Grammy Award

Grammy Award

The Grammy Awards (originally the Gramophone Awards), presented by the Recording Academy (an association of Americans professionally involved in the recorded music industry) for outstanding achievements in the recording industry, is one of four major music awards shows held annually in the United States (the Billboard Music Awards, the American Music Awards, and the Rock and Roll Hall of Fame Induction Ceremony, make up the rest). However, the Grammys, usually held in February, (last of what are considered the "big three" music awards shows, including the BMA and AMA shows) are considered the approximate equivalent to the Oscars, in the music world.

Like the Oscars, the Grammys, which currently have 108 categories within 30 genres of music (such as pop, gospel, and rap), are voted upon by peers - voting members of the Recording Academy - rather than being based upon popularity (as with the AMAs) or sales and chart achievements (the BMAs).

The awards are named for the trophy which the winner receives - a small gilded statuette of a gramophone, handcrafted by Billings Artworks. The awards ceremony features performances by prominent artists, and some of the more prominent Grammys are presented in a widely-viewed televised ceremony.

Some feel that because Grammy voters tend to vote conservatively, and are marketed to by record companies, the most widely-recognized Grammys tend to go to either well-established artists or those being hyped by the recording industry. Hence, the Grammys are not taken seriously by some musicians and music fans. In fact, many artists who are placed in high regard, artistically, by many fans and critics (such as Elvis Presley, Mariah Carey, Garth Brooks, Pink Floyd, Kenny Rogers, The Rolling Stones, Led Zeppelin, Radiohead, ) have been awarded very few Grammys.

Of the "big three" music awards shows, the Grammys are the highest rated.

Unlike the Academy Awards, for which the eligibility period begins January 1, the eligibility period for the Grammys begins October 1, which results in September being considered the Christmas sales period for the music industry (in which artists generally release big albums to qualify for the next year's Grammy). So, for example, John Lennon & Yoko Ono's album Double Fantasy was released in November, 1980, a month-and-a-half too late to qualify for the 1981 Grammys, and thus eligible for the 1982 awards (it eventually won the Grammy Award for Album of the Year).

The Grammys are currently broadcast on CBS.

Grammy Records

Pat Metheny and the Pat Metheny Group have won 16 Grammys in total, including six consecutive awards for six consecutive albums. Metheny, as of the 2004 Grammy Awards, holds the record for Grammy wins in the most different categories:

  1. Best Jazz Fusion Performance (1983, 1984, 1985, 1988, 1990)
  2. Best Instrumental Composition (1991)
  3. Best Contemporary Jazz Performance/Album (1993, 1994, 1996, 1999, 2003)
  4. Best Jazz Instrumental Performance, Individual or Group (1998, 2000)
  5. Best Rock Instrumental Performance (1999)
  6. Best Jazz Instrumental Solo (2001)
  7. Best New Age Album (2004)

Session drummer Hal Blaine played on six consecutive records which won Record of the Year:

  1. 1966 Herb Alpert & the Tijuana Brass - "A Taste of Honey"
  2. 1967 Frank Sinatra - "Strangers in the Night"
  3. 1968 5th Dimension - "Up, Up and Away"
  4. 1969 Simon & Garfunkel - "Mrs. Robinson"
  5. 1970 5th Dimension - "Aquarius/Let the Sunshine In"
  6. 1971 Simon & Garfunkel - "Bridge Over Troubled Water"

Legendary Opera Diva Leontyne Price has won 18 awards

Soul and R&B legend Aretha Franklin has won 11 awards for Best Female R&B Vocal Performance, including 8 consecutive (and the first 8 ever awarded) awards in the category:

  1. 1968 - "Respect"
  2. 1969 - "Chain of Fools"
  3. 1970 - "Share Your Love With Me"
  4. 1971 - "Don't Play That Song"
  5. 1972 - "Bridge Over Troubled Water"
  6. 1973 - Young, Gifted, and Black
  7. 1974 - "Master of Eyes"
  8. 1975 - "Ain't Nothing Like The Real Thing"
  9. 1982 - "Hold On, I'm Comin'"
  10. 1986 - "Freeway of Love"
  11. 1988 - Aretha

Conductor Sir Georg Solti holds the record for most Grammys won, having won a total of thirty-eight awards before his death in 1997.

The most Grammys won in a single night is eight -- a record shared by Michael Jackson (1984), and Carlos Santana (2000).

Christopher Cross (Grammy Awards of 1981) and Norah Jones (Grammy Awards of 2003) are the only artists to receive the "Big Four" (Record of the Year, Album of the Year, Song of the Year, and Best New Artist) in a single ceremony.

Béla Fleck has been nominated in more categories than any other musician, namely country, pop, jazz, bluegrass, classical, folk, and spoken word, as well as composition and arranging.

Award categories

  • Record of the Year
  • Album of the Year
  • Song of the Year
  • Best New Artist
  • Grammy Hall of Fame
  • Grammy Legend Award
  • Grammy Lifetime Achievement Award
  • Grammy Tech Award
  • Grammy Trustees Award

Alternative

  • Best Alternative Music Album

Blues

  • Best Traditional Blues Album
  • Best Contemporary Blues Album

Children's

  • Best Album for Children
  • Best Musical Album for Children
  • Best Spoken Word Album for Children

Classical

  • Best Orchestral Performance
  • Best Classical Vocal Performance
  • Best Classical Performance, Operatic or Choral
  • Best Opera Recording
  • Best Choral Performance
  • Best Classical Performance - Instrumental Soloist or Soloists (with or without orchestra)
  • Best Instrumental Soloist(s) Performance (with orchestra)
  • Best Instrumental Soloist Performance (without orchestra)
  • Best Small Ensemble Performance (with or without conductor)
  • Best Chamber Music Performance
  • Best Classical Contemporary Composition
  • Best Classical Album
  • Best Classical Crossover Album
  • Best New Classical Artist

Comedy

  • Best Comedy Album
  • Best Spoken Comedy Album

Composing and arranging

  • Best Instrumental Composition
  • Best Song Written for a Motion Picture, Television or Other Visual Media (now in the "Film/TV/Media" field)
  • Best Score Soundtrack Album for a Motion Picture, Television or Other Visual Media (now in the "film/TV/media" field)
  • Best Arrangement
  • Best Instrumental Arrangement
  • Best Instrumental Arrangement Accompanying Vocalist(s)
  • Best Vocal Arrangement for Two or More Voices

Country

  • Best Female Country Vocal Performance
  • Best Male Country Vocal Performance
  • Best Country Performance, Duo or Group - Vocal or Instrumental
  • Best Country Performance by a Duo or Group with Vocal
  • Best Country Collaboration with Vocals
  • Best Country Instrumental Performance
  • Best Country & Western Recording
  • Best Country & Western Single
  • Best Country Song
  • Best Country Album
  • Best Bluegrass Album
  • Best New Country & Western Artist

Dance

  • Best Dance Recording (previously in "Pop")
  • Best Electronic/Dance Album

Disco

  • Best Disco Recording

Film/TV/Media

  • Best Compilation Soundtrack Album for a Motion Picture, Television or Other Visual Media
  • Best Song Written for a Motion Picture, Television or Other Visual Media (previously in the "composing and arranging" field)
  • Best Score Soundtrack Album for a Motion Picture, Television or Other Visual Media (previously in the "composing and arranging" field)

Folk

  • Best Ethnic or Traditional Folk Recording
  • Best Traditional Folk Album
  • Best Contemporary Folk Album
  • Best Native American Music Album
  • Best Hawaiian Music Album

Gospel

  • Best Gospel Performance
  • Best Gospel Performance, Traditional
  • Best Gospel Performance, Contemporary
  • Best Gospel Vocal Performance, Female
  • Best Gospel Vocal Performance, Male
  • Best Gospel Vocal Performance by a Duo or Group, Choir or Chorus
  • Best Soul Gospel Performance
  • Best Soul Gospel Performance, Traditional
  • Best Soul Gospel Performance, Contemporary
  • Best Soul Gospel Performance, Female
  • Best Soul Gospel Performance, Male
  • Best Soul Gospel Performance, Male or Female
  • Best Soul Gospel Performance by a Duo or Group, Choir or Chorus
  • Best Inspirational Performance
  • Best Pop/Contemporary Gospel Album
  • Best Rock Gospel Album
  • Best Traditional Soul Gospel Album
  • Best Contemporary Soul Gospel Album
  • Best Southern, Country or Bluegrass Gospel Album
  • Best Gospel Choir or Chorus Album

Historical

  • Best Historical Album

Jazz

  • Best Jazz Vocal Performance, Female
  • Best Jazz Vocal Performance, Male
  • Best Jazz Vocal Performance, Duo or Group
  • Best Jazz Instrumental Solo
  • Best Jazz Instrumental Album, Individual or Group
  • Best Large Jazz Ensemble Album
  • Best Jazz Fusion Performance
  • Best Original Jazz Composition
  • Best Jazz Vocal Album
  • Best Contemporary Jazz Album
  • Best Latin Jazz Album

Latin

  • Best Latin Recording
  • Best Latin Pop Album
  • Best Traditional Tropical Latin Album
  • Best Mexican/Mexican-American Album
  • Best Latin Rock/Alternative Album
  • Best Tejano Album
  • Best Salsa Album
  • Best Merengue Album
  • Best Salsa/Merengue Album

Musical Show

  • Best Musical Show Album
  • Best Sound Track Album or Recording of Original Cast From a Motion Picture or Television

Music Video

  • Best Short Form Music Video
  • Best Long Form Music Video
  • Best Concept Music Video
  • Best Performance Music Video
  • Video of the Year

New Age

  • Best New Age Album

Packaging and notes

  • Best Album Cover
  • Best Album Cover - Classical
  • Best Album Cover - Other Than Classical
  • Best Album Cover, Graphic Arts
  • Best Album Cover, Photography
  • Best Recording Package
  • Best Boxed or Special Limited Edition Package
  • Best Album Notes
  • Best Album Notes - Classical

Polka

  • Best Polka Album

Pop

  • Best Vocal Performance, Female
  • Best Vocal Performance, Male
  • Best Performance by a Vocal Group
  • Best Performance by a Chorus
  • Best Performance by a Vocal Group or Chorus
  • Best Instrumental Performance
  • Best Female Pop Vocal Performance
  • Best Male Pop Vocal Performance
  • Best Contemporary (R&R) Solo Vocal Performance - Male or Female
  • Best Pop Performance by a Duo or Group with Vocal
  • Best Contemporary Performance by a Chorus
  • Best Pop Collaboration with Vocals
  • Best Performance by an Orchestra - for Dancing
  • Best Performance by an Orchestra or Instrumentalist with Orchestra - Primarily Not Jazz or for Dancing
  • Best Pop Instrumental Performance
  • Best Pop Instrumental Performance with Vocal Coloring
  • Best Contemporary Song
  • Best Pop Vocal Album
  • Best Pop Instrumental Album

Production and engineering

  • Best Engineered Album, Non-Classical
  • Best Engineered Album, Classical
  • Best Engineered Recording - Special or Novel Effects
  • Best Remixed Recording, Non-Classical
  • Producer of the Year, Non-Classical
  • Producer of the Year, Classical
  • Remixer of the Year, Non-Classical

R&B

  • Best Female R&B Vocal Performance
  • Best Male R&B Vocal Performance
  • Best R&B Solo Vocal Performance, Male or Female
  • Best R&B Performance by a Duo or Group with Vocals
  • Best Traditional R&B Vocal Performance
  • Best R&B Instrumental Performance
  • Best Urban/Alternative Performance
  • Best Rhythm & Blues Recording
  • Best R&B Song
  • Best R&B Album
  • Best Contemporary R&B Album

Rap

  • Best Rap Performance
  • Best Rap Solo Performance
  • Best Female Rap Solo Performance
  • Best Male Rap Solo Performance
  • Best Rap Performance by a Duo or Group
  • Best Rap/Sung Collaboration
  • Best Rap Song
  • Best Rap Album

Reggae

  • Best Reggae Album

Rock

  • Best Female Rock Vocal Performance
  • Best Male Rock Vocal Performance
  • Best Rock Vocal Performance, Solo
  • Best Rock Performance by a Duo or Group with Vocal
  • Best Rock Instrumental Performance
  • Best Hard Rock Performance
  • Best Metal Performance
  • Best Hard Rock/Metal Performance Vocal or Instrumental
  • Best Rock Song
  • Best Rock Album

Surround Sound

  • Best Surround Sound Album

Spoken

  • Best Spoken Word Album
  • Best Spoken Comedy Album

Traditional Pop

  • Best Traditional Pop Vocal Album

World

  • Best World Music Album
  • Best Traditional World Music Album
  • Best Contemporary World Music Album

Awards by year

Years reflect the year in which the awards were presented, for music released in the previous year.

Grammy Awards by year
1959 | 1960 | 1961 | 1962 | 1963 | 1964 | 1965 | 1966 | 1967 | 1968 | 1969 | 1970 | 1971 | 1972 | 1973 | 1974 | 1975 | 1976 | 1977 | 1978 | 1979 | 1980 | 1981 | 1982 | 1983 | 1984 | 1985 | 1986 | 1987 | 1988 | 1989 | 1990 | 1991 | 1992 | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006



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. CBS has run several stories concerning Sudoku, including on the Early Show in Summer 2005, and on the CBS Evening News that autumn, on October 26. Years reflect the year in which the awards were presented, for music released in the previous year. The stunt was cleverly timed to coincide with a major road expansion, where an imposed 40 mph speed restriction allowed drivers to safely view the puzzle whilst driving. World. The puzzle was carved into a hillside in Chipping Sodbury, near Bristol, England, in view of the M4 motorway. Traditional Pop. A Sky One publicity stunt to promote the programme with the world's largest Sudoku puzzle went awry when the 275 foot (84 m) square puzzle was found to have 1,905 correct solutions.

Spoken. The audience at home was in a separate interactive competition. Surround Sound. Conferring was permitted although the lack of acquaintance of the players with each other inhibited an analytical discussion. Rock. Each player had a hand-held device for entering numbers corresponding to answers for four cells. Reggae. Nine teams of nine players (with one celebrity in each team) representing geographical regions competed to solve a puzzle.

Rap. It was presented by Carol Vorderman. R&B. As a one-off, the world's first live TV Sudoku show, Sudoku Live, was broadcast on 1 July 2005 on Sky One. Production and engineering. On 2 August 2005 the BBC's programme guide Radio Times started to feature a weekly Super Sudoku. Pop. From July 2005 Channel 4 included a daily Sudoku game in their Teletext service (at page 391).

Polka. Recognizing the different psychological appeals of easy and difficult puzzles The Times introduced both side by side on 20 June 2005. Packaging and notes. A simpler explanation is that the puzzle attracts and retains readers—Sudoku players report an increasing sense of satisfaction as a puzzle approaches completion. New Age. Sudoku became particularly prominent in newspapers soon after the 2005 general election leading some commentators to suggest that it was filling the gaps previously occupied by election coverage. Music Video. The rapid rise of Sudoku from relative obscurity in Britain to a front-page feature in national newspapers attracted commentary in the media (see References below) and parody (such as when The Guardian's G2 section advertised itself as the first newspaper supplement with a Sudoku grid on every page [16]).

Musical Show. Newspapers competed to promote their Sudoku puzzles, with The Times and the Daily Mail each claiming to have been the first to feature Sudoku. Latin. As the name Sudoku became well-known in Britain, the Daily Mail adopted it in place of its earlier name "Codenumber". Jazz. By April and May 2005 the puzzle had become popular in these publications and it was rapidly introduced to several other national British newspapers including The Independent, The Guardian, The Sun (where it was labelled Sun Doku), and The Daily Mirror. Historical. That newspaper already had plans for taking advantage of their market lead, and a first Sudoku book was already on the stocks before any other national UK papers had realised just how popular Sudoku might be.

Gospel. Until then the Times had kept very quiet about the huge daily interest that its daily Sudoku competition had aroused. Folk. The Telegraph continued to splash the puzzle on its front page, realizing that it was gaining sales simply by its presence. Film/TV/Media. There is no doubt that it was not until the British Daily Telegraph introduced the puzzle on a daily basis on 23 February 2005 with the full front-page treatment advertising the fact, that the other UK national newspapers began to take real interest. Disco. The immense surge in popularity of Sudoku in British newspapers and internationally has led to it being dubbed in the world media in 2005 the "fastest growing puzzle in the world".

Dance. Nationwide News Pty Ltd began publishing the puzzle in The Daily Telegraph of Sydney on 20 May 2005; five puzzles with solutions were printed that day. Country. The Daily Telegraph introduced its first Sudoku by its puzzle compiler Michael Mepham on 19 January 2005 and other Telegraph Group newspapers took it up very quickly. Composing and arranging. Three days later The Daily Mail began to publish the puzzle under the name "Codenumber". Comedy. The puzzles by Pappocom, Gould's software house, have been printed daily in the Times ever since.

Classical. Knowing that British newspapers have a long history of publishing crosswords and other puzzles, he promoted Sudoku to The Times in Britain, which launched it on 12 November 2004 (calling it Su Doku). Children's. Over 6 years he developed a computer program to produce puzzles quickly. Blues. In 1997, retired Hong Kong judge Wayne Gould, 59, a New Zealander, saw a partly completed puzzle in a Japanese bookshop. Alternative. Sudoku has been called the "Rubik's cube of the 21st century".

Béla Fleck has been nominated in more categories than any other musician, namely country, pop, jazz, bluegrass, classical, folk, and spoken word, as well as composition and arranging. Within the context of puzzle history, parallels are often cited to Rubik's Cube, another logic puzzle popular in the 1980s. Christopher Cross (Grammy Awards of 1981) and Norah Jones (Grammy Awards of 2003) are the only artists to receive the "Big Four" (Record of the Year, Album of the Year, Song of the Year, and Best New Artist) in a single ceremony. It is also often included in puzzle anthologies, such as The Giant 1001 Puzzle Book (under the title Nine Numbers). The most Grammys won in a single night is eight -- a record shared by Michael Jackson (1984), and Carlos Santana (2000). Additionally, Kappa reprints Nikoli Sudoku in GAMES Magazine under the name Squared Away; the New York Post, USA Today, The Boston Globe, Washington Post, and San Francisco Chronicle now also publish the puzzle. Conductor Sir Georg Solti holds the record for most Grammys won, having won a total of thirty-eight awards before his death in 1997. Bringing the process full-circle, Dell Magazines, which publishes the original Number Place puzzle, now also publishes two Sudoku magazines: Original Sudoku and Extreme Sudoku.

Soul and R&B legend Aretha Franklin has won 11 awards for Best Female R&B Vocal Performance, including 8 consecutive (and the first 8 ever awarded) awards in the category:. Yoshimitsu Kanai published his computerized puzzle generator under the name Single Number for the Apple Macintosh [13] in 1995 in Japanese and English, for the Palm (PDA) [14] in 1996, and for the Mac OS-X [15] in 2005. Legendary Opera Diva Leontyne Price has won 18 awards. At least one publisher still uses that title. Session drummer Hal Blaine played on six consecutive records which won Record of the Year:. In 1989, Loadstar/Softdisk Publishing published DigitHunt on the Commodore 64, which was apparently the first home computer version of Sudoku. Metheny, as of the 2004 Grammy Awards, holds the record for Grammy wins in the most different categories:. Within Japan, Nikoli still holds the trademark for the name Sudoku; other publications in Japan use alternative names.

Pat Metheny and the Pat Metheny Group have won 16 Grammys in total, including six consecutive awards for six consecutive albums. It is now published in mainstream Japanese periodicals, such as the Asahi Shimbun. . In 1986, Nikoli introduced two innovations which guaranteed the popularity of the puzzle: the number of givens was restricted to no more than 32 and puzzles became "symmetrical" (meaning the givens were distributed in rotationally symmetric cells). The Grammys are currently broadcast on CBS. At a later date, the name was abbreviated to Sudoku (数独, pronounced SUE-dough-coo; sū = number, doku = single); it is a common practice in Japanese to take only the first kanji of compound words to form a shorter version. So, for example, John Lennon & Yoko Ono's album Double Fantasy was released in November, 1980, a month-and-a-half too late to qualify for the 1981 Grammys, and thus eligible for the 1982 awards (it eventually won the Grammy Award for Album of the Year). The puzzle was named by Kaji Maki (鍜治 真起), the president of Nikoli.

Unlike the Academy Awards, for which the eligibility period begins January 1, the eligibility period for the Grammys begins October 1, which results in September being considered the Christmas sales period for the music industry (in which artists generally release big albums to qualify for the next year's Grammy). The puzzle was introduced in Japan by Nikoli in the paper Monthly Nikolist in April 1984 as Suuji wa dokushin ni kagiru (数字は独身に限る), which can be translated as "the numbers must be single" or "the numbers must occur only once" (独身 literally means "single; celibate; unmarried"). Of the "big three" music awards shows, the Grammys are the highest rated. The puzzle was first published in New York by the specialist puzzle publisher Dell Magazines in its magazine Dell Pencil Puzzles and Word Games, under the title Number Place (which we can only assume Garns named it). In fact, many artists who are placed in high regard, artistically, by many fans and critics (such as Elvis Presley, Mariah Carey, Garth Brooks, Pink Floyd, Kenny Rogers, The Rolling Stones, Led Zeppelin, Radiohead, ) have been awarded very few Grammys. Although likely inspired by the Latin square invention of Leonhard Euler, Garns added a third dimension (the regional restriction) to the mathematical construct and (unlike Euler) presented the creation as a puzzle, providing a partially-completed grid and requiring the solver to fill in the rest. Hence, the Grammys are not taken seriously by some musicians and music fans. The puzzle was designed by Howard Garns, a retired architect and freelance puzzle constructor, and first published in 1979.

Some feel that because Grammy voters tend to vote conservatively, and are marketed to by record companies, the most widely-recognized Grammys tend to go to either well-established artists or those being hyped by the recording industry. The inverse problem—the fewest givens that render a solution unique—is unsolved, although the lowest number yet found for the standard variation without a symmetry constraint is 17, a number of which have been found by Japanese puzzle enthusiasts [11] [12], and 18 with the givens in rotationally symmetric cells. The awards ceremony features performances by prominent artists, and some of the more prominent Grammys are presented in a widely-viewed televised ceremony. Since this applies to Latin squares in general, most variants of Sudoku have the same maximum. The awards are named for the trophy which the winner receives - a small gilded statuette of a gramophone, handcrafted by Billings Artworks. The maximum number of givens that can be provided while still not rendering the solution unique is four short of a full grid; if two instances of two numbers each are missing and the cells they are to occupy form the corners of an orthogonal rectangle, and exactly two of these cells are within one region, there are two ways the numbers can be assigned. Like the Oscars, the Grammys, which currently have 108 categories within 30 genres of music (such as pop, gospel, and rap), are voted upon by peers - voting members of the Recording Academy - rather than being based upon popularity (as with the AMAs) or sales and chart achievements (the BMAs). The number of valid Sudoku solution grids for the 16×16 derivation is not known.

However, the Grammys, usually held in February, (last of what are considered the "big three" music awards shows, including the BMA and AMA shows) are considered the approximate equivalent to the Oscars, in the music world. Russell and Jarvis also showed that when symmetries were taken into account, there were 5,472,730,538 solutions [10] (sequence A109741 in OEIS). The Grammy Awards (originally the Gramophone Awards), presented by the Recording Academy (an association of Americans professionally involved in the recorded music industry) for outstanding achievements in the recording industry, is one of four major music awards shows held annually in the United States (the Billboard Music Awards, the American Music Awards, and the Rock and Roll Hall of Fame Induction Ceremony, make up the rest). The derivation of this result was considerably simplified by analysis provided by Frazer Jarvis and the figure has been confirmed independently by Ed Russell. Best Contemporary World Music Album. The result was derived through logic and brute force computation. Best Traditional World Music Album. This number is equal to 9! × 722 × 27 × 27,704,267,971, the last factor of which is prime.

Best World Music Album. Nonetheless, the number of valid Sudoku solution grids for the standard 9×9 grid was calculated by Bertram Felgenhauer in 2005 to be 6,670,903,752,021,072,936,960 [9] (sequence A107739 in OEIS). Best Traditional Pop Vocal Album. There are significantly fewer valid Sudoku solution grids than Latin squares because Sudoku imposes the additional regional constraint. Best Spoken Comedy Album. A valid Sudoku solution grid is also a Latin square. Best Spoken Word Album. The puzzle is then completed by assigning an integer between 1 and 9 to each vertex, in such a way that vertices that are joined by an edge do not have the same integer assigned to them.

Best Surround Sound Album. In this case, two distinct vertices labelled by and are joined by an edge if and only if:. Best Rock Album. The vertices can be labelled with the ordered pairs , where x and y are integers between 1 and 9. Best Rock Song. The graph in question has 81 vertices, one vertex for each cell of the grid. Best Hard Rock/Metal Performance Vocal or Instrumental. The aim of the puzzle in its standard form is to construct a proper 9-colouring of a particular graph, given a partial 9-colouring.

Best Metal Performance. Solving Sudoku puzzles (as well as any other NP-hard problem) can be expressed as a graph colouring problem. Best Hard Rock Performance. This gives some indication of why Sudoku is difficult to solve, although on boards of finite size the problem is finite and can be solved by a deterministic finite automaton that knows the entire game tree. Best Rock Instrumental Performance. The general problem of solving Sudoku puzzles on n2 x n2 boards of n x n blocks is known to be NP-complete [8]. Best Rock Performance by a Duo or Group with Vocal. Here are some of the more notable single-instance variations:.

Best Rock Vocal Performance, Solo. Top Notch claim this as a feature designed to defeat solving programs. Best Male Rock Vocal Performance. It is debatable whether these are true Sudoku puzzles: although they purportedly have a single linguistically valid solution, they cannot necessarily be solved entirely by logic, requiring the solver to determine the embedded words. Best Female Rock Vocal Performance. The Code Doku [6] devised by Steve Schaefer has an entire sentence embedded into the puzzle; the Super Wordoku [7] from Top Notch embeds two 9-letter words, one on each diagonal. Best Reggae Album. Recent variants have just that, often in the form of a word reading along a main diagonal once solved; determining the word in advance can be viewed as a solving aid.

Best Rap Album. Alphabetical variations have also emerged; there is no functional difference in the puzzle unless the letters spell something. Best Rap Song. Sequential grids, as opposed to overlapping, are also published, with values in specific locations in grids needing to be transferred to others. Best Rap/Sung Collaboration. Often, no givens are to be found in overlapping regions. Best Rap Performance by a Duo or Group. [5] Puzzles with twenty or more overlapping grids are not uncommon in some Japanese publications.

Best Male Rap Solo Performance. In The Times and The Sydney Morning Herald this form of puzzle is known as Samurai SuDoku. Best Female Rap Solo Performance. Five 9×9 grids which overlap at the corner regions in the shape of a quincunx is known in Japan as Gattai 5 (five merged) Sudoku. Best Rap Solo Performance. Puzzles constructed from multiple Sudoku grids are common. Best Rap Performance. Some such variants forsake standard givens entirely.

Best Contemporary R&B Album. Other kinds of extra restrictions can be mathematical in nature, such as requiring the numbers in delineated segments of the grid to have specific sums or products (an example of the former being Killer Su Doku in The Times), demarcating all places arithmetically adjacent digits appear orthogonally adjacent in the grid, providing the parity of all cells, requiring the Lo Shu Square to appear in the solution, and so on. Best R&B Album. [3] [4] In this variant, all the numbers must appear in all the concentric rings as well as in all pairs of adjacent wedges. Best R&B Song. Also found is the Circular Sudoku, also known as Target Sudoku, invented by Essex mathematician Peter Higgins. Best Rhythm & Blues Recording. Another dimension in use is digits with the same relative location within their respective regions; such puzzles are usually printed in colour, with each disjoint group sharing one colour for clarity.

Best Urban/Alternative Performance. The Daily Mail also features Super Sudoku X in its Weekend magazine: an 8×8 grid in which rows, columns, main diagonals, 2×4 blocks and 4×2 blocks contain each number once. Best R&B Instrumental Performance. The aforementioned Number Place Challenger puzzles are all of this variant, as are the Sudoku X puzzles in the Daily Mail, which use 6×6 grids. Best Traditional R&B Vocal Performance. Often the restriction takes the form of an extra "dimension"; the most common is for the numbers in the main diagonals of the grid to also be required to be unique. Best R&B Performance by a Duo or Group with Vocals. Another common variant is for additional restrictions to be enforced on the placement of numbers beyond the usual row, column, and region requirements.

Best R&B Solo Vocal Performance, Male or Female. Larger grids are also possible, with Daily SuDoku's 12×12-grid Monster SuDoku [2], the Times likewise offers a 12×12-grid Dodeka sudoku with 12 regions each being 4×3, Dell regularly publishing 16×16 Number Place Challenger puzzles (the 16×16 variant often uses 1 through G rather than the 0 through F used in hexadecimal), and Nikoli proffering 25×25 Sudoku the Giant behemoths. Best Male R&B Vocal Performance. Puzzle Championship had a Sudoku with parallelogram regions that wrapped around the outer border of the puzzle, as if the grid were toroidal. Best Female R&B Vocal Performance. [1] Even the 9×9 grid is not always standard, with Ebb regularly publishing some of those with nonomino regions (also known as a jigsaw variation); the 2005 U.S. Remixer of the Year, Non-Classical. Although the 9×9 grid with 3×3 regions is by far the most common, numerous variations abound: sample puzzles can be 4×4 grids with 2×2 regions; 5×5 grids with pentomino regions have been published under the name Logi-5; the World Puzzle Championship has previously featured a 6×6 grid with 2×3 regions and a 7×7 grid with six heptomino regions and a disjoint region; Daily SuDoku features new 4×4, 6×6, and simpler 9×9 grids every day as Daily SuDoku for Kids.

Producer of the Year, Classical. The challenge to Sudoku programmers is teaching a program how to build clever puzzles, such that they may be indistinguishable from those constructed by humans; Wayne Gould required six years of tweaking his popular program before he believed he achieved that level. Producer of the Year, Non-Classical. The Guardian famously claimed that because they were hand-constructed, their puzzles would contain "imperceptible witticisms" that would be very unlikely in computer-generated Sudoku. Best Remixed Recording, Non-Classical. The Sudoku puzzles printed in most UK newspapers are apparently computer-generated but employ symmetrical givens; The Guardian licenses and publishes Nikoli-constructed Sudoku puzzles, though it does not include credits. Best Engineered Recording - Special or Novel Effects. Dell Number Place Challenger (see Variants below) puzzles also list authors .

Best Engineered Album, Classical. Nikoli Sudoku are hand-constructed, with the author being credited; the givens are always found in a symmetrical pattern. Best Engineered Album, Non-Classical. The puzzle generator was written with Visual C++, and although it had options to generate a more Japanese-style puzzle, with symmetry constraints and fewer numbers, Dell opted not to use those features, at least not until their recent publication of Sudoku-only magazines. Best Pop Instrumental Album. Wei-Hwa Huang claims that he was commissioned by Dell to write a Number Place puzzle generator in the winter of 2000; prior to that, he was told, the puzzles were hand-made. Best Pop Vocal Album. They also have no authoring credits — that is, the name of the constructor is not printed with any puzzle.

Best Contemporary Song. It is commonly believed that Dell Number Place puzzles are computer-generated; they typically have over 30 givens placed in an apparently random scatter, some of which can possibly be deduced from other givens. Best Pop Instrumental Performance with Vocal Coloring. Building a Sudoku with symmetrical givens is a simple matter of placing the undefined givens in a symmetrical pattern to begin with. Best Pop Instrumental Performance. (This technique is adaptable to composing puzzles other than Sudoku as well.) Great caution is required, however, as failing to recognize where a number can be logically deduced at any point in construction—regardless of how tortuous that logic may be—can result in an unsolvable puzzle when defining a future given contradicts what has already been built. Best Performance by an Orchestra or Instrumentalist with Orchestra - Primarily Not Jazz or for Dancing. This technique gives the constructor greater control over the flow of puzzle solving, leading the solver along the same path the compiler used in building the puzzle.

Best Performance by an Orchestra - for Dancing. Such an undefined given can be assumed to not hold any particular value as long as it is given a different value before construction is completed; the solver will be able to make the same deductions stemming from such assumptions, as at that point the given is very much defined as something else. Best Pop Collaboration with Vocals. Building a Sudoku puzzle by hand can be performed efficiently by pre-determining the locations of the givens and assigning them values only as needed to make deductive progress. Best Contemporary Performance by a Chorus. It is possible to set starting grids with more than one solution and to set grids with no solution, but such are not considered proper Sudoku puzzles; as in most other pure-logic puzzles, a unique solution is expected. Best Pop Performance by a Duo or Group with Vocal. Some online versions offer several difficulty levels.

Best Contemporary (R&R) Solo Vocal Performance - Male or Female. This estimation allows publishers to tailor their Sudoku puzzles to audiences of varied solving experience. Best Male Pop Vocal Performance. Computer solvers can estimate the difficulty for a human to find the solution, based on the complexity of the solving techniques required. Best Female Pop Vocal Performance. It is based on the relevance and the positioning of the numbers rather than the quantity of the numbers. Best Instrumental Performance. A puzzle with a minimum number of givens may be very easy to solve, and a puzzle with more than the average number of givens can still be extremely difficult to solve.

Best Performance by a Vocal Group or Chorus. Perhaps surprisingly, the number of givens has little or no bearing on a puzzle's difficulty. Best Performance by a Chorus. Published puzzles often are ranked in terms of difficulty. Best Performance by a Vocal Group. A very fast solver is usually required for most trial-and-error puzzle-creation algorithms. Best Vocal Performance, Male. This is the method now preferred by many Sudoku programmers, mainly by virtue of its speed.

Best Vocal Performance, Female. This method can be directly applied to solving Sudoku problems, counting all possible solutions for most puzzles rapidly. Best Polka Album. A highly efficient way of solving such constraint problems is Donald Knuth's Dancing Links Algorithm. Best Album Notes - Classical. Backtracking may be applied when alternate values cannot otherwise be excluded. Best Album Notes. A constraint program specifies the constraints of the puzzle (the fact that every number in each row, each column, and each 3×3 region must be unique, and the provided "givens"); a finite domain solver applies the constraints successively to narrow down the solution space until a solution is found.

Best Boxed or Special Limited Edition Package. Another alternative uses finite domain constraint programming. Best Recording Package. A more efficient program could keep track of potential values for cells, eliminating impossible values until only one value remains for a cell, then filling that cell in and using that information for more eliminations, and so on until the puzzle is solved. Best Album Cover, Photography. Although far from computationally efficient, this "brute force" method will find a solution, given sufficient computation time (even a fairly naive implementation will typically not take a noticeable amount of time). Best Album Cover, Graphic Arts. If a cell cannot be filled, the program backs up one level (from that cell) and tries the next value at the higher level (hence the name backtracking).

Best Album Cover - Other Than Classical. This continues until a conflict occurs, in which case the next alternative value is used for the last cell changed. Best Album Cover - Classical. Typically this involves assigning a value (say, 1, or the nearest available number to 1) to the first available cell (say, the top left hand corner) and then moves on to assign the next available value (say, 2) to the next available cell. Best Album Cover. It is also fairly simple to build a backtracking search. Best New Age Album. Given the self-imposed constraints of most Sudoku publishers, this method generally succeeds.

Video of the Year. These programs emulate the human logic to solve a puzzle without resorting to guesses. Best Performance Music Video. For most computer programmers, coding the search for cell values based on elimination, contingencies and multiple contingencies (required for harder Sudoku) is relatively straightforward. Best Concept Music Video. The proverbial Holy Grail is to find a technique which minimises counting, marking up, and rubbing out. Best Long Form Music Video. The what-if approach can be confusing unless you are well organised.

Best Short Form Music Video. Writing candidate numbers into empty cells can be time-consuming. Best Sound Track Album or Recording of Original Cast From a Motion Picture or Television. The counting of regions, rows, and columns can feel boring. Best Musical Show Album. Ideally one needs to find a combination of techniques which avoids some of the drawbacks of the above elements. Best Salsa/Merengue Album. The two main approaches to analysis are "candidate elimination" and "what-if".

Best Merengue Album. When using marking, a couple of similar rules applied in a specified order can solve any Sudoku puzzle, without performing any kind of backtracking. Best Salsa Album. For example, if a digit appears only one time in the mark-ups written inside one region, then it is clear that the digit should be there, even if the cell has other digits marked as well. Best Tejano Album. When using marking, additional analysis can be performed. Best Latin Rock/Alternative Album. When only one marking is missing, that has to be the value of the cell.

Best Mexican/Mexican-American Album. Thus a cell will start empty and as more constraints become known it will slowly fill. Best Traditional Tropical Latin Album. An alternative technique that some find easier is to mark up those numbers that a cell cannot be. Best Latin Pop Album. There are two popular notations: subscripts and dots. Best Latin Recording. Many find it useful to guide this analysis by marking candidate numbers in the blank cells.

Best Latin Jazz Album. From this point, it is necessary to engage in some logical analysis. Best Contemporary Jazz Album. Scanning stops when no further numbers can be discovered. Best Jazz Vocal Album. Puzzles which can be solved by scanning alone without requiring the detection of contingencies are classified as "easy" puzzles; more difficult puzzles, by definition, cannot be solved by basic scanning alone. Best Original Jazz Composition. Particularly challenging puzzles may require multiple contingencies to be recognized, perhaps in multiple directions or even intersecting—relegating most solvers to marking up (as described below).

Best Jazz Fusion Performance. When those cells all lie within the same row (or column) and region, they can be used for elimination purposes during cross-hatching and counting (Contingency example at Puzzle Japan). Best Large Jazz Ensemble Album. Advanced solvers look for "contingencies" while scanning—that is, narrowing a number's location within a row, column, or region to two or three cells. Best Jazz Instrumental Album, Individual or Group. Scanning consists of two basic techniques:. Best Jazz Instrumental Solo. Scans may have to be performed several times in between analysis periods.

Best Jazz Vocal Performance, Duo or Group. Scanning is performed at the outset and periodically throughout the solution. Best Jazz Vocal Performance, Male. The strategy for solving a puzzle may be regarded as comprising a combination of three processes: scanning, marking up, and analysing. Best Jazz Vocal Performance, Female. Each number in the solution therefore occurs only once in each of three "directions" or "scopes", hence the "single numbers" implied by the puzzle's name. Best Historical Album. The goal is to fill in the empty cells, one number in each, so that each column, row, and region contains the numbers 1–9 exactly once.

Best Gospel Choir or Chorus Album. Some cells already contain numbers, known as "givens" (or sometimes as "clues"). Best Southern, Country or Bluegrass Gospel Album. The puzzle is most frequently a 9×9 grid, made up of 3×3 subgrids called "regions" (other terms include "boxes", "blocks", and the like when referring to the standard variation; even "quadrants" is sometimes used, despite this being an inaccurate term for a 9×9 grid). Best Contemporary Soul Gospel Album. The puzzles are often available free from published sources and also may be custom-generated using software. Best Traditional Soul Gospel Album. The level of difficulty of the puzzles can be selected to suit the audience.

Best Rock Gospel Album. Sudoku is recommended by some teachers as an exercise in logical reasoning. Best Pop/Contemporary Gospel Album. The attraction of the puzzle is that the completion rules are simple, yet the line of reasoning required to reach the completion may be complex. Best Inspirational Performance. Numerals are used throughout this article. Best Soul Gospel Performance by a Duo or Group, Choir or Chorus. Dell Magazines, the puzzle's originator, has been using numerals for Number Place in its magazines since they first published it in 1979.

Best Soul Gospel Performance, Male or Female. Any set of distinct symbols will do; letters, shapes, or colours may be used without altering the rules (Penny Press' Scramblets and Knight Features Syndicate's Sudoku Word both use letters). Best Soul Gospel Performance, Male. The numerals in Sudoku puzzles are used for convenience; arithmetic relationships between numerals are absolutely irrelevant. Best Soul Gospel Performance, Female. In Japanese, the word is pronounced [sɯːdokɯ]; in English, it is usually spoken with an Anglicised pronunciation, [səˈdəʊkuː] (BrE) [səˈdoʊkuː] (AmE) (suh-DOE-koo) or [ˈsuːdəʊku] (BrE) [ˈsuːdoʊku] (AmE) (SOO-doe-koo). Best Soul Gospel Performance, Contemporary. title.

Best Soul Gospel Performance, Traditional. S. Best Soul Gospel Performance. Other Japanese publishers refer to the puzzle as Nanpure (Number Place), the original U. Best Gospel Vocal Performance by a Duo or Group, Choir or Chorus. Ltd in Japan. Best Gospel Vocal Performance, Male. The name Sudoku is the Japanese abbreviation of a longer phrase, "suji wa dokushin ni kagiru (数字は独身に限る)," meaning "the digits must remain single"; it is a trademark of puzzle publisher Nikoli Co.

Best Gospel Vocal Performance, Female. . Best Gospel Performance, Contemporary. The first world championship will be in Lucca(Italy) from 10 to 12 March 2006. Best Gospel Performance, Traditional. puzzle magazine in 1979, Sudoku initially caught on in Japan in 1986 and attained international popularity in 2005. Best Gospel Performance. S.

Best Hawaiian Music Album. Although first published in a U. Best Native American Music Album. Completing the puzzle requires patience and logical ability. Best Contemporary Folk Album. Each row, column, and region must contain only one instance of each numeral. Best Traditional Folk Album. The aim of the canonical puzzle is to enter a numerical digit from 1 through 9 in each cell of a 9×9 grid made up of 3×3 subgrids (called "regions"), starting with various digits given in some cells (the "givens").

Best Ethnic or Traditional Folk Recording. Sudoku (Japanese: 数独, sūdoku), sometimes spelled Su Doku, is a logic-based placement puzzle, also known as Number Place in the United States. Best Score Soundtrack Album for a Motion Picture, Television or Other Visual Media (previously in the "composing and arranging" field). and . Best Song Written for a Motion Picture, Television or Other Visual Media (previously in the "composing and arranging" field). or,. Best Compilation Soundtrack Album for a Motion Picture, Television or Other Visual Media. or,.

Best Disco Recording. Wei-Hwa Huang created a meta-Sudoku, where the object is to finish drawing the 5×5 grid's pentomino-region borders so as to leave a uniquely solvable puzzle with no identically-shaped regions. Best Electronic/Dance Album. Puzzle Championship includes a variant called Digital Number Place: rather than givens, most cells contain a partial given—a segment of a number, with the numbers drawn as if part of a seven-segment display. Best Dance Recording (previously in "Pop"). The 2005 U.S. Best New Country & Western Artist. A three-dimensional Sudoku puzzle was invented by Dion Church and published in the Daily Telegraph in May 2005.

Best Bluegrass Album. This approach may be frowned on by logical purists as trial and error (and most published puzzles are built to ensure that it will never be necessary to resort to this tactic,) but it can arrive at solutions fairly rapidly. Best Country Album. The what-if approach requires a pencil and eraser. Best Country Song. Nishio is a limited form of this approach: for each candidate for a cell, the question is posed: will entering a particular number prevent completion of the other placements of that number? If the answer is yes, then that candidate can be eliminated. Best Country & Western Single. In logical terms, this is known as reductio ad absurdum.

Best Country & Western Recording. The steps above are repeated unless a duplication is found or a cell is left with no possible candidate, in which case the alternative candidate is the solution. Best Country Instrumental Performance. In the what-if approach, a cell with only two candidate numbers is selected, and a guess is made. Best Country Collaboration with Vocals. For example, if (p,q) can only appear in 2 cells (within a specific row, column, region scope), other candidates in the 2 cells can be eliminated. Best Country Performance by a Duo or Group with Vocal. Other candidates in the matched cells can be eliminated.

Best Country Performance, Duo or Group - Vocal or Instrumental. A second related principle is also true — if each cell within a set of cells (in a row, column or region scope) contains the same set of candidate numbers, and if the number of cells is equal to the quantity of candidate numbers, the cells and numbers are matched and only those numbers can appear in matched cells. Best Male Country Vocal Performance. The principle is true for all quantities of candidate numbers. Best Female Country Vocal Performance. This principle also works with candidate number subsets—if three cells have candidates (p,q,r), (p,q), and (q,r) or even just (p,r), (q,r), and (p,q), all of the set (p,q,r) elsewhere in the scope can be deleted. Best Vocal Arrangement for Two or More Voices. The placement of these numbers anywhere else in the matching scope would make a solution for the matched cells impossible; thus, the candidate numbers (p,q,r) appearing in unmatched cells in the row, column or region scope can be deleted.

Best Instrumental Arrangement Accompanying Vocalist(s). For example, cells are said to be matched within a particular row, column, or region (scope) if two cells contain the same pair of candidate numbers (p,q) and no others, or if three cells contain the same triplet of candidate numbers (p,q,r) and no others. Best Instrumental Arrangement. Cells with identical sets of candidate numbers are said to be matched if the quantity of candidate numbers in each is equal to the number of cells containing them; essentially, these are perfectly coincident contingencies. Best Arrangement. One of the most common elimination tactics is "unmatched candidate deletion". Best Score Soundtrack Album for a Motion Picture, Television or Other Visual Media (now in the "film/TV/media" field). If these patterns can be identified, elimination of candidate possibilities external to the grid framework can sometimes be achieved.

Best Song Written for a Motion Picture, Television or Other Visual Media (now in the "Film/TV/Media" field). Only certain "closed circuit" or "n×n grid" possibilities exist (which have acquired peculiar names such as "X-wing" and "Swordfish", among others; see List of Sudoku terms and jargon for more information). Best Instrumental Composition. Each set of candidate numbers, 1–9, must ultimately be in an independently self-consistent pattern. This is the basis for advanced analysis techniques that require inspection of the entire set of possibilities for a given candidate number. Best Spoken Comedy Album. A given set of n cells in any particular block, row, or column can only accommodate n different numbers. This is the basis for the "unmatched candidate deletion" technique, discussed below. Best Comedy Album. There are a number of elimination tactics, all of which are based on the simple rules given above, which have important and useful corollaries, including:

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    Best New Classical Artist. After each answer has been achieved, another scan may be performed—usually checking to see the effect of the latest number. Best Classical Crossover Album. In elimination, progress is made by successively eliminating candidate numbers from one or more cells to leave just one choice. Best Classical Album. Using a pencil would then be recommended. Best Classical Contemporary Composition. Dexterity is required in placing the dots, since misplaced dots or inadvertent marks inevitably lead to confusion and may not be easy to erase without adding to the confusion.

    Best Chamber Music Performance. The dot notation has the advantage that it can be used on the original puzzle. Best Small Ensemble Performance (with or without conductor). The second notation is a pattern of dots with a dot in the top left hand corner representing a 1 and a dot in the bottom right hand corner representing a 9. Best Instrumental Soloist Performance (without orchestra). If using the subscript notation, solvers often create a larger copy of the puzzle or employ a sharp or mechanical pencil. Best Instrumental Soloist(s) Performance (with orchestra). The drawback to this is that original puzzles printed in a newspaper usually are too small to accommodate more than a few digits of normal handwriting.

    Best Classical Performance - Instrumental Soloist or Soloists (with or without orchestra). In the subscript notation the candidate numbers are written in subscript in the cells. Best Choral Performance. It also can be the case (typically in tougher puzzles) that the easiest way to ascertain the value of an individual cell is by counting in reverse—that is, by scanning the cell's region, row, and column for values it cannot be, in order to see which is left. Best Opera Recording. Counting 1–9 in regions, rows, and columns to identify missing numbers. Counting based upon the last number discovered may speed up the search. Best Classical Performance, Operatic or Choral. It is important to perform this process systematically, checking all of the digits 1–9.

    Best Classical Vocal Performance. For fastest results, the numbers are scanned in order of their frequency. Best Orchestral Performance. This process is then repeated with the columns (or rows). Best Spoken Word Album for Children. Cross-hatching: the scanning of rows (or columns) to identify which line in a particular region may contain a certain number by a process of elimination. Best Musical Album for Children.

    Best Album for Children. Best Contemporary Blues Album. Best Traditional Blues Album. Best Alternative Music Album.

    Grammy Trustees Award. Grammy Tech Award. Grammy Lifetime Achievement Award. Grammy Legend Award.

    Grammy Hall of Fame. Best New Artist. Song of the Year. Album of the Year.

    Record of the Year. 1988 - Aretha. 1986 - "Freeway of Love". 1982 - "Hold On, I'm Comin'".

    1975 - "Ain't Nothing Like The Real Thing". 1974 - "Master of Eyes". 1973 - Young, Gifted, and Black. 1972 - "Bridge Over Troubled Water".

    1971 - "Don't Play That Song". 1970 - "Share Your Love With Me". 1969 - "Chain of Fools". 1968 - "Respect".

    1971 Simon & Garfunkel - "Bridge Over Troubled Water". 1970 5th Dimension - "Aquarius/Let the Sunshine In". Robinson". 1969 Simon & Garfunkel - "Mrs.

    1968 5th Dimension - "Up, Up and Away". 1967 Frank Sinatra - "Strangers in the Night". 1966 Herb Alpert & the Tijuana Brass - "A Taste of Honey". Best New Age Album (2004).

    Best Jazz Instrumental Solo (2001). Best Rock Instrumental Performance (1999). Best Jazz Instrumental Performance, Individual or Group (1998, 2000). Best Contemporary Jazz Performance/Album (1993, 1994, 1996, 1999, 2003).

    Best Instrumental Composition (1991). Best Jazz Fusion Performance (1983, 1984, 1985, 1988, 1990).

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