Uhlelo lwePythagorean |

Uhlelo lwePythagorean - yakhiwe ngendlela yezibalo zePythagoreans. ukubonakaliswa kobudlelwane obujwayelekile kakhulu (ubude) phakathi kwezinyathelo zomculo. izinhlelo. Abanye ososayensi bamaGreki baye baqinisekisa ukuthi u-2/3 wentambo enwetshiwe ku-monochord, enyakaziswayo, inikeza umsindo ncamashi ingxenye yesihlanu emsulwa ngaphezu kwesisekelo. iphimbo, “okuvela ekudlidlizeni kwayo yonke intambo, u-3/4 wentambo unikeza ilitha, nengxenye yentambo – i-octave. Ukusebenzisa lezi zibalo, Ch. ar. amanani wesihlanu ne-octave, ungakwazi ukubala imisindo ye-diato-nich. noma chromatic. i-gamma (ngezingxenyana zeyunithi yezinhlamvu, noma ngendlela yama-coefficients wesikhawu ebonisa isilinganiso sefrikhwensi ye-oscillation yomsindo ophezulu ukuya kumafrikhwensi alo ophansi, noma ngesimo sethebula lamafrikhwensi wokudlidliza wemisindo). Isibonelo, isikali C-dur esizotholwa ku-P. inkulumo elandelayo:

Ngokwenganekwane, uP. okokuqala kwatholakala kuwusizo. ukusetshenziswa ekushumeni ilire lika-Orpheus. E-Dr. E-Greece, yayisetshenziselwa ukubala ubudlelwano bephimbo phakathi kwemisindo lapho kushunwa i-cithara. Ngolwesithathu. ekhulwini leminyaka, lesi simiso sasisetshenziswa kabanzi ukulungisa izitho zomzimba. P. s. yasebenza njengesisekelo sokwakhiwa kwezimiso zomsindo ochwepheshe baseMpumalanga. I-Middle Ages (isibonelo, i-Jami ku-Treatise on Music, ingxenye yesi-2 yekhulu le-15). Ngokuthuthukiswa kwe-polyphony, izici ezithile ezibalulekile ze-P. ukulandelana, ikakhulukazi, kugcizelela, kuthuthukise amandla adonsela phansi e-semitone; ngesikhathi esifanayo, ngenani lama-harmonics. ongwaqa, lawa maphimbo athathwa njengashube kakhulu, angamanga. Ngohlelo oluhlanzekile, noma lwemvelo, lawa ma-harmonic amasha, ayisici, ahlonziwe. ukuthambekela kwephimbo endaweni yokugcina impahla: kuyancishiswa (uma kuqhathaniswa no-P. s.) b. 3 kanye b. 6 futhi kwandiswa m. 3 futhi m. 6 (5/4, 5/3, 6/5, 8/5, ngokulandelana, esikhundleni sika-81/64, 27/16, 32/27 kanye no-128/81 ku-P. s). Ukuthuthukiswa okuqhubekayo kwe-polyphony, ukuvela kobudlelwane obusha, obuyinkimbinkimbi yethoni, kanye nokusetshenziswa kabanzi kwemisindo elinganayo ye-enharmonic kuphinde kunciphise inani lemisindo; kwatholakala ukuthi uP. - uhlelo oluvulekile, okungukuthi, ukuthi i-12 yesihlanu ayihambisani ngokuphakama nomsindo wangempela (isibonelo, iphenduka ibe phezulu kuno-c yasekuqaleni ngesikhawu esibizwa ngokuthi ikhefana le-Pythagorean futhi elilingana ne-1/9 ithoni ephelele); ngakho-ke, P.s. ayikwazi ukusetshenziselwa ama-enharmonics. ama-modulations. Lesi simo saholela ekubonakaleni kwesistimu ye- temperament efanayo. Ngesikhathi esifanayo, njengoba kuboniswa ucwaningo lwe-acoustic, lapho udlala izinsimbi ezinephimbo elingashintshile lemisindo (isibonelo, i-violin) otd. izwi P.s. thola uhlelo lokusebenza ngaphakathi kohlaka lwesistimu yendawo. Diff. i-cosmological, i-geometric imibono eyavela ngesikhathi sokudala i-P. s ilahlekelwe ngokuphelele incazelo yayo.

References: I-Garbuzov NA, i-Zonal nature of pitch hearing, M.-L., 1948; I-Acoustic yomculo, u-ed. Ihlelwe ngu-NA Garbuzova. Moscow, 1954. Ubuhle bomculo wasendulo. Isingeniso. indatshana kanye nokuqoqwa kwemibhalo ka-AF Losev, eMoscow, ngo-1961; Barbour JM, Ukuphikelela kwePythagorean 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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