Symmetrical frets |

symmetrical frets - frets, cov nplai uas yog nyob ntawm qhov sib npaug ntawm qhov octave. Ib yam li lwm yam kev ntxhov siab, S. l. yog tsim los ntawm lub hauv paus ntawm ib qho chaw. Element (abbreviated li CE). Txawm li cas los xij, tsis zoo li, piv txwv li, los ntawm qhov loj lossis me, S. l. yog tsim tsis nyob rau hauv lub hauv paus ntawm ib tug loj los yog me triad, tab sis nyob rau hauv lub hauv paus ntawm consonance (los yog central kev sib raug zoo) uas tshwm sim los ntawm kev faib ntawm 12 semitones rau hauv 2, 3, 4 los yog 6 qhov sib npaug. Li no 4 possibilities – 12:6, 12:4, 12:3, 12:2 thiab, raws li, 4 lub ntsiab. laj S.l. Lawv muaj npe raws li lawv CE (xws li ib tug loj yog lub npe tom qab nws CE – loj triad): kuv – tag nrho-tone (CE 12: 6 = tag nrho-tone rau-tone); II – txo, los yog tsawg zaus (CE 12: 4 = ntse xya chord); III – nce, lossis ntau dua terts (CE 12: 3 = nce triad); IV – tritone (los yog ob hom, lub sij hawm ntawm BL Yavorsky) (CE 12: 2 = tritone). Nyob ntawm qhov tshwj xeeb. Cov qauv ntawm cov nplai III thiab IV hom frets tau muab faib ua ntau yam. subtypes. Theoretically muaj peev xwm faib 12:12 muab ib qho ntxiv ntawm S. l. (V) - txwv, tab sis tsis muaj vaj tse. structural thiab yog li sawv sib nrug. Pivot table S. l.:

Theoretical S. qhov kev piav qhia ntawm l. txais nyob rau hauv txoj kab nrog rau kev zoo nkauj. kab lig kev cai ntawm txoj kev xav ntawm proportions, uas muab lawv nyob rau hauv ib tug natural kev twb kev txuas nrog rau lwm yam hom ntawm modal systems - cov hom ntawm cov loj-me system thiab lub Nrab Hnub nyoog. fret. Qhov kev piav qhia uas muaj rau txhua tus yog tias txhua hom hom, nyob ntawm nws cov CE, sib raug rau ib qho ntawm cov lej uas tau paub txij thaum ub los - lej lej, sib haum xeeb thiab geometric. Cov lej tsim los ntawm lawv, uas muab CE ntawm txhua qhov ntawm cov tshuab no, tau muab rau hauv cov ntsiab lus ntawm cov coefficients ntawm cov lej. kev hloov pauv.

Daim ntawv thov piv txwv S. l. hauv suab paj nruag liter-re (cov lej qhia cov lej ntawm S. l. hauv cov suab paj nruag piv txwv):

1. MI Glinka. "Ruslan thiab Lyudmila", nplai ntawm Chernomor. 2. NA Rimsky-Korsakov. "Sadko", 2nd painting. 3. NA Rimsky-Korsakov. "Golden Cockerel", qaib ntxhw (tus naj npawb 76, tuav 5-10). 4. NA Rimsky-Korsakov. “Snow Maiden”, Leshy's theme (tus nab npawb 56-58). 5. IB Cherepnin. Kawm piano. op. 56 no 4. 6. IP Stravinsky. “Firebird” (nqe 22-29). 7. IB Stravinsky. "Parsley", lub ntsiab lus ntawm Petrushka (saib hauv Art. Polyaccord). 8. SV Protopopov. "Crow thiab Cancer" rau lub suab nrog piano. 9. O. Messiaen. “20 views…”, Tsis muaj 5 (saib tsab xov xwm Polymodality). 10. AK Lyadoi. “Los ntawm Apocalypse” (tus naj npawb 7). 11. O. Messiaen. L'Ascension rau lub cev, 4th txav. 12. A. Webern. Variations rau fp. op. 27, 4th ntu (saib hauv Art. Dodecaphony).

Saib kuj cov lus Tritone hom, Nce hom, Txo hom, Hom-tone tag nrho.

S. l. - ib yam ntawm cov qauv (modality) nrog rau pentatonic, diatonic, decomp. yam nyuaj frets. S. l. branched tawm los ntawm cov European systems loj thiab me (cov preforms ntawm sl yog transposing sequences, vaj huam sib luag-tert cycles ntawm tonalities, figuration, thiab anharmonicity ntawm sib npaug-interval consonances). Thawj cov qauv ntawm S. l. yog random nyob rau hauv cov xwm (qhov ntxov tshaj plaws, ua ntej 1722, nyob rau hauv lub sarabande ntawm 3rd English suite ntawm JS Bach, tuav 17-19: des2 (ces2)-bl-as1-g1-f1-e1-d1-cis1. Kev siv C L. raws li ib tug tshwj xeeb qhia tau hais tias pib nyob rau hauv lub xyoo pua 19th (ntau hom thiab tag nrho-tone scale nyob rau hauv lub bass Sanctus ntawm loj Es-dur los ntawm Schubert, 1828; nce hom thiab tag nrho-tone scale nyob rau hauv lub bass nyob rau hauv lub opera Vajtswv thiab Bayadere los ntawm Auber, 1830, nyob rau hauv 1835 post nyob rau hauv St. Petersburg nyob rau hauv lub title La Bayadère nyob rau hauv kev hlub; kuj los ntawm Chopin). Dargomyzhsky, NA Rimsky-Korsakov, PI Tchaikovsky, AK Lyadov, VI Rebikov, AN Skryabin, IF Stravinsky, AN Cherepnin, thiab kuj SS Prokofiev, N. Ya. Myaskovsky, DD Shostakovich, SV Protopopov, MIVErikovsky, SE Feinberg, AN Alexandrov thiab lwm yam. composers rau S. l. F. Liszt, R. Wagner, K. Debussy, B. Bartok hais lus; tshwj xeeb tshaj yog dav thiab nthuav dav S. l. tsim los ntawm O. Messiaen. Nyob rau hauv lub suab paj nruag S. txoj kev xav ntawm l. Ameslikas tau piav raws li hom tshwj xeeb txawv teb chaws (piv txwv li, hauv G. Kapellen, 1908, "Suav tag nrho cov suab paj nruag" tau ua qauv qhia los ntawm tus sau ua "exoticism exoticism"). Nyob rau hauv Lavxias teb sab theoretical musicology thawj qhov kev piav qhia ntawm S. l. (nyob rau hauv lub npe "circular" modulating sequences, "circles" ntawm loj thiab me thib peb) belongs rau Rimsky-Korsakov (1884-85); thawj theoretical S. qhov kev piav qhia ntawm l. tau thov los ntawm BL Yavorsky thaum pib. 20th caug xyoo Los ntawm txawv teb chaws. theorists txoj kev xav ntawm S. l. tsim los ntawm Messiaen (“Modes of Limited Transposition”, 1944) thiab E. Lendvai (“System of Axes”, ntawm qhov piv txwv ntawm Bartok's music, 1957).

References: Rimsky-Korsakov NA, Phau ntawv qhia txog kev sib haum xeeb, St. Petersburg, 1886, tib yam, Poln. coll. soj., vol. IV, M., 1960; Yavorsky BL, Tus qauv ntawm kev hais lus suab paj nruag, ntu 1-3, (M., 1908); Kastalsky AD, Nta ntawm pej xeem-Lavxias teb sab suab paj nruas system, M. – Pg., 1923, 1961; AM, A. Cherepnin (notography), “Contemporary Music”, 1925, No 11; Protopopov SV, Cov ntsiab lus ntawm cov qauv ntawm kev hais lus suab paj nruag, ntu 1-2, M., 1930; Tyutmanov IA, Ib co nta ntawm modal-harmonic style ntawm HA Rimsky-Korsakov, nyob rau hauv cov phau ntawv: Kev tshawb fawb thiab methodological sau ntawv ntawm lub xeev Saratov. kev conservatory, vol. 1-4, Saratov, 1957-61; Budrin B., Qee cov lus nug ntawm Rimsky-Korsakov cov lus sib haum xeeb hauv kev ua yeeb yam hauv thawj ib nrab ntawm 90s, Kev Ua Haujlwm ntawm Lub Tsev Haujlwm Saib Xyuas Kev Ua Yeeb Yam ntawm Moscow Conservatory, vol. 1, 1960; Sposobin IV, Lectures on the course of harmony, M., 1969; Kholopov Yu. N., Symmetric hom nyob rau hauv theoretical systems ntawm Yavorsky thiab Messiaen, nyob rau hauv phau ntawv: Suab paj nruag thiab Modernity, vol. 7, M., 1971; ib. Mazel LA, Teeb meem ntawm classical harmony, M., 1972; Tsukkerman VA, Qee cov lus nug ntawm kev sib haum xeeb, hauv nws phau ntawv: Suab paj nruag-theoretical essays thiab etudes, vol. 2, M., 1975; ib. Capellen G., Ein neuer exotischer Musikstil, Stuttg., 11; nws, Fortschrittliche Harmonie- und Melodielehre, Lpz., 1906; Busoni F., Entwurf einer neuen Дsthetik der Tonkunst, Triest, 1908 (Russian translation: Busoni F., Sketch of a new aesthetics of musical art, St. Petersburg, 1907); Schönberg A., Harmonielehre.W., 1912; Setacio1911i G., Note ed appunti al Trattato d'armonia di C. de Sanctis…, Mil. – NY, (1); Weig1923 B., Harmonielehre, Bd 1-1, Mainz, 2; Hbba A., Neue Harmonielehre…, Lpz., 1925; Messiaen O., Technique de mon langage musical, v. 1927-1, P., (2); Lendvai E., Einführung in die Formenund Harmoniewelt Bartoks, hauv: Byla Bartuk. Weg und Werk, Bdpst, 1944; Reich W., Alexander Tcsherepnin, Bonn, (1957).

Yu. H. Kholopov