Golden ratio |

Chikamu Chendarama mumhanzi - inowanikwa muzvizhinji. music prod. kubatanidzwa kwezvinhu zvakakosha zvekuvakwa kwese kana zvikamu zvayo nezvinonzi. golden ratio. Pfungwa yeZ. ne. ndeyemunda we geometry; Z. s. inonzi kupatsanurwa kwechikamu muzvikamu zviviri, neKrom yose inobatana nechikamu chikuru sechikamu chikuru kune chiduku (harmonic division, kupatsanurwa mukunyanyisa uye pakati pechiyero). Kana rose richiratidzwa nebhii a, chikamu chikuru nebhii b, uye chikamu chidiki nebhii c, reshiyo iyi inotaridzwa nechikamu a:b=b:c. Mukutaura kwenhamba, chiyero b:a chikamu chinoenderera, chinenge chakaenzana ne0,618034 ...

Munguva yeRenaissance, zvakasimbiswa kuti Z. s. inowana application mukuratidza. art-wah, kunyanya mukuvaka. Zvaizivikanwa kuti reshiyo yakadaro yezvikamu inopa fungidziro yekuwirirana, chiyero, nyasha. Vanyori vechikoro cheNetherlandish (J. Obrecht) vakashandisa Z. ne. muzvigadzirwa zvavo.

Kuedza kwekutanga kuona kuratidzwa kwaZ. mumimhanzi yakagadzirwa ser. Muzana remakore rechi19 musayendisiti wokuGermany A. Zeising, uyo akazivisa zvisina kururama Z. s. chiyero chepasi rose, chepasi rose, chinoratidzwa mune zvese muhunyanzvi uye mune zvakasikwa. Zeising yakawana kuti pedyo neZ. s. reshiyo inoburitsa hutatu hukuru (nguva yechikamu cheshanu chakazara, chikamu chikuru chetatu sechikamu chikuru, chetatu chidiki sechikamu chidiki).

Kuratidzwa kwakajeka kwehukama hweZ ne. mumimhanzi yakawanikwa pakutanga. Muzana remakore rechi20 muongorori weRussia EK Rosenov mumunda wemimhanzi. mafomu. Maererano naRozenov, zvinotokanganisa nguva iyo melodic. mhedziso inowanzowanikwa panzvimbo iri padyo nenzvimbo Z. ne. Kazhinji pedyo nenzvimbo Z. ine. Kushandura pfungwa kunowanikwawo muzvikamu zvakakura zvemimhanzi. mafomu (Z. s. inozviratidza muyero yenguva yezvikamu, izvo, munyaya yekuchinja kwe tempo, hazvienderani nehuwandu hwehuwandu hwezviyero) uye kunyange muchikamu chimwe chete chinoshanda. Kunyange zvazvo kuongorora kwaRosenov dzimwe nguva kunotsanangurwa zvakanyanya uye kwete pasina kutambanudza, kazhinji, maonero ake pamusoro pekuratidzwa kweZ. mumimhanzi yaibereka zvibereko uye yakapfumisa pfungwa yenguva pfupi mise. mapatani.

Gare gare Z. pamwe. VE Ferman, LA Mazel, nevamwe vakadzidza mimhanzi mumimhanzi. chiratidzo chekugara, ext. kupedzisa rwiyo. Akaratidza kuti panguva Z. ne. nguva yemimhanzi inogona kunge iri melodic. iyo yepamusoro kwete yenguva yose chete, asiwo yemutsara wechipiri, kuti iyi pfungwa inogona kuva nguva iyo mutsara wechipiri unokura zvakasiyana kubva kune wekutanga (izvi zviratidzo zvezs zvinogona kubatanidzwa). Pachiyero che sonata allegro uye muzvikamu zvitatu-zvikamu, maererano naMazel, pfungwa Z. ine. mumhanzi wekirasi kazhinji inowira pakutanga kwekudzokorora (kuguma kwebudiriro), mumhanzi wevanyori verudo inowanikwa mune reprise, padyo nekodha. Mazel akaunza pfungwa yeZ ne. munguva yekuongorora mimhanzi. mabasa; Zvishoma nezvishoma, yakanyatsopinda muhupenyu hwezuva nezuva hwezizi. musicology.

References: Rozenov EK, Pakushandiswa kwemutemo we "golden division" kumumhanzi, "Izvestiya SPb. Society for Musical Meetings, 1904, no. June-Chikunguru-Nyamavhuvhu, p. 1-19; Timding GE, The Golden Section, trans. kubva kuGermany, P., 1924; Mazel L., Chiitiko mukudzidza kwechikamu chegoridhe muzvivakwa zvemumhanzi muchiedza chekuongorora kwakawanda kwemafomu, Dzidzo Yemimhanzi, 1930, Nha 2.