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SIL International

SIL International (formerly known as the Summer Institute of Linguistics) is an evangelical Christian nonprofit organization whose main purpose is to study, develop and document languages, especially those that are lesser-known, in order to expand linguistic knowledge, promote literacy, translate the Christian Bible into local languages, and aid minority language development.

Based on its language documentation work, SIL publishes a database, Ethnologue, of its research into the world's languages, and develops and publishes software programs for language documentation, such as FieldWorks Language Explorer (FLEx) and Lexique Pro.

Its main offices in the United States are located at the International Linguistics Center in Dallas, Texas.

History
William Cameron Townsend, a Presbyterian minister, founded the organization in 1934, after undertaking a Christian mission with the Disciples of Christ among the Kaqchikel Maya people in Guatemala in the early 1930s. In 1933, he turned to Mexico with the purpose of translating the Bible into indigenous languages there, as he had done for Kaqchikel. Townsend established a working relationship with the Mexican Secretariat of Public Education under the government of President Lázaro Cárdenas (in office 1934–1940) and founded SIL to educate linguist-missionaries to work in Mexico. Because the Mexican government did not allow missionary work through its educational system, Townsend founded Wycliffe Bible Translators in 1942 as a separate organization from SIL. Wycliffe Bible Translators focused on Bible translation and missionary activities, whereas SIL focused on linguistic documentation and literacy education.

Having initiated collaboration with the Mexican education authorities, Townsend started the institute as a small summer training-session in Sulphur Springs, Arkansas, in 1934 to train missionaries in basic linguistic, anthropological, and translation principles. Through the following decades the SIL linguists worked at providing literacy education to indigenous people of Mexico, while simultaneously working with the Wycliffe Bible Translators on Bible translation. One of the students at the first summer institute in its second year, 1935, Kenneth Lee Pike (1912–2000), would become the foremost figure in the history of SIL. He served as SIL's president from 1942 to 1979, then as president emeritus until his death in 2000.

The Mexican branch, Instituto Lingüístico de Verano, was established in 1948.

In 2016, Michel Kenmogne from Cameroon became president.

SIL said it had 1,350 language projects in 98 countries and 4,200 staff from 84 countries.

Contributions
SIL's principal contribution to linguistics has been the data that have been gathered and analyzed from over 1,000 minority and endangered languages, many of which had not been previously studied academically. SIL endeavors to share both the data and the results of analysis in order to contribute to the overall knowledge of language. This has resulted in publications on languages such as Hixkaryana and Pirahã, which have challenged the universality of some linguistic theories. SIL's work has resulted in over 20,000 technical publications, all of which are listed in the SIL Bibliography. Most of these are a reflection of linguistic fieldwork.

SIL's focus has not been on the development of new linguistic theories, but tagmemics, though no longer promoted by SIL, was developed by Kenneth Pike, who also coined the words emic and etic, more widely used today in anthropology.

Another focus of SIL is literacy work, particularly in indigenous languages. SIL assists local, regional, and national agencies that are developing formal and informal education in vernacular languages. These cooperative efforts enable new advances in the complex field of educational development in multilingual and multicultural societies.

SIL provides instructors and instructional materials for linguistics programs at several major institutions of higher learning around the world. In the United States, these include Dallas International University, Biola University, Moody Bible Institute, and Dallas Theological Seminary. Other universities with SIL programs include Trinity Western University in Canada, Charles Darwin University in Australia, and Universidad Ricardo Palma in Lima, Peru.

The organization has recently established a new Language and Culture Documentation Services Unit that aims to preserve and revitalize languages threatened by extinction. The creation of this department reflects a growing interest in documenting endangered languages and incorporates a multidisciplinary approach of anthropology and linguistics.

Affiliations
SIL has Consultative Status with UNESCO as an NGO, and has Special Consultative Status with the United Nations Economic and Social Council (ECOSOC) as an advocate for ethnolinguistic communities.

The organization is a member of the Forum of Bible Agencies International and Micah Network, and is a founding member of Maaya, the World Network for Linguistic Diversity.

Ethnologue and ISO 639-3 codes
Ethnologue: A Guide to the World's Languages has been published by SIL since 1951.

From the 13th edition (1997) onwards, the entire contents of the published book were also shared online. From the 17th edition onwards (2013) the publication shifted to a web-centric paradigm, meaning that the website is now the primary means by which the database is accessed. Among other advantages, this greatly facilitates user contributions. A new edition is now published every February. The 27th edition was released in February 2024 and lists 7,164 languages.

Starting with the 16th edition (2009), Ethnologue uses the ISO 639-3 standard, which assigns 3-letter codes to languages; these were derived in part from the 3-letter codes that were used in the Ethnologue 's 15th edition. SIL is the registration authority for the ISO 639-3 standard.

With the publication of the 17th edition (2016), Ethnologue launched a subscription service, but claiming that the paywall would only affect 5% of users. Users who contribute over 100 accepted changes are rewarded with lifetime free access.

A comprehensive review of the 16th, 17th and 18th editions acknowledged that "[Ethnologue] is at present still better than any other nonderivative work of the same scope" except that "[it] fails to disclose the sources for the information presented.

Software
SIL has developed widely used software for linguistic research.
 * Adapt It is a tool for translating text from one language into a related language after performing limited linguistic analysis.
 * In the field of lexicon collection, ShoeBox, the newer ToolBox (Field Linguist's Toolbox), and Lexique Pro have largely been replaced by FieldWorks Language Explorer (FLEx Windows and Linux)  for linguists and WeSay (also Windows and Linux)  for non-professionals. SIL also provides a "Webonary" website for publishing dictionaries.
 * Graphite is a smart-font technology and rendering system.
 * Keyman is a keyboard software solution for typing over 2000 of the world's languages and can be used to make custom keyboards.

Fonts
SIL has developed several widely used font sets that it makes available as free software under the SIL Open Font License (OFL). The names of SIL fonts reflect the Biblical mission of the organization "charis" (Greek for "grace"), "doulos" (Greek for "servant") and "gentium" (Latin for "of the nations"). These fonts have become standard resources for linguists working on the documentation of the world's languages. Most of them are designed only for specific writing systems, such as Ethiopic, Devanagari, New Tai Lue, Hebrew, Arabic, Khmer, Yi, Myanmar, Coptic, and Tai Viet, or some more technical notation, such as cipher musical notation or IPA. Fonts that support Latin include:
 * Gentium: "a typeface family designed to enable the diverse ethnic groups around the world who use the Latin, Cyrillic and Greek scripts to produce readable, high-quality publications. It supports a wide range of Latin- and Cyrillic-based alphabets."
 * Doulos SIL: "a Unicode serif font similar in design to Times/Times New Roman. It contains a comprehensive inventory of glyphs needed for almost any Roman- or Cyrillic-based writing system, whether used for phonetic or orthographic needs. In addition, there is provision for other characters and symbols useful to linguists. It contains near-complete coverage of all the characters defined in Unicode 7.0 for Latin and Cyrillic."
 * Charis SIL: "a Unicode-based font family that supports the wide range of languages that use the Latin and Cyrillic scripts. It is specially designed to make long texts pleasant and easy to read, even in less than ideal reproduction and display environments."
 * Andika: "a sans serif Unicode font designed especially for literacy use and the needs of beginning readers. The focus is on clear letterforms that will not be easily confused with one another. It supports near-complete coverage for Latin and Cyrillic."

Recognitions
The 1947 Summer Meeting of the Linguistic Society of America passed a resolution that the work of SIL "should be strongly commended by our Society and welcomed as one of the most promising developments in applied linguistics in this country."

SIL holds formal consultative status with UNESCO and the United Nations, and has been publicly recognized by UNESCO for their work in many parts of Asia. SIL also holds non-governmental organization status in many countries.

SIL's work has received appreciation and recognition in a number of international settings. In 1973, SIL was awarded the Ramon Magsaysay Award for International Understanding. This foundation honors outstanding individuals and organizations working in Asia who manifest greatness of spirit in service to the peoples of Asia. UNESCO Literacy Prizes have been awarded to SIL's work in a number of countries: Australia (1969), Cameroon (1986), Papua New Guinea (1979), Philippines (1991).

Criticism
In 1979, SIL's agreement was officially terminated by the Mexican government after critiques from anthropologists regarding the combination of education and missionary activities in indigenous communities, though SIL continued to be active in that country. At a conference of the Inter-American Indian Institute in Mérida, Yucatán, in November 1980, delegates denounced the Summer Institute of Linguistics, charging that it was using a scientific name to conceal its Protestant agenda and an alleged capitalist view that was alien to indigenous traditions. This led to the agreement with the Ecuadoran government being terminated in 1980, although a token presence remained. In the early 1990s, the Confederation of Indigenous Nationalities of Ecuador (CONAIE) demanded the expulsion of SIL from the country. SIL was also expelled from Brazil, Mexico, and Panama, and restricted in Colombia and Peru.

The organization's focus on language description, language development and Bible translation, and the missionary activities carried out by many of its field workers have been criticized by linguists and anthropologists who argue that SIL aims to change indigenous cultures, which exacerbates the problems that cause language endangerment and language death. Linguists have argued that the missionary focus of SIL makes relations with academic linguists and their reliance on SIL software and knowledge infrastructure problematic in that respective goals, while often overlapping, also sometimes diverge considerably.

SIL does not consider efforts to change cultural patterns a form of culture destruction and points out that all their work is based on the voluntary participation of indigenous peoples. In the SIL view, ethnocide is not a valid concept and it would lead to pessimism to characterize culture change resulting from the inevitable progress of civilization as ethnocide. SIL considers itself as actively protecting endangered languages by promoting them within the speech community and providing mother-tongue literacy training. Additionally, their expanded interest in preserving threatened languages has resulted in the creation of a Language and Culture Documentation Services Unit.

Regional offices
Besides the headquarters in Dallas, SIL has offices and locally incorporated affiliated organizations in the following countries:

Africa

 * Cameroon: Yaoundé (central office), Bamenda (regional office), Maroua (regional bureau for the north of the country)
 * Chad: N'Djaména
 * Ethiopia: Addis Ababa
 * Senegal: Dakar (central office), Ziguinchor (regional office), Thies (regional office)
 * Togo: Lomé
 * Kenya: Nairobi (Africa Regional Office)
 * Nigeria: Jos

Americas

 * Brazil: Cuiabá
 * Colombia (1962–2002)
 * Mexico: Instituto Lingüístico de Verano (Mexico), based in the Tlalpan borough of Mexico City
 * Peru: Instituto Lingüístico de Verano (Peru), based in Lima
 * Suriname (1968–2001)

Asia

 * Philippines: Quezon City

Oceania

 * Australia: Kangaroo Ground (Melbourne suburbs)
 * Papua New Guinea: Ukarumpa

title: SIL International


text:
Neartown Houston

Montrose is an area located in west-central Houston, Texas, United States and is one of the city's major cultural areas. Montrose is a 7.5 sqmi area roughly bounded by Interstate 69/U.S. Highway 59 to the south, Allen Parkway to the north, South Shepherd Drive to the west, and Taft to Fairview to Bagby to Highway 59 to Main to the east. Montrose neighborhoods include Cherryhurst, Courtlandt Place, Hyde Park, Montrose, Vermont Commons, North and East Montrose, Mandell Place and Winlow Place. Montrose is also less well known by the moniker Neartown, encompassing Superneighborhood #24.

History
Neartown has many of Houston's oldest neighborhoods. The Neartown Association began in 1963. Houston's urban real estate boom starting in the 1990s transformed Neartown and significantly increased property values.

The City of Houston's Planning Department refers to Neartown as a mixed-use community. Since the 1990s gentrification, musicians and artists are being replaced with higher paid professionals (attorneys, educators, medical professionals) due to higher rents. Montrose has "wound a tortuous course from Silk Stocking and Low Rent and back again." In 1997 Katherine Feser of the Houston Chronicle stated that "Montrose [is] not for starving artists anymore".

On June 6, 2006, a teenage MS-13 gang member named Gabriel Granillo was stabbed to death at Ervan Chew Park.

Culture

The River Oaks Shopping Center, Houston's first shopping center, is located in Neartown, east of River Oaks. Constructed in 1927 and designed by architect Hugh Prather, the center, originally known as River Oaks Community Center, was one of the nation's first automobile-oriented retail centers. Its design, with arcs of retail space on either side of West Gray Avenue, was considered a model for future development. Portions of the historic shopping center were demolished in September 2007 to redevelop the site for bookstore and a parking garage. As of 2008, Landmark Theatres operates the River Oaks Theatre, an "arthouse" theater, located in the center. The theater is the last historic movie theater in Houston that is still being used as it was originally designed.

Cityscape

Neartown was described in 1973 as "old buildings ranging all the way from Victorian Epic to Ramshackle Plywood." Neartown has European-style restaurants and sidewalk cafés along five blocks of Westheimer with many housed in renovated pre-World War I houses. The Neartown neighborhood along Van Buren Street was the Houston Press "Best Hidden Neighborhood" in 2002.

Demographics
In 2015 the Houston city government-defined Neartown/Montrose Super Neighborhood had 31,037 residents. 71% were non-Hispanic white, 18% were Hispanic, 6% were non-Hispanic Asians, 4% were non-Hispanic blacks, and 1% were non-Hispanic others. In 2000 the super neighborhood had 28,015 people. 68% were non-Hispanic whites, 23% were Hispanic, 4% each were non-Hispanic black and Asian, and 2% were non-Hispanic others.

Local government
The community is within the Houston Police Department's Central Patrol Division, headquartered at 61 Riesner. The Neartown Storefront Station is located at 802 Westheimer. The City of Houston purchased the building used for the storefront with federal community development funds. By September 20, 1990, the Neartown Business Alliance spent around $4,000 per year to maintain the storefront.

Houston Fire Department Fire Station 16 serves the area. The fire station is in Fire District 6. The station opened at the intersection of Westheimer Road and Yupon in 1928. The station moved to the intersection of Richmond and Dunlavy in 1979.

City Council District D covers Neartown. As of 2008 Wanda Adams represents the district. Since the City of Houston Redistricting of 2011, Neartown has been represented in Council by Ellen Cohen in District C.

County, state, and federal representation
Harris County Precinct One, as of 2008 headed by El Franco Lee, serves Neartown. The county operates the Neartown Office at 1413 Westheimer Road.

A portion of Neartown is located in District 134 of the Texas House of Representatives. As of 2010, Sarah Davis represents District 134. A portion of Neartown is located in District 147 of the Texas House of Representatives. As of 2008, Garnet F. Coleman represents the district. Neartown is located in District 13 of the Texas Senate. As of 2008 its representative is Rodney Ellis.

The community is located within Texas's 7th congressional district. Since redistricting effective for the 2012 election, Neartown has been redrawn into the Texas 2nd Congressional District, served by Ted Poe. The United States Postal Service operates two post offices, the University Post Office at 1319 Richmond Avenue and the River Oaks Station Post Office at 1900 West Gray Street, in Neartown.

Places of interest

 * Museums
 * Menil Collection art museum
 * Rothko Chapel
 * Houston Center for Photography
 * Byzantine Fresco Chapel Museum
 * Museo Guadalupe Aztlan
 * Museum of Printing History

 * Consulates
 * Consulate-General of the People's Republic of China (closed)
 * Consulate-General of Norway
 * Radio
 * KPFT 90.1 FM, a Pacifica Radio affiliate, located at 419 Lovett Boulevard

 * Community
 * Houston GLBT Community Center
 * Pride Committee of Houston

 * Festivals
 * Houston Greek Festival, usually held in October, on the grounds of the Annunciation Greek Orthodox Cathedral

 * Parades
 * Houston Art Car Parade
 * Houston Gay Pride Parade to commemorate the Stonewall Riots

 * Cathedrals and Churches
 * Annunciation Greek Orthodox Cathedral
 * Chapel of St. Basil at the University of St. Thomas (Texas)(designed by esteemed architect Philip Johnson)

Economy
The headquarters of Baker Hughes is in the America Tower at the American General Center Service Corporation International has its headquarters in Neartown.

On July 1, 1983 Continental Airlines's headquarters were located at the America Tower in Neartown, and would remain there until the relocation to Continental Center I in Downtown Houston, announced by the airline in 1997, that occurred in stages in 1998 and 1999.

Colleges and universities
Neartown is home to the University of Saint Thomas.

Neartown is also close to Rice University, The University of Texas Health Science Center at Houston, the University of Houston, Texas Southern University, Houston Community College Central, and University of Houston–Downtown.

Public schools
Pupils in Neartown are in the Houston Independent School District. Neartown is divided among Trustee District IV, represented by Paula M. Harris as of 2008, Trustee District V, represented by Dianne Johnson as of 2008, and Trustee District VIII, represented by Diana Dávila as of 2008.

Baker Montessori School (formerly Wilson Montessori School, in Neartown), Gregory-Lincoln Education Center (in the Fourth Ward), MacGregor Elementary School, Poe Elementary School (in Boulevard Oaks), and Wharton Elementary School (in Neartown) serve separate sections of Neartown.

Pupils in Neartown reside within the boundaries of three middle-school attendance areas. Lanier Middle School (in Neartown), Cullen Middle School, and Gregory-Lincoln Education Center serve separate sections of Neartown. All Neartown area pupils are zoned to Lamar High School in Upper Kirby.

In Fall 2019 Arabic Immersion Magnet School is scheduled to move into the former High School for the Performing and Visual Arts building.

Histories of schools
For a period, Montrose Elementary School was in Neartown. Southmore Elementary School opened in 1921, Wilson in 1925, Lanier in 1926, Poe in 1928, and Wharton in 1929. Southmore was renamed MacGregor Elementary School in 1930 and Lamar opened in 1937. Ryan opened in 1958 after Yates High School moved to a new campus. Gregory-Lincoln opened in 1966 and its current facility opened in 2007. Before the start of the 2009–2010 school year J. Will Jones, which formerly served a section of Neartown, was consolidated into Blackshear Elementary School, a campus in the Third Ward. During its final year of enrollment J. Will Jones had more students than Blackshear.

Previously Ryan Middle School served a segment of Neartown. In March 2013 the HISD board voted to close Ryan Middle School and move all students into the zone of Cullen Middle School. The High School for the Performing and Visual Arts moved to Downtown Houston in 2019.

Private schools
Neartown is home to the Annunciation Orthodox School (a K-8 private school) and The Harris School. The Kinkaid School was located in the Neartown area until 1957 when the school moved to Piney Point Village.

Public libraries
The administrative offices of the Houston Public Library are located in the Marston Building in Neartown. The City of Houston spent $1.3 million to renovate the Marston Building to accommodate HPL staff. The administration moved to the building after the Central Library was scheduled to close in 2006.

The Eleanor K. Freed-Montrose Neighborhood Library of Houston Public Library is at 4100 Montrose Boulevard.

Media
The Houston Chronicle is the area regional newspaper. The River Oaks Examiner is a local newspaper distributed in the community.

Health services
Legacy Community Health Services and Montrose Counseling Center  are located in Neartown. In 2006 the Metropolitan Multi-Service Center was moved from the Houston Department of Health and Human Services to the Houston Parks and Recreation Department. It became the West Gray Adaptive Recreation Center.

Parks and recreation
Ervan Chew Park, a fenced-in, approximately 9000 sqft park, is located at 4502 Dunlavy Street. The park (originally Herbert D. Dunlavy Park) was acquired by the City of Houston in 1945. In February 2000 the park was renamed for Ervan Chew, a Chinese-American Eagle Scout who grew up in the area and won the Silver Beaver Award, which was delivered by Ronald Reagan, in 1986; Chew died at age 42, on January 19, 1999. Chew Park has a basketball half court, small soccer (football) field, a dog park and a baseball diamond. Ervan Chew Park has little league games and dog parties. The Neartown Little League, located in Neartown, holds its games at Chew Park. Chew Park was the first park to let dogs run without leashes in a special zone. The Friends of Ervan Chew Park funded the dog zone, which was dedicated in May 2004.

Notable residents

 * Denton Cooley
 * Walter Cronkite
 * Clark Gable
 * Howard Hughes
 * Lyndon B. Johnson
 * Mirabeau B. Lamar (the site for Lamar's family home is now Woodrow Wilson Montessori School)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Neartown Houston


text:
Method of successive substitution

In modular arithmetic, the method of successive substitution is a method of solving problems of simultaneous congruences by using the definition of the congruence equation. It is commonly applied in cases where the conditions of the Chinese remainder theorem are not satisfied.

There is also an unrelated numerical-analysis method of successive substitution, a randomized algorithm used for root finding, an application of fixed-point iteration.

The method of successive substitution is also known as back substitution.

Example One
Consider the simple set of simultaneous congruences
 * x ≡ 3 (mod 4)
 * x ≡ 5 (mod 6)

Now, for x ≡ 3 (mod 4) to be true, x = 3 + 4j for some integer j. Substitute this in the second equation
 * 3+4j ≡ 5 (mod 6)

since we are looking for a solution to both equations.

Subtract 3 from both sides (this is permitted in modular arithmetic)
 * 4j ≡ 2 (mod 6)

We simplify by dividing by the greatest common divisor of 4,2 and 6. Division by 2 yields:
 * 2j ≡ 1 (mod 3)

The Euclidean modular multiplicative inverse of 2 mod 3 is 2. After multiplying both sides with the inverse, we obtain:
 * j ≡ 2 × 1 (mod 3)

or
 * j ≡ 2 (mod 3)

For the above to be true: j = 2 + 3k for some integer k. Now substitute back into 3 + 4j and we obtain
 * x = 3 + 4(2 + 3k)

Expand:
 * x = 11 + 12k

to obtain the solution

x ≡ 11 (mod 12)

Example 2 (An Easier Method)
Although the method utilized in the preceding example is coherent, it does not work for every problem.

Consider these four systems of congruences: In order to proceed in finding an expression that represents all the solutions that satisfies this system of linear congruences, it is important to know that a (mod b) has an analogous identity:
 * x ≡ 1 (mod 2)
 * x ≡ 2 (mod 3)
 * x ≡ 3 (mod 5)
 * x ≡ 4 (mod 11)
 * a (mod b) ⇔ bk + a, ∀k ∈ Z, where k is an arbitrary constant.

PROCEDURE
1. Begin by rewriting the first congruence as an equation: 2. Rewrite the second congruence as an equation, and set the equation found in the first step equal to this equation, since x will substitute the x in the second congruence: Because a must be a positive nonnegative inverse, we need a positive a. Thus, we add whatever our current modulus is to a, which is a = -1 + 3 = 2.
 * x = 2a + 1, ∀a ∈ Z
 * x ≡ 2 (mod 3)
 * x = 2a + 1 ≡ 2 (mod 3)
 * 2a ≡ 1 (mod 3)
 * a ≡ 2−1 (mod 3)
 * a = -1.

3. We now rewrite a = 2 in terms of our current modulus: 4. We now substitute our current value of a into our equation that we found in step 1 with respect to x: ∴ x = 6b + 5.
 * a = 2 (mod 3)
 * ∴ a = 3b + 2
 * x = 2a + 1
 *  = 2(3b + 2) + 1, ∀b ∈ Z
 * = 6b + 5.

5. We now substitute our new value for x into the x in our third linear congruence, and rewrite 3 (mod 5) to its equivalent expression: Because b = -2, we add our current to modulus to it in order to obtain b = 3.
 * x ≡ 3 (mod 5)
 * = 6b + 5 ≡ 3 (mod 5)
 * = 6b + 5 = 5b + 3
 * = b = -2.

∴ b = 5c + 3.

6. We again substitute our new value for b into our equation that we found in step 4 with respect to x: ∴ x = 30c + 23, ∀c ∈ Z
 * x = 6b + 5
 * = 6(5c + 3) + 5
 * = 30c + 23

7. We now substitute our new value for x into the x of our final linear congruence, rewriting 4 (mod 11) to its equivalent expression: Adding our current modulus to the value that c represents, our new c = 10.
 * x ≡ 4 (mod 11)
 * = 30c + 18 ≡ 4 (mod 11)
 * = 30c + 23 = 11c + 4
 * = 19c = -19
 * = c = -1.

∴ c = 11d + 10, ∀d ∈ Z.

8. Our final step is to substitute c into the equation with respect to x that we found in step 6: ∴ 330d + 323 represents all solutions that satisfies the system of congruences with which we began.
 * x = 30c + 23
 * = 30(11d + 10) + 23
 * = 330d + 323.

Checking Our Work
To check that our answer is correct, we deduce whether each respective residue is conceived when we compute 323 by the modulo of each congruence:

323 ≡ 1 (mod 2) 323 ≡ 2 (mod 3) 323 ≡ 3 (mod 5) 323 ≡ 4 (mod 11) An alternative method would be to deduce whether each modulus divides the difference of 323 and each congruence's respective residue:
 * 323 = 161 * 2 + 1
 * 323 = 107 * 3 + 2
 * 323 = 64 * 5 + 3
 * 323 = 29 * 11 + 4

2 | (323 - 1) is true.

3 | (323 - 2) is true.

5 | (323 - 3) is true.

11 | (323 - 4) is true.

Another way to solve the system of linear congruences is to use the Chinese Remainder Theorem, and it will give us the same result.

Example 3 (Similar Method Utilized Above but with a Twist)
When solving a system of linear congruences using the method utilized in the above example, there will be situations where solving for a variable will produce a rational.

The key to solving for the variable is to add the current modulus to the other side of the equation, until a multiple of the coefficient of the variable that is being solved for

is procured. Here is an example:
 * x ≡ 2 (mod 3)
 * x ≡ 3 (mod 5)
 * x ≡ 2 (mod 7)

PROCEDURE
1. Rewrite the first linear congruence to its equivalent equation: 2. Rewrite the second congruence as an equation, and set the expression equal to the expression found in the preceding step: This is where the method used in example 2 appears to have troubles, but I found a solution: Add whatever the current modulus is to the side of the equation where the variable is not, until the coefficient is able to divide it. The reason why we can do this is because of the definition of a congruence class Thus,
 * x ≡ 2 (mod 3)
 * x = 3a + 2, ∀a ∈ Z.
 * x ≡ 3 (mod 5)
 * x = 5a + 3, ∀a ∈ Z
 * 3a + 2 = 5a + 3
 * -1 = 2a

3. Add 5, which is our modulus, to -1, to obtain: 4. Rewrite a = 2 as its equivalent modular equation 5. Substitute our current a into the equation procured in step 1 with respect to x: 6. Finally, rewrite the third congruence, and set it equal to the equation incurred in the preceding step, solving for b. Substituting for x, we have Add our current modulus, which is 7, to -6, until a multiple of 8 is conceived: Thus, Rewriting b in terms of its modulus, we have 7. Substitute our new equation b for b in the equation with respect to x we conceived in step 6: ∴ 105c + 23 represents all solutions that satisfies the system of congruences with which we began.
 * -1 + 5 = 4
 * 4 = 2a
 * a = 2.
 * a = 2 becomes a = 5b + 2, ∀b ∈ Z.
 * x = 3a + 2 = 3 (5b + 2) + 2 = 15b + 8.
 * ∴ x = 15b + 8.
 * x ≡ 2 (mod 7) can be rewritten as x = 7b + 2
 * 15b + 8 = 7b + 2
 * 8b = -6
 * -6 + 7 = 1 + 7 = 8.
 * 8b = 8
 * b = 1.
 * b = 7c + 1, ∀c ∈ Z
 * x = 15b + 8
 * = 15 (7c + 1) + 8
 * = 105c + 23
 * ∴ x = 105c + 23.

Checking Our Work
To check that our answer is correct, we deduce whether each respective residue is conceived when we compute 23 by the modulo of each congruence:

23 ≡ 2 (mod 3) 23 ≡ 3 (mod 5) 23 ≡ 2 (mod 7)
 * 23 = 7 * 3 + 2
 * 23 = 4 * 5 + 3
 * 23 = 3 * 7 + 2

General algorithm
In general:
 * write the first equation in its equivalent form
 * substitute it into the next
 * simplify, use the modular multiplicative inverse if necessary
 * continue until the last equation
 * back substitute, then simplify
 * rewrite back in the congruence form

If the moduli are coprime, the Chinese remainder theorem gives a straightforward formula to obtain the solution.

title: Method of successive substitution


text:
Raymond Leppard

Raymond John Leppard (11 August 1927 – 22 October 2019) was a British-American conductor, harpsichordist, composer and editor. In the 1960s, he played a prime role in the rebirth of interest in Baroque music; in particular, he was one of the first major conductors to perform Baroque opera, reviving works by Claudio Monteverdi and Francesco Cavalli. He conducted operas at major international opera houses and festivals, including the Glyndebourne Festival where he led the world premiere of Nicholas Maw's The Rising of the Moon, the Metropolitan Opera and the Royal Opera House. He composed film scores such as Lord of the Flies and Alfred the Great.

Life and career
Leppard (pronounced LEPP-ard) was born in London and grew up in Bath, Somerset, where he was educated at the City of Bath Boys' School, now known as the Beechen Cliff School. He studied harpsichord and viola at Trinity College, Cambridge, and became interested in choral conducting.

In 1952, he made his London debut at Wigmore Hall in London, conducted his own Leppard Ensemble. He became closely associated with the Goldsbrough Orchestra, which became the English Chamber Orchestra in 1960. Also, he gave recitals as harpsichordist, and was a fellow of Trinity College and a lecturer in music from 1958 to 1968. He retired from his post as Director of Music at Trinity College in 1968.

His interest in early music prompted him to prepare several realisations of scores from the period. While musicologists considered his editions controversial, his performances were important for introducing early operatic masterpieces to the general public. In 1962, he prepared a performing score of Monteverdi's L'incoronazione di Poppea for a production at the Glyndebourne Festival. He subsequently edited Monteverdi's other surviving stage works, L'Orfeo and Il ritorno d'Ulisse in patria, as well as operas by Francesco Cavalli and Jean-Philippe Rameau. He conducted several of his realisations both in the theatre and in the recording studio.

In 1963, he composed the original film score for Peter Brook's Lord of the Flies, the adaptation of William Golding's novel. His other film work included composing the score to Alfred the Great (1969), and arranging the music for Laughter in the Dark (1969) and The Hotel New Hampshire (1984).

In November 1969, he made his American debut conducting the Westminster Choir and the New York Philharmonic, at which occasion he also appeared as soloist in Joseph Haydn's Harpsichord Concerto in D major. In 1973 he became principal conductor of the BBC Northern Symphony Orchestra in Manchester (now the BBC Philharmonic), a position he retained until 1980.

Leppard conducted Britten's Billy Budd at the Metropolitan Opera and the San Francisco Opera, as well as Gluck's Alceste and Handel's Alcina at the New York City Opera. He also conducted at the Royal Opera House in London, in Paris, at the Hamburg State Opera, the Santa Fe Opera, in Stockholm and Geneva.

In September 1986 Raymond Leppard conducted the BBC Symphony Orchestra, Singers and Chorus at the Last Night of the Proms in the Royal Albert Hall, London.

At Glyndebourne, he conducted the world premiere of Nicholas Maw's The Rising of the Moon. From 1987 to 2001, Leppard was the music director of the Indianapolis Symphony Orchestra, where he collaborated with concertmaster Hidetaro Suzuki. From 2004 to 2006, he served as music advisor to the Louisville Orchestra.

In 1973, the Republic of Italy conferred upon him the title of Commendatore della Republica Italiana for services to Italian music. He received an Honorary Degree of a Doctor of Letters by the University of Bath in 1973. He was appointed a Commander of the Order of the British Empire (CBE) by Queen Elizabeth II in 1983. Leppard became an American citizen in 2003. He died in Indianapolis on 22 October 2019. He bequeathed his extensive archive of opera realisations to the Royal Conservatoire of Scotland.

title: Raymond Leppard


text:
Viktor Belenko

Viktor Ivanovich Belenko (Виктор Иванович Беленко; February 15, 1947 – September 24, 2023) was a Russian-born American aerospace engineer and Soviet pilot who defected in 1976 to the West while flying his MiG-25 "Foxbat" jet interceptor and landed in Hakodate, Japan. George H. W. Bush, the Director of Central Intelligence at the time, called the opportunity to examine the plane up close an "intelligence bonanza" for the West. Belenko later became a U.S. aerospace engineer.

Early life and defection

Belenko was born in Nalchik, Russian SFSR, in a Russian family (his passport states his ethnicity as Russian). Lieutenant Belenko was a pilot with the 513th Fighter Regiment, 11th Air Army, Soviet Air Defence Forces based in Chuguyevka, Primorsky Krai. On 6 September 1976, he successfully defected to the West by flying his MiG-25 jet fighter to Hakodate Airport, Hokkaido Japan.

This was the first time that Western military intelligence were able to get a close look at the aircraft and its specifications, and many secrets and surprises were revealed. His defection caused significant damage to the Soviet Air Force. Belenko was granted asylum by U.S. President Gerald Ford, and a trust fund was set up for him, which granted him a very comfortable living in later years. The US government debriefed him for five months after his defection and employed him as a consultant for several years thereafter. Belenko had brought with him the pilot's manual for the MiG-25 since he expected to assist US pilots in evaluating and testing the aircraft.

Belenko was not the only pilot to have defected from the Soviet Union in this way or even the first to defect from a Soviet-bloc country. He might have been aware of the US government's policy of awarding large cash prizes to defecting pilots of communist countries. In March and May 1953,  two Polish Air Force pilots flew MiG-15s to Denmark. Later in 1953, North Korean pilot No Kum Sok flew his MiG-15 to a US air base in South Korea; the MiG is in the permanent collection of the National Museum of the U.S. Air Force, displayed in its original owner markings. Later, Soviet Captain Aleksandr Zuyev flew his MiG-29 to Trabzon, Turkey, on 20 May 1989. That MiG-29 was promptly returned to the Soviets.

Aftermath
The MiG-25's arrival in Japan was a windfall for Western military planners. The Japanese government had originally allowed the United States to examine the plane and to conduct ground tests of the radar and engines only; however, it subsequently allowed the US to dismantle the plane to examine it extensively. The plane was moved by a US Air Force C-5 Galaxy cargo aircraft from Hakodate to Hyakuri Air Base on 25 September, and by then, experts had determined that the plane was an interceptor, not a fighter-bomber, which was a welcome reassurance for Japanese defense planners.

On 2 October 1976, the Japanese Government announced that it would ship the aircraft in crates from the port of Hitachi and billed the Soviets US$40,000 for crating services and airfield damage at Hakodate. The Soviets responded with a request to return the plane via their own Antonov An-22 aircraft after a rigorous inspection of the crates. The Japanese government refused, and the Soviets finally submitted to the Japanese terms on 22 October 1976. The aircraft was moved from Hyakuri to the port of Hitachi on 11 November 1976 on a convoy of trailers. It left in 30 crates aboard the Soviet cargo ship Taigonos on 15 November 1976 and arrived about three days later in Vladivostok. A team of Soviet technicians had been allowed to view subassemblies at Hitachi, and upon finding 20 missing parts, one being film of the flight to Hakodate, the Soviets attempted to charge Japan US $10 million. Neither the Japanese nor the Soviet bill is known to have been paid.

A senior diplomat described the Soviet position as "sulky about the whole affair." The CIA concluded at the time that "both countries seem anxious to put the problem behind them" and speculated that the Soviets were reluctant to cancel a series of upcoming diplomatic visits because "some useful business is likely to be transacted, and because the USSR, with its political standing in Tokyo so low, can ill-afford setbacks in Soviet–Japanese economic cooperation."

Life in the United States
In 1980, the US Congress enacted S. 2961, authorizing citizenship for Belenko. It was signed into law by President Jimmy Carter on 14 October 1980, as Private Law 96-62.

After his defection, Belenko co-wrote a 1980 autobiography, MiG Pilot: The Final Escape of Lieutenant Belenko with Reader's Digest writer John Barron.

U.S. citizenship
The U.S. Congress passed an act in 1980 to give Belenko citizenship. Eager to escape attention, he took the surname Schmidt and moved around often, mostly living in small towns across the Midwest. He worked as a consultant to aerospace companies and government agencies. His marriage to Coral Garaas ended in divorce. Along with his son Paul Schmidt, Mr. Belenko is survived by another son, Tom Schmidt, and four grandchildren. Though his Soviet wife appealed for his return after his defection and the biography that was written in the US with his collaboration (MiG Pilot: the Final Escape of Lt. Belenko) confirms that he had a wife and son in the USSR, Belenko told his son that this was untrue and that it was Soviet propaganda.

Belenko started a new life in the United States and married a music teacher from North Dakota, Coral. They had two sons. The marriage ended in a divorce later on. Belenko allegedly also had a son from his first marriage. He never divorced his first wife and allegedly never provided child support to her after his defection, but Belenko denied this. Russian journalists reached out to his Russian wife and she claimed in an interview that Belenko never contacted her after his defection and never provided child support. Belenko's repeated claims that this was simply Soviet propaganda were false. He never provided any evidence that he provided financial support to his child.

Belenko almost never appeared in interviews during his life in the United States. He feared for his life until the day he died. However, in a brief and informal bar interview in 2000, he said that he was happy in the United States, remarking, "[Americans] have tolerance regarding other people's opinion. In certain cultures, if you do not accept the mainstream, you would be booted out or might disappear. Here we have people—you know, who hug trees, and people who want to cut them down—and they live side by side!" In this interview he also claimed that he visited Moscow but did not provide any evidence of his trip.

The Soviet Union repeatedly spread false stories about Belenko being killed in a car accident, returning to Russia, being arrested and executed, or otherwise brought to justice.

Viktor Belenko died in a nursing home in the small town of Rosebud, Illinois on September 24, 2023, at the age of 76. However, journalists learned about his death only at the end of November. The former pilot's son, Paul Schmidt, told the newspaper that his father had died after a short illness. There was no memorial service.

title: Viktor Belenko


text:
Gene Tyranny

Robert Nathan Sheff (January 1, 1945 – December 12, 2020 ), known professionally as "Blue" Gene Tyranny, was an American avant-garde composer and pianist.

"His memorable pseudonym, coined during his brief stint with Iggy and the Stooges, was derived partly from Jean, his adoptive mother’s middle name," wrote Steve Smith, in his New York Times obituary for Tyranny. "It also referred to what he called 'the tyranny of the genes' — a predisposition to being 'strongly overcome by emotion,' he said in Just for the Record: Conversations With and About ‘Blue’ Gene Tyranny, a documentary film."

Early life
Tyranny was born Joseph Gantic in San Antonio on January 1, 1945, to William and Eleanor Gantic. Later that year, after his birth father, an Army paratrooper, went missing in the Asian theater of World War II, his mother put him up for adoption. He was adopted by Dorothy and Meyer Sheff of San Antonio, who changed his name to Robert Nathan Sheff. Tyranny was raised in the Lutheran church. He studied piano with Meta Hertwig and Rodney Hoare, and composition with Otto Wick and Frank Hughes.

Career
Tyranny began his performance career in high school, playing pieces by major composers (such as John Cage) with Philip Krumm in a concert series in San Antonio. He toured with the Carla Bley Band in 1977 and the Prime Movers (which included Iggy Pop and Michael Erlewine) as well as Iggy & The Stooges. "After releasing the album Raw Power in 1973, [Pop] invited his former bandmate to join him on tour," Steve Smith noted in his New York Times obituary for Tyranny. "Mr. Tyranny accepted, performing with red LED lights woven into his hair." He performed on albums by Laurie Anderson (Strange Angels), David Behrman (On the Other Ocean), John Cage (Cheap Imitation and Empty Words), Peter Gordon, and Robert Ashley (Perfect Lives, Dust, Celestial Excursions), with whom he frequently collaborated.

He taught at Mills College from 1971 to 1982, where his students included composer Hsiung-Zee Wong, and also worked at the Center for Contemporary Music at Mills. He moved to New York in 1983 and received a Bessie in 1988 and in 1989 a Composer Fellowship from the NY Foundation for the Arts.

Tyranny was a contributor for AllMusic, reviewing albums and creating biographies for many notable contemporary artists.

According to Kyle Gann in the Village Voice, Tyranny had "Cecil Taylor's keyboard energy [and] Morton Feldman's ear." "The most original aspect of [his] works," wrote Gann, "is the way they create continuity: they're tonal, yet rigorously asymmetrical. They satisfy the ear without letting it take anything for granted. They evolve...with the labyrinthine irreversibility of deep psychic forces." In another Voice article, Gann was lyrical in his evocation of Tyranny's virtuosity: "God plays the piano through this man. Science cannot explain the speed with which trillions of inspired brain impulses zip through his...hands, resulting in note-perfect works...the 1988 Kitchen improv-with-delay [The Intermediary Following Traces of the Song]...I called 'the most inspired piano performance I've ever heard.' It still is. At his schmaltziest ("Sunrise or Sunset in Texas") he's like Keith Jarrett on an extremely good day. At his best, it's like listening to Ives improvise 'Hawthorne' from the Concord Sonata."

In October 2020, Just for the Record: Conversations With and About "Blue" Gene Tyranny, a documentary film directed by David Bernabo, premiered at the TUSK Festival 2020. In a review of the film for The Wire, Joshua Minsoo Kim wrote, "Hearing Tyranny talk and learning how he lived his life encourages one to go the same way."

Tyranny died in hospice in Long Island City, Queens, on December 12, 2020, of complications of diabetes.

In David Bernabo's documentary film Just for the Record: Conversations With and About ‘Blue’ Gene Tyranny, Tyranny said music was a source of solace, but also a means “of deeply informing myself that there’s another world. Music is my way of being in the world.”

Discography

 * Out of the Blue (1977 Lovely Music LML 1061 [LP], 2007 Unseen Worlds UW01 [CD])
 * Real Life and the Movies, Vol. 1 (1981 Fun Music 21 [cassette])
 * The Intermediary (1982 Lovely Music [LP] 1063, 2008 Lovely Music [CD])
 * Country Boy Country Dog (How To Discover Music in the Sounds of Your Daily Life) (1994 Lovely Music LCD 1065)
 * Free Delivery (1999 Lovely Music LCD 1064)
 * Take Your Time (2003 Lovely Music LCD 1066)
 * The Somewhere Songs/The Invention of Memory (2008 Mutable 17529-2 [CD])
 * Detours (2012 Unseen Worlds UW07 [CD])
 * Degrees of Freedom Found (2021 Unseen Worlds UW35 [CD])

Listening

 * Art of the States: "Blue" Gene Tyranny Meditation: Nothing's Changed, Everything's Changed (1961/2002)
 * "Blue" Gene Tyranny at Roulette TV (2008) A Letter From Home (1974)

title: Gene Tyranny


text:
Olaf of York

Olaf of York may refer to:

 * Olaf Gothfrith's son, i.e. Amlaíb mac Gofrith
 * Olaf Sihtric's son, i.e. Amlaíb Cuaran

title: Olaf of York


text:
T-square

A T-square is a technical drawing instrument used by draftsmen primarily as a guide for drawing horizontal lines on a drafting table. The instrument is named after its resemblance to the letter T, with a long shaft called the "blade" and a short shaft called the "stock" or "head". T-squares are available in a range of sizes, with common lengths being 18 inch, 24 inch, 30 inch, 36 inch and 42 inch.

In addition to drawing horizontal lines, a T-square can be used with a set square to draw vertical or diagonal lines. The T-square usually has a transparent edge made of plastic which should be free of nicks and cracks in order to provide smooth, straight lines.

T-squares are also used in various industries, such as construction. For example, drywall T-squares are typically made of aluminum and have a 48 inch tongue, allowing them to be used for measuring and cutting drywall. In woodworking, higher-end table saws often have T-square fences attached to a rail on the front side of the table, providing improved accuracy and precision when cutting wood.

title: T-square


text:
Talk:Rodolphe Kreutzer

Untitled
I know the Kreutzer excercises very well- and have played many of them. They are pretty hard!
 * That's true,indeed!I've also played his work very well.After the double stop,difficult musics are attacking to the player!So I've created the guidance!Please check it.Naotyan 07:13, 27 June 2007 (UTC)

Merge!
Merge Rudolph Kreutzer? (Will do this properly later...) Schissel | Sound the Note! 01:10, 14 August 2006 (UTC)

title: Talk:Rodolphe Kreutzer


text:
Morton Subotnick

Morton Subotnick (born April 14, 1933) is an American composer of electronic music, best known for his 1967 composition Silver Apples of the Moon, the first electronic work commissioned by a record company, Nonesuch. He was one of the founding members of California Institute of the Arts, where he taught for many years.

Subotnick has worked extensively with interactive electronics and multi-media, co-founding the San Francisco Tape Music Center with Pauline Oliveros and Ramon Sender, often collaborating with his wife Joan La Barbara. Morton Subotnick is one of the pioneers in the development of electronic music and multi-media performance and an innovator in works involving instruments and other media, including interactive computer music systems. Most of his music calls for a computer part, or live electronic processing; his oeuvre utilizes many of the important technological breakthroughs in the history of the genre.

Early career
Subotnick was born in Los Angeles, California, and graduated from the University of Denver. In the early 1960s, Subotnick taught at Mills College and with Ramon Sender, he co-founded the San Francisco Tape Music Center. During this period he also collaborated with Anna Halprin on two works (the 3 legged stool and Parades and Changes) and acted as music director of the Actors Workshop.

In 1966 Subotnick was instrumental in getting a Rockefeller Grant to join the Tape Center with the Mills Chamber Players (a chamber group at Mills College with performers Nate Rubin (violin); Bonnie Hampton (cello); Naomi Sparrow (piano) and Subotnick on clarinet). The grant required that the Tape Center relocate to a host institution that became Mills College. Subotnick, however, did not stay with the move, but went to New York with the Actor's Workshop to become the first music director of the Lincoln Center Rep Company in the Vivian Beaumont Theater at Lincoln Center. Along with Len Lye, he became an artist in residence at the newly formed Tisch School of the Arts at NYU. The School of the Arts provided him with a studio and a Buchla Synthesizer (now at the Library of Congress). He then helped to develop the Electric Circus and the Electric Ear, and became their artistic director. At the same time he created Silver Apples of the Moon, The Wild Bull, and Touch.

Silver Apples of the Moon
Early electronic music was made using wave generators and tape-manipulated sounds. Subotnick was among the first composers to work with electronic instrument designer Don Buchla. Buchla's modular voltage-controlled synthesizer, which he called the Electric Music Box and which was constructed partly based on suggestions by Subotnick and Sender, was both more flexible and easier to use, and its sequencing ability was integral to Subotnick's music.

In the late 1960s, a time when much United States' academic "avant-gardist" electronic music was highly abstract, (largely concerned with pitch and timbre, where (metric) rhythm might be an afterthought or of no consequence, and simple patterned structures were largely avoided), Subotnick broke with this direction by including sections with metric rhythms – those based on pulses and beats. Both Silver Apples of the Moon and 1968's The Wild Bull (another Nonesuch-commissioned work for tape; they have since been combined on a Wergo CD ) have been choreographed by dance companies around the world.

In 1969 Subotnick was invited to be part of a team of artists to move to Los Angeles to plan a new school. Mel Powell as Dean, Subotnick as Associate Dean, and a team of four other pairs of artists carved out a new path of music education and created the now famous California Institute of the Arts. Subotnick remained Associate Dean of the music school for 4 years and then, resigning from that position, became the head of the composition program where, a few years later, he created a new media program that introduced interactive technology and multimedia into the curriculum. In 1978 Subotnick, with Roger Reynolds and Bernard Rands, produced 5 annual internationally acclaimed new music festivals.

Approach to music
Where previous electronic music had used non-traditional structures, Subotnick's electronic compositions are structured more like the classical music for acoustic instruments with which audiences are familiar, but with nontraditional timbres and pitch manipulations no orchestra could produce. He has also written for acoustic instruments, and he has studied with Darius Milhaud and Leon Kirchner at Mills College in Oakland, California.

In addition to music in the electronic medium, Subotnick has written for symphony orchestra, chamber ensembles, theater and multimedia productions. His "staged tone poem” The Double Life of Amphibians, a collaboration with director Lee Breuer and visual artist Irving Petlin, utilizing live interaction between singers, instrumentalists and computer, was premiered at the 1984 Olympics Arts Festival in Los Angeles.

The concert version of Jacob’s Room, a mono drama commissioned by Betty Freeman for the Kronos Quartet and singer Joan La Barbara, received its premiere in San Francisco in 1985. Jacob's Room, Subotnick's multimedia opera chamber opera (directed by Herbert Blau with video imagery by Steina and Woody Vasulka, featuring Joan La Barbara), received its premiere in Philadelphia in April 1993 under the auspices of The American Music Theater Festival. The Key To Songs, for chamber orchestra and computer, was premiered at the 1985 Aspen Music Festival. Return, commissioned to celebrate the return of Halley's Comet, premiered with an accompanying sky show in the planetarium of Griffith Observatory in Los Angeles in 1986. Subotnick's recent works—among them Jacob's Room, The Key to Songs, Hunger, In Two Worlds, And the Butterflies Begin to Sing and A Desert Flowers—utilize computerized sound generation, specially designed software Interactor and "intelligent" computer controls which allow the performers to interact with the computer technology.

All My Hummingbirds Have Alibis (1994) was an interactive concert work and a CD-ROM (perhaps the first of its kind), Making Music (1995), Making More Music (1998) were his first works for children, and an interactive 'Media Poem', Intimate Immensity, premiered at the Lincoln Center Festival in NY (1997). The European premiere (1998) was in Karlsruhe, Germany. A string quartet with CDROM, Echoes from the Silent Call of Girona (1998), was premiered in Los Angeles by Southwest Chamber Music.

Subotnick was commissioned to complete a larger version of the opera, Jacobs Room. This premiered in 2010 at the Bregenz Festival in Austria.

Subotnick is developing tools for young children to create music. He has authored a series of six CDROMs for children, mounted a children's website and he is developing a related school program. Subotnick's Pitch Painter for iPad and iPhone (not available on App Store) is a musical finger painting app which presents a new intuitive way for kids to create music.

Subotnick is working with the Library of Congress as they are preparing an archival presentation of his electronic works. He tours extensively throughout the U.S. and Europe as a lecturer and composer/performer. Morton Subotnick is published by Schott Music. Students of his include Ingram Marshall, Mark Coniglio, Carl Stone, Rhys Chatham, Charlemagne Palestine, Ann Millikan, Nicholas Frances Chase, Brian Evans, Julia Stilman-Lasansky, John King, Lois V Vierk, Betty Ann Wong, and Jeremy Zuckerman.

Personal life
Subotnick is married to Joan La Barbara, a singer and composer. Subotnick's older son, Steven Subotnick, is an animator; his younger son, Jacob Subotnick, is a sound designer and his daughter, Tamara Winer, is a psychiatric social worker.

Awards

 * Guggenheim Fellowship
 * Rockefeller Grants (3)
 * Meet the Composer (2)
 * American Academy of Arts and Letters Composer Award
 * Brandies Award
 * Deutscher Akademischer Austauschdienst Künstlerprogramm (DAAD), Composer in Residence in Berlin
 * Lifetime Achievement Award (SEAMUS at Dartmouth)
 * ASCAP: John Cage Award
 * ACO: Lifetime Achievement
 * Honorary Doctorate from the California Institute of the Arts

Selected works

 * Sonata for viola and piano (1959–60)
 * Silver Apples of the Moon (National Recording Registry inductee) (1967)
 * The Wild Bull (1968)
 * Touch (1969)
 * Sidewinder (1971)
 * Four Butterflies (1973)
 * Until Spring (1975)
 * A Sky of Cloudless Sulfur (1978)
 * Axolotl (1981)
 * A Fluttering of Wings (1981)
 * An Arsenal of Defense for solo viola and "electronic ghost score" (1982)
 * Trembling (1983)
 * The Key to Songs (1985)
 * Jacob's Room (1986)
 * and the butterflies begin to sing (1988)
 * All My Hummingbirds Have Alibis (1991)
 * Echoes from the Silent Call of Girona (1998)
 * Gestures (1999–2001)
 * Then Now and Forever (2008)
 * The Other Piano (2007)
 * Jacob's Room Opera (2010)
 * From Silver Apples of the Moon to A Sky of Cloudless Sulphur (2009 – 2013)
 * Jacob's Room Monodrama (2013)

Listening

 * Interview with Dublab
 * Interview with RedBull Music Academy
 * Mars Millennium Project 2030: Artist: Morton Subotnick
 * Morton Subotnick interview
 * Art of the States: Morton Subotnick Echoes from the Silent Call of Girona (1998)
 * Morton Subotnick Interview NAMM Oral History Library (2005)

title: Morton Subotnick


text:
French curve

A French curve is a template usually made from metal, wood or plastic composed of many different curved segments. It is used in manual drafting and in fashion design to draw smooth curves of varying radii. The curve is placed on the drawing material, and a pencil, knife or other implement is traced around its curves to produce the desired result. They were invented by the German mathematician Ludwig Burmester and are also known as Burmester (curve) set.

Clothing design
French curves are used in fashion design and sewing alongside hip curves, straight edges and right-angle rulers. Commercial clothing patterns can be personalized for fit by using French curves to draw neckline, sleeve, bust and waist variations.

title: French curve