Xenharmony
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Xenharmony
Xenharmonic music is music that uses a tuning system that is unlike the 12-tone equal temperament scale. It was named by Ivor Darreg, from Xenia (Greek ξενία), ''hospitable,'' and Xenos (Greek ξένος) ''foreign.'' He stated that it was "intended to include just intonation and such temperaments as the 5-, 7-, and 11-tone, along with the higher-numbered really-microtonal systems as far as one wishes to go." John Chalmers, author of ''Divisions of the Tetrachord'', wrote, "The converse of this definition is that music which can be performed in 12-tone equal temperament without significant loss of its identity is not truly ''microtonal''." Thus xenharmonic music may be distinguished from twelve-tone equal temperament, as well as use of intonation and equal temperaments, by the use of unfamiliar intervals, harmonies, and timbres.. Theorists other than Chalmers consider xenharmonic and non-xenharmonic to be subjective. Edward Foote, in his program notes for ''6 degrees of t ...
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Microtonal
Microtonal music or microtonality is the use in music of microtones—intervals smaller than a semitone, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of twelve equal intervals per octave. In other words, a microtone may be thought of as a note that falls between the keys of a piano tuned in equal temperament. In ''Revising the musical equal temperament,'' Haye Hinrichsen defines equal temperament as “the frequency ratios of all intervals are invariant under transposition (translational shifts along the keyboard), i.e., to be constant. The standard twelve-tone ''equal temperament'' (ET), which was originally invented in ancient China and rediscovered in Europe in the 16th century, is determined by two additional conditions. Firstly the octave is divided into twelve semitones. Secondly the octave, the most fundamental of all intervals, is postulated to be pure (beatless), as described by the ...
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Xenharmonic Versus Microtonal P4
Xenharmonic music is music that uses a tuning system that is unlike the 12-tone equal temperament scale. It was named by Ivor Darreg, from Xenia (Greek ξενία), ''hospitable,'' and Xenos (Greek ξένος) ''foreign.'' He stated that it was "intended to include just intonation and such temperaments as the 5-, 7-, and 11-tone, along with the higher-numbered really-microtonal systems as far as one wishes to go." John Chalmers, author of ''Divisions of the Tetrachord'', wrote, "The converse of this definition is that music which can be performed in 12-tone equal temperament without significant loss of its identity is not truly ''microtonal''." Thus xenharmonic music may be distinguished from twelve-tone equal temperament, as well as use of intonation and equal temperaments, by the use of unfamiliar intervals, harmonies, and timbres.. Theorists other than Chalmers consider xenharmonic and non-xenharmonic to be subjective. Edward Foote, in his program notes for ''6 degrees of ton ...
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Lou Harrison
Lou Silver Harrison (May 14, 1917 – February 2, 2003) was an American composer, music critic, music theorist, painter, and creator of unique musical instruments. Harrison initially wrote in a dissonant, ultramodernist style similar to his former teacher and contemporary, Henry Cowell, but later moved toward incorporating elements of non-Western cultures into his work. Notable examples include a number of pieces written for Javanese style gamelan instruments, inspired after studying with noted gamelan musician Kanjeng Notoprojo in Indonesia. Harrison would create his own musical ensembles and instruments with his partner, William Colvig, who are now both considered founders of the American gamelan movement and world music; along with composers Harry Partch and Claude Vivier, and ethnomusicologist Colin McPhee. The majority of Harrison's works and custom instruments are written for just intonation rather than the more widespread equal temperament, making him one of the most p ...
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Wendy Carlos
Wendy Carlos (born Walter Carlos, November 14, 1939) is an American musician and composer best known for her electronic music and film scores. Born and raised in Rhode Island, Carlos studied physics and music at Brown University before moving to New York City in 1962 to study music composition at Columbia University. Studying and working with various electronic musicians and technicians at the city's Columbia-Princeton Electronic Music Center, she helped in the development of the Moog synthesizer, Robert Moog's first commercially available keyboard instrument. Carlos came to prominence with ''Switched-On Bach'' (1968), an album of music by Johann Sebastian Bach performed on a Moog synthesizer, which helped popularize its use in the 1970s and won her three Grammy Awards. Its commercial success led to several more albums, including further synthesized classical music adaptations, and experimental and ambient music. She composed the score to two Stanley Kubrick films – ''A Cloc ...
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Elodie Lauten
Elodie Lauten (October 20, 1950 – June 3, 2014) was a French-born American composer described as postminimalist or a microtonalist. Biography Born in Paris, France as Genevieve Schecroun, and educated in Paris at the Lycée Claude Monet, the Conservatoire (piano) and the Institut d’Etudes Politiques.Obituary
nytimes.com; accessed March 4, 2015.
Her father was (né Raphaël Schecroun), an n-born jazz musician; her mother was a classical pianist. Lauten was classically trained as a pianist since age 7. She con ...
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Annie Gosfield
Annie Gosfield (born September 11, 1960 in Philadelphia) is a New-York-based composer who works on the boundaries between notated and improvised music, electronic and acoustic sounds, refined timbres and noise. She composes for others and performs with her own group, taking her music to festivals, factories, clubs, art spaces and concert halls. Much of her work combines acoustic instruments with electronic sounds, incorporating unusual sources such as satellite sounds, machine sounds, detuned or out-of-tune samples and industrial noises. Her work often contains improvisation and frequently uses extended techniques and/or altered musical instruments. She won a 2012 Berlin Prize. Work Gosfield's work includes large-scale compositions, opera, orchestral work, chamber music, electronic music, video projects, and music for dance. She uses traditional notation, improvisation and extended techniques to explore relationships between music and noise. Her music is often inspired by n ...
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Logarithms
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of is , or . The logarithm of to ''base''  is denoted as , or without parentheses, , or even without the explicit base, , when no confusion is possible, or when the base does not matter such as in big O notation. The logarithm base is called the decimal or common logarithm and is commonly used in science and engineering. The natural logarithm has the number  as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base and is frequently used in computer science. Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. They were rapidly adopted by navigators, scientists, engineers, surveyors and others to perform high-accur ...
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The Apples In Stereo
The Apples in Stereo, styled as The Apples in stereo, are an American pop/rock band associated with Elephant 6 Collective, a group of bands also including Neutral Milk Hotel, The Olivia Tremor Control, Elf Power, Of Montreal, and Circulatory System. The band is largely a product of lead vocalist/guitarist/producer Robert Schneider, who writes the majority of the band's music and lyrics. Currently, The Apples in Stereo also includes longstanding members John Hill (rhythm guitar) and Eric Allen (bass), as well as more recent members John Dufilho (drums), John Ferguson (keyboards), and Ben Phelan (keyboards/guitar/trumpet). The band's sound draws comparisons to the psychedelic rock of The Beatles and The Beach Boys during the 1960s, as well as to bands such as Electric Light Orchestra and Pavement, and also draws from lo-fi, garage rock, new wave, R&B, bubblegum pop, power pop, punk, electro-pop and experimental music. The band is also well known for their appearance in a ''T ...
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Robert Schneider
Robert Peter Schneider (born March 9, 1971) is an American musician and mathematician. He is the lead singer, songwriter, guitarist and producer of rock/pop band the Apples in Stereo and has produced and performed on albums by Neutral Milk Hotel, the Olivia Tremor Control and a number of other psychedelic and indie rock bands. Schneider co-founded The Elephant 6 Recording Company in 1992. He received a PhD in mathematics from Emory University in 2018. , he is an Assistant Professor of Mathematical Sciences at Michigan Technological University. Life and career Early life After spending the first six years of his life in Cape Town, South Africa, Robert Schneider's family moved to Ruston, Louisiana. In Louisiana, Schneider befriended Bill Doss, Will Cullen Hart and Jeff Mangum, and began discovering and playing music with them. After graduating from Ruston High School, where he was Junior and Senior class president, and spending two years at Centenary College in Shrevep ...
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Non-Pythagorean Scale
Robert Peter Schneider (born March 9, 1971) is an American musician and mathematician. He is the lead singer, songwriter, guitarist and producer of rock/pop band the Apples in Stereo and has produced and performed on albums by Neutral Milk Hotel, the Olivia Tremor Control and a number of other psychedelic and indie rock bands. Schneider co-founded The Elephant 6 Recording Company in 1992. He received a PhD in mathematics from Emory University in 2018. , he is an Assistant Professor of Mathematical Sciences at Michigan Technological University. Life and career Early life After spending the first six years of his life in Cape Town, South Africa, Robert Schneider's family moved to Ruston, Louisiana. In Louisiana, Schneider befriended Bill Doss, Will Cullen Hart and Jeff Mangum, and began discovering and playing music with them. After graduating from Ruston High School, where he was Junior and Senior class president, and spending two years at Centenary College in Shreveport, ...
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Elaine Walker (composer)
Elaine Walker is a composer, electronic musician and author born in 1969. She wrote a physics/philosophy book, “Matter Over Mind: Cosmos, Chaos, and Curiosity” (2016). She specializes in microtonal music, including founding ZIA, an all electronic band, and performing with D.D.T. She has performed with Number Sine.Homepage
, ''ZIASpace.com''.
She describes: "I compose microtonal music strictly by ear and leave it to others to analyze, so you won't find ratios or mathematics here."


Life

Raised in southern New Mexico "by two loving mathematicians, Elaine grew to love the desert in all of its glory and wide openness". Her father was . Walker has a Music
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George De La Warr
George Walter de la Warr (19 August 1904 – 31 March 1969) was born in the Northern England, and in later life became a civil engineer in the pay of Oxfordshire County Council. In 1953 he resigned from this post to work within the discredited field of radionics, in which he was a pioneer. His devices were denounced by medical experts.Williams, William F. (2000). '' Encyclopedia of Pseudoscience: From Alien Abductions to Zone Therapy''. Facts on File Inc. p. 37. "Radionics"
The Skeptic's Dictionary.


Career

Warr was influenced by the devices of . He claimed to have invented a camera that could detect and cure diseases by remote control. In June 1960, he was sued in th ...
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