W_1$ and then going around the table clockwise from her. They are not interchangeable: if the women are $W_1,W_2$, and $W_3$, a seating arrangement in which they sit in the order $W_1W_2W_3$ is distinguishable from one in which they sit in the order $W_2W_1W_3$.
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