Pythagorean system |

Pythagorean system - yakagadzirwa maererano nenzira yePythagoreans masvomhu. kutaura kweiyo yakajairika frequency (hurefu) hukama pakati pematanho emimhanzi. zvirongwa. Mamwe masayendisiti echiGreek akasimbisa zvine simba kuti 2/3 yetambo yakatambanudzwa pane monochord, yakazunguzwa, inopa ruzha chaizvo cheshanu chakachena pamusoro pechigadziko. inzwi, “kusimuka kubva pakudengenyeka kwetambo yose, 3/4 yetambo inopa chikamu, nehafu yetambo - octave. Uchishandisa huwandu uhu, Ch. arr. yechishanu uye octave kukosha, unogona kuverenga manzwi e diato-nich. kana chromatic. gamma (muzvikamu zvetambo, kana muchimiro che interval coefficients inoratidza reshiyo yeoscillation frequency yeinzwi repamusoro kune frequency yeyakaderera, kana muchimiro chetafura yekuzunguza frequencies yemanzwi). Semuenzaniso, chiyero cheC-dur chichagamuchira muP. chirevo chinotevera:

Maererano nengano, P.s. yakatanga kuwanikwa inoshanda. kushandiswa mukugadzirisa mbira dzaOrpheus. MuGreece, raishandiswa kuverenga hukama hwenzwi pakati pemanzwi pakugadzirisa cithara. NeChitatu. zana remakore, iyi system yakashandiswa zvakanyanya kugadzirisa nhengo. P. s. yakashanda sehwaro hwokuvakwa kwezvitsigiso zvenzwi nenyanzvi dzokuMabvazuva. Middle Ages (semuenzaniso, Jami muChibvumirano cheMumhanzi, 2 hafu yezana ramakore rechi 15). Nekuvandudzwa kwepolyphony, zvimwe zvakakosha zveP s zvakaratidzwa: mataurirwo einzwi eiyi system anonyatso ratidza kubatana kunoshanda pakati pemanzwi mune melodic. kutevedzana, kunyanya, kusimbisa, kuwedzera semitone gravitation; panguva imwe chete, muhuwandu hweharmonics. makonzonenzi, aya mazwi anoonekwa seakanyanya kusimba, enhema. Muurongwa hwakachena, kana kuti hwomuzvarirwo, aya matsva, anotsinhirana, akaonekwa. matauriro eimba yekuchengetera zvinhu: yakatetepa (mukuenzanisa neP. s.) b. 3 uye b. 6 uye akawedzera m. 3 uye m. 6 (5/4, 5/3, 6/5, 8/5, zvichiteerana, panzvimbo ye81/64, 27/16, 32/27 uye 128/81 muP. s). Kuwedzera kukwidziridzwa kwepolyphony, kubuda kwehukama hutsva, hwakaoma kunzwisisa hwematoni, uye kushandiswa kwakapararira kwemazwi enharmonic akaenzana anowedzera kuderedza kukosha kwephonatory s; zvakaonekwa kuti P.s. - iyo yakavhurika sisitimu, kureva, kuti mairi yechigumi nembiri haienderane mukukwirira nezwi rekutanga (somuenzaniso, inoshanduka kuva yakakwirira kupfuura yepakutanga c nenguva inonzi Pythagorean comma uye yakaenzana ne12/1. yezwi rose); saka, P. s. haigone kushandiswa kune enharmonics. modulations. Mamiriro ezvinhu aya akaita kuti pave nechimiro chechimiro chechimiro chakafanana. Panguva imwecheteyo, sezvinoratidzwa nekutsvakurudza kweacoustic, paunenge uchiridza zviridzwa zvine ruzha rusina kugadzikana (somuenzaniso, violin) otd. izwi P.s. tsvaga application mukati megadziriro yezone system. Diff. cosmological, geometric pfungwa dzakamuka mukusika P. s dzakarasa zvadzinoreva zvachose.

References: Garbuzov NA, Zonal chimiro chekunzwa kwegomba, M.-L., 1948; Musical Acoustics, ed. Yakarongedzwa naNA Garbuzova. Moscow, 1954. Ancient musical aesthetics. Intro. rondedzero uye muunganidzwa wezvinyorwa naAF Losev, Moscow, 1961; Barbour JM, The persistence of the Pythagorean tuning system, “Scripta mathematica” 1933, v. 1, no 4; Bindel E., Die Zahlengrundlagen der Musik im Wandel der Zeiten, Bd 1, Stuttg., (1950).

YH Rags