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[ "The measurements made of the orbital decay of the PSR B1913 +16 system were a near perfect match to Einstein 's equations .", "The observations made of the orbital decay of this star system was a near perfect match to Einstein 's equations ." ]
[ "The flow of matter from one stellar body to another often leads to the creation of an accretion disk about the recipient star .", "This flow of matter from one stellar body to another is known as an accretion disk ." ]
[ "In the decade following its discovery the system 's orbital period had decreased by about 76 millionths of a second per year - this means that the pulsar was approaching its maximum separation more than a second earlier than it would have if the orbit had remained the same .", "This means the pulsar was approaching its maximum separation more than a second earlier than it would have if the orbit had remained the same ." ]
[ "Pulsars also create a `` wind '' of relativistically outflowing particles , which in the case of binary pulsars can blow away the magnetosphere of their companions and have a dramatic effect on the pulse emission .", "Millisecond pulsars ( or MSP 's ) create a sort of `` wind '' , which in the case of binary pulsars can blow away the magnetosphere of the neutron stars and have a dramatic effect on the pulse emission ." ]
[ "Pulses from this system are now tracked to within 15 μs .", "Pulses from this system have been tracked , without glitches , to within 15 μs since its discovery ." ]
[ "Data collected by Taylor and Joel M. Weisberg and their colleagues of the orbital period of PSR B1913 +16 supported this relativistic prediction ; they reported in 1982 and subsequently that there was a difference in the observed minimum separation of the two pulsars compared to that expected if the orbital separation had remained constant .", "Data collected by Taylor and his colleagues of the orbital period of PRS B1913 +16 supported this relativistic prediction ." ]
[ "When the two bodies are in close proximity , the gravitational field is stronger , the passage of time is slowed - and the time between pulses ( or ticks ) is lengthened .", "When the two bodies are close , the gravitational field is stronger , and the passage of time is slowed ." ]
[ "It was concluded that the pulsar was orbiting another star very closely at a high velocity , and that the pulse period was varying due to the Doppler effect : As the pulsar was moving towards us , the pulses would be more frequent ; and conversely , as it moved away from us fewer would be detected in a given time period .", "It was concluded that the simplest explanation was that the pulsar was orbiting another star very closely at a high velocity ." ]
[ "The Hallstatt culture was succeeded by the La Tène culture of central Europe , which was overrun by the Roman Empire , though traces of La Tène style are still to be seen in Gallo-Roman artefacts .", "They came from the Hallstatt and La Tène cultures ." ]
[ "The four are Irish Gaelic , Scottish Gaelic , Welsh , and Breton ; plus two recent revivals , Cornish ( one of the Brythonic languages ) and Manx ( one of the Goidelic languages ) .", "Today , the Celtic languages that remain are the Breton , Cornish , Welsh and Gaelic languages ." ]
[ "Hire supermodel Adriana Lima to star in it . ''", "Adriana Lima ( born June 12 , 1981 ) is a Brazilian supermodel ." ]
[ "In ZoneAlarm , program access is controlled by way of `` zones '' , into which all network connections are divided .", "In ZoneAlarm , program access is controlled by way of `` zones '' , into which all Computer networking connections are divided ." ]
[ "SmartDefense Advisor , a service that is also available in the free version of ZoneAlarm , helps the user with certain types of alerts .", "SmartDefense Advisor is a service only available in premium versions of ZoneAlarm that helps the user with certain types of alerts ." ]
[ "ZoneAlarm is a personal firewall software application originally developed by Zone Labs , which was acquired in March 2004 by Check Point .", "ZoneAlarm is a software firewall originally developed by Zone Labs , which was acquired in March 2004 by Check Point ." ]
[ "It includes an inbound intrusion detection system , as well as the ability to control which programs can create outbound connections .", "It includes an inbound intrusion detection system , as well as the ability to control which programs can create outbound connections-the latter not available in the Windows XP Service Pack 2 firewall ." ]
[ "Operating System Firewall , OSFirewall for short , is a feature in paid ZoneAlarm versions only .", "Operating System Firewall , OSFirewall for short , is a feature in ZoneAlarm paid versions only ." ]
[ "In 1943 , the Yanceys recorded for Session Records , and went back into the studio to record the album Pure Blues for Atlantic Records in 1951 .", "In 1943 , the Yanceys recorded for Session Records , and went back into the studio to record the album Pure Blues for Atlantic Records ." ]
[ "Because Jimmy Yancey was a great boogie-woogie\\/blues piano player , Estelle recorded several times with her husband .", "Because Jimmy Yancey was a great boogie-woogie\\/blues piano player , but a poor singer , Estelle recorded frequently with her husband ." ]
[ "Yancey , born Estella Harris in Cairo , Illinois , grew up in Chicago , where she sang in church choirs and learned how to play the guitar .", "Yancey , born Estelle Harris , grew up in Chicago , where she sang in church choirs and learned how to play the guitar ." ]
[ "She often sang with him at informal get-togethers and house parties in the 1940s and performed with him at Carnegie Hall , New York in 1948 .", "She often sang with him at meetings and house parties in the 1930s and 1940s and performed with him at Carnegie Hall , New York in 1948 ." ]
[ "Mama Yancey 's recordings with other pianists include `` Mama Yancey , singer , Don Ewell , pianist '' for Windin ' Ball Recordings ( 1952 ) , `` Chicago -- The Living Legends : South Side Blues '' for the Riverside label ( 1961 ) , `` Mama Yancey sings , Art Hodes plays Blues '' for Verve Records in 1965 , Maybe I 'll Cry with Erwin Helfer for the Red Beans label in 1983 , recorded at ages 86-87 , and `` The Blues of Mama Yancey : Axel Zwingenberger and the Friends of Boogie Woogie , vol .", "Mama Yancey 's recordings with other pianists include `` South Side Blues '' for the Riverside label ( 1961 ) , some records with Art Hodes for Verve Records in 1965 , and Maybe I 'll Cry with Erwin Helfer for the Red Beans label in 1983 , recorded at age 87 ." ]
[ "In 1925 , when she was 29 , she married Jimmy Yancey , who had traveled the U.S. and Europe as a vaudeville dancer .", "In 1917 , when she was 21 , she married Jimmy Yancey ." ]
[ "The first match of the relaunched SV Austria Salzburg was played on 29 July 2006 against Lieferinger SV , another Salzburg football club .", "The first match of the new SV Austria Salzburg was played on 29 July 2006 against Lieferinger SV , another football club from the city of Salzburg ." ]
[ "SV Austria Salzburg won 6-0 , and went on to win the championship and promotion to 1 .", "SV Austria Salzburg won 6-0 ." ]
[ "SV Austria Salzburg is an Austrian association football club , based in the city of Salzburg .", "The club claims to preserve the tradition of SV Austria Salzburg ." ]
[ "He was a leader of the Republican Party ( the `` GOP '' ) and founder of the Progressive Party .", "He was a member of the Republican Party ." ]
[ "Subtropical Storm Nicole was the first subtropical storm to receive a name using the standard hurricane name list that did not become a tropical cyclone .", "Subtropical Storm Nicole was the fourteenth named storm and first subtropical cyclone to form during the 2004 Atlantic hurricane season ." ]
[ "In 1972 and 1973 , four subtropical storms were named using the Phonetic alphabet , while all other subtropical cyclones remained unnamed .", "Initially , however , the phonetic alphabet was used to name subtropical cyclones ." ]
[ "The park was designated a UNESCO Biosphere Reserve in 1981 .", "It is also a UNESCO Biosphere Reserve ." ]
[ "During the Age of Discovery , mutiny particularly meant open rebellion against a ship 's captain .", "During the Age of Discovery , mutiny meant open rebellion against a ship 's captain ." ]
[ "In a ceremony at the White House on June 21 , 2000 , his surviving family was presented with his Medal of Honor by President Bill Clinton .", "In a ceremony at the White House on June 21 , 2000 , his family was presented with his medal by President Bill Clinton ." ]
[ "Twenty-one other Asian Americans also received the medal during the ceremony , all but seven of them posthumously .", "Twenty-one other Asian Americans also received the medal during the ceremony , but only seven of them were still alive ." ]
[ "Kuroda volunteered to join the all-Nisei 442nd Regimental Combat Team .", "Kuroda volunteered to be part of the all-Nisei 442nd Regimental Combat Team ." ]
[ "A 1990s review of service records for Asian Americans who received the Distinguished Service Cross during World War II led to Kuroda 's award being upgraded to the Medal of Honor .", "Kuroda 's award was upgraded to the Medal of Honor ." ]
[ "For these actions , he was posthumously awarded the Army 's second-highest decoration , the Distinguished Service Cross .", "For his actions in October 1944 , Kuroda was awarded the Army 's second-highest decoration , the Distinguished Service Cross ( DSC ) ." ]
[ "In those churches which follow the Rite of Constantinople ( e.g. Eastern Orthodox and Eastern Catholics ) , the forty days of Lent are counted differently ; also , the date of Easter is calculated differently in the East than in the West ( see Computus ) .", "Churches in the Byzantine tradition ( e.g. Eastern Orthodox and Eastern Catholic ) count the days of Lent differently ." ]
[ "On 21 January 1992 , he died of cancer at the age of 55 .", "He died on 21 January 1992 , of cancer at the age of 55 ." ]
[ "Three years after Mabo died , that being the traditional mourning period for the people of Murray Island , a gathering was held in Townsville for a memorial service .", "Three years after Mabo died , which is the traditional mourning period for the people of Murray Island , a memorial service was held in Townsville ." ]
[ "The time he spent on the campus had a massive impact on his life .", "The time he spent on the university campus had a major impact on his life ." ]
[ "Five months later , on 3 June 1992 , the High Court announced its historic decision , namely overturning the legal doctrine of terra nullius - which is a term applied to the attitude of the British towards land ownership on the continent of Australia . ''", "Five months later , on 3 June 1992 , the High Court overturned the legal doctrine of terra nullius - which was the term applied to the attitude of the British Empire towards land ownership on the continent of Australia ." ]
[ "Mabo worked on a number of jobs before becoming a gardener with James Cook University in Townsville , Queensland at the age of 31 .", "He worked on a number of jobs before becoming a gardener with James Cook University in Townsville , when he was 31 years old ." ]
[ "Eddie Koiki Mabo ( c. 29 June 1936 - 21 January 1992 ) was an Australian man from the Torres Strait Islands known for his role in campaigning for Indigenous land rights and for his role in a landmark decision of the High Court of Australia which overturned the legal doctrine of terra nullius ( `` land belonging to nothing , no one '' ) which characterised Australian law with regards to land and title .", "Eddie Koiki Mabo ( c. 29 June 1936 - 21 January 1992 ) was an Indigenous Australian activist from the Torres Strait Islands ." ]
[ "In 1974 , this culminated in a discussion he had with Noel Loos and Henry Reynolds , who recalled Mabo 's reaction : In 1981 a land rights conference was held at James Cook University and Mabo made a speech to the audience where he explained the land inheritance system on Murray Island .", "Mabo made a speech to the audience where he explained the indigenous customary land inheritance system on Murray Island ." ]
[ "Mabo was named `` Eddie Koiki Sambo '' but he changed his surname to `` Mabo '' when he was adopted by his maternal uncle , Benny Mabo .", "He changed his surname to Mabo when he was adopted by his mother 's brother , Benny Mabo ." ]
[ "Cornbread is a generic name for any number of quick breads containing cornmeal .", "Cornbread or Johnny cake is a name for any number of `` quick breads '' - bread leavened chemically instead of by yeast - containing cornmeal ." ]
[ "Deuterostomes are distinguished by their embryonic development ; in deuterostomes , the first opening ( the blastopore ) becomes the anus , while in protostomes it becomes the mouth .", "Deuterostomes are distingued by their embryo : in deuterostomes , the first opening ( the blastopore ) becomes the anus , while in protostomes it becomes the mouth ." ]
[ "Pope Gregory VIII ( Latin : Gregorius VIII ; c. 1100\\/1105 - 17 December 1187 ) , born Alberto di Morra , was Pope from 25 October to his death in 1187 .", "Pope Gregory VIII ( Latin : Gregorius Octavus ; c. 1100 - 17 December 1187 ) , born Alberto di Morra , was an Italian priest of the Roman Catholic Church and the 174th Pope from 25 October 1073 until he died in 1085 ." ]
[ "On 21 October 1187 , the day after the death of Pope Urban III , Alberto di Morra was elected pope and took the name Gregory VIII in honor of Pope Gregory VII .", "Cardinal Morra was elected pope on 11 October 1187 ." ]
[ "Alberto di Morra was born about 1105 in Benevento , Italy .", "Alberto di Morra was born in Benvenuo , Italy ." ]
[ "It is present among many cultures throughout history both as decorative motifs and as art pieces themselves .", "It is present in many cultures throughout history both as decorative motifs and as art pieces themselves ." ]
[ "Islamic art , in its prohibition of depicting religious figures , is a prime example of this geometric pattern-based art , which existed centuries before the movement in Europe and in many ways influenced this Western school .", "Islamic art , in its prohibition of depicting religious figures , is a prime example of this geometric pattern-based art ." ]
[ "Other examples of pioneer abstractionists such as Kasimir Malevich and Piet Mondrian have also embraced this approach towards abstract painting .", "Other examples of pioneer abstractionists such as Kazimir Malevich and Piet Mondrian have also embraced this approach towards abstract painting ." ]
[ "However , geometric abstraction can not only be seen as an invention of 20th century avant-garde artists or movements .", "Geometric abstraction is not just an invention of 20th century avant-garde artists or movements ." ]
[ "Geometric abstraction is a form of abstract art based on the use of geometric forms sometimes , though not always , placed in non-illusionistic space and combined into non-objective ( non-representational ) compositions .", "Geometric abstraction is a form of abstract art based on the use of geometric forms in non-representational compositions ." ]
[ "Aligned with and often used in the architecture of Islamic civilations spanning the 7th century-20th century , geometric patterns were used to visually connect spirituality with science and art , both of which were key to Islamic thought of the time .", "Geometric patterns were often used in the architecture of Islamic civilisations from the 7th century-20th century , to visually connect spirituality with science and art ." ]
[ "Expressionist abstract painting , as practiced by artists such as Jackson Pollock , Franz Kline , Clyfford Still , and Wols , represents the opposite of geometric abstraction .", "Expressionist abstract painting , as practiced by artists such as Jackson Pollock , is the opposite of geometric abstraction ." ]
[ "Thallium ( I ) sulfate is colorless , odorless , and tasteless , but highly toxic .", "Thallium ( I ) sulfate is colorless , odorless , and tasteless ." ]
[ "The thallium ( I ) cation is very similar to potassium and sodium cations , which are essential for life .", "This is because the size of the thallium ion is very similar to the size of the potassium ion ." ]
[ "Thallium ( I ) sulfate is created by the reaction of thallium metal with sulfuric acid followed by crystallization .", "It is made by dissolving thallium ore or thallium metal in sulfuric acid ." ]
[ "Thallium ( I ) sulfate ( Tl2SO4 ) or thallous sulfate is the sulfate salt of thallium in the common +1 oxidation state , as indicated by the Roman numeral I . It is often referred to as simply thallium sulfate , but it is more correct to add the I to specify the oxidation state , given that thallium ( III ) sulfate also exists and has some laboratory uses .", "The thallium is in its +1 oxidation state ." ]
[ "Thallium ( I ) sulfate is soluble in water and its toxic effects are derived from the thallium ( I ) cation .", "It has thallium and sulfate ions in it ." ]
[ "Thallium ( I ) sulfate , after entering the body , concentrates itself in the kidneys , liver , brain , and other tissues in the body .", "It gets deposited in the kidney , liver , brain , and similar places ." ]
[ "The city Eisenach left the district in 1998 and became a district-free city .", "The city of Eisenach left the district in 1998 and became a district-free city ." ]
[ "The district was created in 1994 by merging the previous districts Eisenach and Bad Salzungen , and a few municipalities from the district Bad Langensalza .", "The district was set up in 1994 by joining the old districts of Eisenach and Bad Salzungen , and a few municipalities from the district Bad Langensalza ." ]
[ "The district is named after the Wartburg , a castle near Eisenach most famous as the place of residence of Ludwig , Landgrave of Thuringia and his wife , Saint Elizabeth of Hungary ; and , as Martin Luther 's refuge in 1521 .", "The district is named after the Wartburg , a castle near Eisenach most famous as Martin Luther 's refuge in 1521 ." ]
[ "Jurassic Park is a science fiction novel written by Michael Crichton .", "Jurassic Park is a 1991 book by Michael Crichton ." ]
[ "It was at the end of the 7th century and among the Irish that the compiling of these Annals was first begun - see the Annals of the Four Masters , the Annals of Ulster , the Annals of Innisfallen and the Annales Cambriae or Annals of Wales , one of the earliest sources for King Arthur .", "The writing of these Annals was begun at the end of the 7th century and among the Irish - see the Annals of the Four Masters , the Annals of Ulster , the Annals of Innisfallen and the Annales Cambriae or Annals of Wales , one of the earliest sources for King Arthur ." ]
[ "Cicero states that from the earliest period down to the pontificate of Publius Mucius Scaevola ( c. 132 BCE ) , it was usual for the pontifex maximus to record on a white tablet ( album ) , which was exhibited in an open place at his house , so that the people might read it , first , the name of the consuls and other magistrates , and then the noteworthy events that had occurred during the year ( per singulos dies , as Servius says ) .", "52 ) tells that from the earliest period down to the pontificate of Publius Mucius Scaevola ( c. 131 BC ) , it was usual for the pontifex maximus to record on a white tablet ( album ) , which was exhibited in an open place at his house , so that the people might read it ." ]
[ "These records were called in Cicero 's time the Annales maximi .", "In Cicero 's time these records were called Annales Maximi ." ]
[ "Arrived at this stage of development , the Annals now began to lose their primitive character , and henceforward became more and more indistinguishable from the Chronicles , though the term was still used for many documents , such as the Annals of Waverley .", "But the term was still used for many documents , such as the Annals of Waverley ." ]
[ "In Middle Ages , when the order of the liturgical feasts was partly determined by the date of Easter , the custom was early established in the Western Church of drawing up tables to indicate that date for a certain number of years or even centuries .", "In the Middle Ages in the Western Church there were written tables to show that date of Easter for a certain number of years or even centuries ." ]
[ "Annals ( Latin annālis , yearly from annus , a year ) are a concise form of historical representation which record events chronologically , year by year .", "Annals ( Latin Annales , from annus , a year ) are a short form of historical writing which record events chronologically , year by year ." ]
[ "With Arundel as his advisor , Henry began a military campaign , confiscating land from those who opposed him and ordering his soldiers to destroy much of Cheshire .", "With Arundel as his advisor , Henry Bolingbroke began a military campaign , took land from those who opposed him and ordering his soldiers to destroy much of Cheshire ." ]
[ "Henry consulted with Parliament frequently , but was sometimes at odds with the members , especially over ecclesiastical matters .", "Henry consulted with Parliament frequently , but was sometimes at odds with them , especially over religious matters ." ]
[ "Instead , Henry would be required to ask for the lands from Richard .", "Instead , Henry had to ask for the lands from Richard ." ]
[ "After some hesitation , Henry met with the exiled Thomas Arundel , former Archbishop of Canterbury , who had lost his position because of his involvement with the Lords Appellant .", "Henry met with the exiled Thomas Arundel , former Archbishop of Canterbury ." ]
[ "His father , John of Gaunt , was the third son of Edward III , and enjoyed a position of considerable influence during much of the reign of Henry 's cousin Richard II , whom Henry eventually deposed .", "His father , John of Gaunt , was the third son of King Edward III , and had a lot of power in the reign of King Richard II ." ]
[ "He was born at Bolingbroke Castle in Lincolnshire , hence his other name , Henry ( of ) Bolingbroke \\ / ˈbɒlɪŋbrʊk \\ / .", "He was born at Bolingbroke Castle in Lincolnshire , which is why he was often called `` Henry Bolingbroke '' ." ]
[ "Henry IV ( 15 April 1367 - 20 March 1413 ) was King of England and Lord of Ireland ( 1399-1413 ) .", "Henry IV ( April 3 1367 - March 20 1413 ) was a king of England ." ]
[ "Henry quickly gained enough power and support to have himself declared King Henry IV , imprison King Richard ( who died in prison under mysterious circumstances ) and bypass Richard 's seven-year-old heir-presumptive , Edmund de Mortimer .", "Henry gained enough power and support to have himself declared King Henry IV ." ]
[ "Without explanation , Richard canceled the legal documents that would have allowed Henry to inherit Gaunt 's land automatically .", "The next year John of Gaunt died , and Richard would not allow Henry to inherit Gaunt 's land ." ]
[ "Gina Gillespie ( born September 20 , 1951 ) is a former American child actress who had a brief but extensive career in television and film during her childhood and youth .", "Gina Gillespie ( born September 20 , 1951 ) is a former American child actress ." ]
[ "It is the most populous commune in the Ardèche department although it is not the capital which is the smaller town of Privas .", "This commune has the most people living in it of the Ardèche département , although it is not the préfecture ( capital ) , which can be found in the smaller town of Privas ." ]
[ "Kavaguti began skating at the age of five because her mother was a fan of ice dancing .", "She began skating at the age of five because her mother was a fan of ice dancing ." ]
[ "From 2003 , she studied and majored in international relations at St. Petersburg State University , completing her degree in June 2007 .", "She studied international relations at St. Petersburg State University , completing her degree in June 2007 ." ]
[ "Japan does not allow dual nationality , so she was obliged to give up her Japanese citizenship and may reapply to get it back only after ten years .", "Japan does not allow dual nationality , so she was obliged to give up her Japanese citizenship in order to compete for Russia ." ]
[ "In addition to her native Japanese , Kavaguti is also fluent in Russian and English .", "In addition to her native Japanese , she is also fluent in Russian and English ." ]
[ "She originally competed as a singles skater for Japan , then switched to pairs after being inspired by the Russian pair skater Elena Berezhnaya at the 1998 Winter Olympics in Nagano , Japan .", "She switched to pairs after the 1998 Winter Olympics in Nagano , Japan ." ]
[ "Yuko Kavaguti ( also : Kawaguchi , Japanese : Kawaguchi Yūko ( 川口 悠子 ? )", "Yuko Kavaguti Russian : Юко Кавагути , born November 20 , 1981 - ) , also known as Yūko Kawaguchi ( 川口 悠子 , Kawaguchi Yūko ? )" ]
[ "While a piece of Western music generally has a home key , a passage within it may modulate to another key , which is usually closely related to the home key ( in the Baroque and early Classical eras ) , that is , close to the original around the circle of fifths .", "A piece of Western music usually has a home key , and a passage within it may modulate to another key , which is usually closely related to the home key ." ]
[ "Double-flats and double-sharps are used in music as accidentals , but they are never placed in the key signature ( in music that uses equal temperament ) , due to notational convention and because reading the music would become unnecessarily difficult .", "Double-flats and double-sharps are used in music as accidentals , but they are never placed in the key signature ( in music that uses equal temperament ) , because it would make reading the key signature very difficult ." ]
[ "When the key is near the top of the circle ( a key signature of zero or few accidentals ) , the notation of both keys is straightforward .", "When the key is near the top of the circle ( a key signature of zero or few accidentals ) , the writing of both keys is easy - a small number of extra sharps or flats is added ." ]
[ "So the theoretical key of D ♭ minor is usually practically notated by a key signature of C ♯ minor .", "So the theoretical key of D ♭ minor is usually written with the key signature of C ♯ minor ." ]
[ "In each of the bottom three places on the circle of fifths the two enharmonic equivalents can be notated and so do not classify as ` theoretical keys ' : But when a relative key ascends the opposite side of the circle from its home key , then theory suggests that double-sharps and double-flats would have to be incorporated into the notated key signature .", "In each of the bottom three places on the circle of fifths the two enharmonic equivalents can both be written without double-sharps or double-flats and so do not classify as ` theoretical keys ' : But when a relative key is on the opposite side of the circle from its home key , then in theory modulating to that key would involve adding so many sharps or flats that double-sharps and double-flats would have to be written in the key signature ." ]
[ "The following six keys ( which are the parallel major\\/minor keys of those above ) would require one , two or three double-sharps or double-flats : For example , pieces in the major mode commonly modulate up a fifth to the dominant ; for a key with sharps in the signature this leads to a key whose key signature has an additional sharp .", "The following six keys ( which are the parallel major\\/minor keys of those above ) would require one , two or three double-sharps or double-flats : For example , if a piece in E major were to modulate up a fifth to B major , which is next to it on the circle and on the same side of the circle , the notation is clear and simple ; an extra sharp is added to make five sharps ." ]
[ "Under equal temperament the scales sound exactly the same ; such key pairs are said to be enharmonically equivalent .", "Key pairs like this are called enharmonically equivalent ." ]
[ "In order to write that passage with a new key signature , it would become necessary to recast the new section using the enharmonically equivalent key signature of A ♭ major .", "To avoid theoretical keys , the new section would usually be written in the enharmonically equivalent key signature of A ♭ major ." ]
[ "A piece in C ♯ which performs this modulation would lead to the theoretical key of G ♯ , requiring an eighth sharp , meaning an F in place of the F ♯ already present .", "But the next modulation would be to a theoretical key of G ♯ which would need an eighth sharp - for the previous F ♯ note to become F in the key signature ." ]
[ "In music theory , a theoretical key or impossible key is a key and scale which exists in theory and practice , but whose corresponding key signature make its notation impractical .", "In music theory , theoretical keys or impossible keys are keys with key signatures that make writing in them very hard , because they contain one or more double-flats or double-sharps ." ]
[ "For example , the key of D ♭ minor is not conventionally used in notated music , because its corresponding key signature would contain a B ( submediant ) .", "For example , the key of D ♭ minor is not usually used to write music down , because its key signature would contain a B . An equal-tempered scale of D ♭ minor has exactly the same notes as the C ♯ minor scale ." ]