Izinhlobo zokucushwa komculo

Sonke sikujwayele ukuthi kunamanothi ayi-12 ku-octave: okhiye abamhlophe abayi-7 nabamnyama aba-5. Futhi wonke umculo esiwuzwayo, kusukela ku-classical kuya ku-hard rock, wakhiwe yilawa manothi angu-12.

Ingabe kwakuhlala kunje? Ingabe umculo wawuzwakala kanje ngesikhathi sika-Bach, eNkathini Ephakathi noma e-Antiquity?

Umhlangano wokuhlukanisa

Amaqiniso amabili abalulekile:

• ukuqoshwa komsindo kokuqala emlandweni kwenziwa engxenyeni yesibili yekhulu lesi-XNUMX;
• kuze kube sekuqaleni kwekhulu lesi-XNUMX, isivinini esishesha kakhulu okwakungadluliswa ngaso ulwazi kwakuyijubane lehhashi.

Manje ake sisheshe siye phambili emakhulwini ambalwa eminyaka adlule.

Ake sithi u-abbot wesigodlo esithile (asimbize ngokuthi uDominic) weza nombono wokuthi kuyadingeka ukucula izingoma futhi wenze ama-canons yonke indawo futhi njalo ngendlela efanayo. Kodwa akakwazi ukubiza isigodlo sezindela esingumakhelwane futhi acule inothi lakhe elithi “A” kubo ukuze bacule eyabo. Khona-ke ubuzalwane bonke benza imfoloko yokulungisa, ekhiqiza inothi labo elithi "la". U-Dominic umema imfundamakhwela enesiphiwo somculo endaweni yakhe. Imfundamakhwela enemfoloko yokushuna ephaketheni elingemuva le-cassock yayo ihlezi phezu kwehhashi futhi izinsuku ezimbili nobusuku obubili, ilalele ukukhala komoya nokukhala kwezinselo, igibela esigodlweni sezindela esingumakhelwane ukuze ihlanganise umkhuba wabo womculo. Yiqiniso, imfoloko yokulungisa igobe kusukela ekugxumeni, futhi inikeze inothi elithi "la" ngokungalungile, futhi novice ngokwakhe, ngemva kohambo olude, akakhumbuli kahle ukuthi amanothi nezikhathi kwakuzwakala kanjalo endlini yezindela yakhe.

Ngenxa yalokho, ezindlini zezindela ezimbili ezingomakhelwane, izilungiselelo zezinsimbi zomculo namazwi okucula zihluka.

Uma sishesha ukudlulela ekhulwini lesi-XNUMX, sizothola ukuthi ngisho nokubhala kwakungasekho ngaleso sikhathi, okusho ukuthi, kwakungekho mibhalo enjalo ephepheni lapho noma ubani ayenganquma ngokusobala ukuthi yini azoyicula noma ayidlale. Ukuqanjwa ngaleso sikhathi kwakungekona okomqondo, ukunyakaza komculo kwakuboniswa cishe kuphela. Khona-ke, ngisho noma u-Dominic wethu oneshwa wathumela ikhwaya yonke esigodlweni sezindela esingumakhelwane ukuze kuxoxwe ngokushintshana kokuhlangenwe nakho komculo, kwakungeke kwenzeke ukuqopha lokhu okuhlangenwe nakho, futhi ngemva kwesikhathi esithile wonke ama-harmonies azoshintsha ohlangothini olulodwa noma kwenye.

Kungenzeka yini, ngokudideka okunjalo, ukukhuluma nganoma yiziphi izinhlaka zomculo ngaleso sikhathi? Okuxakayo, kungenzeka.

Uhlelo lwePythagorean

Lapho abantu beqala ukusebenzisa izinsimbi zomculo ezinezintambo zokuqala, bathola amaphethini athakazelisayo.

Uma uhlukanisa ubude bentambo ngesigamu, khona-ke umsindo owenzayo uhambisana kakhulu nomsindo wentambo yonke. Ngemva kwesikhathi eside, lesi sikhawu (inhlanganisela yemisindo emibili enjalo) sabizwa octave (Isithombe 1).

Abaningi babheka eyesihlanu njengenhlanganisela elandelayo evumelanayo. Kodwa ngokusobala kwakungenjalo emlandweni. Kulula kakhulu ukuthola enye inhlanganisela evumelanayo. Ukuze wenze lokhu, udinga nje ukuhlukanisa intambo hhayi ku-2, kodwa ibe izingxenye ezi-3 (Fig. 2).

Lesi silinganiso manje sesisaziwa ngokuthi i-duodecima  (isikhawu esiyinhlanganisela).

Manje asinayo nje imisindo emisha emibili - i-octave ne-duodecimal - manje sinezindlela ezimbili zokuthola imisindo emisha eyengeziwe. Ihlukanisa ngo-2 no-3.

Singathatha, isibonelo, umsindo we-duodecimal (okungukuthi 1/3 yeyunithi yezinhlamvu) futhi sihlukanise le ngxenye yeyunithi yezinhlamvu kakade. Uma sihlukanisa ngo-2 (sithola u-1/6 weyunithi yezinhlamvu yasekuqaleni), khona-ke kuzoba khona umsindo oyi-octave ephakeme kune-duodecimal. Uma sihlukanisa ngo-3, sithola umsindo oyi-duodecimal ukusuka ku-duodecimal.

Awukwazi ukuhlukanisa intambo kuphela, kodwa futhi uhambe ngendlela ehlukile. Uma ubude bentambo bukhuphuka izikhathi ezi-2, khona-ke sithola umsindo we-octave ephansi; uma ukhuphuka izikhathi ezi-3, khona-ke i-duodecima iphansi.

Ngendlela, uma umsindo we-duodecimal wehliswa nge-octave eyodwa, okungukuthi. ukwandisa ubude izikhathi ezingu-2 (sithola i-2/3 yobude bezintambo zangempela), khona-ke sizothola okwesihlanu okufanayo (Fig. 3).

Njengoba ubona, ingxenye yesihlanu iyisikhawu esithathwe ku-octave ne-duodecim.

Ngokuvamile, owokuqala owaqagela ukusebenzisa izinyathelo zokuhlukanisa ngo-2 nango-3 ukuze akhe amanothi ubizwa ngokuthi i-Pythagoras. Ukuthi ngabe kunjalo ngempela yini kunzima ukusho. Futhi uPythagoras ngokwakhe ungumuntu ocishe abe yinganekwane. Izincwadi zokuqala ezilotshiwe zencwadi yakhe esizaziyo zalotshwa eminyakeni engu-200 ngemva kokufa kwakhe. Yebo, futhi kungenzeka ukucabanga ukuthi abaculi ngaphambi kukaPythagoras basebenzisa lezi zimiso, abazange bazenzele (noma abazange babhale phansi). Lezi zimiso zitholakala emhlabeni wonke, zinqunywa imithetho yemvelo, futhi uma abaculi bangekhulu lokuqala belwela ukuzwana, babengenakuze bazidlule.

Ake sibone ukuthi hlobo luni lwamanothi esiwatholayo ngokuhamba ngababili noma ngabathathu.

Uma sihlukanisa (noma siphindaphinda) ubude beyunithi yezinhlamvu ngo-2, khona-ke sizohlala sithola inothi eliyi-octave ephakeme (noma ephansi). Amanothi ahluke nge-octave abizwa ngokufana, singasho ukuthi ngeke siwathole amanothi "amasha" ngale ndlela.

Isimo sihluke kakhulu ekuhlukaniseni ngo-3. Ake sithathe “yenza” njengenothi lokuqala futhi sibone ukuthi izinyathelo zamawele amathathu zisiholela kuphi.

Siyibeka ku-axis duodecim ye-duodecimo (umkhiwane 4).

Ungafunda kabanzi mayelana namagama esiLatini wamanothi lapha. Inkomba ethi π ezansi kwenothi isho ukuthi lawa angamanothi esikali sePythagorean, ngakho kuzoba lula ngathi ukuwahlukanisa namanothi ezinye izikali.

Njengoba ubona, kwakusohlelweni lwePythagorean lapho kwavela khona ama-prototypes awo wonke amanothi esiwasebenzisayo namuhla. Futhi hhayi umculo kuphela.

Uma sithatha amanothi ayi-5 aseduze “sokwenza” (kusuka kokuthi “fa” kuye ku-“la”), sithola lokho okubizwa ngokuthi i-pentatonic - uhlelo lwesikhawu, olusetshenziswa kabanzi kuze kube namuhla. Amanothi ayi-7 alandelayo (kusuka ku-“fa” kuye ku-“si”) azonikeza i-diatonic. Yilawa manothi manje asebekwe okhiye abamhlophe bepiyano.

Isimo esinokhiye omnyama siyinkimbinkimbi kancane. Manje kunokhiye owodwa kuphela phakathi kuka-“do” kanye “no-re”, futhi kuye ngezimo, kubizwa ngokuthi yi-C-sharp noma i-D-flat. Kuhlelo lwe-Pythagorean, i-C-sharp ne-D-flat kwakungamanothi amabili ahlukene futhi awakwazanga ukubekwa kukhiye ofanayo.

ukushuna kwemvelo

Yini eyenza abantu bashintshe uhlelo lwePythagorean lube yimvelo? Okuxakayo ukuthi, ingeyesithathu.

Ekushuneni kwePythagorean, ingxenye enkulu yesithathu (isibonelo, i-interval do-mi) ayihambisani. Emfanekisweni wesi-4, sibona ukuthi ukuze siphume kunothi elithi "yenza" siye kunothi elithi "mi", sidinga ukuthatha izinyathelo ezi-4 ze-duodecimal, sihlukanise ubude bezintambo izikhathi ezingu-4 3. Akumangalisi ukuthi imisindo emibili enjalo izoba nokuncane okufanayo, ungwaqa omncane, okungukuthi, ungwaqa.

Kodwa eduze kakhulu kwesithathu kwePythagorean kukhona okwesithathu kwemvelo, okuzwakala njengongwaqa kakhulu.

I-Pythagorean yesithathu

Okwesithathu okungokwemvelo

Abaculi bekhwaya, lapho lesi sikhawu sivela, ngokuziphendulela bathatha ungwaqa wesithathu wemvelo.

Ukuze uthole okwesithathu kwemvelo ocingweni, udinga ukuhlukanisa ubude bayo ngo-5, bese unciphisa umsindo ovelayo ngama-octave angu-2, ngakho ubude bentambo buzoba ngu-4/5 (Fig. 5).

Njengoba ubona, kwavela ukuhlukaniswa kwentambo ibe izingxenye ezingu-5, okwakungekho ohlelweni lwePythagorean. Yingakho ingxenye yesithathu yemvelo ingenakwenzeka ohlelweni lwePythagorean.

Ukushintsha okulula okunjalo kuholele ekubuyekezweni kwalo lonke uhlelo. Ngemva kwesesithathu, zonke izikhawu ngaphandle kwe-prima, imizuzwana, okwesine nokwesihlanu zishintshe umsindo wazo. Kwakhiwe zemvelo (ngezinye izikhathi ibizwa ngokuthi ihlanzekile) isakhiwo. Kuvele ukuthi kunongwaqa kunePythagorean, kodwa akuyona into kuphela leyo.

Into eyinhloko efikile emculweni ngokulungiswa kwemvelo i-tonality. Okukhulu nokuncane (kokubili njengama-chords nanjengokhiye) kwenzeke kuphela ekuhleleni kwemvelo. Okusho ukuthi, ngokusemthethweni, i-triad enkulu ingabuye iqoqwe kusukela kumanothi wesistimu yePythagorean, kodwa ngeke ibe nekhwalithi evumela ukuthi uhlele i-tonality ohlelweni lwePythagorean. Akukona nje ukuqondana ukuthi emculweni wasendulo indawo yokugcina impahla yayikhona monody. I-Monody ayiyona nje ingoma ye-monophonic, ngomqondo othile kungathiwa i-monophony, ephika ngisho nethuba lokuhambisana ne-harmonic.

Asikho isidingo sokuchaza incazelo enkulu nencane kubaculi.

Kwabangewona abaculi, ukuhlolwa okulandelayo kungaphakanyiswa. Bandakanya noma iyiphi isiqephu sakudala kusukela kokwakudala kwe-Viennese kuya maphakathi nekhulu lama-95. Ngamathuba angu-99,9% kuzoba kokukhulu noma okuncane. Vula umculo wesimanje odumile. Izoba kokukhulu noma okuncane okungenzeka kube ngu-XNUMX%.

Isikali esithambile

Kuye kwaba nemizamo eminingi yokulawula isimo sengqondo. Ngokuvamile, isimo sengqondo sinoma yikuphi ukuchezuka kwesikhawu kusuka kokuhlanzekile (kwemvelo noma kwePythagorean).

Inketho ephumelele kakhulu kwakuyi-equal temperament (RTS), lapho i-octave ivele ihlukaniswe ngezikhawu ezingu-12 "ezilinganayo". "Ukulingana" lapha kuqondwa kanje: inothi ngalinye elilandelayo linani elifanayo lezikhathi eziphakeme kunedlule. Futhi sesiphakamise inothi izikhathi eziyi-12, kufanele size ku-octave ehlanzekile.

Ngemva kokuxazulula inkinga enjalo, sithola inothi elingu-12 isimo sengqondo esilinganayo (noma i-RTS-12).

Kodwa kungani isimo sengqondo sasidingeka?

Iqiniso liwukuthi uma ekuhlelweni kwemvelo (okungukuthi, kwathathelwa indawo nomsindo olinganayo) ukushintsha ithonikhi - umsindo "esibala" kuwo ukuguquguquka kwezwi - isibonelo, kusukela kunothi "yenza" kuya kunothi " re”, khona-ke bonke ubudlelwano besikhashana buzophulwa. Lesi isithende sika-Achilles sakho konke ukulungisa okuhlanzekile, futhi indlela kuphela yokulungisa lokhu ukwenza zonke izikhawu zibe kancane, kodwa zilingane enye nenye. Khona-ke uma uthuthela kukhiye ohlukile, empeleni, akukho okuzoshintsha.

Uhlelo oluthambile lunezinye izinzuzo. Isibonelo, ingadlala umculo, kokubili okubhalwe ngesilinganiso semvelo, kanye nePythagorean.

Kumaminithi, okusobala kakhulu ukuthi zonke izikhawu ngaphandle kwe-octave kulolu hlelo zingamanga. Yiqiniso, indlebe yomuntu nayo ayilona ithuluzi elikahle. Uma amanga engabonakali, ngakho-ke ngeke sikwazi ukukubona. Kodwa intukuthelo efanayo yesithathu ikude kakhulu nemvelo.

Okwesithathu okungokwemvelo

Okwesithathu ulaka

Ingabe zikhona izindlela zokuphuma kulesi simo? Ingabe lolu hlelo lungathuthukiswa?

Yini okulandelayo?

Ake sibuyele kuDominic wethu kuqala. Singasho yini ukuthi esikhathini sangaphambi kokuqoshwa komsindo kwakunezingoma zomculo ezingaguquki?

Ukucabanga kwethu kubonisa ukuthi noma inothi elithi “la” lishintsha, khona-ke zonke izakhiwo (ukuhlukanisa intambo zibe izingxenye ezi-2, 3 nezi-5) zizohlala zinjalo. Lokhu kusho ukuthi amasistimu azovela afane. Vele, isigodlo esisodwa sezindela singasebenzisa okwesithathu kwePythagorean ekusebenzeni kwayo, kanti eyesibili - eyemvelo, kepha ngokunquma indlela yokwakhiwa kwayo, sizokwazi ukucacisa ngokusobala ukwakheka komculo, ngakho-ke amathuba ezigodlo ezihlukene azowenza. abe ngokomculo.

Manje yini elandelayo? Okuhlangenwe nakho kwekhulu le-12 kubonisa ukuthi ukusesha akuzange kume ku-RTS-12. Njengomthetho, ukwakhiwa kwama-tunings amasha kwenziwa ngokuhlukanisa i-octave hhayi ku-24, kodwa ngenani elikhulu lezingxenye, isibonelo, zibe ngu-36 noma XNUMX. Le ndlela iwumshini kakhulu futhi ayikhiqizi. Sibonile ukuthi ukwakhiwa kuqala endaweni yokuhlukaniswa okulula kwentambo, okungukuthi, ixhunywe nemithetho ye-physics, ngokudlidliza kwalolu chungechunge olufanayo. Kuphela ekupheleni kokwakhiwa, amanothi atholiwe athathelwa indawo athambile. Kodwa-ke, uma sithukuthela ngaphambi kokwakha okuthile ngezilinganiso ezilula, khona-ke umbuzo uphakama: yini esiyithukuthelisayo, sichezuka kumaphi amanothi?

Kodwa kukhona nezindaba ezinhle. Uma ukuze wakhe kabusha isitho kusuka kunothi elithi "yenza" kuya kunothi elithi "re", uzodinga ukusonta amakhulu amapayipi namashubhu, manje, ukuze wakhe kabusha i-synthesizer, mane ucindezele inkinobho eyodwa. Lokhu kusho ukuthi empeleni akudingeki ukuthi sidlale ngendlela engahambisani nomculo, singasebenzisa izilinganiso ezimsulwa futhi sizishintshe lapho kuphakama isidingo.

Kodwa kuthiwani uma sifuna ukudlala hhayi ngezinsimbi zomculo ze-elekthronikhi, kodwa ku-"analog"? Kungenzeka yini ukwakha izinhlelo ezintsha ze-harmonic, usebenzise esinye isimiso, esikhundleni sokuhlukaniswa kwemishini ye-octave?

Yebo, ungakwazi, kodwa lesi sihloko sikhulu kangangokuthi sizobuyela kuso ngesinye isikhathi.

Umbhali - Roman Oleinikov

Umbhali uzwakalisa ukubonga kwakhe kumqambi u-Ivan Soshinsky ngezinto zomsindo ezinikeziwe