Composers Domenico Scarlatti and John Cage come from different sonic worlds. Scarlatti died 13 years before Beethoven was born. Cage was born 85 years after Beethoven died. In his sonatas, Scarlatti (born in 1685) devoted himself to exploiting the capacities of the harpsichord. Cage (who died in 1992), for his part, devised multiple ways to alter the sound of today’s grand piano — the sort of instrument that Beethoven could only dream of — by inserting foreign objects into its strings.

Swiveling between two grand pianos, David Greilsammer plays music by both composers for the third program of the PUC 125 series in Princeton University’s Richardson Auditorium on Tuesday, December 1, at 6 and 9 p.m. Greilsammer uses an unadulterated concert grand for the Scarlatti. For the Cage, he turns to a “prepared” piano inside of which he has placed nuts, bolts, rubber, and plastic, according to the composer’s instructions.

In a telephone interview from Geneva, Switzerland, Greilsammer explains how he came to devise a program consisting of works by Scarlatti and Cage, musical strangers. “For many years I had been performing Scarlatti in some recitals and Cage in others. One day I was thinking about new programs, and it struck me how similar the sonatas of these two composers are, and I realized that I had to create a project with these two.”

Greilsammer differentiates the classical sonatas of Haydn, Mozart, and Beethoven from those of Scarlatti and Cage. In the classical period, he says, “Sonatas were becoming huge and heavy” and followed rules. “They were symmetrical. If there was a four-measure question, it would require a four-measure reply; rarely would there be a phrase of seven measures. And with classical sonatas, you know for sure that the themes will come back at the end.”

“Scarlatti sonatas consist of two short parts,” Greilsammer says. “He didn’t follow any rule of symmetry. He did what he wanted. Maybe there would be a new theme a few seconds before the end of a piece. That’s what makes these pieces so wild and modern, almost 300 years after they were written.”

“It’s fascinating that in the first part of the 20th century, Cage writes sonatas that follow the same kind of unusual pattern that Scarlatti used,” Greilsammer continues. “Cage never acknowledged that he knew Scarlatti. These two have absolutely nothing to do with each other, but they wrote in the same pattern. Their sonatas are adventurous, and crazy, full of surprises all of the time, not following what others around them were doing.”

“Both men were pioneers,” Greilsammer says. Scarlatti wrote almost 600 sonatas. I wanted to select the more striking ones. I kept hearing imaginary bridges to Cage in my head. When I perform this program I do not stop between pieces. I play entire sonatas, alternating composers. The connections are extraordinary.” The Scarlatti selections cover his entire compositional career. The Cage pieces come from the composer’s “Sonatas and Interludes,” a set of 20 pieces written between 1946 and 1948.

Although Scarlatti made no attempt to alter the sound of the harpsichord, he created novel sonorities on the instrument. His compositional standbys included crossing hands, dissonances, wide leaps, repeated notes requiring rapidly changing fingers on a single key, runs using double notes, cluster chords using five or more notes at a time, and other techniques.

Exploring new sonic territory in the 1930s, at a time when many composers were still writing romantic music, Cage modified the sound of the piano by “preparing” it with foreign objects. “Cage transformed the piano into something new,” Greilsammer says. “He was able to create a band of four or five percussionists in one instrument.” Furthermore, he documented exactly how to prepare the piano for each piece.

For the majority of notes on a grand piano, depressing a single key sends a hammer-like mechanism toward three strings inside the instrument. “Cage left a precise map that shows what to do with every single string inside the piano,” Greilsammer says. “Sometimes he specifies whether the nut or bolt should be positioned between the first and second strings, or between the second and third strings, and how many inches the hardware should be from the hammers.”

“If you don’t do this right, it doesn’t sound good,” Greilsammer says. “Cage had a particular sound in his mind; he makes a lot of sense. He was smart.”

“It used to take me four hours to prepare the piano at first,” Greilsammer says. “Now I can do it in one hour. I’ve learned how to keep the hardware in place. And I’ve learned how not to let stuff fall out of position or move during performance.”

“There’s a difference from one piano to another,” Greilsammer says. “Cage said that you have to readjust from one piano to another. I used to worry about how to get into Cage’s mind. It’s strange to explain. You need to develop a sensibility to his thinking.” Now, when Greilsammer confronts a piano he has prepared for the first time, he can tell whether it produces the sound that he looks for in performing Cage’s works.

“It has become obvious to me when the sound of the prepared piano is not right, and I will readjust. When you play Cage, you need to be open-minded about performing all kinds of music. If you just care about playing traditional classical or romantic music it won’t work.”

Greilsammer makes no attempt to delegate preparing the piano to someone else. “I have to do it myself. I don’t let anybody else do it. I develop an intense relationship to the piano. I have a kit with the necessary hardware. I know what sound each object will produce.

“The Cage sonatas use screws, nuts, and bolts of different sizes; the longest is four inches; the shortest is a half inch. I choose the length of the screws. There are pieces of rubber and plastic. I buy everything in a hardware store and cut the objects if necessary.

“When you put nuts around the bolts it creates a tambourine effect. Inserting rubber makes the sound of an African tom-tom. An eraser gives the boom of a big percussion instrument. There’s no wood in the sonatas, though Cage specifies it elsewhere,” he says.

Greilsammer has recorded his Scarlatti/Cage encounter for Sony Classical.

In addition to the Scarlatti/Cage program, Greilsammer appears in public, conducting and soloing with the Geneva Camerata, a 30-member ensemble founded in 2013. Greilsammer is the music and artistic director of GeCa. “All of its musicians are amazing individual soloists able to perform music of all styles — baroque, even on period instruments; and avant garde on modern instruments. They play jazz and blues, and use electronic effects. They can improvise,” he says. This season GeCa gives more than 40 concerts in Geneva, and will tour in Mexico and China. Plans are underway for a United States tour in 2016-’17.

Greilsammer has performed Mozart extensively. In 2012-’13 he played and conducted all of Mozart’s 27 piano concertos. In 2008, in a single 12-hour concert that began at 10 a.m., he played all 18 Mozart sonatas, taking some of the repeats, and including the Fantasie in C minor, K. 475. “I did it in six chapters with three sonatas at each session,” he says.

When I observe that the accompanying figures in his online Mozart performances are more staccato than is common, he says, “I try to go for a light approach. I don’t like the romantic approach for Haydn, Mozart, or Beethoven. You can’t swing if there’s too much pedal. I like tempos on the fast side for Mozart. I like to play his music with clarity and spark.”

Born in Israel to professor parents in Tel Aviv, Greilsammer, 38, is the eldest of five brothers. His father’s field is political science; his mother’s is history. Greilsammer’s first languages were Hebrew and French. “My dad was born and raised in Paris, so thanks to him I am fluent in French,” he says. English was an early addition. He began his piano studies at age 6.

A Juilliard student, Greilsammer lived in New York for nine years. For four years at the beginning of his career as a professional performer, he lived in Paris. Geneva is his current home.

Greilsammer’s participation in the third PUC 125 concert thrusts him into an experience where barriers between audience and performers dissolve. Listeners surround performing musicians on the stage. Performers chat with their auditors, rather than addressing them. Their experience is amplified by one of the three overhead works of art created by Marsha Levin-Rojer, who has made the constructions specifically for the PUC 125 set of concerts.

Levin-Rojer says about her work “As one who draws, I tend to see the world through line. I move easily between two and three dimensions.” She calls the piece that accompanies Greilsammer’s concert “Counterpoint.” It consists, she says, “of approximately 20,000 glass beads threaded on steel wire and twisted to celebrate the rich interplay of musical phrases.”

A veteran of the two enticing PUC 125 concerts that have taken place so far this season, I treat Greilsammer to my eyewitness account of the series so far. He is game about participating. Enthusiastically, he responds, “I like to talk to audiences.”

David Greilsammer, “Piano and Prepared Piano. Scarlatti/Cage sonatas: Journey Between Two Worlds,” Richardson Auditorium in Alexander Hall, Princeton University. Tuesday, December 1, 6 and 9 p.m. $25; $10 students. 609-258-9220 and www.princetonuniversityconcerts.org.

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