The ''Studies for Player Piano'' is a series of 49
études for
player piano by American composer
Conlon Nancarrow. Often exploring complex rhythmic variations beyond the ability of a human pianist, these compositions are some of the best-known and celebrated compositions by Nancarrow, even though they are generally not considered a set of compositions, but rather individual compositions that were given the same title and status. The dates of composition are unknown, but approximate ranges have been given according to best evidence.
Composition
Nancarrow's ''Studies for Player Piano'' were started when Nancarrow himself was first experimenting with the possibilities of the player piano. Most of these studies were never given a formal premiere and, given that Nancarrow lived his life in relative isolation, his studies became better known after the 80s. Furthermore, most of his studies were arranged for many different ensembles and instruments, including two pianos, small orchestra, string quartet, xylophone, vibraphone and celesta, synthesizers and computers.
1948: Boogie-Woogie Suite
It is suspected that the ''Study No. 3'' was Nancarrow's first composition for player piano composed between 1948 and 1949. This study was later compiled from the three initial parts into a five movement suite entitled ''Boogie-Woogie Suite'' in 1962. Its fourth movement included fragments of the second movement of Nancarrow's ''Suite for Orchestra'', composed in 1945. It was arranged for piano, piano four-hands, chamber orchestra and small orchestra. This study was expanded and finished as Nancarrow's ''Piece for Ligeti'', in an hommage to
György Ligeti on 17 October 1988, at the
Hamburgische Staatsoper
The Hamburg State Opera (in German: Staatsoper Hamburg) is a German opera company based in Hamburg. Its theatre is near the square of Gänsemarkt. Since 2015, the current ''Intendant'' of the company is Georges Delnon, and the current ''Genera ...
. Of the two available versions of the third study, the ''Boogie-Woogie Suite'' remains the better known and more recorded one. A photocopy of the first version of the study is available at the
Lincoln Center Library
The New York Public Library for the Performing Arts, Dorothy and Lewis B. Cullman Center, at 40 Lincoln Center Plaza, is located in Manhattan, New York City, at the Lincoln Center for the Performing Arts on the Upper West Side, between the Metro ...
. The suite was first performed in
Mexico City's
Palacio de Bellas Artes on 30 July 1962.
The suite consists of five movements featuring different music styles. The first movement features a hasty
boogie-woogie in which up to seven layers of melodic and rhythmic structures are superimposed. The second movement features a
blues
Blues is a music genre and musical form which originated in the Deep South of the United States around the 1860s. Blues incorporated spirituals, work songs, field hollers, shouts, chants, and rhymed simple narrative ballads from the Afr ...
, with a twelve-bar ostinato in the bass line which is repeated ten times. The third movement also has a blues character with canonic passages. The fourth movement features a
jazz style, whereas the fifth movement comes back to an even more rushed boogie-woogie.
1949 to 1950
The first study came right after, entitled ''Rhythm Study No. 1 for Player Piano'' and finished between 1949 and 1950. It was published in ''New Music Edition'', a quarterly of modern composition, in Los Angeles in October 1951. The study has more than two hundred tempo changes. It was premiered together with Studies Nos. 1 and 2, in
Mexico City's
Palacio de Bellas Artes on 30 July 1962.
Nancarrow's ''Study No. 2'' was composed circa 1950 and premiered together with Nos. 1 and 2. It is a slow blues with two melodic bass parts in tempo ratio of 3:5. However, Nancarrow also composed three additional version of the same study, entitled by himself ''Didactical Study No. 2x'', ''Didactical Study No. 2y'' and ''Didactical Study No. 2z''. These versions are also known as 2b, 2c and 2d, respectively, 2a being the main study. This way, 2x (2b) has a tempo ratio of 5:9, 2y (2c) has a tempo ratio of 4:7 and 2z (2d) has a tempo ratio of 5:7.
Some publishers and record companies use the title ''Study No. 2a'' in order to differentiate it from Nancarrow's ''Study No. 2A'' (sometimes also erroneously entitled ''Study No. 2b'', as it would lead to confusion), an extended version of the fourth movement of his 1945 ''Suite for Orchestra''. This extended version arranged for player piano was also composed in 1950 and was later included in the set decades later as an afterthought.
1951 to 1960
Between 1951 and 1965, Nancarrow wrote the studies nos. 4 to 30. Some of these compositions have been dated according to evidence, but Nancarrow never left a date in any of his originals. In these studies, Nancarrow explored the possibilities of
polyrhythm,
prolation canons and the usage of
irrational numbers, such as the
square root of two. However, he still used different musical styles, including
jazz or
blues
Blues is a music genre and musical form which originated in the Deep South of the United States around the 1860s. Blues incorporated spirituals, work songs, field hollers, shouts, chants, and rhymed simple narrative ballads from the Afr ...
.
The ''Study No. 4'' is a study with jazzy melody lines which features canonlike elements. However, it is not a strict canon, as the rhythmic patterns are not followed. It was premiered in a performance at
Ann Arbor, Michigan
Ann Arbor is a city in the U.S. state of Michigan and the county seat of Washtenaw County, Michigan, Washtenaw County. The 2020 United States census, 2020 census recorded its population to be 123,851. It is the principal city of the Ann Arbor ...
, at the
ONCE Festival of New Music
Once means a one-time occurrence.
Once may refer to:
Music
* ''Once'' (Pearl Jam song), a 1991 song from the album ''Ten''
* ''Once'' (Roy Harper album), a 1990 album by Roy Harper
* ''Once'' (The Tyde album), a 2001 debut album by The Tyd ...
, on 18 February 1962. It was arranged for the ballet ''Crises'', by
Merce Cunningham and
John Cage
John Milton Cage Jr. (September 5, 1912 – August 12, 1992) was an American composer and music theorist. A pioneer of indeterminacy in music, electroacoustic music, and non-standard use of musical instruments, Cage was one of the leading fi ...
, and again for piano four-hands. The ''Study No. 5'' was premiered in the same festival as the ''Study No. 4''. It is a study of repeated and rapid runs and chordal motifs, superimposed over two ostinato rhythmic and melodic lines in the bass at tempos 5:7. It starts with only two voices but ends up with thirteen. It was also arranged for ''Crises'' and, later on, for chamber orchestra. The ''Study No. 6'' has a rather
blues
Blues is a music genre and musical form which originated in the Deep South of the United States around the 1860s. Blues incorporated spirituals, work songs, field hollers, shouts, chants, and rhymed simple narrative ballads from the Afr ...
y style, with a tune on top of a quasi-ostinato bass line, which tempo ratios of 4:5:6, shifting back and forth every four notes along the whole movement. It was first performed in
Kassel
Kassel (; in Germany, spelled Cassel until 1926) is a city on the Fulda River in northern Hesse, Germany. It is the administrative seat of the Regierungsbezirk Kassel and the district of the same name and had 201,048 inhabitants in December 2020 ...
, in Summer 1982, and has since been arranged for a
Marantz
Marantz is a company that develops and sells high-end audio products. The company was founded in New York, but is now based in Japan.
The first Marantz audio product was designed and built by Saul Marantz in his home in Kew Gardens, New York. ...
computer-piano, chamber orchestra, piano four-hands, two pianos and small orchestra. Amongst the arrangers is British composer
Thomas Adès.
Of all of Nancarrow's early compositions for player piano, ''Study No. 7'' is probably one of the longest. It takes 6 minutes to perform. According to American music scholar
Kyle Gann
Kyle Eugene Gann (born November 21, 1955, in Dallas, Texas) is an American professor of music, critic, analyst, and composer who has worked primarily in the New York City area. As a music critic for ''The Village Voice'' (from 1986 to 2005) and ...
, it is one of the few studies approaching the sonata form. One of the most complex early compositions, the study features striking rhythmic pattern together with melodic lines. The eight-part composition ends with racing arpeggios. It was originally presented with a longer beginning and a shorter ending. It was first performed together with the first three studies in
Mexico City, on 30 July 1962 and has been arranged for a
Marantz
Marantz is a company that develops and sells high-end audio products. The company was founded in New York, but is now based in Japan.
The first Marantz audio product was designed and built by Saul Marantz in his home in Kew Gardens, New York. ...
computer-piano, chamber orchestra, piano four-hands, two pianos and two disc-pianos.
The ''Study No. 8'' is probably one of the most important early studies, because it features some of the most representative traits of Nancarrow's music: canons and continual tempo changes. These techniques were further developed along his musical career. The study is in three parts and is considered the first acceleration study. It was also the first time Nancarrow used bar lines and conventional notation. The first performance of the work was the one in 1962 in
Mexico City. The following studies would continue to explore varied meters and tempos. Among them, the ''Study No. 9'', which can be described as a collage with three repeating loops at different tempos. As his previous studies, the bass line is in ostinato and the ratios used in the study are 3:4:5. It was also premiered in the performance of the studies 7 and 8, in Mexico City and was arranged for chamber orchestra, piano four-hands and two pianos.
The last study to feature jazz characteristics is ''Study No. 10''. It has a blues melody and complex rhythmic patterns, given the continually changing
time signature. The first version of this study was in
ABA form. However, in Nancarrow's circa-1980 revision of the study, the first section was dropped. This later revision is now considered authoritative. The ''Study No. 11'' is an isorhythmic study which uses a technique from the 14th century
motet
In Western classical music, a motet is mainly a vocal musical composition, of highly diverse form and style, from high medieval music to the present. The motet was one of the pre-eminent polyphonic forms of Renaissance music. According to Margar ...
s. It uses conventional notation and features a sequence of repeating 120 chords. There are up to thirty tempo changes in the first page alone. The ''Study No. 12'' is the first one to receive an unofficial subtitle: the ''flamenco'' study, because of its influence by Spanish
flamenco. The study imitates the guitar arpeggios used in flamenco music. This study was arranged for chamber orchestra in 1995. These three studies were first performed at the Mexico City event in which most of his other studies to date were performed.
''Seven Canonic Pieces''
The studies 13 to 19 constitute a cycle of canons composed before 1960 entitled ''Siete piezas canónicas'' ( es, Seven Canonic Pieces). The whole cycle of canons was first performed in the
Mexico City's
Palacio de Bellas Artes, on 30 July 1962. All of these canons have at least one characteristic in common: the prolation of the different parts.
The ''Study No. 13'' is the preliminary study for the whole set. Nancarrow became displeased with the result and decided to withdraw it and to never publish it. However, he made it available as a recording. The rest of the canons were published, starting with ''Study No. 14'' which is a canon 4/5, in which the first part begins at a tempo of ♩ = 88, followed shortly thereafter by the second part, two octaves and a fifth higher at tempo ♩ = 110. The ''Study No. 15'' is a canon 3/4, in which the two parts are three octaves apart and the faster meter alternates in a way that both parts begin and end simultaneously. The ''Study No. 16'' explores deeper into the concept of two-part prolation canons. It is a sketch of a canon 3/5. There are two sections, the second 5/3 as fast as the first, and then the two are played simultaneously as a third section. The ''Study No. 17'' is a three-part canon with ratios 12/15/20. The ''Study No. 18'' is, again, a two-part canon with ratios 3/4. The second voice begins when the first has gone 1/3 of its way, but it is played 1/3 faster, so it catches up and finishes together with the first part. It is largely seen as a precursor of ''Study No. 40b''. Finally, the ''Study No. 19'' has the same tempo ratios than ''Study No. 17''. It is a three-part canon with ratios 12/15/20, and its second and third part entries are set in a way that all three parts end up simultaneously.
1961 to 1965
Chronologically, the next composition to be finished was the ''Study No. 21'', the canon X. It is an acceleration study where one voice progressively slows down while the other speeds up. The study starts with a bass line playing a 12-tone row at about 4 notes per second, immediately followed by the other voice, playing thirty-nine notes per second. Then the bass line starts to speed up and the treble line slows down progressively, reaching the same tempo halfway through the piece. The piece ends up with one of the lines playing 120 notes per second. It was presumably written in 1961 and was first performed in the Mexico City performance in 1962. The ''X'' alludes to the tempo acceleration and deceleration of both parts in the canon. It was also arranged for synthesizer, Marantz computer-piano, two disc-pianos and two voices. Following, ''Study No. 22'', a canon with ratios of 1%/1½%/2¼%; this means that the lowest voice starts at a given tempo and accelerates 1% over time, the second voice does so at 1½% and the third voice at 2¼%. The three voices accelerate until the middle of the piece, where they decelerate at the same rate and get to the end of the piece at the same initial speeds. This canon was first performed in
Kassel, Germany, in Summer 1982.
The ''Study No. 23'' is a two-part composition which turns three-part halfway in the study. As in ''Study No. 21'', Nancarrow also experimented with constant acceleration and deceleration changes. The treble accelerated part is considered to be "unplayable". The study was also first performed in Kassel in 1982. The ''Study No. 24'' is a three-part canon 14/15/16 which, unlike other pieces by Nancarrow, is predominantly tonal. It features rapid repetitions, chains of trills and glissandi. It has been called a "masterpiece" by American scholar
Kyle Gann
Kyle Eugene Gann (born November 21, 1955, in Dallas, Texas) is an American professor of music, critic, analyst, and composer who has worked primarily in the New York City area. As a music critic for ''The Village Voice'' (from 1986 to 2005) and ...
. It was first performed on 30 May 1964, in
Ojai, California
Ojai ( ; Chumash: ''’Awhaỳ'') is a city in Ventura County, California. Located in the Ojai Valley, it is northwest of Los Angeles and east of Santa Barbara. The valley is part of the east–west trending Western Transverse Ranges and is ...
. ''Study No. 25'' is one of Nancarrow's most elaborate studies. It features many "idiomatic" traits of the player piano: glissandos, arpeggios, lightning-fast zagged patterns and rapid sequences. Its ending is a 12-second section in which 1028 notes are played with the sustain pedal held down, sometimes even getting to two hundred notes per second. However, even though it has canonic elements, it is mostly a rhapsodic piece. It was premiered at the
Pro Musica Nova
Pro Musica Nova was a biennial festival for contemporary music sponsored by Radio Bremen from 1958 to 2001. It was founded by Hans Otte. A number of experimental and electronic composers contributed.
History
From 1960 it was held in alternate yea ...
festival in
Bremen
Bremen (Low German also: ''Breem'' or ''Bräm''), officially the City Municipality of Bremen (german: Stadtgemeinde Bremen, ), is the capital of the German state Free Hanseatic City of Bremen (''Freie Hansestadt Bremen''), a two-city-state consis ...
, on 15 May 1976.
The ''Study No. 26'' is actually the only study where all voices have no rhythmic differentiation. The canon is 1/1, which means that all the notes have the same tempo. It starts with one voice and ends up with seven. The study has been arranged for 7 hands on two to four pianos, piano four-hands, small orchestra and chamber ensemble. It was first performed at the Kassel event in 1982. In the ''Study No. 27'', Nancarrow came back to the acceleration canons. This study is a canon 5%/6%/8%/11%/, and consists of an ostinato bass line at a constant speed, with up to eight voices accelerating and decelerating at different speeds. Nancarrow himself saw the study as "the ticking of an ontological clock (world clock) with events running along beside it at different speeds". This study was premiered at the
Pro Musica Nova
Pro Musica Nova was a biennial festival for contemporary music sponsored by Radio Bremen from 1958 to 2001. It was founded by Hans Otte. A number of experimental and electronic composers contributed.
History
From 1960 it was held in alternate yea ...
festival in
Bremen
Bremen (Low German also: ''Breem'' or ''Bräm''), officially the City Municipality of Bremen (german: Stadtgemeinde Bremen, ), is the capital of the German state Free Hanseatic City of Bremen (''Freie Hansestadt Bremen''), a two-city-state consis ...
, on 15 May 1976, just like ''Study No. 25''.
The ''Study No. 28'' is another one of those complex pieces by Nancarrow. It is one of the few pieces which have actual rules and correlations between tempo and pitch. To serve as a guide for listeners, Nancarrow also added chords at regular intervals to provide a temporal orientation. It was first performed in the
National Autonomous University of Mexico
The National Autonomous University of Mexico ( es, Universidad Nacional Autónoma de México, UNAM) is a public research university in Mexico. It is consistently ranked as one of the best universities in Latin America, where it's also the bigges ...
, in
Mexico City, on 23 October 1990. The ''Study No. 29'' is the first piece in which Nancarrow tried to work on a prepared piano, in the style of
John Cage
John Milton Cage Jr. (September 5, 1912 – August 12, 1992) was an American composer and music theorist. A pioneer of indeterminacy in music, electroacoustic music, and non-standard use of musical instruments, Cage was one of the leading fi ...
. However, Nancarrow dismissed the idea of putting preparations in a piano for this study. It has up to eight parts and resembles the ticking of clocks at different speeds. The study is in ABABABABABABAB form with different acceleration ratios interacting with each other. Nancarrow never liked the piece and was initially willing to withdraw it. He commented: "I should have thrown it away a long time ago, but I never had the heart." The study was first performed in
Köln
Cologne ( ; german: Köln ; ksh, Kölle ) is the largest city of the German western state of North Rhine-Westphalia (NRW) and the fourth-most populous city of Germany with 1.1 million inhabitants in the city proper and 3.6 million ...
, on 15 October 1988.
Finally, the ''Study No. 20'' was among the last studies from this period to be composed. With this study, Nancarrow started to use characteristics in notation other than the traditional ones. Sometimes unofficially subtitled ''Cloud'', it features a style that is very closely related to that of
Iannis Xenakis and
György Ligeti. This study is a study on note durations, with eight voices being very close together. It was presumably composed around 1965, and is strikingly similar to Ligeti's ''Monument'' for two pianos, written in 1976. This study was first performed in
Aptos, California
Aptos (Ohlone for "The People") is an unincorporated town in Santa Cruz County, California. The town is made up of several small villages, which together form Aptos: Aptos Hills-Larkin Valley, Aptos Village, Cabrillo, Seacliff, Rio del Mar, and S ...
, on 27 August 1977 and has been arranged for two pianos and for piano four-hands. The last study from 1965 is ''Study No. 30'', which was rejected by the composer for him having problems with the preparations, because the preparations did not stay with the strings of an
upright piano. After this study, Nancarrow decided to go back to the unprepared piano. Nancarrow recorded the piece, but never published the score and discarded it, for he was not pleased with the result. This study was first performed in public in the same even as ''Study No. 28'', in the
National Autonomous University of Mexico
The National Autonomous University of Mexico ( es, Universidad Nacional Autónoma de México, UNAM) is a public research university in Mexico. It is consistently ranked as one of the best universities in Latin America, where it's also the bigges ...
, in
Mexico City, on 23 October 1990.
1966 to 1969
The ''Study No. 31'' is a canon 21/24/25. It has three differentiated parts, called "movements" by
Kyle Gann
Kyle Eugene Gann (born November 21, 1955, in Dallas, Texas) is an American professor of music, critic, analyst, and composer who has worked primarily in the New York City area. As a music critic for ''The Village Voice'' (from 1986 to 2005) and ...
, which follow a sequence of "fast-slow-fast". However, these movements are not marked in any way in the original score. This study was arranged for string quartet in 2003. The ''Study No. 32'' is a canon 5/6/7/8, in which all the different voices are not assigned a particular speed for the whole movement, but rather each voice is played at different speeds. This study was arranged for piano four-hands and chamber ensemble. From ''Study No. 33'' on, Nancarrow became more and more fascinated by irrational tempos. This is a canon /2, which means that the different layers have no common denominator. As in the previous study, the different speeds are alternated between the parts of the composition. Considered one of the most important studies by Nancarrow himself, this study was completed circa 1968 and was arranged for string quartet in 2003. All of these three studies were given a first performance at the
Kassel
Kassel (; in Germany, spelled Cassel until 1926) is a city on the Fulda River in northern Hesse, Germany. It is the administrative seat of the Regierungsbezirk Kassel and the district of the same name and had 201,048 inhabitants in December 2020 ...
event, in Summer 1982.
The longest and most important study by Nancarrow, ''Study No. 37'' was initially conceived in 1965 and was finished in 1969. It takes up to 10 minutes to perform. It is a complex canon
150 150 may refer to:
*150 (number), a natural number
*AD 150, a year in the 2nd century AD
*150 BC, a year in the 2nd century BC
*150 Regiment RLC
*Combined Task Force 150
See also
* List of highways numbered 150
The following highways are numbered ...
/
160
Year 160 ( CLX) was a leap year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Atilius and Vibius (or, less frequently, year 913 '' Ab urbe condita''). ...
/
168
Year 168 ( CLXVIII) was a leap year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Apronianus and Paullus (or, less frequently, year 921 ''Ab urbe co ...
/
180
__NOTOC__
Year 180 ( CLXXX) was a leap year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Rusticus and Condianus (or, less frequently, year 933 '' Ab ...
/
187
Year 187 ( CLXXXVII) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Quintius and Aelianus (or, less frequently, year 940 ''Ab urbe c ...
/
200
__NOTOC__
Year 200 ( CC) was a leap year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Severus and Victorinus (or, less frequently, year 953 '' Ab ur ...
/
210
Year 210 ( CCX) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Faustinus and Rufinus (or, less frequently, year 963 ''Ab urbe condita ...
/
225
__NOTOC__
Year 225 ( CCXXV) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Fuscus and Domitius (or, less frequently, year 978 ''Ab ...
/
240
__NOTOC__
Year 240 ( CCXL) was a leap year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Sabinus and Venustus (or, less frequently, year 993 ''Ab u ...
/
250
__NOTOC__
Year 250 ( CCL) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Traianus and Gratus (or, less frequently, year 1003 ''Ab u ...
/
262
__NOTOC__
Year 262 (Roman numerals, CCLXII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Gallienus and Faustianus (or, less fre ...
/
281, that is, a twelve-part canon. These twelve different speeds correspond to the ratios of the vibrations in the notes of a
7-limit just chromatic scale. It was first performed in
Graz
Graz (; sl, Gradec) is the capital city of the Austrian state of Styria and second-largest city in Austria after Vienna. As of 1 January 2021, it had a population of 331,562 (294,236 of whom had principal-residence status). In 2018, the popul ...
on 31 October 1982 and has since been arranged at least four times: for twelve synthesizers, for computer, xylophone and vibraphone, for computer and xylophone installation and for 12 spatially distributed stereo channels.
The other three studies were begun between 1966 and 1969, but were completed between 1969 and 1976. The ''Study No. 34'', which was completed circa 1969, is a canon
/
/
. This means that it is a 9/10/11; however, each part is also subdivided into 4/5/6. It was premiered in
Mexico City on 23 October 1990 and was arranged for string trio in 2004. The ''Study No. 36'' is a canon 17/18/19/20 in which all of its four voices have exactly the same score with different fixed speeds: its first voice plays at tempo 85, its second at 90, its third at 95 and its fourth at 100. The four parts meet in the middle of the composition. Therefore, the fourth voice ends first, then the third, then the second and, finally, the first. It was finished in 1970. Finally, the ''Study No. 35'' is a comeback by Nancarrow to a rather jazzy style. It was finished between 1975 and 1978, even though it was performed before it was finished. These two studies were first performed in the
Bremen
Bremen (Low German also: ''Breem'' or ''Bräm''), officially the City Municipality of Bremen (german: Stadtgemeinde Bremen, ), is the capital of the German state Free Hanseatic City of Bremen (''Freie Hansestadt Bremen''), a two-city-state consis ...
event, on 15 May 1976.
1970 to 1982
From here, Nancarrow started to work on other creative ways to develop his compositions. The ''Study No. 40'' is a study for two player pianos. It is divided into two parts: ''40a'' and ''40b''. The study ''a'' is a canon
e/
Ï€ for only one player piano, which makes a profuse use of glissandi. The study ''b'', however, is a canon
, for two synchronized player pianos. This means that the two pianos play the same score, but the second piano starts approximately 20 seconds away from the first, but a bit faster, in a way that both pianos end up simultaneously. It has been unofficially subtitled ''Transcendental''. It was completed in 1975 and was first performed in the
Pro Musica Nova
Pro Musica Nova was a biennial festival for contemporary music sponsored by Radio Bremen from 1958 to 2001. It was founded by Hans Otte. A number of experimental and electronic composers contributed.
History
From 1960 it was held in alternate yea ...
event, in 1976. The ''Study No. 41'', again for two player pianos, is divided into three parts: ''41a'', ''41b'' and ''41c''. The first canon is
for the first piano, the second canon is