Mhando dzemimhanzi tunings

Isu tese takajaira kuti kune gumi nemaviri manotsi mune octave: 12 makiyi machena uye mashanu matema. Uye mimhanzi yose yatinonzwa, kubva ku classical kusvika ku hard rock, inoumbwa ne7 manotsi aya.

Zvakagara zvakadaro here? Mimhanzi yainzwika seizvi here panguva yaBach, kuMiddle Ages kana muAntiquity?

Classification gungano

Zvinhu zviviri zvakakosha:

• ekutanga marekodhi munhoroondo akaitwa muhafu yechipiri yezana ramakore rechiXNUMX;
• kusvika pakutanga kwezana ramakore rechiXNUMX, kukurumidza kukurumidza uko ruzivo rwaigona kufambiswa kwaive kumhanya kwebhiza.

Zvino ngatikurumidzei mberi mazana mashoma apfuura.

Ngatitii abbot yeimwe monastery (ngatimutii Dominic) akauya nepfungwa yekuti zvakakosha kuimba nziyo uye kuita canons kwese uye nguva dzose nenzira imwechete. Asi haakwanise kudaidza imba yemamongi yevavakidzani oimba chinyorwa chake "A" kwavari kuti vatarise yavo. Ipapo hukama hwese vanogadzira forogo yekugadzira, iyo inoburitsa chaizvo chinyorwa chavo "la". Dominic anokoka mutambi ane chipo chemumhanzi panzvimbo yake. Mutsvaki ane forogo yekugezera muhomwe yekuseri kwekasisoki yake anogara pabhiza uye kwemazuva maviri neusiku huviri, achiteerera kurira kwemhepo uye kurira kwemahwanda, anomhanya achienda kune imwe imba yemamongi yakavakidzana kuti abatanidze tsika yavo yekuimba. Ehezve, forogo yekugadzira yakakotama kubva pakusvetuka, uye inopa iyo noti "la" zvisizvo, uye novice pachake, mushure merwendo rurefu, haayeuke zvakanaka kana zvinyorwa nepakati zvainzwika seizvi mumusha wake wemamongi.

Somugumisiro, mumamongi maviri akavakidzana, zvigadziro zvezviridzwa zvemimhanzi uye manzwi ekuimba anoshanduka kuva akasiyana.

Kana tikakasira kumberi kusvika kuzana ramakore rechiXNUMX, tinozoona kuti kunyangwe notation yakanga isipo panguva iyoyo, ndiko kuti, pakanga pasina zvinyorwa zvakadaro pabepa izvo chero munhu aigona kuziva zvekuimba kana kutamba. Notion munguva iyoyo yakanga isiri yepfungwa, kufamba kwerwiyo kwairatidzwa chete zvishoma. Zvino, kunyangwe kana Dominic wedu asina rombo akatumira kwaya yese kune yakavakidzana yemamongi kune yekusiyirana yekutsinhana kwechiitiko chemumhanzi, hazvingaite kurekodha chiitiko ichi, uye mushure menguva yakati kuwirirana kwese kwaizochinja mune imwe nzira kana imwe.

Zvinoita here, nekuvhiringidzika kwakadaro, kutaura nezve chero zvimiro zvemimhanzi panguva iyoyo? Oddly zvakakwana, zvinogoneka.

Pythagorean system

Vanhu pavakatanga kushandisa zviridzwa zvine tambo zvokutanga, vakawana mapatani anonakidza.

Kana iwe ukakamura kureba kwetambo nepakati, ipapo ruzha rwainoita rwunonyatsoenderana nekunzwika kwetambo yese. Pave paya, nguva iyi (kusanganiswa kwemanzwi maviri akadai) yakadanwa pasi pasi (Mufananidzo 1).

Vazhinji vanorangarira yechishanu kuva musanganiswa unotevera unowirirana. Asi sezviri pachena izvi zvakanga zvisina kudaro munhau. Zviri nyore kuwana imwe inowirirana musanganiswa. Kuti uite izvi, iwe unongoda kuparadzanisa tambo kwete mu 2, asi muzvikamu zvitatu (Fig. 3).

Reshiyo iyi yava kuzivikanwa kwatiri se duodecima  (composite interval).

Ikozvino hatingori neruzha ruviri rutsva - octave uye duodecimal - ikozvino tave nenzira mbiri dzekuwana mamwe manzwi matsva. Inopatsanurwa ne2 ne3.

Tinogona kutora, semuenzaniso, duodecimal ruzha (kureva 1/3 yetambo) topatsanura chikamu ichi chetambo kare. Kana tikakamura na 2 (tinowana 1/6 yetambo yepakutanga), ipapo pachava neruzha rwunoita octave yakakwirira kudarika duodecimal. Kana tikakamura na3, tinowana ruzha rwuri duodecimal kubva kuduodecimal.

Iwe haugoni kungoparadzanisa tambo, asiwo enda kune imwe nzira. Kana kureba kwetambo kunowedzera ne2 nguva, zvino tinowana inzwi re octave pasi; kana ukawedzera nekatatu, ipapo duodecima yakaderera.

Nenzira, kana duodecimal inzwi rakaderedzwa neoctave imwe, kureva. kuwedzera urefu ne2 nguva (tinowana 2/3 yehupamhi hwetambo yepakutanga), ipapo tichawana imwe yechishanu (Fig. 3).

Sezvauri kuona, cheshanu inguva inotorwa kubva kune octave uye duodecim.

Kazhinji, wekutanga akafungidzira kushandisa nhanho dzekuparadzanisa na2 uye ne3 kuvaka manotsi anonzi Pythagoras. Kana zviri izvo chaizvoizvo zvakaoma kutaura. Uye Pythagoras pachake anenge munhu wengano. Nhoroondo dzepakutanga-tanga dzebasa rake dzatinoziva dzakanyorwa makore 200 afa. Hongu, uye zvinokwanisika kufungidzira kuti vaimbi vasati vashandisa Pythagoras mitemo iyi, havana kungozvigadzira (kana kuti havana kunyora) ivo. Mitemo iyi ndeyepasi rose, inorayirwa nemitemo yezvakasikwa, uye kana vaimbi vomumazana emakore apakuvamba vaivavarira kutsinhirana, vaisagona kuinzvenga.

Ngationei kuti rudzii rwezvinyorwa zvatinowana nekufamba tiri vaviri kana vatatu.

Kana tikagovanisa (kana kuwanda) kureba kwetambo na 2, saka tichagara tichiwana chinyorwa chinoti octave yakakwirira (kana yakaderera). Zvinyorwa zvinosiyana neoctave zvinonzi zvakafanana, tinogona kutaura kuti hatisi kuzowana "matsva" manotsi nenzira iyi.

Mamiriro ezvinhu akasiyana nekupatsanura na 3. Ngatitorei “ita” sechinyorwa chekutanga uye tione kuti nhanho dziri mumatatu matatu dzinotisvitsa kupi.

Isu tinoiisa paaxis duodecim ye duodecimo (fig. 4).

Iwe unogona kuverenga zvakawanda nezvechiLatin mazita ezvinyorwa pano. Indekisi π iri pazasi pechinyorwa inoreva kuti aya ndiwo manotsi echiyero chePythagorean, saka zvichava nyore kwatiri kuti tisiyanise kubva pane zvinyorwa zvezvimwe zviyero.

Sezvauri kuona, yaive muPythagorean system iyo prototypes yezvinyorwa zvese zvatinoshandisa nhasi zvakaonekwa. Uye kwete mimhanzi chete.

Kana tikatora zvinyorwa zvishanu zviri padhuze kuti “ita” (kubva “fa” kuenda “la”), tinowana anonzi pentatonic - iyo interval system, iyo inoshandiswa zvakanyanya kusvika nhasi. Manotsi manomwe anotevera (kubva “fa” kuenda “si”) achapa diatonic. Ndiwo manotsi aya atova pamakiyi machena epiyano.

Mamiriro ezvinhu ane makiyi madema akanyanya kuoma. Ikozvino pane kiyi imwe chete pakati pe "do" uye "re", uye zvichienderana nemamiriro ezvinhu, inonzi kana C-yakapinza kana D-flat. MuPythagorean system, C-yakapinza uye D-flat aive manotsi maviri akasiyana uye aisagona kuiswa pakiyi imwechete.

natural tuning

Chii chakaita kuti vanhu vachinje hurongwa hwePythagoras kune hwechisikigo? Zvinoshamisa kuti, chikamu chechitatu.

Mukugadzirisa kwePythagorean, iyo huru yechitatu (semuenzaniso, iyo nguva do-mi) inopesana. Mumufananidzo 4, tinoona kuti kuti tiwane kubva pachinyorwa "ita" kune chinyorwa "mi", tinoda kutora 4 duodecimal matanho, kuparadzanisa urefu hwetambo ne 4 3 nguva. Hazvishamisi kuti mitsindo miviri yakadaro ichange iine zvishoma zvakafanana, consonance duku, kureva, consonance.

Asi pedyo zvikuru nePythagorean yechitatu pane chetatu chechisikigo, iyo inonzwika zvakanyanya zvakanyanya.

Pythagorean wechitatu

Natural wechitatu

Vaimbi vekwaya, pakaonekwa nguva iyi, vakanyatsotora makonzonendi echitatu.

Kuti uwane chetatu chechisikigo pane tambo, unoda kuparadzanisa urefu hwayo ne5, uye wozodzikisa inzwi rinoguma ne 2 octaves, saka urefu hwetambo huchava 4/5 (Fig. 5).

Sezvaunogona kuona, kupatsanurwa kwetambo muzvikamu zvishanu kwakaonekwa, iyo yakanga isiri muPythagorean system. Ndicho chikonzero chetatu chetatu chisingagoneki muPythagorean system.

Kutsiva kwakapfava kwakadaro kwakatungamira kudzokororo yehurongwa hwese. Kutevera chechitatu, nguva dzose kunze kweprima, masekondi, mana uye yechishanu zvakashandura inzwi razvo. Yakagadzirwa dzinongoitika (dzimwe nguva inonzi sheer) mamiriro. Zvakazove zvakanyanya kuenderana kupfuura Pythagorean, asi handizvo chete.

Chinhu chikuru chakauya kumimhanzi ine tuning yakasikwa ndeye tonality. Zvikuru uye zvidiki (zvese semakodhi uye sekiyi) zvakave zvinogoneka mukugadzirisa kwechisikigo. Ndiko kuti, zvakarongeka, katatu huru inogonawo kuunganidzwa kubva pane zvinyorwa zvePythagorean system, asi haizove nehuhu hunokubvumira kuronga tonality muPythagorean system. Hazvisi zvemasanga kuti mumimhanzi yekare ndiyo yainyanya kuchengeterwa zvinhu monody. Monody haisi kungoimba monophonic, neimwe nzira inogona kutaurwa kuti ndeye monophony, iyo inoramba kunyange mukana wekubatana kwekubatana.

Hapana chikonzero chekutsanangura zvinorehwa nemukuru nediki kuvaimbi.

Kune vasiri vaimbi, kuedza kunotevera kunogona kutaurwa. Sanganisira chero chidimbu chekare kubva kuViennese classics kusvika pakati pezana ramakore rechi95. Neine mukana we99,9% ichave iri muhombe kana mudiki. Batidza mimhanzi yemazuva ano ine mukurumbira. Ichave mune yakakura kana diki ine mukana weXNUMX%.

Chikero chakapfava

Pakave nekuedza kwakawanda kwehunhu. Kazhinji kutaura, hunhu ndiko kutsauka kwechinguva kubva kukachena (zvakasikwa kana Pythagorean).

Sarudzo yakanyanyobudirira yaive yakaenzana temperament (RTS), apo octave yakangopatsanurwa kuita gumi nembiri "yakaenzana" nguva. "Kuenzana" pano kunonzwisiswa sezvinotevera: chinyorwa chimwe nechimwe chinotevera inhamba yakafanana yenguva dzakakwirira kudarika yapfuura. Uye tasimudza chinyorwa ka12, isu tinofanirwa kusvika kune yakachena octave.

Tapedza dambudziko rakadaro, tinowana 12-noti equal temperament (kana RTS-12).

Asi nei kushatirwa kwaidiwa zvachose?

Icho chokwadi ndechekuti kana mukugadzirisa kwechisikigo (kureva, yakatsiviwa neyakafanana nehasha) kushandura tonic - ruzha kubva patino "verenga" tonality - semuenzaniso, kubva pachinyorwa "ita" kune chinyorwa " re", ipapo hukama hwese hwepakati huchatyorwa. Ichi ndicho chitsitsinho cheAchilles chezvose zvakachena tunings, uye nzira chete yekugadzirisa izvi ndeyokuita kuti nguva dzose dzive zvishoma, asi dzakaenzana kune imwe neimwe. Zvino kana iwe uchienda kune imwe kiyi, muchokwadi, hapana chinoshanduka.

The tempered system ine zvimwe zvakanakira. Semuenzaniso, inogona kuridza mimhanzi, zvese zvakanyorerwa chiyero chechisikigo, uye chePythagorean.

Pamaminuses, chinonyanya kuoneka ndechekuti nguva dzese kunze kweiyo octave mune ino system ndeyenhema. Chokwadika, nzeve yomunhu haisati iri chigadziko chakafanira. Kana manyepo ari microscopic, saka isu hatigone kuzviona. Asi chetatu chehasha chimwe chetecho chiri kure kwazvo nechakasikwa.

Natural wechitatu

Hasha yechitatu

Pane nzira dzekubuda nadzo mumamiriro aya here? Hurongwa uhu hunogona kuvandudzwa here?

Chii chakazoitika?

Ngatidzokere kuna Dominic wedu kutanga. Tinogona here kutaura kuti munguva iyo isati yarekodhwa ruzha pakanga paine mimwe mimhanzi yakagadziriswa tunings?

Mafungiro edu anoratidza kuti kunyangwe chinyorwa "la" chikachinja, zvese zvivakwa (kukamura tambo kuita 2, 3 uye 5 zvikamu) zvicharamba zvakafanana. Izvi zvinoreva kuti masisitimu anozove akafanana. Ehe, imwe monastery inogona kushandisa yechitatu yePythagorean mukuita kwayo, uye yechipiri - iyo yechisikigo, asi nekuona nzira yekuvakwa kwayo, isu tichakwanisa kunyatsoziva chimiro chemimhanzi, uye nekudaro mikana iyo mamongi akasiyana achaita. kuva nemimhanzi.

Saka chii chinotevera? Chiitiko chezana remakore rechi12 chinoratidza kuti kutsvaga hakuna kumira paRTS-12. Sezvo mutemo, kugadzirwa kwetunings kutsva kunoitwa nekukamura octave kwete mu24, asi muhuwandu hukuru hwezvikamu, semuenzaniso, mu36 kana XNUMX. Iyi nzira ndeye mechanistic uye haina zvibereko. Isu taona kuti zvivakwa zvinotanga munzvimbo yekupatsanurwa kuri nyore kwetambo, kureva kuti, zvakabatana nemitemo yefizikisi, nekudengenyeka kwetambo imwechete iyi. Chete pamagumo ezvivakwa, zvinyorwa zvakagamuchirwa zvakatsiviwa neakasununguka ane hasha. Kana, zvisinei, isu takatsamwa tisati tavaka chimwe chinhu muzvikamu zvakapfava, zvino mubvunzo unomuka: chii chatiri kushatisa, kubva pane zvinyorwa zvatinotsauka?

Asi kunewo mashoko akanaka. Kana kuti uvakezve nhengo kubva pachinyorwa "ita" kune chinyorwa "re", iwe unofanirwa kumonya mazana emapombi nemachubhu, ikozvino, kuvakazve synthesizer, ingodzvanya bhatani rimwe. Izvi zvinoreva kuti isu hatifanirwe kutamba mune zvishoma kunze kwehunyoro hunyoro, tinogona kushandisa mareshiyo akachena toashandura kechipiri chinodiwa chinomuka.

Asi zvakadini kana tichida kutamba kwete pazviridzwa zvemagetsi, asi pa "analog"? Zvinogoneka here kuvaka masisitimu matsva eHarmonic, shandisa imwe misimboti, pachinzvimbo cheiyo mechanistic division yeoctave?

Hongu, unogona, asi nyaya iyi yakakura zvekuti tichazodzokera kwairi imwe nguva.

Munyori - Roman Oleinikov

Munyori anoratidza kuonga kwake kumunyori Ivan Soshinsky nokuda kwezvinyorwa zvekuteerera zvakapiwa