Menene consonance?

A cikin bayanin da ya gabata, mun gano yadda sauti ke aiki. Bari mu maimaita wannan dabara:

SAUTI = RUWAN KASA + DUK ABINDA YA WUCE

Bugu da ƙari, yayin da Jafanawa ke sha'awar furen ceri, za mu kuma yaba da jadawali na amsa mitar - sifa mai girman girman sauti (Hoto 1):

Ka tuna cewa axis a kwance yana wakiltar farar (mitar oscillation), kuma axis na tsaye yana wakiltar ƙara (amplitude).

Kowane layi na tsaye mai jituwa ne, jigon farko yawanci ana kiransa asali. An tsara masu jituwa kamar haka: na biyu masu jituwa sau 2 ya fi sautin asali sau XNUMX, na uku shine uku, na huɗu shine hudu, da sauransu.

Don taƙaitawa, maimakon “yawanci nth harmonic" za mu ce kawai "nth masu jituwa”, kuma maimakon “ainihin mitar” – “mitar sauti”.

Don haka, duban mitar amsawa, ba zai yi mana wahala ba mu amsa tambayar, menene ra'ayin.

Yadda za a ƙidaya zuwa rashin iyaka?

Consonance a zahiri yana nufin "sautin haɗin gwiwa", sautin haɗin gwiwa. Menene sautuna daban-daban guda biyu za su yi kama da juna?

Bari mu zana su akan ginshiƙi ɗaya ƙarƙashin juna (Fig. 2):

Anan ga amsar: wasu daga cikin masu jituwa na iya yin daidai da mitar. Yana da ma'ana a ɗauka cewa yawancin mitoci masu daidaitawa, yawancin sautunan "na kowa" suna da, sabili da haka, ƙarin saɓani a cikin sautin wannan tazara. Don zama cikakke daidai, yana da mahimmanci ba kawai adadin madaidaicin madaidaicin ba, amma menene rabon duk matches masu sautin sauti, wato, adadin adadin matching zuwa jimlar adadin sautin harmonics.

Muna samun tsari mafi sauƙi don ƙididdige ma'anar magana:

inda N_zuw shine adadin madaidaicin masu jituwa,  N_{na kowa} shine jimlar adadin sauti masu jituwa (yawan mitocin sauti daban-daban), da fursunoni kuma shine abin da muke so. Don zama daidai a lissafin, yana da kyau a kira adadin ma'auni na mitar magana.

To, al'amarin karami ne: kuna buƙatar ƙididdigewa N_zuw и N_{na kowa}, raba ɗaya da ɗayan, kuma a sami sakamakon da ake so.

Matsalar kawai ita ce duka jimlar adadin masu jituwa har ma da adadin madaidaicin jituwa ba shi da iyaka.

Menene zai faru idan muka raba rashin iyaka ta rashin iyaka?

Bari mu canza ma'auni na ginshiƙi na baya, "tashi" daga gare ta (Fig. 3)

Mun ga cewa jituwa masu jituwa suna faruwa akai-akai. Ana maimaita hoton (Fig. 4).

Wannan maimaitawa zai taimake mu.

Ya ishe mu mu lissafta ma'auni (1) a cikin ɗaya daga cikin dige-gefe rectangles (misali, a cikin na farko), sa'an nan, saboda maimaitawa kuma a kan dukan layi, wannan rabo zai kasance iri ɗaya.

Don sauƙi, za a yi la'akari da mitar ainihin sautin sauti na farko (ƙananan) daidai da haɗin kai, kuma za a rubuta yawan sautin asali na sauti na biyu a matsayin juzu'i mara lahani.  .

Bari mu lura a cikin ƙididdiga cewa a cikin tsarin kiɗa, a matsayin mai mulkin, ana amfani da sauti daidai, rabon mitoci wanda aka bayyana ta wasu juzu'i.  . Misali, tazarar na biyar shine rabo  , kwata –  , Triton -   da dai sauransu.

Bari mu lissafta rabo (1) a cikin rectangular farko (Fig. 4).

Yana da sauƙi a ƙidaya adadin masu jituwa. A bisa ka'ida, akwai biyu daga cikinsu, ɗaya na cikin ƙananan sauti, na biyu - zuwa babba, a cikin siffa 4 an yi musu alama a ja. Amma duka waɗannan jigogi suna yin sauti a mitar guda ɗaya, bi da bi, idan muka ƙidaya adadin mitoci masu daidaitawa, to za a sami irin wannan mitar guda ɗaya kawai.

Menene jimillar adadin mitocin sauti?

Mu yi gardama kamar haka.

Dukkan jituwa na ƙananan sauti an tsara su a cikin lambobi duka (1, 2, 3, da sauransu). Da zarar duk wani jituwa na saman sautin ya zama lamba, zai zo daidai da ɗaya daga cikin jituwa na ƙasa. Duk masu jituwa na sautin na sama nau'i ne na ainihin sautin , don haka mita n-th harmonic zai kasance daidai da:

wato, zai zama lamba (tun m lamba ce). Wannan yana nufin cewa sautin na sama a cikin rectangle yana da jituwa tun daga farkon (sautin asali) zuwa n- Oh, saboda haka, sauti n mitoci.

Tunda duk masu jituwa na ƙananan sauti suna cikin lambobi, kuma bisa ga (3), daidaituwa ta farko tana faruwa a mitar. m, Sai dai itace cewa ƙananan sauti a cikin rectangle zai ba da m mitoci masu sauti.

Ya kamata a lura cewa mitar daidaitawa m mun sake ƙidaya sau biyu: lokacin da muka ƙidaya mitocin sautin sama da lokacin da muka ƙidaya mitocin ƙananan sautin. Amma a zahiri, mitar ɗaya ce, kuma don amsa daidai, za mu buƙaci mu rage mitar “karin” ɗaya.

Jimlar duk mitocin sauti a cikin rectangle za su kasance:

Madadin (2) da (4) zuwa dabara (1), muna samun magana mai sauƙi don ƙididdige ra'ayin:

Don jaddada ma'anar waɗanne sautunan da muka ƙididdige su, zaku iya nuna waɗannan sautuna a maƙallan fursunoni:

Amfani da irin wannan tsari mai sauƙi, zaku iya ƙididdige ma'anar kowane tazara.

Kuma yanzu bari mu yi la'akari da wasu kaddarorin na mitar consonance da misalan lissafinsa.

Kayayyaki da misalai

Da farko, bari mu lissafta baƙaƙe don mafi sauƙi tazara kuma mu tabbata cewa dabara (6) tana “aiki”.

Wane tazara ne mafi sauƙi?

Tabbas prima. Bayanan kula guda biyu suna sauti tare. A kan ginshiƙi zai yi kama da haka:

Mun ga cewa kwata-kwata duk mitocin sauti sun zo daidai. Don haka, dole ne maƙasudin ya zama daidai da:

Yanzu bari mu musanya rabo ga unison  a cikin dabara (6), muna samun:

Lissafin ya zo daidai da amsar "da hankali", wanda ake tsammani.

Bari mu dauki wani misali a cikinsa wanda amsar da ta dace ta kasance a bayyane - octave.

A cikin octave, sautin na sama ya ninka sau 2 sama da na ƙasa (bisa ga mitar sautin asali), bi da bi, akan jadawali zai yi kama da haka:

Ana iya gani daga jadawali cewa kowane jitu na biyu ya zo daidai, kuma amsar da ta dace ita ce: ma'anar ita ce 50%.

Mu lissafta shi da dabara (6):

Kuma kuma, ƙimar ƙididdigewa tana daidai da " ilhama ".

Idan muka ɗauki bayanin kula azaman ƙaramar sauti to kuma yi ƙirƙira ƙimar baƙar magana ga duk tazara tsakanin octave akan jadawali (sauki tazara), muna samun hoto mai zuwa:

Mafi girman ma'auni na ma'auni shine a cikin octave, na biyar da na huɗu. A tarihi sun yi nuni ga “cikakkun” baƙaƙe. Ƙanana da manyan sulusi, da ƙanana da babba na shida sun ɗan yi ƙasa kaɗan, waɗannan tazarar ana ɗaukarsu “marasa cikawa” baƙaƙe. Sauran tazara suna da ƙaramin ma'auni na yarda, bisa ga al'ada suna cikin ƙungiyar dissonances.

Yanzu mun lissafta wasu kaddarorin ma'aunin ma'aunin mitar, waɗanda suka fito daga dabarar lissafinsa:

1. Mafi hadaddun rabo  (yawan lambar m и n), ƙarancin tazara.

И m и n a cikin dabara (6) suna cikin ma'auni, don haka, yayin da waɗannan lambobin ke ƙaruwa, ma'aunin ma'aunin magana yana raguwa.

2. Haɗin sama na tazara daidai yake da madaidaicin ƙasa na tazara.

Don samun tazarar ƙasa maimakon tazarar sama, muna buƙatar a cikin rabo   canza m и n. Amma a cikin dabara (6), babu shakka babu abin da zai canza daga irin wannan maye.

3. Ma'auni na mitar haɗin kai na tazara bai dogara da wane bayanin da muke gina ta ba.

Idan kun canza bayanin kula guda biyu ta tazara ɗaya sama ko ƙasa (misali, gina na biyar ba daga bayanin kula ba. to, amma daga bayanin kula zo), sai kuma rabo  tsakanin bayanin kula ba zai canza ba, saboda haka, ma'aunin ma'aunin ma'aunin magana zai kasance iri ɗaya.

Za mu iya ba da wasu kaddarorin masu ba da izini, amma a yanzu za mu taƙaita kanmu ga waɗannan.

Physics da lyrics

Hoto na 7 yana ba mu ra'ayi na yadda consonance ke aiki. Amma shin haka ne da gaske muke fahimtar ma'anar tazara? Shin akwai mutanen da ba sa son cikakkiyar ma'ana, amma mafi ƙarancin jituwa suna da daɗi?

Haka ne, irin waɗannan mutane tabbas sun wanzu. Kuma don bayyana wannan, ya kamata a bambanta ra'ayoyi guda biyu: jiki yarda и fahimta consonance.

Duk abin da muka tattauna a wannan talifin yana da alaƙa da jin daɗin jiki. Don ƙididdige shi, kuna buƙatar sanin yadda sautin yake aiki, da yadda jijjiga daban-daban ke ƙara. Haɗin kai na jiki yana ba da abubuwan da ake buƙata don fahimtar yarda, amma baya ƙayyade shi 100%.

Ƙaddamar da fahimta an ƙaddara shi da sauƙi. An tambayi mutum ko yana son wannan baƙon? Idan haka ne, to, a gare shi yana da lamuni. idan ba haka ba, rashin fahimta ne. Idan aka ba shi tazara guda biyu don kwatantawa, to muna iya cewa ɗaya daga cikinsu zai yi kama da mutum a halin yanzu ya fi baƙar magana, ɗayan kuma ya ragu.

Za a iya ƙididdige baƙar magana? Ko da mun ɗauka cewa yana yiwuwa, to, wannan lissafin zai zama mai rikitarwa mai rikitarwa, zai haɗa da ƙarin rashin iyaka - rashin iyaka na mutum: kwarewarsa, halayen ji da kuma iyawar kwakwalwa. Wannan rashin iyaka ba shi da sauƙin magancewa.

Koyaya, bincike a wannan yanki yana ci gaba. Musamman ma, mawaki Ivan Soshinsky, wanda da kirki samar da audio kayan ga wadannan bayanin kula, ya ɓullo da wani shirin da za ka iya gina wani mutum taswirar fahimtar consonances ga kowane mutum. A halin yanzu ana haɓaka shafin mu-theory.info, inda kowa zai iya gwadawa kuma a gano fasalin jinsa.

Kuma duk da haka, idan akwai fahimtar fahimtar juna, kuma ya bambanta da na zahiri, menene ma'anar lissafin karshen? Za mu iya sake fasalin wannan tambaya ta hanya mai ma'ana: ta yaya waɗannan ra'ayoyin biyu suka danganci?

Nazarin ya nuna cewa alaƙar da ke tsakanin matsakaicin fahimtar magana da jin daɗin jiki yana kan tsari na 80%. Wannan yana nufin cewa kowane mutum yana iya samun halayensa na ɗaiɗaikun, amma ilimin lissafi na sauti yana ba da babbar gudummawa ga ma'anar magana.

Tabbas, binciken kimiyya a wannan fanni yana nan a farkon farkonsa. Kuma a matsayin tsarin sauti, mun ɗauki wani tsari mai sauƙi mai sauƙi na mahara masu jituwa, kuma an yi amfani da lissafin consonance mafi sauƙi - mita, kuma ba a la'akari da abubuwan da ke cikin aikin kwakwalwa wajen sarrafa siginar sauti ba. Amma gaskiyar cewa ko da a cikin tsarin irin waɗannan sauƙaƙan an sami babban matsayi na alaƙa tsakanin ka'idar da gwaji yana da kwarin gwiwa sosai kuma yana ƙarfafa ƙarin bincike.

Aiwatar da hanyar kimiyya a fagen jituwa na kiɗa ba'a iyakance ga ƙididdigewa ba, har ila yau yana haifar da sakamako mai ban sha'awa.

Misali, tare da taimakon hanyar kimiyya, ana iya siffanta jituwar kiɗan ta hoto, a gani. Za mu yi magana game da yadda za mu yi hakan a gaba.

Mawallafi - Roman Oleinikov