Pythagorean system |
Pythagorean qhov system - formulated raws li txoj kev ntawm Pythagoreans lej. qhia txog qhov feem ntau zaus (qhov siab) kev sib raug zoo ntawm cov kauj ruam ntawm cov suab paj nruag. tshuab. Lwm cov kws tshawb fawb Greek tau tsim kev pom zoo tias 2/3 ntawm txoj hlua ncab ntawm ib qho monochord, vibrated, muab lub suab raws nraim ib qho dawb huv thib tsib saum lub hauv paus. suab nrov, "tsim los ntawm kev vibration ntawm tag nrho cov hlua, 3/4 ntawm txoj hlua muab quart, thiab ib nrab ntawm txoj hlua - ib qho octave. Siv cov khoom no, Ch. arr. thib tsib thiab octave qhov tseem ceeb, koj tuaj yeem suav cov suab ntawm diato-nich. los yog chromatic. gamma (nyob rau hauv feem ntawm ib txoj hlua, los yog nyob rau hauv daim ntawv ntawm lub sij hawm coefficients qhia qhov piv ntawm lub oscillation zaus ntawm lub suab sab sauv mus rau lub zaus ntawm lub qis dua, los yog nyob rau hauv daim ntawv ntawm ib lub rooj ntawm vibration frequencies ntawm lub suab). Piv txwv li, qhov ntsuas C-dur yuav tau txais hauv P. s. cov lus hauv qab no:
Raws li cov lus dab neeg, P. s. xub pom cov tswv yim. daim ntawv thov nyob rau hauv tuning lub lyre ntawm Orpheus. Hauv tebchaws Greece, nws tau siv los suav cov suab sib raug zoo ntawm lub suab thaum kho lub cithara. Hnub Wednesday. xyoo pua, qhov system no tau siv dav rau kev kho lub cev. P. s. ua lub hauv paus rau kev tsim kho suab tshuab los ntawm theorists ntawm Sab Hnub Tuaj. Nruab Nrab Hnub nyoog (piv txwv li, Jami hauv Treatise ntawm Suab paj nruag, 2nd ib nrab ntawm lub xyoo pua 15th). Nrog rau txoj kev loj hlob ntawm polyphony, qee yam tseem ceeb ntawm P. s tau tshwm sim: lub suab intonations ntawm qhov system no zoo qhia txog kev sib txuas ntawm cov suab hauv suab paj nruag. sequences, tshwj xeeb, hais txog, txhim khu semitone gravitation; Nyob rau tib lub sij hawm, nyob rau hauv ib tug xov tooj ntawm harmonics. consonances, cov intonations yog perceived raws li nruj heev, tsis tseeb. Nyob rau hauv ib tug ntshiab, los yog tej yam ntuj tso, system, cov tshiab, yam ntxwv harmonics, raug txheeb xyuas. warehouse tendencies ntawm intonation: nws yog nqaim (piv nrog P. s.) b. 3i ib b. 6 thiab m. 3 i m. 6 (5/4, 5/3, 6/5, 8/5, raws li, tsis yog 81/64, 27/16, 32/27 thiab 128/81 hauv P. s). Kev txhim kho ntxiv ntawm polyphony, qhov tshwm sim ntawm cov tshiab, ntau txoj kev sib raug zoo tonal, thiab kev siv cov suab sib npaug sib npaug ntxiv txwv tus nqi ntawm phonatory s; tau pom tias P. s. - lub kaw lus qhib, piv txwv li, nyob rau hauv nws 12th thib tsib tsis coincide nyob rau hauv qhov siab nrog lub suab qub (piv txwv li, nws hloov tawm kom siab tshaj qhov qub c los ntawm lub caij nyoog hu ua Pythagorean comma thiab sib npaug li 1/9. ntawm tag nrho cov suab); yog li ntawd, P.s. tsis tuaj yeem siv rau enharmonics. modulations. Qhov xwm txheej no tau coj mus rau qhov pom ntawm lub cev temperament. Nyob rau tib lub sijhawm, raws li qhia los ntawm kev tshawb fawb acoustic, thaum ua si cov twj paj nruag nrog lub suab tsis ruaj ntawm lub suab (piv txwv li, violin) otd. intonation P. s. nrhiav daim ntawv thov nyob rau hauv lub moj khaum ntawm cheeb tsam system. Qhov txawv. cosmological, geometric cov tswv yim uas tshwm sim nyob rau hauv tus txheej txheem ntawm kev tsim P. s tau tag nrho lawv lub ntsiab lus.
References: Garbuzov NA, Zonal xwm ntawm lub suab hnov, M.-L., 1948; Suab paj nruag Acoustics, ed. Edited los ntawm NA Garbuzova. Moscow, 1954. Ancient suab paj nruag aesthetics. Intro. sau ntawv thiab sau cov ntawv los ntawm AF 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).
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