The Klavierübung (Piano Tutorial, BV A 3), by the Italian pianist and composerFerruccio Busoni, is a compilation of piano exercises and practice pieces, comprising transcriptions of works by other composers and original compositions of his own.
Busoni worked on the Klavierübung at various times during the last seven years of his life, and with it, he hoped to pass on his accumulated knowledge of keyboard technique. The Klavierübung is not a comprehensive or systematic graduated course of study, nor is it intended for beginning or intermediate students. Instead it assumes the student has mastered standard piano technique and has reached a virtuoso level. Busoni proceeds by adding refinements, short cuts, and unusual solutions for pianistic problems encountered in a performing artist's repertoire. The included exercises and examples reflect Busoni's own special, but diverse, interests and abilities.[1]
Assessment
Edward J. Dent, author of the first definitive biography of Busoni, had this to say about the exercises and studies in the Klavierübung: "...they are all extraordinarily interesting and stimulating. They are interesting too as helping to elucidate some of Busoni's other compositions, for the studies show how certain of his harmonic devices grew out of purely pianistic principles based on definite positions of the hands on the keyboard. Every one of the studies has genuine musical originality, and even the exercises to be repeated in all keys are a good deal more musical than such forms of torture are generally made to be."[2]
Publication of the first edition
The Klavierübung was first published by Breitkopf & Härtel in separate parts beginning in 1918. Part 2 appeared in 1919, and parts 3 and 4 two years later. The fifth, and what was to be the final part, appeared in 1922. Kindermann, who prepared the first extensive catalog of Busoni's works in 1980, refers to this "First Edition" as Klavierübung in fünf Teilen [Piano Tutorial in Five Parts],[3] and Breitkopf & Härtel later republished a collected edition under this name ca. 1996.[4]
Original plan of the work
Part 1 (Sechs Klavierübungen und Präludien) consists of six tutorials (numbered I - VI). Tutorials I to V were written in three days (10–12 September 1917), and tutorial VI one month later. The first piece of Part 2 was written on 7 November 1917, and the remainder from 4 to 10 June 1918. It consists of three tutorials (VII to IX).
Each tutorial begins with exercises and moves on to short original pieces and adaptions or transcriptions of excerpts from the repertory. For instance, the first tutorial starts with traditional scales (although the fingerings are unorthodox), then adds two excerpts which require power and speed: the first is from Liszt's Totentanz, and the second is based on two bars in Busoni's "Turandots Frauengemach" [Turandot's Bedchamber] (Book 4 from Elegien, BV 249). This is followed by two original compositions: a 16-bar "Tempo di Valse" and a 33-bar "Preludio," both of which emphasize legato scales at moderate speed. Busoni frequently lists at the bottom one or more pieces from the repertoire as examples (in German: Beispiele) suitable for further study. In the case of the "Preludio," the Beispiel is Alkan's first etude from Etudes dans tous les tons majeurs, (Op. 35).
The first tutorial exemplifies a blueprint which is used for the subsequent tutorials, each emphasizing a different aspect of piano technique. These include, in addition to the "simple" scales of the first tutorial: forms derived from scales (chords incorporated into scales); chromatic "sliding-finger" (or "sixth-finger") technique; repeated notes; arpeggios and broken chords; examples of "three-hands"; trills; examples with arpeggios; and further examples of "three hands."[5]
Difficulties completing
Because of distractions, including ill health, and other concerns, not least being the work on his lifelong masterpiece, the opera Doktor Faust (unfinished at the time of his death in 1924), many planned components of the Klavierübung were delayed or never fully realized. For instance, the foreword was not written until July 1920, and did not appear until the publication of Part 3 in 1921. Part 2 contains material which should have been included in Part 1, in tutorials V [arpeggios] and VI ["for three hands"]. Part 3 presents additional material appropriate to Part 1, as appendices. A "Chromaticon" for Part 4, mentioned in a footnote to the foreword, had to be abandoned, and was hurriedly replaced with his edition of Eight Etudes by Cramer (BV B 53) first published in 1897. Part 5 likewise consists of already existing pieces. Perhaps, if Busoni had lived longer, he would have included much more. For example, there are no tutorials on the very important technique of pedalling, for which he was particularly well known.[6]
Publication of a second edition
From December 1923 to January 1924 Busoni did manage to reorganize and enrich the material for a second edition of 284 pages. Entitled Klavierübung in zehn Büchern [Piano Tutorial in Ten Books], it was published posthumously in 1925 as Volume VIII of the Bach-Busoni Edition. Only a small number of copies of the second edition were printed, and until recently, it has been a major rarity. Fortunately, it is now available online (see, for example, this page at the International Music Score Library Project).
Significance of the second edition
The second edition is particularly important, since it contains all Busoni's last piano compositions. Two of these are not found elsewhere and are of special interest, since they were intended as source material for the unfinished final scene of Doktor Faust:[7]
"Study for the Third Pedal" [No.7 from Seven Short Pieces for the Cultivation of Polyphonic Playing, Book 9]
Annotated listing of contents
Busoni did not typically disclose the source of the extracts on which he based many of the pieces in the Klavierübung. They are often simply titled, for example, "Nach Bach" or "Nach Schubert." Fortunately, both Beaumont[8] and Sitsky[9] have provided fairly detailed descriptions of the contents of both the first and second editions. Some of this information is inserted here as annotations between square brackets.
Klavierübung in Five Parts (First Edition)
Klavierübung in fünf Teilen
Part 1: Six Piano Tutorials and Preludes
Sechs Klavierübungen und Präludien (der Klavierübung erster Teil.) (score)
I. [Scales]
[exercises and pieces employing unusual and unorthodox fingerings: the thumb passing under the fifth finger; the fifth finger passing over the thumb; or not using the thumb at all]
[Busoni also published an edition of Totentanz, BV B 72, which is based on an earlier manuscript of Liszt's and includes a De Profundis section.] (Sitsky, pp. 226-230)
(d) Allegretto, p. 6.
[scales in alternating hands, broken chords in the other hand]
[based on two measures from the final page of Turandot's Frauengemach, No.4 from Busoni's Elegien, BV 249 (score)] (Beaumont, p. 303)
(e) Tempo di Valse, p. 6.
(f) Preludio. Allegro [in E major], p. 7.
[This piece also appears in the Second Edition, Book 9, as No.1 in Sieben kurze Stücke zur Pflege des polyphonen Spiels.]
Beispiel: Alkan, Etudes dans tous les tons majeurs, [Op. 35] No.1 (score)
[Piano music "à trois mains" ("for three hands") combines three musical lines (written on three staves), which sounds as though it is played by three hands, but nevertheless is actually played by two.]
(a) Preludio. Alla Tarantella, pp. 34-35.
[short piece based on the middle (Allegro) section of All'Italia (no.2) from Elegien, BV 249] (score)
Beispiel: Liszt, Norma-Fantasie. [Réminiscences de Norma, S.394] (score)
[excerpt from the fifth movement of the C-sharp minor Quartet Op. 131 (score), transcribed for piano; consists of the first 24 bars, jumps to the fermata at bar 45 and proceeds to the cadence at the beginning of the first ending at bar 66] (Sitsky, p 278)
Beispiele: Schubert-Liszt, Das Sterbeglöcklein.
[Schubert song, D.871, transcribed for solo piano]
[No.3 from Liszt's Sechs Melodien (6 Melodies), S.563]
Liszt, Valse a capriccio sur Lucia e Parisina (Erste Fassung) [S.401]
Beispiel: Alkan, Etudes dans les tons majeurs: C dur Stück. [Op. 35, No.4] (score)
(b) Preludio. Andante tranquillo, pp. 24-25.
[excerpt based on Busoni's Improvisation on "Wie wohl ist mir" for two pianos (BV 271; score), beginning at bar 10] (Beaumont, p. 303)
(c) Tempo di Valse, elegantemente, pp. 26-29.
[After 2 bars of introduction the piece is essentially identical to the 28-bar Intermezzo in A-flat major from Busoni's Fourth Ballet Scene (first version of 1892, BV 238; score); it then modulates into a new 24-bar middle section, and finally returns to A-flat major in the 19-bar conclusion.] (Beaumont, p. 303)
(a) Perpetuum mobile et infinitum. Studie nach Bach (aus "an die Jugend"). Allegro non troppo, pp. 30-31.
[An endlessly repeating 24-bar loop extracted from the "Fuga figurata" of Book 2 of Busoni's An die Jugend, BV 254 (score). The piece combines themes from the prelude and the fugue of Bach's Prelude and Fugue No.5 in D major (BWV 850) from the Well-Tempered Clavier, Book 1 (score)]
[16-bar excerpt beginning just before bar 57 of Liszt's transcription of Schubert's song Erlkönig in 12 Lieder von Franz Schubert, S.558/4 (score)] (Sitsky, p 293)
(c) Aus meinem "Concerto". Trattenuto e fantasticamente, pp. 34-35.
Busoni, Indianisches Tagebuch, Nr. 2. [BV 267, No.2] (score)
Busoni, IV. Ballet-Szene (Galopp). [BV 238a, No.2] (score)
(j) Transcriptions-Studie nach Liszt. Quasi Galopp, sempre da Capo, pp. 30-31.
[60-bar indefinitely repeating excerpt from Busoni's piano transcription of Liszt's Mephisto Waltz for orchestra (S.110), BV B 61 (beginning on p. 27 of the complete score)] (Sitsky, p 243)
(k) Variations-Studie nach Paganini-Liszt, 1. [Vivo], pp.32-36.
[Busoni's concert transcription of Liszt's Paganini Etude No.4 "Arpeggio," BV B 74 (score). In this edition the Liszt version is omitted, and the original tempo indication "Vivo" was inadvertently removed.] (Sitsky, p 243)
(l) Variations-Studie nach Paganini-Liszt, 2. Vivace moderato tutto staccato, pp. 37-44.
[Busoni's concert transcription of Liszt's Paganini Etude No.6 "Thema mit Variationen," BV B 67 (score). This transcription was first published by Breitkopf & Härtel in 1914. That edition includes the two Liszt versions printed on staves above Busoni's transcription, and the Paganini original, below. In this edition the Liszt and Paganini versions are omitted.]
[The following section (m) also appears in the Second Edition, Book 3 "Chordal (broken chords" as section (d).]
(m) Nachsatz zur V. Übung. [Appendix to tutorial V.], pp. 45-46.
[6 further arpeggio exercises]
["chains of all types of 7th chords and their derivatives"] (Sitsky, p. 167)
(n) Anhang. 7 Variationen nach einem Motiv von Beethoven, p. 47.
[Appendix: Seven variations on a motive of Beethoven.]
[Footnote:] In verschiedenen Tonarten zu üben. Auch in Moll. [To be practiced in different keys. Also in minor.]
Acht Etüden von Cramer (der Klavierübung vierter Teil.) (score)
[Busoni's edition of the Cramer etudes was originally published in 1897 by Schlesinger (BV B 53). That edition is faithful to the originals, except the slow introduction of No.5 is omitted, and suggested changes to Etudes 4 to 8 are indicated with ossias. The etudes were republished in this edition of the Klavierübung without alteration. They are also included in the Second Edition, Book 7, but the versions of Etudes 4 to 8 in that edition include the ossias in the text without notification and contain musical and pianistic changes as well.] (Sitsky, p 284)
[Variations on the Prelude in C minor, Op.28, No.20 (Chopin score). The Ten Variations were also published separately as catalog no. EB 5230 (BV 213a). The variations are played continuously; they are not numbered in the score, but are numbered here according to Sitsky (pp. 56-58).]
(1) Sostenuto [Introduction]
(2) Largo [Chopin Prelude]
(3) [var. 1] Sostenuto (alla breve)
(4) [var. 2] Poco più vivo, leggiero scherzoso
(5) [var. 3] (En Carillon)
(6) [var. 4] continuando. dolce
(7) [var. 5] Sotto voce e poi sempre aumentando
(8) [var. 6] [no marking, begins on p. 10, 4th beat of first measure]
(9) [var. 7] Fantasia: Tempo libero. - Andante. [2 bars] - Tempo libero. - Presto.
(10) [var. 8] [begins at the second bar of the "Allegro deciso"; 6 measures serving as introduction to var. 9]
(11) [var. 9] Scherzo finale - (Vivace misurato) [fugue-like]
(12) [var. 10] (Hommage à Chopin) Tempo di Valse, tranquillo moderato.
(13) Tempo dello Scherzo. [conclusion based on var. 9]
[Note: The "Faustian" introduction (1) employs the technique of symmetrical harmony which Busoni had been developing over the previous twelve years. These four bars were so important to him that he later requested that they be played as introduction to the variations of 1888 (BV 213)] (Beaumont, p. 298.)
(b) Sechs Varianten zu Etüden und Präludien von Chopin, pp. 23-31.
[Six Variants of Etudes and Preludes by Chopin]
"Erst der Spiegel der Variante vom Urbild zeigt das Interessante." (Ferruccio Busoni)
(1) [unmarked] [Variant of Etude, Op. 10 No.1 - broken chords in both hands]
(2) Moderato [Variant of Etude Op. 10 No.2 - chromatic figure played by thumb and second finger]
(3) Agitato [Variant of Op. 10, No.9 - broken figures in the right hand]
(4) Moderato vivace [Variant of Etude Op. 10, No.7 - begins more simply than Chopin, ends more difficulty, with both hands playing sixteenth-note chords]
(5) Allegro [Variant of Etude Op. 10, No.8 - Chopin's passage work is extended]
[Assigned the Kindermann catalog number BV 293 (score), this piece is a shortened version of the Scherzoso from the Concertino for Piano, BV 292. The middle section of the Scherzoso is replaced with a sequential passage.]
[11 connected exercises in a series of keys with variants of techniques introduced in Part 1]
(e) (Scales.) 2. Übereinanderstellung verschiedener Tonarten. [Superimposed keys], pp. 47-48.
[Footnote:] "Sind von jeder Halbton stufe aus zu wiederholen." [To be repeated in half-tone steps.]
[Bitonal scale exercises with different, but related keys in the right and left hand, e.g., C major and A major, etc.; hands in similar and contrary motion]
[This set concludes with a "Faustian" cadence.] Beaumont, p. 304)
(f) (Scales.) 3. Presto volante, pp. 49-51.
[7 single-note scale exercises on a single stave, in different keys and patterns, played by alternating hands; the 8th exercise is on two staves with scales in simultaneous octaves played with alternating hands, finishing with diverging stepwise chords in both hands]
(g) Anhang. Terzen [Appendix. Thirds], p. 52
[5 scale exercises: broken thirds; double thirds split between two hands; double thirds in both hands; split chromatic thirds; split chromatic thirds with sliding fingers]
[This section should studied together with a similar section in Busoni's edition of the Well-Tempered Clavier, Book 1 (score)] (Sitsky, p. 166)
Klavierübung in Ten Books (Second Edition)
Title page:
Klavierübung in zehn Büchern von Ferruccio Busoni. Zweite umgestaltete und bereicherte Ausgabe.
[Piano Tutorial in Ten Books by Ferruccio Busoni. Second reorganized and enriched edition.]
[4 exercises using the thumb; 3 exercises not using the thumb; employ unusual and unorthodox fingerings: the thumb passing under the fifth finger; the fifth finger passing over the thumb; or not using the thumb at all]
[11 connected exercises in a series of keys with variants of the same techniques]
(c) [Superimposed keys], pp. 7-8.
[Bitonal scale exercises with different, but related keys in the right and left hand, e.g., C major and A major, etc.; hands in similar and contrary motion]
[This set concludes with a "Faustian" cadence.] Beaumont, p. 304)
(d) Presto volante, pp. 9-11.
[7 single-note scale exercises on a single stave, in different keys and patterns, played by alternating hands; the 8th exercise is on two staves with scales in simultaneous octaves played with alternating hands, finishing with diverging stepwise chords in both hands]
(e) [Thirds], p. 12.
[5 scale exercises: broken thirds; double thirds split between two hands; double thirds in both hands; split chromatic thirds; split chromatic thirds with sliding fingers]
[This section should studied together with a similar section in Busoni's edition of the Well-Tempered Clavier, Book 1 (score)] (Sitsky, p. 166)
Book 2: Forms derived from scales
Zweites Buch. Von Tonleitern abgeleitete Formen, pp. 13–26. (score)
Beispiel: Alkan, Etudes dans les tons majeurs: C dur Stück. [Op. 35, No.4] (score)
(k) Preludio. Andante tranquillo, pp. 43-44.
[excerpt based on Busoni's Improvisation on "Wie wohl ist mir" for two pianos (BV 271; score), beginning at bar 10] (Beaumont, p. 303)
(l) Tempo di Valse, elegantemente, pp. 45-48.
[After 2 bars of introduction the piece is essentially identical to the 28-bar Intermezzo in A-flat major from Busoni's Fourth Ballet Scene (first version of 1892, BV 238; score); it then modulates into a new 24-bar middle section, and finally returns to A-flat major in the 19-bar conclusion.] (Beaumont, p. 303)
[Piano music "à trois mains" ("for three hands") combines three musical lines (written on three staves), which sounds as though it is played by three hands, but nevertheless is actually played by two.]
[transcription of the Barcarole from the Tales of Hoffmann] (score) (Sitsky, p 289; Beaumont, p. 303)
(c) Nach Beethoven. Presto, pp. 55-56.
[excerpt from the fifth movement of the C-sharp minor Quartet Op. 131 (score), transcribed for piano; consists of the first 24 bars, jumps to the fermata before the "a tempo" at bar 44 and proceeds to the cadence at the beginning of the first ending at bar 65] (Sitsky, p 278)
Beispiele: Schubert-Liszt, Das Sterbeglöcklein.
[Schubert song, D.871, transcribed for solo piano]
[No.3 from Liszt's Sechs Melodien (6 Melodies), S.563]
Liszt, Valse a capriccio sur Lucia e Parisina (Erste Fassung) [S.401]
(d) Perpetuum mobile et infinitum. Studie nach Bach (aus "an die Jugend"). Allegro non troppo, pp. 57-58.
[An endlessly repeating 24-bar loop extracted from the "Fuga figurata" of Book 2 of Busoni's An die Jugend, BV 254 (score). The piece combines themes from the prelude and the fugue of Bach's Prelude and Fugue No.5 in D major (BWV 850) from the Well-Tempered Clavier, Book 1 (score)]
[16-bar excerpt beginning just before bar 57 of Liszt's transcription of Schubert's song Erlkönig in 12 Lieder von Franz Schubert, S.558/4 (score)] (Sitsky, p 293)
(f) Aus meinem "Concerto". Trattenuto e fantasticamente, pp. 61-62.
[The following piece is not included in the First Edition]
(i) Veloce e leggiero, pp. 84-88.
[This extended piece, composed 1–3 January 1924, is Busoni's last piano composition (score). The music was also intended for Busoni's unfinished opera Doktor Faust, and Antony Beaumont used it for his completion of the opera.] (Beaumont, p. 305)
["A sinister five-page essay in Busoni's best spectral style..."] (Sitsky, p 168)
[transcription of the Presto from the Mendelssohn-Liszt Wedding March & Elfin Chorus, S.410 (score)] (Sitsky, p 243)
(h) Nach Bizet. Allegro deciso, pp. 110-111.
[consists of the first 68-bars of Busoni's Kammer Fantasie über Carmen, BV 284 (score) with 6-bars added to provide an ending] (Sitsky, p 279)
(i) Nach Liszt. Quasi Galopp, sempre da Capo, pp. 112-113.
[60-bar indefinitely repeating excerpt from Busoni's piano transcription of Liszt's Mephisto Waltz for orchestra (S.110), BV B 61 (beginning on p. 27 of the complete score)] (Sitsky, p 243)
(j) Allegro, pp. 114-117.
"...another fierce-looking study in staccato chords...." (Sitsky, p 170)
[Busoni's edition of the Cramer etudes was originally published in 1897 by Schlesinger (BV B 53). That edition is faithful to the originals, except the slow introduction of No.5 [recte No. 6] is omitted, and possible changes to Etudes 4 to 8 are indicated with ossias. The etudes republished in the Klavierübung (First Edition, Part 4) are identical to those in the Schlesinger edition. However, in this edition Etudes 4 to 8 include the ossias in the text without notification and contain musical and pianistic changes as well.] (Sitsky, p 284)
Acht Etüden nach Cramer, pp. 118-150.
1. Allegro non tanto
2. Comodo: Behaglich
3. En Carillon: Moderato
4. Allegro di Bravura
5. Répétition: Allegrissimo
6. Allegro moderato
7. Scherzando: Piùttosto moderato
8. Finale: Molto agitato quasi presto
Book 8: Variations and Variants on Chopin
Achtes Buch. Variationen und Varianten zu Chopin (score)
(a) Neun Variationen über ein Präludium von Chopin, pp. 151-167.
[The same as Zehn Variationen über ein Präludium von Chopin (BV 213a, except the "Fantasia" section is omitted (score)] (Sitsky, p 57)
[The variations are played without pause; they are not numbered in the score, but are numbered here according to Sitsky.]
(1) Sostenuto [Introduction]
(2) Largo [Chopin Prelude]
(3) [var. 1] Sostenuto (alla breve)
(4) [var. 2] poco più vivo, legg. scherzoso
(5) [var. 3] (En Carillon)
(6) [var. 4] continuando. dolce
(7) [var. 5] sotto voce e poi sempre aumentando
(8) [var. 6] [no marking, begins on p. 159, 4th beat of first measure]
[The Fantasia section is omitted here; it is included in the 1st edition of the Klavierübung.]
(9) [var. 7] deciso. [6 measures serving as introduction to var. 8]
(10) [var. 8] Scherzo finale - (Vivace misurato) [fugue-like]
(11) [var. 9] (Hommage à Chopin) Tempo di Valse, tranquillo moderato.
(12) Tempo dello Scherzo. [conclusion based on var. 8]
[Note: The "Faustian" introduction (1) employs the technique of symmetrical harmony which Busoni had been developing over the previous twelve years. These four bars were so important to him that he later requested that they be played as introduction to the variations of 1888 (BV 213)] (Beaumont, p. 298.)
(b) Varianten zu Etüden und Präludien von Chopin, pp. 168-177.
[Six Variants of Etudes and Preludes by Chopin]
"Erst der Spiegel der Variante vom Urbild zeigt das Interessante." (Ferruccio Busoni)
(1) [unmarked] [Variant of Etude, Op. 10 No.1 - broken chords in both hands]
(2) Moderato [Variant of Etude Op. 10 No.2 - chromatic figure played by thumb and second finger]
[followed with a page of suggested variants (not found in the First Edition)]
(3) Agitato [Variant of Op. 10, No.9 - broken figures in the right hand]
(4) Moderato vivace [Variant of Etude Op. 10, No.7 - begins more simply than Chopin, ends more difficulty, with both hands playing sixteenth-note chords]
(5) Allegro [Variant of Etude Op. 10, No.8 - Chopin's passage work is extended]
[Chopin's passage work is shifted to from the left to the right hand; the entire piece is transcribed and is performable.]
Book 9: Seven Short Pieces for the Cultivation of Polyphonic Playing
Neuntes Buch. Sieben kurze Stücke zur Pflege des polyphonen Spiels (score)
(a) Sieben kurze Stücke zur Pflege des polyphonen Spiels, pp. 178-202.
[Nos.1 and 7 were added to extend Fünf kurze Stücke zur Pflege des polyphonen Spiels auf dem Pianoforte, BV 296. The pieces follow a cycle of keys of ascending fourths.] (Sitsky, p. 170)
7. Mit Anwendung des III. Pedals (Steinway & Sons Sostenuto-Pedal.) Andante tranquillo. [in F major]
[This piece is written on 4 staves, two for the Hauptstimme [principal part] and two for the Liegende Töne [Held notes]. Busoni finished it on 13 November 1923 in Paris. It is dedicated to Leonhard Tauber, who was his host while he was in Paris. The music was intended for the moment of Faust's death at the end of the final scene of his unfinished opera Doktor Faust.] (Beaumont, p. 306.)
(b) Perpetuum mobile (nach des Concertino II. Satze), pp. 203-213.
[Assigned the Kindermann catalog number BV 293 (score), this piece is a shortened version of the Scherzoso from the Concertino for Piano, BV 292. The middle section of the Scherzoso is replaced with a sequential passage.]
Kindermann, Jürgen (1980). Thematisch-chronologisches Verzeichnis der Werke von Ferruccio B. Busoni. Studien zur Musikgeschichte des 19. Jahrhunderts, vol. 19. Regensburg: Gustav Bosse Verlag. ISBN3-7649-2033-5
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Bahasa BahauBPS: 0428 6Dituturkan diIndonesiaWilayahKutai Barat, Kalimantan TimurPenutur19.000 (SIL, 2007) Rumpun bahasaAustronesia Melayu-PolinesiaKayan-MurikKayanBahasa Bahau Kode bahasaISO 639-1-ISO 639-2-ISO 639-3bhvBPS (2010)0428 6QIDQ3502039 Status konservasi C10Kategori 10Kategori ini menunjukkan bahwa bahasa telah punah (Extinct)C9Kategori 9Kategori ini menunjukkan bahwa bahasa sudah ditinggalkan dan hanya segelintir yang menuturkannya (Dormant)C8bKategori 8bKategori ini men...
Function that is its own inverse For the archaic use of this term, see exponentiation. An involution is a function f : X → X that, when applied twice, brings one back to the starting point. In mathematics, an involution, involutory function, or self-inverse function[1] is a function f that is its own inverse, f(f(x)) = x for all x in the domain of f.[2] Equivalently, applying f twice produces the original value. General properties Any involution is a bijection. The iden...
American media personality (1923–2023) For the activist group Sea Shepherd's ship, see MY Bob Barker. For the prison supply company, see Bob Barker Company. For the rugby player, see Bob Barker (rugby union). Bob BarkerBarker in 1975BornRobert William Barker(1923-12-12)December 12, 1923Darrington, Washington, U.S.DiedAugust 26, 2023(2023-08-26) (aged 99)Los Angeles, California, U.S.Resting placeForest Lawn Memorial Park, Hollywood HillsCitizenship United States Rosebud Sioux Tribe Educ...
Diplomatic crisis over nuclear weapons 1994 North Korean nuclear crisisPart of Inter-Korean conflictFlight Operations aboard the USS Kitty Hawk on 4 December 1994Date12 March 1993 – 21 October 1994LocationKorean PeninsulaSea of JapanResult Agreed Framework signed between United States and North Korea Temporary suspension of North Korean nuclear weapons program Cessation of Team Spirit exercisesBelligerents North Korea United States South KoreaCommanders and leaders Kim Il S...
Questa voce o sezione sull'argomento guerra è priva o carente di note e riferimenti bibliografici puntuali. Commento: diverse note non sono affidabili: la 5 e la 6, la numero 3 non funziona più, la 11. Sebbene vi siano una bibliografia e/o dei collegamenti esterni, manca la contestualizzazione delle fonti con note a piè di pagina o altri riferimenti precisi che indichino puntualmente la provenienza delle informazioni. Puoi migliorare questa voce citando le fonti più precisamente. Se...
Romanian swimmer Noémi LungNoemi Lung in 1988Personal informationFull nameNoemi Lung ZahariaNationalityRomanianBorn (1968-05-16) May 16, 1968 (age 55)Baia Mare, RomaniaHeight1.75 m (5 ft 9 in)Weight65 kg (143 lb)SportSportSwimmingStrokesButterfly and medleyCollege teamFlorida Atlantic University (USA)CoachGheorghe Demeca[1][2] Medal record Representing Romania Olympic Games 1988 Seoul 400 m medley 1988 Seoul 200 m medley World Championships...
Pour les articles homonymes, voir Buch. Cet article est une ébauche concernant une localité autrichienne. Vous pouvez partager vos connaissances en l’améliorant (comment ?) selon les recommandations des projets correspondants. Buch Héraldique Administration Pays Autriche Land Vorarlberg District(Bezirk) Brégence Code postal A-6960 Immatriculation B Indicatif 43+ Code Commune 8 02 08 Démographie Population 602 hab. (1er janvier 2016) Densité 98 hab./km2 Géographie Coo...
Controlling robots from a distance Justus security robot patrolling in Kraków Telerobotics is the area of robotics concerned with the control of semi-autonomous robots from a distance, chiefly using television, wireless networks (like Wi-Fi, Bluetooth and the Deep Space Network) or tethered connections. It is a combination of two major subfields, which are teleoperation and telepresence. Teleoperation Teleoperation indicates operation of a machine at a distance. It is similar in meaning to t...
1964 single by the Beatles This article is about the song by the Beatles. For other uses, see I Should Have Known Better (disambiguation). I Should Have Known BetterUS picture sleeve (reverse)Single by the Beatlesfrom the album A Hard Day's Night A-sideA Hard Day's NightReleased13 July 1964 (1964-07-13)Recorded25–26 February 1964StudioEMI, LondonGenrePop rock[1]Length2:44LabelCapitolSongwriter(s)Lennon–McCartneyProducer(s)George MartinThe Beatles US singles chro...
This article is about the Bobby Brown album. For other albums with similar titles, see Masterpiece (disambiguation). This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: The Masterpiece album – news · newspapers · books · scholar · JSTOR (August 2012) (Learn how and when to remove this message) 2012 studio a...
Moveable bridge with a counterweight which keeps the span(s) balanced during the upswing Bascule bridgeThis animation shows the movement of a double-leaf bascule.AncestorDrawbridge, Plate girder bridge, cantilever bridgeRelatedLift bridge, swing bridgeDescendantNoneCarriesPedestrian, bicycle, automobile, truck, light rail, heavy railSpan rangeShortMaterialSteelMovableYesDesign effortMediumFalsework requiredSite and prefabrication specific A bascule bridge (also referred to as a drawbridge or ...
Sokrates ΣωκράτηςSokratesLahirc. 469 / 470 SMDeme Alopece, AthenaMeninggal399 SM (umur sekitar 71)AthenaKebangsaanYunaniEraFilsafat kunoKawasanFilsafat BaratAliranYunani klasikMinat utamaEpistemologi, EtikaGagasan pentingMetode Sokrates, Ironi Kematian Sokrates, lukisan karya pelukis Jacques-Louis David (1787).Sokrates (Yunani: Σωκράτης, Sǒkratēs) (sekitar 470 SM–399 SM) adalah salah seorang filsuf dari Yunani.[1] Ia merupakan salah satu pemikir antropos...
