Movable counterpoint |
Movable counterpoint - ib hom kev sib cav sib ceg, kev sib xyaw ua ke ntawm polyphonic ntawm cov suab paj nruag (sib txawv, nrog rau tib yam, zoo sib xws, teeb tsa hauv daim ntawv ntawm kev coj ua), qhia txog kev tsim ntawm ib lossis ob peb. derivative compounds raws li ib tug tshwm sim ntawm ib tug hloov nyob rau hauv thawj qhov sib piv los ntawm rearranging (tsiv, hloov) cov unchanging suab paj nruag. Nyob ntawm txoj kev hloov kho, raws li cov lus qhia ntawm SI Taneyev, muaj peb hom P. to .: vertically movable, raws li kev hloov pauv hauv qhov qub. qhov piv ntawm suab paj nruag nyob rau hauv qhov siab, – ib tug derivative kev twb kev txuas (saib suab paj nruas piv txwv b, c, d, e) yog tsim los ntawm kev hloov lub suab paj nruag mus rau ib tug los yog lwm lub sij hawm nce los yog down (ie vertically); kab rov tav txav tau, raws li kev hloov pauv ntawm lub sijhawm nkag ntawm ib lub suab paj nruag, lub suab txheeb ze rau lwm tus, - kev sib txuas sib txuas (saib piv txwv f, g) yog tsim los ntawm kev hloov ntawm ib qho ntawm cov suab paj nruag. suab rau qee qhov kev ntsuas (beats ntawm ib qho kev ntsuas) rau sab xis lossis sab laug (ie, kab rov tav);
SI Taneev. Los ntawm phau ntawv "Mobile counterpoint ntawm kev sau nruj".
doubly mobile, combining cov khoom ntawm yav dhau los 2, – ib tug derivative compound (saib piv txwv h, i, j) yog tsim raws li ib tug tshwm sim ntawm ib txhij. hloov nyob rau hauv qhov siab piv thiab qhov piv ntawm lub sij hawm ntawm kev nkag ntawm melodic. votes (ie vertically thiab horizontally).
Nyob rau hauv kev zoo nkauj Nyob rau hauv relation mus polyphony, raws li ib tug hloov dua siab tshiab ntawm ib tug ua ke ntawm unchanging ntsiab, raws li ib tug kev sib koom ua ke ntawm kev rov ua dua tshiab thiab rov ua dua, qhov kev rov ua dua tshiab tsis ncav cuag ib theem ntawm qhov sib txawv, thiab kev rov ua dua yog enriched nrog cov qauv tshiab, nws hloov tawm. los ua ib qho ntawm qhov tshwm sim ntawm qhov tshwj xeeb ntawm polyphonic. xav (saib Polyphony).
Qhov txiaj ntsig zoo tshaj plaws thiab kev faib tawm yog ntsug-P. rau. Yog li, nws yog technical. polygonal hauv paus. canons ntawm qeb 1 (tshwj tsis yog rau cov uas lub suab nkag mus rau tib lub sijhawm thiab nyob rau tib txoj kev).
Piv txwv li, nyob rau hauv ib lub quadruple. fp. Nyob rau hauv lub canon ntawm AV Stanchinsky, ntsug permutations tshwm sim, lub system ntawm uas yuav tsum tau qhia los ntawm cov nram qab no tswvyim:
Ntawm no Rl nyob rau hauv kev sib raug zoo rau R (saib Risposta, Proposta) thiab R3 nyob rau hauv relation to R2 nkag mus rau sab sauv octave; R2 nkag mus rau qis thib tsib hauv kev sib raug zoo rau R1; 1st thawj compound b + a1, nws cov derivatives a2 + b1 thiab b2 + a3, 2nd pib compound c + b1, nws cov derivatives b2 + c1, ca + b3; ob chav counterpoint ntawm duodecym tau siv (Iv = -11; saib hauv qab). Permutations nyob rau hauv ntsug-P. k. - cov cuab yeej ntawm infinite canons (tshwj tsis yog canons hauv kuv yuav txais) thiab canonical. sequences ntawm qeb 1. Piv txwv li, nyob rau hauv lub jubilant-sounding ob-headed. Nyob rau hauv qhov kawg canon qhia los ntawm MI Glinka nyob rau hauv lub climactic xaus ntawm lub coda los ntawm overture mus rau lub opera Ruslan thiab Lyudmila, lub suab tsim cov nram qab no permutations:
Ntawm no: thawj qhov sib xyaw b + a1 (bars 28-27, 24-23, 20-19 los ntawm qhov kawg ntawm kev overture), cov derivative a + b1 (bars 26-25, 22-21); ob chav octave counterpoint tau siv (ntau dua, qhov thib tsib decimals, Iv = -14). Piv txwv ntawm ntsug-P. vim in canon. sequences: ob-headed. invention ib-moll No. 13 Thiab. C. Bach, tuav 3-4 (nce hauv vib nas this); Cov suab paj nruag nrov heev ntawm 3rd ib feem ntawm cantata "John ntawm Damascus" los ntawm Taneyev muaj cov piv txwv tsis tshua muaj ib ntu ntawm plaub lub suab: nyob rau hauv tus naj npawb 13 raws li cov khoom ntawm cov kev loj hlob ntawm lub ntsiab lus (ib theem zuj zus hauv peb, hauv qhov tseeb nrog ob npaug ntawm cov suab), nyob rau hauv tus lej 15 raws li qhov pib ntawm lub ntsiab lus (teeb meem los ntawm kab rov tav hloov chaw). Vertical-P. vim – ib tug cwj pwm ntawm complex fugues thiab fugues nrog ib tug tuav tawm tsam. Piv txwv li, hauv ob chav fugue los ntawm Kyrie hauv Requiem V. A. Mozart, ob lub ntsiab lus sib txawv tsim qhov kev sib txuas pib hauv cov tuav (abbr. – tt.) 1-4; derivative compounds ntawm cov ntsiab lus raws li yuav luag tsis muaj interludes hauv vols. 5-8 (octave permutation), 8-11, 17-20 (nyob rau hauv rooj plaub tom kawg permutation rau duodecime) thiab hais txog. Concentration ntawm contrapuntal. cov tswv yim ( ntsug permutations ntawm 3 lub ntsiab lus) characterizes lub rov tshwm sim ntawm triple fugue hauv C los ntawm FP. Hindemith's "Ludus tonalis" lub voj voog, qhov chaw pib sib txuas hauv vols. 35-37 thiab derivatives hauv vols. 38-40, 43-45, 46-48. Hauv Cis-dur fugue los ntawm 1st ntim ntawm Well-Tempered Clavier los ntawm I. C. Bach lub ntsiab lus ntawm fugue thiab qhov kev tuav pov hwm kev tuav pov hwm tsim thawj qhov sib txuas hauv tt. 5-7, derivatives in vol. 10-12, 19-21, ib. Lub ntsiab lus thiab ob qhov kev tawm tsam nyob hauv fugue los ntawm D. D. Shostakovich C-dur (No 1) los ntawm piano. lub voj voog "24 preludes thiab fugues" ua qhov kev sib txuas pib hauv vols. 19-26, muab los ntawm nws nyob rau hauv vols. 40-47, 48-55, 58-65, 66-73. Vertical-P. vim nws kuj yog qhov tseem ceeb tshaj plaws ntawm txoj kev loj hlob thiab shaping nyob rau hauv fugues nrog polyphonically varied interludes. Piv txwv li, hauv c-moll fugue los ntawm 1st ntim ntawm Bach's Well-Tempered Clavier, 1st interlude (vol. 5-6) – pib, 4th (tt. 17-18) – derivative (Iv = -11, nrog ib nrab ob npaug ntawm lub suab qis), incl. 19 derivative los ntawm qhov pib ntawm 4th interlude (Iv = -14, thiab los ntawm 1st interlude Iv = -3); 2nd interlude (vols. 9-10) – pib, 5th interlude (tt. 22-23) yog ib tug derivative nrog ib tug permutation nyob rau hauv lub Upper ob lub suab. Hauv homophonic thiab sib xyaw homophonic-polyphonic. vertical-P cov ntawv. vim hais tias yuav siv tau nyob rau hauv ib txoj kev los yog lwm yam nyob rau hauv ib qho ntawm lawv seem, eg. Thaum tsim cov ntsiab lus hauv kev taw qhia ntawm 1st txav ntawm Glazunov's 5th symphony (8 vols. mus txog 2 - pib, 4 t. mus txog rau tus naj npawb 2 - derivative). Thaum nthuav tawm lub ntsiab lus sab hauv 1st txav ntawm 4th symphony los ntawm P. THIAB. Tchaikovsky (tus thawj pib nyob rau hauv vol. 122, derivative incl. 128) ntsug permutation yog ib txoj hauv kev zoo nkauj. saturation ntawm lyric. suab paj nruag. Qee zaum kev txav ntsug yog siv nyob rau hauv nruab nrab ntawm cov ntaub ntawv yooj yim (L. Beethoven, fp. lus op. 2 Tsis yog 2, Largo appassionato: tus thawj yog nyob rau hauv nruab nrab ntawm ob daim ntawv, piv txwv li 9, derivatives – in vols. 10 thiab 11); nyob rau hauv sonata kev loj hlob, qhov no yog ib qho tseem ceeb tshaj plaws thiab dav siv txhais tau tias ntawm kev loj hlob motivic (piv txwv li, nyob rau hauv 1st txav los ntawm Es-dur quartet los ntawm V. A. Mozart, K.-V. 428: Original – Vol. 85-86 : kuv. 87-88, 89-90, 91-92). Polyphonic feem ntau siv. kev ua haujlwm ntawm cov khoom siv nrog kev pab ntawm kev hloov ntsug hauv cov ntu rov ua dua, qhov uas lawv pab txhawb rau kev rov ua dua tshiab ntawm lub suab (piv txwv li, hauv Scriabin's paj huam op. 32 No 1 Fis-dur, derivative incl. 25). Feem ntau ntsug permutations yog siv nyob rau hauv xaus. ntu ntawm daim ntawv (piv txwv li, hauv Glinka's Aragonese Jota code: tus thawj yog tus naj npawb 24, qhov derivative yog 25). Vertical-P. vim - ib qho ntawm feem ntau siv polyphonic txhais tau tias. variations (piv txwv li, nyob rau hauv lub thib 3 txav los ntawm Borodin's D-dur quartet: thawj zaug nyob rau hauv lub reprise yog tus naj npawb 4, los yog hais txog. 111, derivative - tus lej 5 lossis lwm yam. 133; hauv No.
Lub Scope ntawm kab rov tav movable thiab doubly movable counterpoints yog ntau txwv. T. n. "counterpoint nrog thiab tsis nres" los ntawm P. Mulu pawg (hais los ntawm SI Taneyev nyob rau hauv "Mobile counterpoint" thiab reproduced nyob rau hauv qhov teeb meem 1 ntawm MV Ivanov-Boretsky's Musical-Historical Reader, No 42) tseem yog tib yam nyob rau hauv nws tus kheej txoj kev piv txwv ntawm suab paj nruag. ntau lawm, tag nrho raws li kab rov tav-P. k :pob. daim tuaj yeem ua tau hauv 2 versions - nrog ncua (thawj) thiab tsis muaj lawv (derivative); Qhov rarity no ua hauj lwm ua ib qho piv txwv zoo ntawm kev ua hauj lwm ntawm cov tswv ntawm lub era ntawm austere style. Nws yog qhov tseem ceeb tshaj plaws uas cov txheej txheem ntawm kab rov tav thiab ob npaug-P. k. underlies ib co canons ntawm qeb 2 (piv txwv li, suab zoo li lub pinnacle ntawm txoj kev loj hlob los ntawm 1st ib feem ntawm lub 5th symphony ntawm DD Shostakovich, ib tug ob chav canon, qhov twg lub ntsiab thiab theem nrab cov ntsiab lus yog ua ke, tooj 32) thiab canonical . sequences ntawm 2nd qeb (piv txwv li, nyob rau hauv lub thib ob ib feem ntawm Myaskovsky's quartet No. 2, vol. 3 thiab seq.). Xyaum feem ntau cov teev hom P. rau. ntsib nyob rau hauv stretches ntawm fugues nrog txawv txav deb ntawm introductions. Piv txwv li, lub ricercar-zoo li fugue hauv C-dur los ntawm 70st ntim ntawm Bach's Well-Tempered Clavier tiag tiag muaj cov txheej txheem nyuaj dua; hauv Credo (Tsis muaj 1) los ntawm Pawg hauv h-moll los ntawm JS Bach, tus thawj - vols. 12-4, derivatives – vol. 9-17, 21-34 : kuv. Nyob rau hauv lub fugue los ntawm Ravel lub qhov ntxa ntawm Couperin suite, tsis tshua muaj zog txav nyob rau hauv strettas tsim mos dissonant suab yam ntxwv ntawm no composer: tt. 37-35 - pib (stretta ntawm lub ncauj lus nyob rau hauv ncaj qha motion nrog ib tug nkag deb ntawm ob yim); tt. 37-39 - derivative nyob rau hauv vertically reversible counterpoint; TT. 41-44 - derivative nyob rau hauv tsis tiav vertically reversible counterpoint; tt. 46-48 - muab tau los ntawm yav dhau los nrog rau kab rov tav offset (qhov nkag deb yog qhov thib yim); tt. 50-58 - derivative nyob rau hauv daim ntawv ntawm peb lub hom phiaj. stretches ob-P. rau.
Kab rov tav txav tau qee zaum pom nyob rau hauv fugues nrog kev tuav pov hwm (xws li, hauv gis-moll fugues los ntawm vol. 1, As-dur thiab H-dur los ntawm vol. 2 ntawm Bach's Well-Tempered Clavier; hauv qhov kawg fugue los ntawm concerto rau 2 FP Stravinsky).
Tshem tawm. kev tshav ntuj txawv cov kab rov tav txav hauv cov suab paj nruag ntawm WA Mozart, piv txwv li. hauv sonata D-dur, K.-V. 576, qw. 28, 63 thiab 70 (qhov kev nkag mus deb yog feem ib-yim, rau-yim thiab peb-yim nrog ntsug permutation).
Zoo heev. txawv-tshaj kab rov tav txav yog qhov tseem ceeb, piv txwv li. in grand fugue Es-dur for organ by JS Bach, BWV 552, vol. 90 e tzk;. nyob rau hauv lub 2nd txav ntawm Glazunov lub 7th symphony, 4 ntsuas mus rau tus naj npawb 16. Nyob rau hauv lub kawg fugue ntawm txoj hlua quintet G-dur op. 14 Taneyev cov ntsiab lus ntawm ob chav fugue nyob rau hauv kev sib txuas derivative yog nqa tawm nrog ib txoj kab rov tav txav (los ntawm 2 tons) thiab ntsug permutation:
Nyob rau hauv par nrog P. to. yuav tsum tau muab ib yam ntawm cov counterpoint complex - counterpoint uas tso cai rau ob npaug: ib tug derivative compound yog tsim los ntawm ob npaug rau ib tug (saib piv txwv k, 1) los yog tag nrho (saib piv txwv li m) suab nrog imperfect consonances (nyob rau hauv suab paj nruag ntawm lub xyoo pua 20th - muaj. lwm qhov sib npaug mus rau pawg). Raws li cov txheej txheem ntawm kev sau, qhov counterpoint, uas tso cai rau ob npaug, yog ze heev rau ntsug-P. rau., vim hais tias lub suab ob npaug yog qhov tseem ceeb ntawm qhov tshwm sim ntawm ntsug permutation ntawm ob lub sijhawm - ib feem peb, thib rau, tus lej. Kev siv ob npaug ntawm cov khoom sib txuas ua ke muab qhov kev xav ntawm compaction, loj ntawm lub suab; Piv txwv li nyob rau hauv prelude thiab fugue rau fp. Glazunov, ua. 101 Tsis muaj 3 qhov recapitulation ntawm cov ntsiab lus ntawm ob chav fugue hauv m. 71 yog tus thawj, hauv m. 93 yog ib qho derivative nrog octave ntsug permutation thiab nrog ob npaug ntawm lub suab; nyob rau hauv Variation VI los ntawm Variations ntawm lub ntsiab ntawm Paganini rau ob pianos. Lutoslavsky nyob rau hauv thawj, lub suab sab sauv txav nrog tertian ob npaug, lub qis ib tug nrog loj triads, nyob rau hauv lub inexact derivative (v. 6) lub suab sab sauv txav nrog parallel me triads, qis dua nrog peb.
P. to. thiab counterpoint, uas tso cai rau ob npaug, tuaj yeem ua ke nrog kev thim rov qab (piv txwv li, hauv kev txhim kho qhov kawg ntawm symphony C-dur "Jupiter" los ntawm WA Mozart, canonical imitation hauv kev txav ncaj qha hauv cov tuav 173-175 yog thawj zaug, nyob rau hauv tuav 187-189 - ib tug derivative nrog inversion thiab ntsug permutation ntawm lub suab, nyob rau hauv tuav 192-194 - ib tug derivative nrog ntsug permutation thiab nrog tsuas yog ib lub suab inverted), tej zaum nyob rau hauv ua ke nrog nrog xws li cov ntaub ntawv ntawm melodic. transformations, xws li nce, txo, tsim complex kev tsim kho. Yog li, lub variation ntawm polyphonic. kev sib xyaw ua ke. kev ntsuas txiav txim qhov tsos ntawm suab paj nruag FP. quintet g-moll (op. 30) Taneyev: saib, piv txwv li, cov lej 72 (thawj) thiab 78 (derivative nrog nce thiab kab rov tav txav), 100 (derivative in doubly P. k.), 220 - hauv qhov kawg ( ua ke ntawm cov ntsiab lus tseem ceeb nrog nws cov plaub hau nce).
Lub tswv yim ntawm counterpoint thiab counterpoint, uas tso cai rau ob npaug, yog tag nrho tsim los ntawm SI Taneev nyob rau hauv nws lub hauv paus ua hauj lwm "Mobile counterpoint ntawm nruj kev sau ntawv". Tus kws tshawb fawb tsim cov ntawv sau uas tso cai rau lej. los ntawm kev txheeb xyuas qhov kev txav ntawm lub suab kom raug thiab txiav txim siab cov xwm txheej ntawm kev sau ntawv P. rau. Qee qhov kev xaiv thiab cov ntsiab lus no: Kuv - lub suab sab saud, II - lub suab qis hauv ob- thiab nruab nrab hauv peb lub suab, III - lub suab qis hauv peb lub suab (cov npe no tau khaws cia hauv cov khoom siv); 0 - prima, 1 - thib ob, 2 - thib peb, 3 - quart, thiab lwm yam. h (luv rau lat. horisontalis) - kab rov tav txav ntawm lub suab; Ih (luv luv rau lat. Performance index horisontalis) - qhov taw qhia ntawm kab rov tav txav, txiav txim siab hauv lub voj voog lossis kev ntaus (saib piv txwv f, g, h, i, j); v (luv rau lat. verticalis) – ntsug ntawm lub suab. Qhov kev txav ntawm lub suab sab saud nce thiab nqis yog ntsuas los ntawm qhov sib thooj nrog tus nqi zoo, kev txav ntawm lub suab sab saud thiab qis dua los ntawm lub caij nyoog nrog lub cim rho tawm (piv txwv li, IIV = 2 - txav ntawm lub suab sab sauv. nce los ntawm ib feem peb, IIV = -7 - txav ntawm lub suab qis los ntawm octave). Hauv ntsug-P. j. ib tug permutation, uas lub suab sab sauv ntawm tus thawj kev twb kev txuas (cov qauv ntawm tus thawj nyob rau hauv ob-lub suab I + II) tuav txoj hauj lwm ntawm lub sab sauv ib tug derivative, yog hu ua ncaj qha (saib piv txwv b, c; ib daim duab denoting direct permutation nyob rau hauv ob lub suab:
). Ib tug permutation, uas lub suab sab sauv ntawm tus thawj occupies txoj hauj lwm ntawm lub qis ib tug derivative, yog hu ua tus opposite (saib piv txwv d, e; nws daim duab:
).
Ob lub taub hau polyphonic ib qho kev sib txuas uas tso cai rau ntsug permutations (tsis yog qhov sib txawv, tab sis kuj - sib piv rau cov ntsiab lus tsis raug - thiab ncaj qha), hu ua. ob chav counterpoint (German doppelter Kontrapunkt); Piv txwv li, nyob rau hauv ob chav Inventions E-dur No 6 JS Bach thawj - hauv vols. 1-4, derivative – in vols. 5-8, IV=-14 + II V=-7
). Peb lub taub hau. ib qho kev sib txuas uas tso cai rau 6 lub suab sib txuas (ib qho ntawm cov suab qub tuaj yeem yog sab sauv, nruab nrab lossis qis hauv qhov kev sib txuas derivative) yog hu ua triple counterpoint (German dreifacher Kontrapunkt, Tripelkontrapunkt). Daim duab denoting permutations hauv triphony:
Piv txwv li, hauv peb lub hom phiaj Inventions f-moll No 9 JS Bach: tus thawj - hauv vols. 3-4, derivatives – in vols. 7–8
nyob rau hauv No. 19 los ntawm Shchedrin's "Polyphonic Notebook" – ib tug derivative nyob rau hauv v. 9. Tib lub hauv paus ntsiab lus underlies me ntsis-siv. quadruple counterpoint (German vierfacher Kontrapunkt, Quadrupelkontrapunkt), tso cai rau 24 lub suab ua haujlwm (saib, piv txwv li, tus lej 5, 6, 7 hauv 1 ntu ntawm cantata "John of Damascus"; tus lej 1, 2, 3, 4 hauv qhov xaus Nyob rau hauv ob lub choir No. 9 ntawm lub cantata "Tom qab nyeem Ntawv Nkauj" los ntawm Taneyev, thiab nyob rau hauv lub fugue nyob rau hauv e-moll los ntawm lub voj voog "24 Preludes thiab Fugues" rau pianoforte Shostakovich - vols. 15-18 thiab 36. -39). Ib qho piv txwv tsis tshua muaj ntawm tsib counterpoint - cov cai ntawm qhov kawg ntawm lub suab paj nruag C-dur ("Jupiter") los ntawm WA Mozart: tus thawj hauv vols. 384-387, ib., vol. 387-391, 392-395, 396-399, 399-402; Permutation tswvyim:
Algebraic. qhov sib npaug ntawm qhov sib txawv ntawm kev txav ntawm ob lub suab (hauv ob lub suab; hauv peb- thiab polyphony - rau txhua khub ntawm lub suab) yog hu ua qhov taw qhia ntawm kev txav ntsug thiab yog txhais los ntawm Iv (luv rau Latin index verticalis; saib piv txwv b , c, d, ib). Iv yog lub ntsiab lus tseem ceeb tshaj plaws hauv cov lus qhia ntawm SI Taneev, vim hais tias nws characterizes tus qauv rau kev siv ntawm lub sij hawm tsim ntawm polyphonic suab. cov ntaub so ntswg, thiab cov yam ntxwv ntawm lub suab coj. Piv txwv li, thaum sau tus thawj compound nyob rau hauv ob chav counterpoint ntawm lub decimal (ie Iv = -9), tsuas yog qhov sib txawv thiab tsis ncaj ntawm lub suab ntawm lub suab yog suav tias yog nyob rau hauv lub moj khaum ntawm kev sau ntawv nruj, thiab tuav lub quart los ntawm lub suab sab sauv thiab tsis muaj los ntawm lub suab qis yog tsis tso cai nyob rau hauv thiaj li yuav zam lub suab nyob rau hauv lub derivative. compound txwv tsis pub los ntawm cov kev cai ntawm no style. Lub permutation tuaj yeem ua tiav txhua lub sijhawm thiab, yog li ntawd, Iv tuaj yeem muaj txiaj ntsig, txawm li cas los xij, hauv kev xyaum, peb hom permutations feem ntau yog: ob chav counterpoint decimals (Iv = -9 lossis -16), duodecimes (Iv = - 11 lossis -18) thiab tshwj xeeb tshaj yog ob chav octave counterpoint (Iv = -7 lossis -14). Qhov no tau piav qhia los ntawm qhov tseeb tias thaum permuting ob chav counterpoint ntawm lub octave, decima thiab duodecima, lub harmonic hloov me ntsis nyob rau hauv lub derivatives. qhov tseem ceeb ntawm qhov kev sib txuas ntawm tus thawj (consonant intervals ntawm tus thawj feem ntau sib haum mus rau consonant intervals nyob rau hauv lub derivative; tib dependence muaj nyob ntawm dissonances). Muaj peev xwm ua kom ntsug permutations ntawm decomp. intervals (ie siv cov nqi sib txawv ntawm Iv) tsim tshwj xeeb contrapuntal art. ib tug txhais tau tias tso cai rau tus composer subtly diversify lub sonority. Ib qho piv txwv zoo tshaj plaws yog g-moll fugue los ntawm 2nd ntim ntawm Bach's Well-Tempered Clavier: lub ntsiab lus thiab qhov kev tawm tsam uas tau tuav tseg yog thawj zaug ua ke hauv cov tuav. 5–9; derivative hauv tt. 13-17 (Iv=-14), 28-32 (Iv=-11), 32-36 (Iv=-2) and 36-40 (Iv=-16); ntxiv, hauv tt. 51-55 nyob rau hauv lub derivative lub ntsiab lus yog doubled los ntawm lub thib rau ntawm saum toj no (Iv = +5), nyob rau hauv tt. 59-63 permutation ntawm Iv = -14 nrog ob npaug ntawm lub ntsiab lus los ntawm ib feem peb ntawm hauv qab no, thiab counteraddition los ntawm ib feem peb ntawm saum toj no (Iv = -2). Hauv suab paj nruag tom qab Bach thiab mus txog rau xyoo pua 20th. feem ntau siv octave permutation yooj yim; Txawm li cas los xij, composers, raws li lub harmonica loj hlob. kev ywj pheej siv cov ntsuas me me uas siv yav dhau los. Tshwj xeeb, lawv muaj nyob rau hauv lub canon. Cov kab ke uas ib qho kev sib xyaw ua ke yog tsim los ntawm cov risposta thiab rov nkag ntawm cov proposta: piv txwv li, nyob rau hauv 2nd txav ntawm Mozart's D-dur quartet, K.-V. 499, qw. 9-12 (Iv = -13); nyob rau hauv 1 lub zog ntawm Glazunov's Symphony No. 8, nr 26, s. 5-8 (Iv = -15); nyob rau hauv lub overture rau lub opera "Meistersingers ntawm Nuremberg", vol. 7 (Iv = -15) and vol. 15 (Iv = -13); nyob rau hauv daim duab 1 ntawm 3rd d. "Cov lus dab neeg ntawm lub nroog tsis pom ntawm Kitezh", tus lej 156, vols. 5-8 (Iv=-10); nyob rau hauv lub 1 lub zog ntawm Myaskovsky's Quartet No. 12, qw.
HA Rimsky-Korsakov. "Cov Dab Neeg ntawm Invisible City ntawm Kitezh thiab Maiden Fevronia", ua III, 1st scene.
Kev sib txuas tsim los ntawm SI Taneyev nrog lub canon (nyob rau hauv phau ntawv "Cov Lus Qhuab Qhia ntawm Canon") ua rau nws ua tau kom raug cais thiab tshawb fawb txiav txim siab cov ntsiab lus ntawm decomp. canon cov ntawv. P.'s theory to. ua lub hauv paus rau kev txhim kho ntxiv ntawm cov lus qhia ntawm Taneyev nyob rau hauv owls. musicology (SS Bogatyrev, "Double Canon" thiab "Reversible Counterpoint").
References: Taneev SI, Movable counterpoint of nruj sau ntawv, Leipzig, 1909, M., 1959; nws tus kheej, Lus Qhuab Qhia ntawm Canon, M., 1929; Ivanov-Boretsky MV, Suab paj nruag thiab keeb kwm nyeem, vol. 1, M., 1929; ib. Bogatyrev SS, Ob chav canon, M.-L., 1947; nws, Reversible counterpoint, M., 1960; Dmitriev AN, Polyphony as a factor of shaping, L., 1962; Pustylnik I. Ya., Movable counterpoint and free sau, L., 1967; Jadassohn S., Lehrbuch des einfachen, doppelten, drei- und vierfachen Contrapunkts, Lpz., 1884, id., in his Musikalische Kompositionslehre, Tl. 1, Bd 2, Lpz., 1926; Riemann H., Lehrbuch des einfachen, doppelten und imitierenden Kontrapunkts, Lpz., 1888. 1921; Prout, E., Ob chav counterpoint thiab canon, L., 1891, 1893.
VP Frayonov
