Dennis Johnson, a composer who in 1959 wrote a trailblazing Minimalist work, a six-hour piano meditation of repeated notes and long pauses that went unheard for 50 years before being rediscovered, died on Dec. 20 in Morgan Hill, Calif. He was 80.
His half brother, Don Wilson, said the cause was complications of dementia.
Until 10 years ago, long after Mr. Johnson had dropped composing for a career as a mathematician, his music was known only by reputation. References to it were found in the writings of the composer La Monte Young, who described Mr. Johnson as one of his closest musical allies when they were students at the University of California, Los Angeles.
Mr. Young is a founder of Minimalism, a genre of composition marked by repetition, gradual development and sometimes spare harmonies. Some of the most important contemporary composers, including John Adams, Steve Reich and Philip Glass, are at times associated with the movement or at least have incorporated such elements in their work.
Mr. Young is credited with composing the first Minimalist work, his String Trio of 1958, which unfolded so slowly that listeners focused less on its sequence of notes than on its long, sustained tones and glacial pace.
A year later, Mr. Johnson produced “November,” his piano work, which also moves glacially, starting with just two notes — a rising minor third — repeated several times before new material is added, in a process that yielded a flow of individual tones, sustained chords and silences.
Mr. Johnson described his compositional method in a 2013 interview with the music magazine The Wire: “I would just sit down at the piano and diddle, and listen, and it would slowly grow, like out of a seed,” he said. “Even now, when I do mathematics, it seems to be that way.”
Mr. Johnson’s innovations were repetition and generally consonant harmonies. Mr. Young has said that “November” influenced his own six-hour magnum opus, “The Well-Tuned Piano” (1964), considered an early landmark of the genre.
But for the next 50 years “November” was virtually unknown. The path to its revival began in 1992, when Mr. Young gave the critic and composer Kyle Gann a cassette tape with a partial performance, by Mr. Johnson, running 112 minutes.
Mr. Gann decided to reconstruct the score, using the tape and a handful of pages that Mr. Johnson had sent him detailing many of the work’s motifs as well as performance instructions. Mr. Gann performed a tag-team version of the piece with the pianist Sarah Cahill at the Second International Conference on Minimalist Music, at the University of Missouri, Kansas City, in 2009.
That performance led to a 2013 recording by R. Andrew Lee for Irritable Hedgehog, a new-music label. Mr. Gann’s reconstruction has also been recorded by the Dutch pianist Jeroen van Veen.
Though the score was unknown to most musicians until the release of Mr. Lee’s recording, its Minimalist qualities — and its influence on Mr. Young — have led to a reconsideration of Minimalism’s early history.
Dennis Lee Johnson was born in Los Angeles on Nov. 19, 1938, to Leroy Johnson, a building contractor, and Eloise (Jeffcoat) Johnson, a seamstress. His parents divorced before he was 8, and when his mother remarried, the family moved to Canoga Park, Calif.
In addition to Mr. Wilson, his half brother, Mr. Johnson is survived by a half sister, Judy Wilson Plouff.
Mr. Johnson’s early talent for mathematics earned him a full scholarship to Phillips Exeter Academy in New Hampshire, where he completed high school. He enrolled as a math student at the California Institute of Technology in 1956. But after a year he became disillusioned, and although he had studied the piano only casually as a child, he decided to transfer to U.C.L.A. to study music.
As part of Mr. Young’s iconoclastic circle, Mr. Johnson produced works that were often whimsical, like “Din,” in which 40 musicians screamed, clapped their hands and shuffled their feet in a darkened hall. They could also be conceptual, like a piece that consisted of a card containing only the word “Listen.” He continued performing for several years, both on the piano and on the hichiriki, a Japanese double reed instrument.
When Mr. Young moved to New York, in 1960, Mr. Johnson remained at U.C.L.A., shifting his focus to ethnomusicology and, by 1962, to mathematical study. But he visited New York several times from 1960 to 1965, and played the hichiriki in early versions of Mr. Young’s performance group, Theater of Eternal Music.
In 1966, Mr. Johnson gave up performing music publicly and began work on his doctorate in math, which he completed two years later. In 1969, he took a two-year position at the Institute of Advanced Study in Princeton, N.J. Beginning in the mid-1970s, he worked for a decade at NASA’s Jet Propulsion Laboratory, near Pasadena, first as a staff researcher and software developer and then as a consultant.
Among his projects at the lab was the radio mapping of Venus — a mathematical reconstruction of the planet’s surface using radar data. He also taught mathematics at the University of California, Berkeley, and continued his own research in advanced algebra and geometry.
His 1983 theorem, the Johnson homomorphism, is still studied in the field of geometric topology. After 1995, Mr. Johnson began working with Roger C. Alperin, a professor of mathematics at San Jose State University, on theoretical projects having to do with “understanding the symmetries of curves related to their geometry,” as Dr. Alperin explained it.
Mr. Johnson’s final mathematical work, a collaboration with Dr. Alperin, was published in the German journal Beiträge zur Algebra und Geometrie (Contributions to Algebra and Geometry) in January 2016.B:
2014香港六和开奖3877【没】【了】【乌】【雅】【丹】【的】【捣】【乱】，【宴】【会】【按】【计】【划】【进】【行】【着】，【金】【政】【民】【的】【态】【度】【摆】【得】【很】【低】，【赢】【得】【北】【地】【不】【少】【大】【臣】【的】【好】【感】。 【黄】【裕】【章】【甚】【至】【与】【身】【旁】【的】【傅】【正】【文】【低】【语】【感】【叹】：“【高】【丽】【这】【位】【皇】【子】，【不】【是】【个】【简】【单】【人】【物】。” “【可】【惜】【了】，【听】【说】【不】【得】【宠】。”【傅】【正】【文】【淡】【然】【一】【笑】，【深】【邃】【的】【眼】【睛】【逡】【巡】【在】【宴】【会】【厅】【中】，【与】【傅】【跬】【的】【神】【色】【倒】【是】【有】【七】【八】【分】【相】【像】。 【金】【政】【民】【在】【高】【丽】【确】【实】
【如】【果】【有】，【那】【么】【便】【再】【无】【可】【能】。 【苏】【梨】【靠】【在】【封】【怀】【瑾】【怀】【里】，【眼】【泪】【一】【串】【串】【流】【下】【来】，【身】【体】【都】【难】【受】【得】【抖】【动】【起】【来】。 【或】【许】【她】【真】【的】【再】【也】【见】【不】【到】【那】【个】【孩】【子】【了】。 “【你】【眼】【睛】【最】【近】【不】【好】，【所】【以】【这】【段】【时】【间】【不】【用】【再】【使】【用】【电】【子】【产】【品】。”【封】【怀】【瑾】【替】【她】【做】【了】【决】【定】。 【封】【怀】【瑾】【下】【意】【识】【地】【朝】【苏】【梨】【探】【过】【手】【来】。【苏】【梨】【猛】【然】【合】【上】【那】【双】【无】【神】【的】【眼】【睛】，【脸】【埋】【入】【自】【己】【曲】
【太】【上】【闻】【言】【微】【微】【一】【惊】，【他】【有】【些】【意】【外】【于】【时】【光】【北】【的】【回】【答】。 【然】【如】【此】【一】【来】，【自】【己】【似】【乎】【并】【没】【有】【什】【么】【理】【由】【可】【以】【拒】【绝】【了】【呢】。 “【既】【想】【去】，【那】【便】【走】【吧】！”【他】【道】。 “【还】【请】【稍】【等】【一】【下】，【我】【还】【要】【回】【去】【带】【一】【本】【书】。” “【那】【是】【一】【本】【怎】【样】【的】【书】？”【太】【上】【问】。 【他】【不】【太】【理】【解】，【心】【想】【都】【这】【个】【时】【候】【了】，【你】【丫】【的】【还】【有】【心】【情】【看】【书】？ 【时】【光】【北】【却】【道】。2014香港六和开奖3877“【温】【子】【言】，【你】【私】【自】【嫁】【给】【皇】【族】【女】【帝】，【本】【族】【长】【没】【来】【问】【罪】，【你】【倒】【是】【反】【而】【声】【讨】【起】【来】，【看】【来】【这】【几】【年】【在】【外】【面】【过】【得】【太】【好】【了】，【让】【你】【养】【成】【了】【目】【无】【尊】【长】【的】【性】【子】！” “【目】【无】【尊】【长】？【敢】【问】【族】【长】，【你】【是】【我】【的】【谁】？”【听】【着】【这】【怒】【吼】【声】，【温】【子】【言】【直】【接】【反】【问】。 “【你】…”【温】【馨】【刚】【想】【继】【续】【说】【话】，【心】【脏】【却】【猛】【然】【一】【痛】，【瞬】【间】【就】【脸】【色】【惨】【白】… “【族】【长】，【快】【来】【人】，
“【这】【不】【是】【重】【点】。”【邵】【行】【深】【说】：“【重】【点】【是】【现】【在】【怎】【么】【办】？” “【啧】【啧】【啧】。”【松】【晟】【睿】【翻】【了】【个】【大】【白】【眼】，“【现】【在】【这】【个】【是】【你】【的】【问】【题】【了】，【就】【不】【是】【重】【点】【了】？” 【他】【顿】【了】【顿】，【又】【道】：“【要】【我】【说】【啊】，【其】【实】【你】【们】【这】【种】【畸】【形】【关】【系】，【断】【了】【也】【好】，【不】【然】【你】【们】【除】【了】【在】【享】【受】【鱼】【水】【之】【欢】【的】【时】【候】，【其】【余】【时】【候】【是】【挺】【担】【惊】【受】【怕】【的】。” 【松】【晟】【睿】【这】【句】【话】【刚】【说】【完】，【那】
【文】【静】【的】【到】【来】【并】【非】【是】【什】【么】【好】【兆】【头】，【何】【诗】【梦】【已】【经】【预】【想】【到】【了】，【但】【没】【有】【想】【到】【她】【如】【此】【大】【胆】。 “【李】【威】【你】【到】【底】【选】【择】【我】【还】【是】【诗】【梦】，【今】【天】【就】【做】【出】【一】【个】【选】【择】。” 【这】【简】【直】【是】***【中】【的】【王】【炸】【牌】，【一】【旦】【打】【出】【了】【没】【有】【人】【可】【以】【阻】【挡】。 【原】【本】【愉】【快】【聊】【天】【的】【何】【震】【东】【一】【家】【脸】【色】【凝】【重】，【刚】【刚】【在】【他】【们】【眼】【里】【是】【一】【个】【好】【女】【婿】【形】【象】【的】【李】【威】，【居】【然】【是】【脚】【踏】【两】【只】【船】【的】
【卫】【家】【一】【行】【人】【中】【随】【着】【马】【车】【越】【走】【越】【远】，【除】【了】【卫】【锦】【明】，【见】【识】【过】【纳】【戒】【的】【神】【奇】，【对】【这】【些】【东】【西】【能】【快】【速】【接】【受】。 【还】【有】【小】【夏】【梦】【单】【纯】【喜】【欢】【亮】【晶】【晶】【的】【墙】【壁】，【基】【本】【上】【是】【震】【惊】【到】【麻】【木】。 【长】【峰】【县】【城】【下】【有】【这】【么】【一】【条】【通】【道】，【如】【此】【的】【宽】【广】，【居】【然】【没】【人】【发】【现】？ 【也】【不】【对】，【地】【窖】【只】【是】【个】【普】【通】【地】【窖】，【没】【任】【何】【机】【关】。 【说】【明】【这】【所】【田】【庄】【在】【被】【高】【飞】【买】【下】【之】【前】，【没】