Tsarin Pythagorean |
Tsarin Pythagorean – tsara bisa ga hanyar Pythagoreans lissafi. bayyana dangantakar mitar (tsawo) mafi yawanci tsakanin matakan kiɗa. tsarin. Sauran masana kimiyya na Girka sun tabbatar da cewa 2/3 na kirtani da aka shimfiɗa akan monochord, girgiza, yana ba da sauti daidai tsantsa na biyar sama da tushe. sautin, "tasowa daga girgizar dukan kirtani, 3/4 na kirtani yana ba da kwata, kuma rabin kirtani - octave. Yin amfani da waɗannan adadi, Ch. arr. dabi'u na biyar da octave, zaku iya lissafin sautin diato-nich. ko chromatic. gamma (a cikin juzu'i na kirtani, ko a cikin nau'i na tazara tazara wanda ke nuna rabon mitar oscillation na sauti na sama zuwa mitar na ƙasa, ko a cikin nau'in tebur na mitar sauti). Misali, ma'aunin C-dur zai karɓa a cikin P. s. magana mai zuwa:
A cewar almara, P.s. na farko samu m. aikace-aikace a kunna leda na Orpheus. A cikin Dr. A Girka, an yi amfani da shi don ƙididdige alaƙar da ke tsakanin sauti lokacin kunna cithara. Ran laraba. karni, an yi amfani da wannan tsarin sosai don daidaita gabobin. P. s. yayi aiki a matsayin tushen gina tsarin sauti ta masu ilimin tunanin Gabas. Tsakanin Zamani (misali, Jami a cikin Treatise on Music, 2nd rabin karni na 15). Tare da haɓakar polyphony, an bayyana wasu mahimman fasalulluka na P. s: ƙayyadaddun sauti na wannan tsarin yana nuna alaƙar aiki tsakanin sautuna a cikin karin waƙa. jerin, musamman, ƙarfafawa, haɓaka haɓakar semitone; a lokaci guda, a cikin adadin masu jituwa. Consonances, wadannan intonations ana tsinkayar a matsayin ma tashin hankali, ƙarya. A cikin tsaftataccen tsari, ko na halitta, an gano waɗannan sabbin halayen jituwa. dabi'un sito na innation: an kunkuntar (idan aka kwatanta da P. s.) b. 3 da b. 6 da tsawo m. 3 da m. 6 (5/4, 5/3, 6/5, 8/5, bi da bi, maimakon 81/64, 27/16, 32/27 da 128/81 a cikin P. s). Ci gaban haɓakar sautin ringi, bullowar sabbin alaƙar tonal mai sarƙaƙƙiya, da yawaitar amfani da daidaitattun sautunan ƙara ƙayyadaddun ƙimar phonatory s; an gano cewa P. s. – buɗaɗɗen tsarin, watau, cewa a cikinsa na 12 na biyar bai zo daidai da tsayi da sautin asali ba (misali, ya zama mafi girma fiye da ainihin c ta wani tazara mai suna Pythagorean waƙafi kuma daidai yake da kusan 1/9). na duka sautin; don haka, P. s. ba za a iya amfani da su don enharmonics. modulations. Wannan yanayin ya haifar da bayyanar tsarin yanayin yanayi iri ɗaya. A lokaci guda, kamar yadda bincike na acoustic ya nuna, lokacin kunna kayan kida tare da sautin da ba daidai ba (misali, violin) otd. innation P. s. nemo aikace-aikace a cikin tsarin tsarin yankin. Bambance-bambance. Cosmological, geometric ra'ayoyin da suka taso a cikin tsarin samar da P. sun rasa ma'anarsu gaba daya.
References: Garbuzov NA, Yanayin yanki na sauraron sauti, M.-L., 1948; Musical Acoustics, ed. Edited by NA Garbuzova. Moscow, 1954. Tsohon kayan ado na kiɗa. Gabatarwa makala da tarin matani na AF Losev, Moscow, 1961; Barbour JM, Dagewar tsarin tuning Pythagorean, “Scripta mathematica” 1933, v. 1, no 4; Bindel E., Die Zahlengrundlagen der Musik im Wandel der Zeiten, Bd 1, Stuttg., (1950).
Farashin YH
