Kodi consonance ndi chiyani?

M'mawu apitawa, tapeza momwe mawu amagwirira ntchito. Tiyeni tibwereze ndondomeko iyi:

SOUND = GROUND TONE + ZONSE ZONSE ZAMBIRI

Kuphatikiza apo, monga momwe anthu aku Japan amasirira maluwa a chitumbuwa, tidzasiliranso ma graph pafupipafupi - mawonekedwe a amplitude-frequency of sound (mkuyu 1):

Kumbukirani kuti nsonga yopingasa imayimira mamvekedwe (mafupipafupi a oscillation), ndipo nsonga yoyimirira imayimira mokweza (makulitsidwe).

Mzere uliwonse woyimirira ndi wa harmonic, woyamba wa harmonic nthawi zambiri umatchedwa wofunika. Ma Harmonics amakonzedwa motere: yachiwiri ya harmonic ndi 2 nthawi zambiri kuposa kamvekedwe kofunikira, yachitatu ndi itatu, yachinayi ndi inayi, ndi zina zotero.

Chifukwa chofupikitsa, m'malo mwa "mafupipafupi nth harmonic" tidzangonena kuti "nth harmonic", ndipo m'malo mwa "mafupipafupi ofunikira" - "mawu pafupipafupi".

Chifukwa chake, poyang'ana kuyankha pafupipafupi, sizingakhale zovuta kuti tiyankhe funso, consonance ndi chiyani.

Momwe mungawerengere mpaka infinity?

Consonance kwenikweni amatanthauza "kumveka kophatikizana", kulira kophatikizana. Kodi maphokoso awiri osiyana angamveke ngati chiyani?

Tiyeni tiwajambule pa tchati chomwecho pansi pa wina ndi mnzake (mkuyu 2):

Nayi yankho: ena mwa ma harmonics amatha kugwirizana pafupipafupi. Ndizomveka kuganiza kuti ma frequency ofananira, m'pamenenso mamvekedwe "odziwika" amakhala, ndipo, chifukwa chake, ma consonance amamvekanso pamawu a nthawi yoteroyo. Kunena zowona, ndikofunikira osati kuchuluka kwa ma harmonics ofananira, koma ndi gawo lotani la ma harmonics onse omwe amamveka, ndiye kuti, chiŵerengero cha chiwerengero chofananira ndi chiwerengero cha ma harmonics omveka.

Timapeza njira yosavuta kwambiri yowerengera consonance:

kumene N_gawo ndi chiwerengero cha ma harmonics ofanana,  N_wamba ndi chiwerengero cha ma harmonics omveka (chiwerengero cha maulendo osiyanasiyana omveka), ndi kuipa ndi consonance yathu yomwe tikufuna. Kuti mukhale olondola masamu, ndi bwino kutchula kuchuluka kwake muyeso wa ma frequency consonance.

Chabwino, nkhaniyi ndi yaing'ono: muyenera kuwerengera N_gawo и N_wamba, gawani wina ndi mzake, ndi kupeza zotsatira zomwe mukufuna.

Vuto lokhalo ndiloti chiwerengero chonse cha ma harmonics komanso ngakhale chiwerengero cha ma harmonics ofananira ndi opanda malire.

Kodi chimachitika ndi chiyani ngati tigawa zopanda malire ndi zopanda malire?

Tiyeni tisinthe sikelo ya tchati yapitayi, "chokani" pamenepo (mkuyu 3)

Timawona kuti ma harmonics ofananira amapezeka mobwerezabwereza. Chithunzicho chikubwerezedwa (mkuyu 4).

Kubwerezabwerezaku kudzatithandiza.

Ndikokwanira kuti tiwerengere chiŵerengero (1) mu imodzi mwa timakona timene timadontho (mwachitsanzo, mu yoyamba), ndiye, chifukwa cha kubwerezabwereza ndi pamzere wonse, chiŵerengerochi chidzakhala chofanana.

Kuti zikhale zosavuta, kusinthasintha kwa kamvekedwe ka mawu oyamba (otsika) kumaonedwa kuti ndi ofanana ndi mgwirizano, ndipo mafupipafupi a kamvekedwe ka mawu achiwiri adzalembedwa ngati gawo losasinthika.  .

Tiyeni tiwone m'makolo kuti m'magulu a nyimbo, monga lamulo, amamveka ndendende zomwe zimagwiritsidwa ntchito, chiŵerengero cha maulendo omwe amafotokozedwa ndi kachigawo kakang'ono.  . Mwachitsanzo, nthawi yachisanu ndi chiŵerengero  , koloko -  , triton -   etc.

Tiyeni tiwerengere chiŵerengero (1) mkati mwa rectangle yoyamba (mkuyu 4).

Ndikosavuta kuwerengera kuchuluka kwa ma harmonics ofanana. Mwamwayi, pali awiri a iwo, imodzi ndi ya phokoso lapansi, yachiwiri - pamwamba, mu mkuyu 4 iwo amalembedwa mofiira. Koma ma harmonics onsewa amamveka pafupipafupi, motsatana, ngati tiwerengera kuchuluka kwa ma frequency ofananira, ndiye kuti padzakhala ma frequency amodzi okha.

Kodi ma frequency amawu ndi otani?

Tiyeni tikangane chonchi.

Ma harmonics onse a mawu otsika amapangidwa ndi manambala athunthu (1, 2, 3, etc.). Mwamsanga pamene harmonic iliyonse ya phokoso lapamwamba ndi chiwerengero chokwanira, chidzagwirizana ndi chimodzi mwa ma harmonics a pansi. Ma harmonics onse a phokoso lapamwamba ndi ma multiples a toni yofunikira , kotero ma frequency n-th harmonic idzakhala yofanana ndi:

ndiko kuti, idzakhala chiwerengero chonse (kuyambira m ndi chiwerengero). Izi zikutanthauza kuti phokoso lapamwamba mu rectangle limakhala ndi ma harmonics kuchokera ku choyamba (mawu ofunikira) mpaka n-o, choncho, phokoso n mafupipafupi.

Popeza ma harmonic onse a mawu otsika amakhala mu manambala ophatikizika, ndipo molingana ndi (3), mwangozi woyamba umachitika pafupipafupi. m, zimakhala kuti phokoso lapansi mkati mwa rectangle lidzapereka m ma frequency amawu.

Ndikoyenera kudziwa kuti coinciding pafupipafupi m tinawerenganso kawiri: tikamawerengera ma frequency a liwu lapamwamba komanso tikamawerengera mafunde apansi. Koma kwenikweni, ma frequency ndi amodzi, ndipo yankho lolondola, tidzafunika kuchotsa pafupipafupi "owonjezera".

Mafuridwe onse amawu amkati mwa rectangle adzakhala:

Kuyika (2) ndi (4) mu formula (1), timapeza mawu osavuta powerengera consonance:

Kuti mutsindike ma consonance omwe tidawerengera, mutha kuwonetsa mawu awa m'mabulaketi kuipa:

Pogwiritsa ntchito njira yosavuta yotere, mutha kuwerengera consonance ya nthawi iliyonse.

Ndipo tsopano tiyeni tikambirane zina katundu wa pafupipafupi consonance ndi zitsanzo zake mawerengedwe.

Katundu ndi zitsanzo

Choyamba, tiyeni tiwerenge ma consonances a magawo osavuta kwambiri ndikuwonetsetsa kuti chilinganizo (6) "chimagwira ntchito".

Ndi nthawi iti yomwe ili yosavuta?

Ndithudi prima. Zolemba ziwiri zimamveka mogwirizana. Pa tchati zidzawoneka motere:

Tikuwona kuti ma frequency onse amawu amagwirizana. Chifukwa chake, consonance iyenera kukhala yofanana ndi:

Tsopano tiyeni tisinthe chiŵerengero cha mgwirizano  mu formula (6), timapeza:

Kuwerengera kumagwirizana ndi yankho la "intuitive", lomwe liyenera kuyembekezera.

Tiyeni titenge chitsanzo china chomwe yankho lachidziwitso liri lodziwikiratu - octave.

Mu octave, phokoso lakumtunda ndilokwera 2 kuposa lapansi (malinga ndi kamvekedwe ka mawu ofunikira), motero, pa graph idzawoneka motere:

Zitha kuwoneka kuchokera pa graph kuti sekondi iliyonse ya harmonic imagwirizana, ndipo yankho lachidziwitso ndilo: consonance ndi 50%.

Tiyeni tiwerenge motsatira ndondomeko (6):

Ndipo kachiwiri, mtengo wowerengeka ndi wofanana ndi "mwachidziwitso".

Ngati titenga cholembacho ngati phokoso lapansi ku ndi kukonza mtengo wa consonance pazigawo zonse za octave pa graph (nthawi zosavuta), timapeza chithunzi chotsatira:

Miyezo yapamwamba kwambiri ya consonance ili mu octave, yachisanu ndi yachinayi. Iwo m'mbiri yakale ankanena za "zangwiro" consonances. Zing'onozing'ono ndi zazikulu zitatu, ndipo zazing'ono ndi zazikulu zisanu ndi chimodzi ndizotsika pang'ono, izi zimatengedwa ngati consonances "zopanda ungwiro". Zina zonsezo zimakhala ndi digiri yotsika ya consonance, mwachizolowezi zimakhala za gulu la dissonances.

Tsopano tikulemba zinthu zina za muyeso wa frequency consonance, zomwe zimachokera ku formula yowerengera:

1. The zovuta chiŵerengero  (nambala zambiri m и n), kukhala ndi makonsonanti ocheperako.

И m и n mu formula (6) ali mu denominator, choncho, pamene manambalawa akuwonjezeka, muyeso wa consonance umachepetsa.

2. Kukwera kwa consonance kwa nthawiyo ndi kofanana ndi kutsika kwa consonance kwa nthawiyo.

Kuti tipeze nthawi yotsika m'malo mwa nthawi yokwera, tifunika mu chiŵerengero   sinthanani m и n. Koma mu chilinganizo (6), palibe chomwe chidzasinthe kuchokera m'malo mwake.

3. Muyezo wa ma frequency consonance a interval sikutengera mawu omwe tikupangira.

Ngati musintha manotsi onse nthawi imodzi mmwamba kapena pansi (mwachitsanzo, pangani chachisanu osati pacholemba ku, koma kuchokera pacholemba ре), ndiye chiŵerengero  pakati pa zolemba sizidzasintha, ndipo chifukwa chake, muyeso wa consonance pafupipafupi udzakhalabe womwewo.

Titha kupereka zina za consonance, koma pakadali pano tingodziletsa tokha ku izi.

Physics ndi mawu

Chithunzi 7 chimatipatsa lingaliro la momwe consonance imagwirira ntchito. Koma kodi umu ndi momwe timadziwiradi consonance ya intervals? Kodi pali anthu omwe sakonda ma consonances angwiro, koma mawu osagwirizana kwambiri amawoneka osangalatsa?

Inde, anthu oterowo alipodi. Ndipo kuti tifotokoze izi, mfundo ziwiri ziyenera kusiyanitsa: kugwirizana kwa thupi и kuzindikira consonance.

Chilichonse chimene takambirana m’nkhani ino n’chokhudza mmene thupi limayendera. Kuti muwerengere, muyenera kudziwa momwe phokoso limagwirira ntchito, komanso momwe ma vibrations osiyanasiyana amawonjezera. Consonance yakuthupi imapereka zofunikira pakuzindikirika kwa consonance, koma sizimatsimikizira 100%.

Consonance yodziwika imatsimikiziridwa mophweka. Munthu amafunsidwa ngati amakonda consonance iyi. Ngati inde, ndiye kuti kwa iye kuli consonance; ngati ayi, ndiye dissonance. Ngati apatsidwa magawo awiri kuti afananize, ndiye kuti tinganene kuti imodzi mwa izo idzawoneka kwa munthuyo panthawiyo, ina yocheperapo.

Kodi consonance yodziwika ingawerengedwe? Ngakhale titaganiza kuti n'zotheka, ndiye kuti kuwerengera kumeneku kudzakhala kovuta kwambiri, kudzaphatikizapo zopanda malire - zopanda malire za munthu: zomwe zinamuchitikira, zizindikiro zakumva ndi luso la ubongo. Kupanda malire kumeneku sikophweka kwambiri kuthana nako.

Komabe, kafukufuku m’derali akupitirirabe. Makamaka, wolemba nyimbo Ivan Soshinsky, amene mokoma amapereka zipangizo zomvetsera pa zolemba izi, wapanga pulogalamu imene mukhoza kumanga munthu mapu a maganizo a consonances kwa munthu aliyense. Tsamba la mu-theory.info likupangidwa pano, pomwe aliyense angayesedwe ndikupeza zomwe amamva.

Ndipo komabe, ngati pali consonance yodziwika, ndipo imasiyana ndi thupi, pali phindu lotani powerengera chomaliza? Tikhoza kukonzanso funsoli m'njira yomangirira: Kodi mfundo ziwirizi zikugwirizana bwanji?

Kafukufuku akuwonetsa kuti kulumikizana pakati pa ma consonance odziwika bwino ndi ma consonance akuthupi ali pa dongosolo la 80%. Izi zikutanthauza kuti munthu aliyense akhoza kukhala ndi mawonekedwe akeake, koma fizikiki yamawu imathandizira kwambiri kutanthauzira kwa consonance.

Inde, kafukufuku wa sayansi m’derali akadali pachiyambi. Ndipo monga phokoso dongosolo, tinatenga chitsanzo chosavuta cha ma harmonics angapo, ndipo mawerengedwe a consonance anagwiritsidwa ntchito mosavuta - pafupipafupi, ndipo sanaganizire za zochitika za ubongo pokonza chizindikiro cha phokoso. Koma mfundo yakuti ngakhale m’kati mwa kufeŵetsa koteroko kugwirizana kwakukulu pakati pa chiphunzitso ndi kuyesa kwapezeka n’kolimbikitsa kwambiri ndipo kumapangitsa kufufuza kwina.

Kugwiritsiridwa ntchito kwa njira ya sayansi mu gawo la mgwirizano wa nyimbo sikumangokhalira kuwerengera kwa consonance, kumaperekanso zotsatira zosangalatsa.

Mwachitsanzo, mothandizidwa ndi njira ya sayansi, mgwirizano wa nyimbo ukhoza kuwonetsedwa mojambula, kuwonetsera. Tidzakambirana za momwe tingachitire izi nthawi ina.

Wolemba - Roman Oleinikov