Hom suab paj nruag tunings

Peb txhua tus tau siv los ntawm qhov tseeb tias muaj 12 daim ntawv hauv octave: 7 lub yuam sij dawb thiab 5 qhov dub. Thiab tag nrho cov suab paj nruag peb hnov, los ntawm classical mus rau lub pob zeb nyuaj, yog tsim los ntawm 12 cov ntawv no.

Puas yog ib txwm zoo li no? Puas yog suab paj nruag suab zoo li no thaum lub sijhawm Bach, hauv Nruab Nrab Hnub nyoog lossis hauv Antiquity?

Classification convention

Ob qhov tseeb tseem ceeb:

• thawj lub suab kaw hauv keeb kwm tau ua nyob rau hauv ib nrab ntawm lub xyoo pua XNUMX;
• mus txog rau thaum pib ntawm lub xyoo pua XNUMX, qhov ceev tshaj plaws uas cov ntaub ntawv tuaj yeem kis tau yog qhov ceev ntawm tus nees.

Tam sim no cia peb ceev ceev rau pem hauv ntej ob peb centuries dhau los.

Piv txwv li tus abbot ntawm ib lub tsev teev ntuj (cia hu nws Dominic) tuaj nrog lub tswv yim tias nws yog ib qho tsim nyog los hu nkauj thiab ua canons nyob txhua qhov chaw thiab ib txwm ua tib yam. Tab sis nws tsis tuaj yeem hu lub tuam tsev nyob sib ze thiab hu nws daim ntawv "A" rau lawv kom lawv kho lawv li. Tom qab ntawd tag nrho cov kwv tij lawv ua ib qho kev sib tw, uas rov tsim dua lawv cov ntawv "la". Dominic caw cov nkauj zoo nkauj tshaj plaws rau novice rau nws qhov chaw. Ib tug novice nrog ib tug tuning diav rawg nyob rau hauv lub hnab tshos tom qab ntawm nws lub cassock zaum ntawm ib tug nees thiab rau ob hnub thiab ob hmo, mloog lub xuav ntawm cua thiab lub claatter ntawm hooves, gallops mus rau ib tug nyob sib ze monastery los koom ua ke lawv cov suab paj nruas xyaum. Ntawm chav kawm, lub diav rawg khoov los ntawm kev dhia, thiab muab cov ntawv "la" tsis raug, thiab cov novice nws tus kheej, tom qab taug kev ntev, tsis nco qab zoo seb cov ntawv sau thiab lub sijhawm ua suab zoo li ntawd hauv nws lub tsev teev ntuj.

Yog li ntawd, nyob rau hauv ob lub tsev teev ntuj nyob sib ze, qhov chaw ntawm cov cuab yeej suab paj nruag thiab cov suab hu nkauj tau sib txawv.

Yog tias peb ceev nrooj mus rau lub xyoo pua XNUMX-XNUMXth, peb yuav pom tias txawm tias cov ntawv sau tsis muaj nyob rau ntawd, uas yog, tsis muaj cov ntawv sau zoo li no rau ntawm daim ntawv uas leej twg tuaj yeem txiav txim siab yam twg los hu nkauj lossis ua si. Cov ntawv sau nyob rau lub sijhawm ntawd tsis yog kev xav, qhov kev txav ntawm lub suab paj nruag tau qhia tsuas yog kwv yees li. Tom qab ntawd, txawm tias peb tsis muaj hmoo Dominic tau xa tag nrho pawg hu nkauj mus rau ib lub tsev teev ntuj nyob sib ze rau kev sib tham ntawm kev sib pauv suab paj nruag, nws yuav tsis muaj peev xwm sau qhov kev paub no, thiab tom qab qee lub sij hawm tag nrho cov kev sib haum xeeb yuav hloov mus rau ib qho lossis lwm qhov.

Puas muaj peev xwm, nrog qhov tsis meej pem, hais txog tej yam suab paj nruag hauv lub sijhawm ntawd? Oddly txaus, nws yog ua tau.

Pythagorean qhov system

Thaum tib neeg pib siv cov cuab yeej ntaus suab paj nruag thawj zaug, lawv pom cov qauv nthuav.

Yog tias koj faib qhov ntev ntawm txoj hlua hauv ib nrab, ces lub suab uas nws ua tau zoo sib haum xeeb nrog lub suab ntawm tag nrho cov hlua. Ntau tom qab, lub sijhawm no (kev sib xyaw ntawm ob lub suab zoo li no) tau hu ua octave (pib 1).

Ntau tus xav txog qhov thib tsib yog qhov kev sib haum xeeb tom ntej. Tab sis pom tau tias qhov no tsis yog qhov tshwm sim hauv keeb kwm. Nws yog qhov yooj yim dua los nrhiav lwm qhov kev sib haum xeeb. Txhawm rau ua qhov no, koj tsuas yog yuav tsum tau faib cov hlua tsis yog 2, tab sis ua 3 ntu (Daim duab 2).

Qhov piv txwv no tam sim no paub rau peb li duodecima ua  (composite interval).

Tam sim no peb tsis muaj ob lub suab tshiab - octave thiab duodecimal - tam sim no peb muaj ob txoj hauv kev kom tau txais ntau thiab ntau lub suab tshiab. Nws faib los ntawm 2 thiab 3.

Peb tuaj yeem coj, piv txwv li, ib lub suab duodecimal (piv txwv li 1/3 ntawm txoj hlua) thiab faib cov hlua ntawm cov hlua no. Yog tias peb faib nws los ntawm 2 (peb tau txais 1/6 ntawm thawj txoj hlua), ces yuav muaj lub suab uas yog octave siab tshaj qhov duodecimal. Yog tias peb faib los ntawm 3, peb tau txais lub suab uas yog duodecimal los ntawm duodecimal.

Koj tuaj yeem tsis tsuas yog faib cov hlua, tab sis kuj mus rau qhov sib txawv. Yog hais tias qhov ntev ntawm txoj hlua yog nce los ntawm 2 zaug, ces peb tau txais ib lub suab octave qis; Yog tias koj nce 3 zaug, ces duodecima qis dua.

Los ntawm txoj kev, yog tias lub suab duodecimal txo qis los ntawm ib qho octave, uas yog. nce qhov ntev los ntawm 2 zaug (peb tau 2/3 ntawm tus thawj hlua ntev), ces peb yuav tau txais tib yam thib tsib (Fig. 3).

Raws li koj tuaj yeem pom, qhov thib tsib yog lub sijhawm los ntawm octave thiab duodecim.

Feem ntau, thawj tus uas kwv yees siv cov kauj ruam ntawm kev faib los ntawm 2 thiab los ntawm 3 los tsim cov ntawv yog hu ua Pythagoras. Txawm hais tias qhov no yog qhov tseeb yog qhov nyuaj heev los hais. Thiab Pythagoras nws tus kheej yog ib tug yuav luag mythical neeg. Cov ntawv sau ntxov tshaj plaws ntawm nws txoj haujlwm uas peb paub tau sau 200 xyoo tom qab nws tuag. Yog lawm, thiab nws muaj peev xwm xav tias cov kws ntaus suab paj nruag ua ntej Pythagoras siv cov ntsiab cai no, tsuas yog tsis tsim (lossis tsis sau) lawv. Cov ntsiab cai no yog universal, dictated los ntawm cov kev cai ntawm xwm, thiab yog hais tias cov suab paj nruag ntawm lub centuries thaum ntxov strove rau kev sib haum xeeb, lawv yuav tsis dhau lawv.

Cia saib seb peb tau txais cov ntawv zoo li cas los ntawm kev taug kev hauv ob lossis peb zaug.

Yog tias peb faib (lossis muab faib) qhov ntev ntawm txoj hlua los ntawm 2, ces peb yuav tau txais ib daim ntawv uas yog octave siab dua (lossis qis dua). Cov ntawv sau uas txawv ntawm ib qho octave yog hu ua tib yam, peb tuaj yeem hais tias peb yuav tsis tau txais cov ntawv "tshiab" li no.

Qhov xwm txheej no txawv heev nrog kev faib los ntawm 3. Cia peb ua "ua" raws li daim ntawv thawj zaug thiab pom qhov twg cov kauj ruam hauv triplets coj peb.

Peb muab tso rau ntawm lub axis duodecim rau duodecimo (daim duab 4).

Koj tuaj yeem nyeem ntxiv txog cov npe Latin ntawm cov ntawv sau ntawm no. Qhov ntsuas π nyob rau hauv qab ntawm daim ntawv txhais tau hais tias cov no yog cov ntawv sau ntawm Pythagorean nplai, yog li nws yuav yooj yim dua rau peb kom paub qhov txawv ntawm cov ntawv ntawm lwm cov nplai.

Raws li koj tuaj yeem pom, nws yog nyob rau hauv Pythagorean system uas cov qauv ntawm tag nrho cov ntawv uas peb siv niaj hnub no tau tshwm sim. Thiab tsis yog suab paj nruag xwb.

Yog tias peb nqa 5 daim ntawv ze tshaj plaws rau "ua" (los ntawm "fa" mus rau "la"), peb tau txais qhov hu ua pentatonic txoj kev - lub caij nyoog nruab nrab, uas tau siv dav rau niaj hnub no. Cov ntawv 7 tom ntej (los ntawm "fa" mus rau "si") yuav muab diatonic. Nws yog cov ntawv no uas tam sim no nyob rau ntawm cov yuam sij dawb ntawm lub piano.

Qhov xwm txheej nrog cov yuam sij dub yog qhov nyuaj me ntsis. Tam sim no tsuas muaj ib qho tseem ceeb ntawm "ua" thiab "re", thiab nyob ntawm qhov xwm txheej, nws yog hu ua C-sharp lossis D-flat. Hauv Pythagorean system, C-sharp thiab D-flat yog ob daim ntawv sib txawv thiab tsis tuaj yeem muab tso rau tib tus yuam sij.

ntuj tuning

Dab tsi ua rau tib neeg hloov Pythagorean system mus rau ntuj? Oddly txaus, nws yog ib tug thib peb.

Hauv Pythagorean tuning, qhov loj thib peb (piv txwv li, lub sijhawm do-mi) yog qhov tsis txaus ntseeg. Hauv daim duab 4, peb pom tias txhawm rau kom tau txais los ntawm daim ntawv "ua" rau daim ntawv "mi", peb yuav tsum ua 4 duodecimal kauj ruam, faib txoj hlua ntev ntawm 4 3 zaug. Nws tsis yog qhov xav tsis thoob tias ob lub suab zoo li no yuav muaj me ntsis sib xws, me me consonance, uas yog, consonance.

Tab sis ze heev rau Pythagorean thib peb muaj qhov thib peb, uas suab ntau dua consonant.

Pythagorean thib peb

Ntuj thib peb

Cov neeg hu nkauj hu nkauj, thaum lub sijhawm no tshwm sim, reflexively coj lub suab lus thib peb.

Txhawm rau kom tau txais lub ntuj thib peb ntawm txoj hlua, koj yuav tsum faib nws qhov ntev los ntawm 5, thiab tom qab ntawd txo cov suab nrov los ntawm 2 octaves, yog li qhov ntev ntawm txoj hlua yuav yog 4/5 (Fig. 5).

Raws li koj tuaj yeem pom, kev faib cov hlua rau hauv 5 ntu tau tshwm sim, uas tsis yog nyob rau hauv Pythagorean system. Yog vim li cas qhov thib peb yog tsis yooj yim sua nyob rau hauv lub Pythagorean system.

Xws li ib qho yooj yim hloov tau coj mus rau kev kho ntawm tag nrho cov system. Tom qab qhov thib peb, txhua lub sijhawm tshwj tsis yog prima, vib nas this, plaub thiab thib tsib hloov lawv lub suab. Tsim tej yam ntuj tso (qee zaum hu ua huv si) qauv. Nws hloov tawm los ua consonantal ntau dua li Pythagorean, tab sis qhov ntawd tsis yog tib qho xwb.

Qhov tseem ceeb uas tau tuaj rau suab paj nruag nrog ntuj tuning yog tonality. Loj thiab me (ob qho tib si raws li chords thiab raws li cov yuam sij) ua tau tsuas yog nyob rau hauv ntuj tuning. Ntawd yog, ua tiav, lub triad loj tuaj yeem sib sau los ntawm cov ntawv sau ntawm Pythagorean system, tab sis nws yuav tsis muaj qhov zoo uas tso cai rau koj los npaj cov tonality hauv Pythagorean system. Nws tsis yog coincidence uas nyob rau hauv ancient sij hawm suab paj nruag lub warehouse tseem ceeb monody. Monody tsis yog hu nkauj monophonic xwb, hauv kev nkag siab nws tuaj yeem hais tias nws yog monophony, uas tsis lees paub txawm tias muaj kev sib haum xeeb.

Tsis muaj ntsiab lus piav qhia lub ntsiab lus ntawm qhov loj thiab me rau cov kws ntaus nkauj.

Rau cov neeg tsis muaj suab paj nruag, qhov kev sim hauv qab no tuaj yeem pom zoo. suav nrog ib qho classical los ntawm Viennese classics mus rau nruab nrab ntawm lub xyoo pua 95th. Nrog rau qhov tshwm sim ntawm 99,9% nws yuav yog nyob rau hauv qhov loj lossis hauv me. Qhib lub suab paj nruag nrov niaj hnub. Nws yuav nyob hauv qhov loj lossis me me nrog qhov tshwm sim ntawm XNUMX%.

Tempered nplai

Muaj ntau qhov kev sim siab ntawm tus cwj pwm. Feem ntau hais lus, temperament yog ib qho kev sib txawv ntawm lub sijhawm los ntawm kev ntshiab (natural lossis Pythagorean).

Qhov kev xaiv ua tau zoo tshaj plaws yog qhov sib npaug (RTS), thaum lub octave tau muab faib ua 12 "sib npaug" ntu. "Equality" ntawm no yog to taub raws li hauv qab no: txhua daim ntawv tom ntej yog tib lub sij hawm ntau dua li yav dhau los. Thiab tau tsa daim ntawv 12 zaug, peb yuav tsum tuaj rau lub octave dawb huv.

Tau daws qhov teeb meem zoo li no, peb tau txais ib daim ntawv 12 sib npaug temperament (los yog RTS-12).

Tab sis vim li cas thiaj xav tau lub siab ntev?

Qhov tseeb yog hais tias nyob rau hauv ib tug natural tuning (xws li, nws twb hloov los ntawm ib tug sib npaug tempered ib tug) hloov lub tonic - lub suab los ntawm peb "suav" lub tonality - piv txwv li, los ntawm daim ntawv "ua" rau daim ntawv " re”, tom qab ntawd txhua qhov kev sib raug zoo ntawm lub sijhawm yuav raug ua txhaum cai. Qhov no yog Achilles lub pob taws ntawm txhua qhov huv si tunings, thiab tib txoj hauv kev los kho qhov no yog ua kom tag nrho cov ntu me me tawm, tab sis sib npaug rau ib leeg. Tom qab ntawd thaum koj tsiv mus rau lwm tus yuam sij, qhov tseeb, tsis muaj dab tsi yuav hloov.

Tempered system muaj lwm yam zoo. Piv txwv li, nws tuaj yeem ua suab paj nruag, ob qho tib si sau rau lub ntuj tsim, thiab rau Pythagorean.

Ntawm cov minuses, qhov pom tseeb tshaj plaws yog tias txhua lub sijhawm tshwj tsis yog lub octave hauv qhov system no yog cuav. Tau kawg, tib neeg pob ntseg tsis yog ib qho khoom siv zoo tagnrho. Yog tias qhov tsis tseeb yog microscopic, ces peb tuaj yeem tsis pom nws. Tab sis tib tempered thib peb yog heev deb ntawm lub ntuj.

Ntuj thib peb

Tempered thib peb

Puas muaj txoj hauv kev tawm ntawm qhov xwm txheej no? Cov kab ke no puas tuaj yeem txhim kho?

Yuav ua li cas yog tom ntej no?

Cia peb rov qab mus rau peb Dominic ua ntej. Peb puas tuaj yeem hais tias nyob rau lub sijhawm ua ntej lub suab kaw muaj qee cov suab paj nruag tuning?

Peb qhov laj thawj qhia tau hais tias txawm tias daim ntawv "la" hloov, ces txhua qhov kev tsim kho (kev faib cov hlua rau hauv 2, 3 thiab 5 ntu) yuav zoo ib yam. Qhov no txhais tau hais tias cov txheej txheem yuav tsum tau hloov mus ua tib yam. Tau kawg, ib lub tsev teev ntuj tuaj yeem siv Pythagorean thib peb hauv nws qhov kev coj ua, thiab qhov thib ob - lub ntuj tsim, tab sis los ntawm kev txiav txim siab ntawm nws txoj kev tsim kho, peb yuav muaj peev xwm txiav txim siab tsis meej txog cov suab paj nruag, thiab yog li muaj peev xwm sib txawv monasteries. muaj suab paj nruag.

Yog li dab tsi ntxiv? Qhov kev paub ntawm lub xyoo pua 12th qhia tau hais tias kev tshawb nrhiav tsis tau nres ntawm RTS-12. Raws li txoj cai, kev tsim cov kev hloov kho tshiab yog ua los ntawm kev faib cov octave tsis yog 24, tab sis mus rau ntau qhov chaw, piv txwv li, rau hauv 36 lossis XNUMX. Txoj kev no yog heev mechanistic thiab unproductive. Peb tau pom tias cov kev tsim kho pib nyob rau hauv thaj tsam ntawm kev faib yooj yim ntawm txoj hlua, uas yog, lawv tau txuas nrog cov kev cai ntawm physics, nrog kev vibrations ntawm tib txoj hlua. Tsuas yog thaum kawg ntawm kev tsim kho, cov ntawv tau txais tau hloov nrog cov tempered zoo. Yog tias, txawm li cas los xij, peb npau taws ua ntej peb tsim ib yam dab tsi hauv qhov sib piv yooj yim, ces cov lus nug tshwm sim: peb tempering dab tsi, los ntawm cov ntawv twg peb deviate?

Tab sis kuj muaj xov xwm zoo. Yog hais tias txhawm rau txhim kho lub cev los ntawm daim ntawv "ua" rau daim ntawv "re", koj yuav tsum twist ntau pua cov kav dej thiab cov raj, tam sim no, txhawm rau txhim kho cov khoom sib txuas, tsuas yog nias ib lub pob. Qhov no txhais tau hais tias peb tsis tas yuav tsum tau ua si hauv me ntsis ntawm lub suab nrov, peb tuaj yeem siv qhov sib piv ntshiab thiab hloov lawv qhov thib ob qhov xav tau tshwm sim.

Tab sis yuav ua li cas yog tias peb xav ua si tsis yog hauv cov twj paj nruag hluav taws xob, tab sis ntawm "analog" sawv daws yuav? Puas yog nws muaj peev xwm tsim kom muaj kev sib haum xeeb tshiab, siv qee lub hauv paus ntsiab lus, es tsis txhob ntawm kev faib tshuab ntawm octave?

Tau kawg, koj tuaj yeem ua tau, tab sis lub ntsiab lus no yog qhov dav heev uas peb yuav rov qab mus rau lwm lub sijhawm.

Tus sau - Roman Oleinikov

Tus sau qhia nws ua tsaug rau tus kws sau paj huam Ivan Soshinsky rau cov khoom siv suab