Chii chinonzi consonance?

Muchinyorwa chakapfuura, takaona kuti ruzha runoshanda sei. Ngatidzokorore fomula iyi:

KURUDZIKA = GROUND TONE + ALL MULTIPLE OVERTONS

Pamusoro pezvo, sezvo maJapan anoyemura maruva echerry, isu tichayemurawo frequency remhinduro graph - iyo amplitude-frequency hunhu hwekurira (Fig. 1):

Rangarira kuti axis yakachinjika inomiririra nzwi (oscillation frequency), uye axis yakatwasuka inomiririra ruzha (amplitude).

Mutsara wega wega wakatwasuka ndeye harmonic, yekutanga harmonic inowanzonzi iyo yakakosha. Harmonics inorongwa sezvinotevera: yechipiri inonzi harmonic inosvika 2 nguva yakakwirira kudarika inzwi rinokosha, yechitatu ndeyetatu, yechina ina, zvichingodaro.

Nekuda kwekupfupika, pachinzvimbo che "frequency nth harmonic" tichangoti "nth harmonic", uye pachinzvimbo che "basic frequency" - "sound frequency".

Saka, tichitarisa pane frequency mhinduro, hazvizove zvakaoma kwatiri kuti tipindure mubvunzo, chii chinonzi consonance.

Nzira yekuverenga sei kune infinity?

Consonance chaizvoizvo inoreva kuti "co-sounding", kurira kwekubatana. Manzwi maviri akasiyana anganzwika sei pamwechete?

Ngativadhirowe pachati imwechete pasi peumwe neumwe (Fig. 2):

Heino mhinduro: mamwe eharmonics anogona kuenderana muhuwandu. Zvine musoro kufunga kuti kana mafekisheni akawanda anoenderana, ndipo paanowedzera manzwi “akajairika”, uye, nokudaro, kuwedzera kwekonzonenzi muruzha rwenguva yakadaro. Kuti zvive zvakanyatsojeka, zvakakosha kwete chete nhamba yekufananidza harmonics, asi ndechipi chikamu chezvose zvinonzwika harmonics mechi, kureva, chiyero chenhamba yekufananidza kusvika kuhuwandu hwekunzwika kwehuronics.

Isu tinowana iyo yakapusa formula yekuverenga consonance:

apo N_sovp ndiyo nhamba yekufananidza harmonics,  N_zvakajairika ndiyo nhamba yese yezvinonzwika harmonics (nhamba yemhando dzakasiyana dzekurira), uye nezvayakaipira uye ndiyo consonance yedu yatinoda. Kuti uve wakarurama wemasvomhu, zviri nani kudaidza huwandu chiyero che frequency consonance.

Zvakanaka, nyaya idiki: iwe unofanirwa kuverenga N_sovp и N_zvakajairika, patsanura imwe neimwe, uye uwane mhedzisiro yaunoda.

Dambudziko chete nderekuti ese ari maviri akazara nhamba yeharmonics uye kunyangwe iyo nhamba yekufananidza harmonics haina magumo.

Chii chinoitika kana tikagovanisa kusaguma nekusingaperi?

Ngatichinje chiyero chechati yapfuura, "ibva" kubva pairi (Fig. 3)

Isu tinoona kuti kuenzanisa kunopindirana kunoitika zvakare uye zvakare. Mufananidzo wacho unodzokororwa (Fig. 4).

Kudzokorora uku kuchatibatsira.

Zvakakwana kuti isu tiverenge reshiyo (1) mune imwe yemakona emakona (somuenzaniso, mune yekutanga), saka, nekuda kwekudzokorora uye pamutsetse wese, chiyero ichi chicharamba chakafanana.

Kuti zvive nyore, kuwanda kwezwi rinokosha rekutanga (pasi) inzwi richaonekwa seyakaenzana nekubatana, uye kuwanda kwezwi rinokosha rezwi rechipiri richanyorwa sechikamu chisingadzivisiki.  .

Ngationei mumabare kuti mumitambo yemimhanzi, sekutonga, inonyatso kurira kunoshandiswa, chiyero chefrequencies icho chinoratidzwa nechimwe chikamu.  . Semuenzaniso, nguva yechishanu ndiyo reshiyo  , makota -  , triton -   etc.

Ngativerengei reshiyo (1) mukati merectangle yekutanga (Fig. 4).

Zviri nyore kuverenga nhamba yekufananidza harmonics. Nenzira, kune maviri azvo, imwe ndeyekunzwika kwepasi, yechipiri - kumusoro, mumufananidzo 4 ivo vakaiswa mutsvuku. Asi ese ari maviri aya maharmonics anonzwika panguva imwe chete, zvichiteerana, kana tikaverenga huwandu hwekufananidza mafrequency, ipapo pachave nekumwe chete kwakadai.

Ndeipi nhamba yese yemanzwi ekurira?

Ngatiite nharo sezvizvi.

Ese maharmonics emutsindo wepasi akarongwa muhuwandu hwakazara (1, 2, 3, nezvimwewo). Pakarepo chero harmonic yezwi repamusoro iri nhamba yakawanda, inopindirana neimwe yeharmonics yepasi. Ese maharmonics emutsindo wepamusoro ndiwo akawanda eiyo toni yakakosha , saka kuwanda n-th harmonic ichave yakaenzana ne:

kureva kuti ichave nhamba yakazara (sezvo m iri nhamba). Izvi zvinoreva kuti mutsindo wepamusoro murectangle une maharmonics kubva kune wekutanga (fundamental toni) kuenda n-o, saka, inzwi n frequency.

Sezvo ese maharmonics emutsindo wepasi ari munhamba dzakakwana, uye zvinoenderana ne (3), kusangana kwekutanga kunoitika pa frequency. m, zvinosvika kuti inzwi rezasi mukati rectangle richapa m manzwi ekurira.

Zvinofanira kucherechedzwa kuti coinciding frequency m takaverengazve kaviri: pataiverenga mafambiro eruzha rwepamusoro uye pataiverenga mafambiro eruzha rwepasi. Asi muchokwadi, iyo frequency ndeye, uye kune mhinduro chaiyo, isu tichada kubvisa imwe "yakawedzera" frequency.

Huwandu hwese kurira kwese kurira mukati merectangle kuchave:

Kutsiva (2) uye (4) kuita fomula (1), tinowana chirevo chakareruka chekuverenga consonance:

Kuti usimbise consonance yatakaverenga, unogona kutaridza manzwi aya mumabhuraketi nezvayakaipira:

Uchishandisa fomula iri nyore, unogona kuverenga consonance yechero nguva.

Uye zvino ngatitarisei zvimwe zvimiro zve frequency consonance uye mienzaniso yekuverenga kwayo.

Properties uye mienzaniso

Kutanga, ngativerengei makonzonenzi enguva dzakareruka uye tive nechokwadi chekuti fomula (6) "inoshanda".

Ndeipi nguva iri nyore?

Chokwadi prima. Zvinyorwa zviviri zvinonzwika pamwe chete. Pane chati ichaita seizvi:

Isu tinoona kuti zvachose kurira kwese kunopindirana. Saka, consonance inofanira kuenzana ne:

Zvino ngatitsive chiyero chekubatana  mufomula (6), tinowana:

Iko kuverenga kunopindirana ne "intuitive" mhinduro, iyo inofanirwa kutarisirwa.

Ngatitorei mumwe muenzaniso umo mhinduro inonzwisisika iri pachena - iyo octave.

Mune octave, ruzha rwepamusoro rwakakwira zvakapetwa ka2 pane rezasi (zvinoenderana nekuwanda kweiyo toni yakakosha), zvichiteerana, pagirafu ichaita seizvi:

Zvinogona kuoneka kubva pagirafu kuti sekondi yega yega harmonic inopindirana, uye mhinduro intuitive ndeyekuti: consonance i50%.

Ngativerengei neformula (6):

Uye zvakare, iyo yakaverengerwa kukosha yakaenzana ne "intuitive".

Kana tikatora chinyorwa sezwi rezasi to uye kuronga kukosha kwekonsonance yezvikamu zvese mukati meoctave pane girafu (nguva dzakareruka), tinowana mufananidzo unotevera:

Izvo zviyero zvepamusoro zvekonsonanti zviri muoctave, yechishanu neyechina. Vakambotaura nezvemakonzonenzi “akakwana”. Zvikamu zvidiki nezvikuru muzvitatu, uye zvidiki uye zvechitanhatu zvikuru zvakadzikira zvishoma, nguva idzi dzinonzi makonzonenzi “asina kukwana”. Dzimwe nguva dzakasara dzine dhigirii yakaderera yekonsonanti, sechinyakare ivo ndeveboka remadissonances.

Zvino isu tinonyora zvimwe zvimiro zveyero ye frequency consonance, iyo inobva kune formula yekuverenga kwayo:

1. Iyo yakanyanya kuoma chiyero  (nhamba zhinji m и n), iyo konzonendi shoma yenguva.

И m и n mufomula (6) dziri mudhinominati, naizvozvo, sezvo nhamba idzi dzichiwedzera, chiyero chekonzoni chinodzikira.

2. Kukwira kwekonzonenzi yepakati yakaenzana nekudzika kwekonzonenzi yepakati.

Kuti tiwane nguva yekudzika panzvimbo yekukwira, tinoda mureshiyo   chinjanisa m и n. Asi mune fomula (6), zvachose hapana chichachinja kubva pakutsiva kwakadaro.

3. Chiyero chefrequency consonance yenguva hazvinei nekuti tiri kuivaka kubva kupi.

Kana ukachinja manotsi ese ari maviri panguva imwechete kumusoro kana pasi (semuenzaniso, gadzira cheshanu kwete kubva panoti to, asi kubva pachinyorwa re), ipapo chiyero  pakati pezvinyorwa hazvizoshanduki, uye nekudaro, chiyero che frequency consonance chicharamba chakafanana.

Tinogona kupa zvimwe zvimiro zvekonsonanti, asi parizvino tichazviganhurira kune izvi.

Physics uye mazwi

Mufananidzo 7 unotipa pfungwa yekuti consonance inoshanda sei. Asi aya ndiwo maonero atinoita chaizvo kuwirirana kwezvikamu? Pane vanhu vasingade makonzonenzi akakwana here, asi iwo anonyanya kusawirirana anoita seanofadza?

Hongu, vanhu vakadaro variko zvechokwadi. Uye kutsanangura izvi, pfungwa mbiri dzinofanira kusiyaniswa: kunzwisiswa kwemuviri и consonance inonzwisisika.

Zvese zvatakurukura munyaya ino zvine chekuita nekuonana kwemuviri. Kuti uiverenge, unofanirwa kuziva kuti ruzha runoshanda sei, uye kuti kudengenyeka kwakasiyana kunowedzera sei. Physical consonance inopa zvinodikanwa zveinonzwisisika consonance, asi haizviratidze 100%.

Konsonanti inonzwisiswa inotsanangurwa zviri nyore. Munhu anobvunzwa kana achifarira consonance iyi. kana hongu, saka kwaari ndiko kubvumirana; kana zvisina kudaro, idissonance. Kana akapiwa mapindiro maviri ekuenzanisa, saka tinogona kutaura kuti imwe yacho ichaita kumunhu panguva ino yakawanda, imwe shoma.

Ko consonance inonzwisisika inogona kuverengerwa here? Kunyange kana tikafunga kuti zvinogoneka, saka kuverenga uku kuchave kwakaoma, kunosanganisira imwe isingaperi - kusakwana kwemunhu: ruzivo rwake, maitiro ekunzwa uye kugona kwehuropi. Iyi infinity haisi nyore kubata nayo.

Zvisinei, tsvakurudzo munharaunda iyi iri kuenderera mberi. Kunyanya, munyori Ivan Soshinsky, uyo anopa nemutsa zvinyorwa zvekuteerera kune zvinyorwa izvi, akagadzira purogiramu iyo iwe unogona kuvaka imwe mepu yemafungiro ekonsonanti kumunhu mumwe nomumwe. Iyo saiti mu-theory.info iri kuvandudzwa, uko chero munhu anogona kuongororwa uye kuona maficha ekunzwa kwavo.

Uye zvakadaro, kana pane inonzwisiswa consonance, uye yakasiyana kubva mumuviri, chii chiri chinangwa pakuverenga iyo yekupedzisira? Tinogona kugadzirisa mubvunzo uyu nenzira inovaka: pfungwa mbiri idzi dzinodyidzana sei?

Zvidzidzo zvinoratidza kuti kuwirirana pakati peavhareji inonzwisiswa consonance uye yepanyama consonance iri pahurongwa hwe80%. Izvi zvinoreva kuti munhu wega wega anogona kunge aine ake ega hunhu, asi fizikisi yeruzha inopa mupiro wakakura kune tsananguro yekonsonanti.

Zvechokwadi, tsvakurudzo yesayenzi munharaunda iyi ichiri pakutanga. Uye sechimiro chenzwi, isu takatora yakapusa modhi yeakawanda harmonics, uye kuverenga kwekonsonanti kwakashandiswa zviri nyore - frequency, uye hatina kufunga nezvehunhu hwekuita kwehuropi mukugadzirisa chiratidzo chezwi. Asi chokwadi chekuti kunyangwe mukati mehurongwa hwekurerutsa kwakadaro hukama hwepamusoro-soro pakati pedzidziso uye kuedza hwakawanikwa hunokurudzira zvikuru uye hunomutsa kumwe kutsvakurudza.

Kushandiswa kwenzira yesainzi mumunda wekuwirirana kwemimhanzi hakugumiri pakuverenga kwekonzoni, kunopawo zvimwe zvinonakidza mhedzisiro.

Semuenzaniso, nerubatsiro rwenzira yesainzi, kuwirirana kwemimhanzi kunogona kufananidzirwa nemifananidzo, kuratidzwa. Tichataura pamusoro pekuita izvi nguva inotevera.

Munyori - Roman Oleinikov