Matsala mai motsi |
Matsala mai motsi - wani nau'i na hadadden ma'anar ƙira, haɗin gwiwar waƙa na polyphonic (mabambanta, da kuma iri ɗaya, kama, wanda aka tsara a cikin nau'i na kwaikwayo), yana ba da shawarar samuwar ɗaya ko da yawa. mahadi na asali sakamakon canji a cikin rabo na farko ta hanyar sake tsarawa (motsi, canzawa) waɗannan karin waƙoƙin da ba su canzawa. Dangane da hanyar sake tsarawa, bisa ga koyarwar SI Taneyev, akwai nau'ikan P. zuwa .: mai motsi a tsaye, dangane da canji a cikin asali. rabon karin waƙa a tsayi, - haɗin haɗin kai (duba misalan kiɗan b, c, d, e) ana samuwa ta hanyar canja wurin waƙar zuwa ɗaya ko wata tazara sama ko ƙasa (watau a tsaye); a kwance mai motsi, dangane da canji a lokacin shigowar waƙar ɗaya, murya dangane da wani, – haɗin haɗin gwiwa (duba misalan f, g) yana samuwa daga ƙaura daga cikin waƙar. muryoyin don takamaiman adadin ma'auni (buga ma'auni) zuwa dama ko hagu (watau a kwance);
SI Taneev. Daga littafin "Mobile counterpoint of tsauraran rubuce-rubuce".
sau biyu ta hannu, hade da kaddarorin 2 da suka gabata, - wani fili mai ƙirƙira (duba misalan h, i, j) yana samuwa a sakamakon lokaci guda. canje-canje a cikin rabo mai tsayi da rabon lokutan shigarwa na melodic. kuri'u (watau a tsaye da a kwance).
A cikin kayan ado Game da polyphony, a matsayin gyare-gyaren haifuwa na haɗuwa da abubuwa marasa canzawa, a matsayin haɗin kai na sabuntawa da maimaitawa, inda sabuntawa ba ya kai wani matsayi na wani nau'i na daban, kuma maimaitawa yana wadatar da sabon salo na tsari, ya juya. ya zama ɗaya daga cikin bayyanar da ƙayyadaddun sautin murya. tunani (duba Polyphony).
Mafi girman ƙimar aiki da rarraba shine a tsaye-P. ku. Don haka, shi mai fasaha ne. tushen polygonal. canons na rukuni na 1 (sai dai waɗanda muryoyin suka shiga tazara iri ɗaya kuma a hanya ɗaya).
Misali, a cikin hudu. fp. A cikin canon na AV Stanchinsky a tsaye permutations tasowa, tsarin wanda za a iya bayyana ta da wadannan makirci:
Anan Rl dangane da R (duba Risposta, Proposta) da R3 dangane da R2 shigar da octave na sama; R2 yana shiga ƙasa ta biyar dangane da R1; Na farko fili na farko b + a1, abubuwan da suka samo asali a1 + b2 da b1 + a2, fili na farko na biyu c + b3, abubuwan da suka samo asalinsa b2 + c1, ca + b2; An yi amfani da maki biyu na duodecym (Iv = -1; duba ƙasa). Ƙaddamarwa a tsaye-P. k. - dukiya na canons marasa iyaka (sai dai canons a cikin zan karɓa) da kuma canonical. jerin jerin nau'ikan 3st. Misali, a cikin jubilant-sauti mai kai biyu. A cikin canon mara iyaka wanda MI Glinka ya gabatar a cikin ƙarshen ƙarshen coda daga overture zuwa wasan opera Ruslan da Lyudmila, muryoyin suna yin abubuwa masu zuwa:
Anan: fili na farko b + a1 (sanduna 28-27, 24-23, 20-19 daga ƙarshen overture), abin da aka samu a + b1 (sanduna 26-25, 22-21); An yi amfani da madaidaicin octave biyu (mafi daidai, adadi na biyar, Iv = -14). Misalai na tsaye-P. saboda a canon. jerin: masu kai biyu. ƙirƙira a-moll No. 13 Kuma. C. Bach, sanduna 3-4 (sauka cikin dakika); Kiɗa mai ban mamaki na kashi na 3 na cantata "Yohanna na Dimashƙu" na Taneyev ya ƙunshi misalan da ba kasafai ba na jeri a cikin muryoyi huɗu: a lamba 13 dangane da kayan ɓangaren haɓaka na jigon (jeri yana saukowa kashi uku, a cikin gaskiya tare da ninka sautunan murya), a lamba 15 dangane da dalilin farko na jigon (rikitaccen matsuguni a kwance). A tsaye-P. saboda – sifa ta hadaddun fugues da fugues tare da ci gaba da adawa. Misali, a cikin fugue biyu daga Kyrie a cikin Requiem V. A. Mozart, jigogi guda biyu masu bambanta suna haifar da haɗin farko a cikin sanduna (abbr. tt) 1-4; abubuwan da suka samo asali na jigogi suna bin kusan ba tare da tsangwama a cikin vols. 5-8 (ctave permutation), 8-11, 17-20 (a cikin na ƙarshe yanayin permutation zuwa duodecime) da sauransu. Hankali contrapuntal. Dabaru (tsaye-tsaye na jigogi 3) suna nuna ramuwar gayya na fugue sau uku a cikin C daga FP. Zagayen “Ludus tonalis” na Hindemith, inda haɗin farko a vols. 35-37 da abubuwan da aka samo asali a cikin juzu'i. 38-40, 43-45, 46-48. A cikin Cis-dur fugue daga juzu'i na 1st na Clavier mai tsananin zafin rai na I. C. Taken Bach na fugue da madaidaicin matsayin da aka riƙe shine haɗin farko a cikin tt. 5-7, abubuwan da aka samo asali a cikin juzu'i. 10-12, 19-21 da ƙari. Jigo da 'yan adawa biyu sun ci gaba da kasancewa a cikin fugue ta D. D. Shostakovich C-dur (No 1) daga piano. sake zagayowar "24 preludes da fugues" sun haɗa haɗin farko a cikin vols. 19-26, an samo daga gare ta a mujalladi. 40-47, 48-55, 58-65, 66-73. A tsaye-P. saboda kuma shine mafi mahimmancin hanyoyin haɓakawa da siffata a cikin fugues tare da bambance-bambancen sautin murya. Misali, a cikin c-moll fugue daga juzu'in 1st na Bach's Well-Tempered Clavier, tsakar 1st (vol. 5-6) - farko, 4th (tt. 17-18) - abin da aka samo asali (Iv = -11, tare da juzu'i biyu na ƙananan murya), gami da. 19 wanda aka samo daga farkon 4th interlude (Iv = -14, kuma daga 1st interlude Iv = -3); Tashar ta biyu (vols. 9-10) - na farko, tazara ta 5 (tt. 22-23) asali ne tare da juzu'i a cikin manyan muryoyi biyu. A cikin homophonic da gauraye homophonic-polyphonic. a tsaye-P siffofin. saboda ana iya amfani da su ta hanya ɗaya ko wata a kowane sashinsu, misali. Lokacin da aka kafa jigon a cikin gabatarwar motsi na 1st na Glazunov's 5th symphony (8 vols. har zuwa lamba 2 - na farko, 4 t. har zuwa lamba 2 - wanda aka samu). Lokacin baje kolin jigon gefe a cikin motsi na 1st na wasan kwaikwayo na 4 na P. DA. Tchaikovsky (asali ya fara a vol. 122, abubuwan da aka samu ciki har da. 128) Juyawar tsaye hanya ce ta waƙa. jikewa na waka. kiɗa. Wani lokaci ana amfani da motsi na tsaye a tsakiyar ginin sassa masu sauƙi (L. Beethoven, fp. sonata op. 2 No 2, Largo appassionato: asalin yana tsakiyar sigar kashi biyu, watau 9, abubuwan da aka samo asali - a cikin juzu'i. 10 da 11); a cikin ci gaban sonata, wannan shine ɗayan mafi mahimmanci kuma mafi yawan hanyoyin da ake amfani da su na haɓaka haɓakawa (misali, a cikin motsi na 1st daga Es-dur quartet na V. A. Mozart, K.-V. 428: asali – vols. 85-86, abubuwan da aka samo asali - vols. 87-88, 89-90, 91-92). Ana amfani da polyphonic sau da yawa. sarrafa kayan tare da taimakon sauye-sauye a tsaye a cikin sassan reprise, inda suke taimakawa wajen sabunta sauti (misali, a cikin waƙar Scriabin op. 32 No 1 Fis-dur, wanda ya haɗa da. 25). Yawancin lokaci ana amfani da juzu'i a tsaye a cikin ƙarshe. sassan tsari (misali, a cikin lambar Aragonese Jota ta Glinka: asalin shine lamba 24, abin da aka samu shine 25). A tsaye-P. domin – daya daga cikin mafi yawan amfani da polyphonic wajen. Bambance-bambance (misali, a cikin motsi na 3 daga D-dur quartet na Borodin: na farko a cikin reprise shine lamba 4, ko sauransu. 111, wanda aka samu - lamba 5 ko makamancin haka. 133; in No.
Iyakar madaidaicin madaidaicin madaidaicin madaidaicin madaidaicin madaidaicin madaidaicin madaidaicin ya fi iyaka. T. n. "Mataki tare da ba tare da tsayawa ba" daga taron P. Mulu (wanda SI Taneyev ya ambata a cikin "Mobile counterpoint" kuma an sake buga shi a fitowa ta 1 na MV Ivanov-Boretsky's Musical-Historical Reader, No 42) ya kasance kawai a hanyarsa misali na kiɗa. samarwa, gabaɗaya bisa horizontally-P. k.: bugu. za a iya yin yanki a cikin nau'ikan 2 - tare da dakatarwa (na asali) kuma ba tare da su ba (na asali); wannan rarity yana aiki azaman misali mai kyau na hanyoyin aiki na masanan zamanin da salon salo. Yana da mahimmanci cewa fasaha na kwance da biyu-P. k. karkashin wasu canons na 2nd category (misali, sauti kamar kololuwar ci gaba daga kashi na 1st na 5th symphony na DD Shostakovich, biyu Canon, inda babban da sakandare jigogi suna hade, lamba 32) da kuma canonical . jerin jerin nau'i na 2 (misali, a cikin kashi na 2 na Myaskovsky's quartet No. 3, vol. 70 et seq.). A zahiri galibin ƙayyadaddun nau'ikan P. zuwa. saduwa a cikin shimfidar fugues tare da tazara masu canzawa na gabatarwa. Misali, ricercar-kamar fugue a cikin C-dur daga juzu'i na 1st na Bach's Well-Tempered Clavier a zahiri ya ƙunshi ci gaba mafi rikitarwa strettas; a Credo (No 12) daga Mass in h-moll ta JS Bach, na asali - vols. 4-9, abubuwan da aka samo asali - vols. 17-21, 34-37. A cikin fugue daga Ravel's Tomb of Couperin suite, rikitattun ƙungiyoyi a cikin strettas suna haifar da sautuka masu taushin hali na wannan mawaki: tt. 35-37 - na farko (stretta a kan batun a cikin motsi kai tsaye tare da nisan shigarwa na biyu na takwas); tt. 39-41 - wanda aka samo asali a cikin madaidaicin juzu'i; TT. 44-46 - abin da aka samo asali a cikin madaidaicin juzu'i wanda bai cika cikakke ba; tt. 48-50 - wanda aka samo daga baya tare da raguwa a kwance (nisa shigarwa shine na takwas); tt. 58-60 - abin da aka samo asali a cikin hanyar manufa uku. mikewa a cikin biyu-P. ku.
A wasu lokuta ana samun motsin kai tsaye a fugues tare da madaidaicin matsayi (misali, a cikin gis-moll fugues daga juzu'i. 1, As-dur da H-dur daga juzu'i na 2 na Bach's Well-Tempered Clavier; a cikin fugue na ƙarshe daga concerto. don 2 FP Stravinsky).
Banda alheri yana bambanta motsi a kwance a cikin kiɗan WA Mozart, alal misali. in sonata D-dur, K.-V. 576, shafi. 28, 63 da 70 (Nisan shigarwa daidai da daya-takwas, shida-takwas da uku-takwas tare da permutation a tsaye).
Babban fasaha. motsi daban-daban na kwance masu duhu suna da mahimmanci, misali. in grand fugue Es-dur na sashin jiki na JS Bach, BWV 552, juzu'i. 90 da guda; a cikin motsi na 2 na Glazunov's 7th symphony, 4 matakan har zuwa lamba 16. A cikin fugue na karshe na kirtani quintet G-dur op. 14 Taneyev jigogi na fugue sau biyu a cikin haɗin haɓaka ana aiwatar da su tare da ƙaura a kwance (ta 2 ton) da jujjuyawar tsaye:
Daidai da P. to. ya kamata a sanya wani nau'i na ma'auni mai mahimmanci - maƙasudin da ke ba da damar ninka biyu: an samar da fili ta hanyar ninka ɗaya (duba misalan k, 1) ko duka (duba misali m) muryoyin da ba daidai ba (a cikin kiɗa na karni na 20 - akwai). duk wani ninki biyu har zuwa gungu). Bisa ga fasaha na tsarawa, ƙididdiga, wanda ke ba da damar sau biyu, yana kusa da tsaye-P. to., Domin sautin murya mai ninki biyu shine ainihin sakamakon juzu'i a tsaye na tazara mai ninki biyu - na uku, na shida, ƙima. Yin amfani da ninki biyu a cikin abubuwan da aka samo asali yana ba da jin dadi, girman sauti; mis a prelude da fugue don fp. Glazunov, da. 101 No 3 da maimaita jigogi na fugue biyu a cikin m. 71 shine asali, a cikin m. 93 abin da aka samo asali ne tare da juzu'i na octave a tsaye kuma tare da ninki biyu na sautuna; a cikin Bambancin VI daga Bambance-bambance akan Jigon Paganini don pianos guda biyu. Lutoslavsky a cikin asali, babbar murya tana motsawa tare da tertian ninki biyu, na ƙasa tare da manyan triads, a cikin abin da ba daidai ba (aya 6) babbar murya tana motsawa tare da ƙananan ƙananan triads, na ƙasa da kashi uku.
P. ku. da counterpoint, wanda damar sau biyu, za a iya hade tare da reversible counterpoint (misali, a cikin ci gaban da karshe na siphony C-dur "Jupiter" WA Mozart, da canonical kwaikwayo a kai tsaye motsi a sanduna 173-175 ne. na farko, a cikin sanduna 187-189 - abin da aka samo asali tare da jujjuyawar muryoyin muryoyi da juzu'i, a cikin sanduna 192-194 - abin da aka samo tare da jujjuyawar tsaye kuma tare da jujjuyawar murya ɗaya kawai), wani lokaci a hade tare da irin waɗannan nau'ikan waƙoƙin waƙa. canje-canje, kamar karuwa, raguwa, samar da gine-gine masu rikitarwa. Don haka, bambancin polyphonic. haduwa a cikin ma'ana. ma'auni yana ƙayyade bayyanar kiɗan FP. quintet g-moll (op. 30) Taneyev: duba, alal misali, lambobi 72 (na asali) da 78 (wanda aka samu tare da karuwa da motsi a kwance), 100 (wanda aka samo a cikin biyu P. k.), 220 - a cikin karshe (na farko). hade da babban jigo tare da karuwarsa sau hudu).
Ka'idar counterpoint da counterpoint, wanda ke ba da damar ninkawa, SI Taneev ya haɓaka shi sosai a cikin ainihin aikinsa na "Tallafi mai tsattsauran ra'ayi". Mai binciken ya kafa bayanin kula da ke ba da izinin lissafi. ta hanyar kwatanta motsin muryoyin daidai da ƙayyadaddun yanayin rubuta P. zuwa. Wasu daga cikin waɗannan zane-zane da ra'ayoyi: I - babbar murya, II - ƙananan murya a cikin biyu- da tsakiya a cikin sautuka uku, III - ƙananan murya a cikin sautuka uku (an adana waɗannan zane-zane a cikin abubuwan da aka samo asali); 0 – prima, 1 – na biyu, 2 – na uku, 3 – quart, da sauransu. h (gajeren don lat. horisontalis) - motsi a kwance na murya; Ih (gajeren lat. index horisontalis) - mai nuna alamar motsi a kwance, ƙaddara a cikin hawan keke ko bugun (duba misalan f, g, h, i, j); v (gajeren lat. verticalis) - motsin murya a tsaye. Motsi na babbar murya sama da ƙasa ana auna ta tazara mai ma'ana tare da ingantacciyar ƙima, motsin babbar murya ƙasa da ƙasa sama ta tazara tare da alamar ragi (misali, IIV=2 - motsi na babbar murya. sama da na uku, IIV=-7 - motsi na ƙananan murya sama da octave). A tsaye-P. j. permutation, wanda babbar murya ta ainihin haɗin kai (ka'idar asali a cikin murya biyu I + II) tana riƙe da matsayi na babba a cikin abin da aka samo asali, ana kiranta kai tsaye (duba misalai b, c; adadi mai nuna alama). karkata kai tsaye cikin murya biyu:
). Ƙwaƙwalwa, wanda babbar murya ta asali ta mamaye matsayin ƙasan ɗaya a cikin abin da aka samo asali, ana kiranta akasin haka (duba misalan d, e; hotonsa:
).
Polyphonic mai kai biyu wani fili wanda ke ba da damar juzu'i na tsaye (ba kawai akasin haka ba, har ma - ya bambanta da ma'anar da ba daidai ba - da kai tsaye), wanda ake kira. biyu counterpoint (Jamus doppelter Kontrapunkt); misali, a cikin Ƙirƙirar E-dur No 6 JS Bach na asali - a cikin juzu'i. 1-4, wanda aka samo asali - a cikin juzu'i. 5-8, IV=-14 + II V=-7
). Kawu uku. haɗin da ke ba da damar haɗakar muryoyin 6 (kowane daga cikin muryoyin asali na iya zama babba, tsakiya ko ƙasa a cikin haɗin da aka samu) ana kiran shi sau uku counterpoint (Jamus dreifacher Kontrapunkt, Tripelkontrapunkt). Alkaluman da ke nuna ruɗani a cikin triphony:
Misali, a cikin Ƙirƙirar Ƙirƙirar manufa uku f-moll No 9 JS Bach: na asali – a vols. 3-4, abubuwan da aka samo asali - a cikin juzu'i. 7-8
a lamba 19 daga littafin Shchedrin's "Polyphonic Notebook" - abin da aka samo asali a cikin aya 9. Wannan ka'ida ta dogara da ƙarancin amfani. Hudu biyu counterpoint (German vierfacher Kontrapunkt, Quadrupelkontrapunkt), kyale 24 murya matsayi (duba, misali, lambobi 5, 6, 7 a cikin 1st part na cantata "John of Damascus"); lambobi 1, 2, 3, 4 a ƙarshe. A cikin mawaƙa biyu na No. 9 na cantata "Bayan Karatun Zabura" ta Taneyev, kuma a cikin fugue a cikin e-moll daga zagayowar "24 Preludes da Fugues" na pianoforte Shostakovich - juzu'i 15-18 da 36 -39). Misalin da ba kasafai ba na maki biyar - lambar wasan karshe na wasan kwaikwayo C-dur ("Jupiter") na WA Mozart: asali a cikin vols. 384-387, abubuwan da aka samo a cikin juzu'i. 387-391, 392-395, 396-399, 399-402; tsarin rugujewa:
Algebraic. jimlar tazarar motsi na muryoyin biyu (a cikin murya biyu; a cikin uku- da polyphony - ga kowane nau'in muryoyin biyu) ana kiranta mai nuna motsi a tsaye kuma Iv ke bayyana shi (gajeren fihirisar Latin verticalis; duba misalai b). , c, d, e). Iv shine ma'anar mafi mahimmanci a cikin koyarwar SI Taneev, saboda ya kwatanta ka'idoji don amfani da tazara da aka kafa tsakanin muryoyin polyphonic. kyallen takarda, da fasali na jagorancin murya. Misali, lokacin rubuta mahaɗin farko a maki biyu na ƙima (watau Iv = -9), kawai akasin motsin muryoyi da kaikaitacce ana ɗauka a cikin tsarin tsattsauran rubuce-rubuce, kuma ba a yarda da riƙe juzu'i ta babbar murya ba ko ɗaya ta ƙaramar murya don guje wa sautuna a cikin abin da aka samo asali. fili da dokokin wannan salon suka haramta. Ana iya aiwatar da mutuncin a kowace tazara kuma, sabili da haka, IV na iya samun duk wata hanya, duk da haka, a cikin matakan permutations (IV = -9 ko -16), Duodcimes ko -11 - - 18 ko -7) kuma musamman madaidaicin octave sau biyu (Iv = -14 ko -XNUMX). An bayyana wannan ta gaskiyar cewa lokacin da ake yin juzu'i biyu na octave, decima da duodecima, jituwa yana canzawa kaɗan a cikin abubuwan da aka samo asali. Mahimman haɗin kai na asali (matsalolin baƙaƙe na asali galibi sun yi daidai da tazara na baƙaƙe a cikin abin da aka samo asali; dogaro iri ɗaya yana wanzuwa tsakanin ɓata lokaci). Ikon yin juzu'i na tsaye akan decomp. tazara (watau amfani daban-daban dabi'u na IV) ya ƙunshi musamman contrapuntal art. wata hanya ce da ke ba wa mawaƙan damar sarrafa sonority a hankali. Ɗaya daga cikin fitattun misalan shine g-moll fugue daga juzu'i na 2 na Bach's Well-Tempered Clavier: jigon da 'yan adawa da aka hana sun zama haɗin farko a sanduna. 5-9; asali a cikin tt. 13-17 (Iv=-14), 28-32 (Iv=-11), 32-36 (Iv=-2) da 36-40 (Iv=-16); bugu da kari, in tt. 51-55 a cikin asalin jigon an ninka shi da na shida daga sama (Iv = +5), a cikin tt. 59-63 permutation a Iv=-14 tare da ninka jigon ta kashi uku daga ƙasa, da ƙari ta uku daga sama (Iv = -2). A cikin kiɗa bayan Bach kuma har zuwa karni na 20. sau da yawa ana amfani da ƙaƙƙarfan ƙazamin octave; duk da haka, mawaƙa, yayin da harmonica ke girma. 'yanci suna amfani da alamun da ba a yi amfani da su ba a baya. Musamman, ana samun su a cikin canon. jeri inda aka samar da fili mai tsauri tsakanin risposta da sake shigar da proposta: misali, a cikin motsi na 2 na Mozart's D-dur quartet, K.-V. 499, shafi. 9-12 (Iv = -13); a cikin 1st motsi na Glazunov Symphony No. 8, lamba 26, juzu'i. 5-8 (Iv = -15); a cikin opera zuwa opera "Meistersingers of Nuremberg", vol. 7 (Iv = -15) da juzu'i. 15 (Iv = -13); a hoto na 1 na d. "Tatsuniyoyi na birnin Kitezh marar ganuwa", lamba 156, vols. 5-8 (Iv=-10); a cikin 1st motsi na Myaskovsky's Quartet No. 12, shafi.
HA Rimsky-Korsakov. "Tale of the Invisible City of Kitezh and the Maiden Fevronia", Act III, 1st scene.
Haɗin da aka kafa ta SI Taneyev tare da canon (a cikin littafin "The Doctrine of Canon") ya sa ya yiwu a daidaita daidaitattun ka'idodin decomp da kimiyya. canon siffofin. Ka'idar P. zuwa. yayi aiki a matsayin tushen ci gaba da cigaban koyarwar Taneyev a cikin owls. musicology (SS Bogatyrev, "Double Canon" da "Reversible Counterpoint").
References: Taneev SI, Madaidaicin madaidaicin rubutu, Leipzig, 1909, M., 1959; nasa, Rukunan Canon, M., 1929; Ivanov-Boretsky MV, Mai karanta kida da tarihi, vol. 1, M., 1929; Bogatyrev SS, Biyu Canon, M.-L., 1947; nasa, Reversible counterpoint, M., 1960; Dmitriev AN, Polyphony a matsayin factor na siffa, L., 1962; Pustylnik I. Ya., Maɓalli mai motsi da rubutu kyauta, L., 1967; Jadassohn S., Lehrbuch des einfachen, doppelten, drei- und vierfachen Contrapunkts, Lpz., 1884, id., A cikin Musikalische Kompositionslehre, Tl. 1, Bd 2, Lpz., 1926; Riemann H., Lehrbuch des einfachen, doppelten und imitierenden Kontrapunkts, Lpz., 1888. 1921; Prout, E., Matsala biyu da canon, L., 1891, 1893.
VP Frayonov
