Lub zog dissonance

Dab tsi yog dissonance? Hauv cov ntsiab lus yooj yim, nws yog qhov tsis sib haum xeeb, tsis txaus siab ua ke ntawm ntau lub suab. Vim li cas thiaj li muaj kev sib xyaw ua ke ntawm cov ntu thiab chords? Lawv tuaj qhov twg los thiab vim li cas lawv thiaj xav tau?

Journey ntawm Odysseus

Raws li peb pom nyob rau hauv daim ntawv dhau los, thaum lub sij hawm Antiquity, lub Pythagorean system dominated. Nyob rau hauv nws, tag nrho cov suab ntawm lub system yog tau los ntawm tsuas yog faib cov hlua rau hauv 2 los yog 3 qhov sib npaug. Lub halving tsuas hloov lub suab los ntawm octave. Tab sis kev faib los ntawm peb ua rau muaj kev sau ntawv tshiab.

Cov lus nug raug cai tshwm sim: thaum twg peb yuav tsum tso tseg qhov kev faib no? Los ntawm txhua daim ntawv tshiab, faib txoj hlua los ntawm 3, peb tuaj yeem tau txais lwm tus. Yog li, peb tuaj yeem tau txais 1000 lossis 100000 suab hauv lub suab paj nruag. Peb yuav tsum nres qhov twg?

Thaum Odysseus, tus hero ntawm ib zaj paj huam Greek thaum ub, rov qab los rau nws Ithaca, ntau yam teeb meem tos nws ntawm txoj kev. Thiab txhua tus ntawm lawv ncua nws txoj kev taug mus txog thaum nws pom tias yuav ua li cas nrog nws.

Ntawm txoj kev mus rau txoj kev loj hlob ntawm cov suab paj nruag systems, ib yam nkaus thiab, muaj obstacles. Rau qee lub sij hawm lawv ua kom qeeb ntawm cov txheej txheem ntawm cov tsos ntawm cov ntawv tshiab, tom qab ntawd lawv tau kov yeej lawv thiab caij nkoj mus, qhov chaw lawv ntsib qhov teeb meem tom ntej. Cov teeb meem no yog dissonances.

Wb sim to taub tias dissonance yog dab tsi.

Peb tuaj yeem tau txais qhov tseeb txhais ntawm qhov tshwm sim no thaum peb nkag siab lub cev qauv ntawm lub suab. Tab sis tam sim no peb tsis xav tau qhov tseeb, nws txaus rau peb piav qhia hauv cov lus yooj yim.

Yog li peb muaj txoj hlua. Peb tuaj yeem faib ua 2 lossis 3 ntu. Yog li peb tau txais octave thiab duodecim. Ib qho octave suab ntau tus consonant, thiab qhov no yog to taub - faib los ntawm 2 yog yooj yim dua faib los ntawm 3. Nyob rau hauv lem, ib tug duodecima yuav suab ntau consonant tshaj ib txoj hlua muab faib ua 5 qhov chaw (xws li kev faib yuav muab ib feem peb tom qab ob octaves), vim kev faib los ntawm 3 yog yooj yim dua, dua li faib los ntawm 5.

Tam sim no cia peb nco ntsoov li cas, piv txwv li, ib qho thib tsib tau tsim. Peb faib cov hlua ua 3 ntu, thiab tom qab ntawd nce qhov ntev ntawm qhov tshwm sim los ntawm 2 zaug (Daim duab 1).

Raws li koj tuaj yeem pom, txhawm rau tsim ib qho thib tsib, peb yuav tsum tsis txhob ua ib qho, tab sis ob kauj ruam, thiab, yog li ntawd, tus thib tsib yuav suab qis dua tus lej octave lossis duodecime. Nrog txhua kauj ruam, peb zoo li yuav txav mus ntxiv thiab deb ntawm daim ntawv qub.

Peb tuaj yeem tsim txoj cai yooj yim rau kev txiav txim siab consonance:

tsawg dua cov kauj ruam peb ua, thiab qhov yooj yim dua cov kauj ruam no lawv tus kheej, lub consonant ntau lub caij yuav.

Cia peb rov qab mus rau kev tsim kho.

Yog li, tib neeg tau xaiv thawj lub suab (kom yooj yim, peb yuav xav tias qhov no rau, txawm hais tias cov Greeks thaum ub lawv tus kheej tsis tau hu nws) thiab pib tsim lwm cov ntawv los ntawm kev faib lossis muab qhov ntev ntawm txoj hlua los ntawm 3.

Thawj tau txais ob lub suab, uas rau rau yog qhov ze tshaj plaws F и ntsev (pib 2). ntsev yog tau yog tias qhov ntev ntawm txoj hlua raug txo los ntawm 3 zaug, thiab F - ntawm qhov tsis sib xws, yog tias nws nce 3 zaug.

Qhov ntsuas π tseem yuav txhais tau tias peb tab tom tham txog cov ntawv sau ntawm Pythagorean system.

Yog tias koj txav cov ntawv no mus rau tib lub octave qhov twg daim ntawv nyob rau, ces lub sijhawm ua ntej lawv yuav raug hu ua plaub (do-fa) thiab thib tsib (do-sol). Cov no yog ob lub sijhawm zoo kawg nkaus. Thaum lub sij hawm hloov los ntawm Pythagorean system mus rau lub ntuj, thaum yuav luag txhua lub sij hawm hloov, kev tsim kho ntawm plaub thiab thib tsib tseem tsis hloov. Kev tsim ntawm tonality mus nrog kev koom tes ncaj qha tshaj plaws ntawm cov ntawv sau no, nws yog nyob rau ntawm lawv qhov tseem ceeb thiab subdominant tau tsim. Cov sijhawm no tau dhau los ua consonant uas lawv tau ua suab paj nruag kom txog rau thaum lub sijhawm romanticism, thiab txawm tias tom qab lawv tau muab lub luag haujlwm tseem ceeb heev.

Tab sis peb digress los ntawm dissonances. Kev tsim kho tsis tau nres ntawm peb daim ntawv no. Sruna txuas ntxiv muab faib ua 3 ntu thiab duodecyma tom qab duodecyma kom tau txais cov suab tshiab thiab tshiab.

Thawj qhov teeb meem tshwm sim ntawm qib tsib, thaum twg rau (Original note) re, fa, sol, la sau ntawv ntxiv E (pib 3).

Nruab nrab sau ntawv E и F ib ntus tau tsim uas zoo li tsis txaus ntseeg rau cov neeg ntawm lub sijhawm ntawd. Lub sijhawm no yog qhov thib ob me me.

Me thib ob mi-fa - harmonic

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Tau ntsib lub sijhawm no, peb txiav txim siab tias yuav suav nrog dab tsi E lub kaw lus tsis tsim nyog lawm, koj yuav tsum nres ntawm 5 sau ntawv. Yog li thawj qhov system tau hloov mus ua 5-nco, nws tau hu ua pentatonic txoj kev. Txhua lub sij hawm nyob rau hauv nws yog heev consonant. Lub pentatonic nplai tseem tuaj yeem pom hauv pej xeem suab paj nruag. Qee zaum, raws li cov xim tshwj xeeb, nws kuj muaj nyob rau hauv classics.

Sij hawm dhau mus, tib neeg tau siv lub suab me me thib ob thiab pom tau tias yog tias koj siv nws nruab nrab thiab mus txog, ces koj tuaj yeem nyob nrog nws. Thiab qhov teeb meem tom ntej no yog kauj ruam 7 (Fig. 4).

Daim ntawv tshiab tau dhau los ua qhov tsis txaus ntseeg uas lawv txawm txiav txim siab tsis muab nws lub npe, tab sis hu nws F ntse (lub npe f#). Tiag tiag ntse thiab txhais tau hais tias lub caij nyoog uas tau tsim ntawm ob daim ntawv no: F и F ntse. Nws suab zoo li no:

Lub interval F thiab F-ntse yog harmonic

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Yog tias peb tsis mus "tshaj qhov ntse", ces peb tau txais 7-sau ntawv system - diatonic. Feem ntau cov suab paj nruag classical thiab niaj hnub no yog 7-kauj ruam, uas yog, lawv tau txais lub Pythagorean diatonic hauv qhov kev hwm no.

Txawm hais tias muaj qhov tseem ceeb ntawm diatonicism, Odysseus tau caij nkoj mus. Tau kov yeej qhov teeb meem ntawm daim ntawv ntse, nws pom qhov chaw qhib uas koj tuaj yeem ntaus ntau li 12 daim ntawv rau hauv qhov system. Tab sis lub 13th tsim ib tug txaus ntshai dissonance - Pythagorean comm.

Pythagorean comma

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Tej zaum peb tuaj yeem hais tias qhov comma yog Scylla thiab Charybdis dov rau hauv ib qho. Nws tsis siv ntau xyoo lossis ntau pua xyoo los kov yeej qhov teeb meem no. Tsuas yog ob peb txhiab xyoo tom qab ntawd, nyob rau hauv lub xyoo pua 12th AD, cov kws ntaus nkauj puas tig mus rau cov tshuab microchromatic, uas muaj ntau dua XNUMX sau ntawv. Tau kawg, nyob rau hauv cov ntaub ntawv no centuries, ib tug neeg tau sim mus ntxiv ob peb lub suab ntxiv rau lub octave, tab sis cov kev sim no yog heev hem tias, hmoov tsis, ib tug tsis tuaj yeem hais txog lawv qhov tseem ceeb hauv kev ua suab paj nruag.

Cov kev sim ntawm lub xyoo pua XNUMX puas tuaj yeem suav tias ua tiav? Puas muaj cov tshuab microchromatic tuaj rau hauv kev siv suab paj nruag? Cia peb rov qab mus rau lo lus nug no, tab sis ua ntej ntawd peb yuav xav txog ob peb qhov kev tsis sib haum xeeb ntxiv, tsis yog los ntawm Pythagorean system lawm.

hma thiab dab ntxwg nyoog

Thaum peb hais txog kev tsis sib haum xeeb los ntawm Pythagorean system, peb yog me ntsis cunning. Ntawd yog, muaj ob qho me me thib ob thiab ntse, tab sis tom qab ntawd lawv hnov ​​lawv txawv me ntsis.

Qhov tseeb yog hais tias cov suab paj nruag ntawm ancient sij hawm yog feem ntau ntawm ib tug monodic warehouse. Cias muab, tsuas yog ib daim ntawv suab ib zaug, thiab ntsug - ib txhij ua ke ntawm ob peb lub suab - yuav luag tsis tau siv. Yog li ntawd, cov neeg nyiam suab paj nruag thaum ub, raws li txoj cai, tau hnov ​​​​me me thib ob thiab lub ntsej muag ntse zoo li no:

Me me thib ob mi-fa - melodic

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Semitone F thiab F ntse - melodic

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Tab sis nrog rau txoj kev loj hlob ntawm txoj kab ntsug, kev sib haum xeeb (ntev) ntu, suav nrog cov tsis sib haum xeeb, tau hnov ​​​​zoo tshaj plaws.

Tus thawj hauv no series yuav tsum tau hu ua triton.

Qhov no yog li cas ib tug tritone suab zoo li

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Nws yog hu ua tritone, tsis yog vim nws zoo li amphibian, tab sis vim hais tias nws muaj raws nraim peb lub suab ntawm lub suab qis mus rau sab sauv (uas yog, rau semitones, rau piano yuam sij). Interestingly, nyob rau hauv Latin nws tseem hu ua tritonus.

Lub sijhawm no tuaj yeem tsim ua ob qho tib si hauv Pythagorean system thiab hauv ntuj. Thiab ntawm no thiab muaj nws yuav suab dissonant.

Txhawm rau tsim nws hauv Pythagorean system, koj yuav tsum faib cov hlua ua 3 ntu 6 zaug, thiab tom qab ntawd muab ob npaug rau qhov ua tau ntev 10 zaug. Nws hloov tawm hais tias qhov ntev ntawm txoj hlua yuav raug qhia raws li ib feem 729/1024. Needless hais, nrog ntau cov kauj ruam, tsis tas yuav tham txog consonance.

Nyob rau hauv ntuj tuning, qhov teeb meem yog me ntsis zoo dua. Lub ntuj tritone tuaj yeem tau raws li hauv qab no: faib qhov ntev ntawm txoj hlua los ntawm 3 ob zaug (piv txwv li, faib los ntawm 9), tom qab ntawd faib los ntawm lwm 5 (tag nrho faib los ntawm 45 ntu), thiab tom qab ntawd muab ob npaug rau 5 zaug. Yog li ntawd, qhov ntev ntawm txoj hlua yuav yog 32/45, uas, txawm hais tias yooj yim me ntsis, tsis cog lus rau consonance.

Raws li cov lus xaiv nyob rau hauv Nruab Nrab Hnub nyoog, lub sijhawm no hu ua "dab ntxwg nyoog hauv suab paj nruag."

Tab sis lwm qhov consonance tau ua qhov tseem ceeb dua rau kev txhim kho suab paj nruag - hma thib tsib.

Hma Quint

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Lub sijhawm no tuaj qhov twg? Vim li cas thiaj xav tau?

Piv txwv tias peb ntaus suab hauv ib qho system los ntawm ib daim ntawv rau. Nws muaj ib daim ntawv ре Nws hloov tawm yog tias peb faib cov rune rau hauv 3 ntu ob zaug (peb ua ob theem duodecimal rau pem hauv ntej). Ib daim ntawv A tsim ib qho txawv me ntsis: kom tau txais nws, peb yuav tsum tau nce txoj hlua 3 zaug (siv ib kauj ruam rov qab los ntawm duodecims), thiab tom qab ntawd faib cov hlua uas tau tshwm sim rau hauv 5 qhov chaw (uas yog, coj lub ntuj thib peb, uas tsuas yog tsis tau. muaj nyob rau hauv lub Pythagorean system). Yog li ntawd, nyob nruab nrab ntawm qhov ntev ntawm cov hlua ntawm cov ntawv sau ре и A peb tsis tau txais qhov piv txwv yooj yim ntawm 2/3 (ntshiab thib tsib), tab sis qhov piv ntawm 40/27 (hma thib tsib). Raws li peb pom los ntawm kev sib raug zoo, lub consonance no tsis tuaj yeem ua consonant.

Vim li cas peb tsis sau ntawv A, uas yuav yog ib tug ntshiab tsib ntawm ре? Qhov tseeb yog tias tom qab ntawd peb yuav muaj ob daim ntawv A - "quint los ntawm re" thiab "natural". Tab sis nrog "quint" A yuav muaj teeb meem tib yam li ре - Nws yuav xav tau nws thib tsib, thiab peb yuav muaj ob daim ntawv E.

Thiab cov txheej txheem no yog unstoppable. Nyob rau hauv qhov chaw ntawm ib lub taub hau ntawm hydra, ob tshwm sim. Los ntawm kev daws ib qho teeb meem, peb tsim ib qho tshiab.

Txoj kev daws teeb meem ntawm hma thib tsib tau dhau los ua radical. Lawv tsim ib tug sib npaug tempered system, qhov twg "thib tsib" A thiab "natural" tau hloov los ntawm ib daim ntawv - tempered A, uas tau muab me ntsis tawm ntawm kev sib tw nrog rau tag nrho lwm cov ntawv, tab sis qhov tawm ntawm lub suab yog NW nyuam qhuav pom, thiab tsis pom tseeb li hauv hma thib tsib.

Yog li tus hma thib tsib, zoo li tus hma uas muaj kev paub txog hiav txwv, tau coj lub nkoj suab paj nruag mus rau ntug hiav txwv uas xav tsis thoob heev - lub cev tsis sib xws.

Keeb Kwm Ntawm Kev Tsis Txaus Siab

Cov keeb kwm luv luv ntawm kev tsis sib haum xeeb qhia peb li cas? Kev paub dab tsi tuaj yeem rub los ntawm kev taug kev ntawm ntau pua xyoo?

• Ua ntej, raws li nws muab tawm, dissonances nyob rau hauv keeb kwm ntawm suab paj nruag ua si tsis muaj tsawg tshaj li consonances. Txawm tias muaj tseeb hais tias lawv tsis nyiam thiab tawm tsam nrog lawv, nws yog lawv cov uas feem ntau muab impetus rau qhov tshwm sim ntawm tshiab suab paj nruas qhia, ua ib tug catalyst rau unexpected discoveries.
• Qhov thib ob, ib qho kev nthuav dav tuaj yeem pom. Nrog txoj kev loj hlob ntawm suab paj nruag, tib neeg kawm hnov ​​consonance nyob rau hauv ntau thiab ntau complex ua ke ntawm suab.

Ob peb tus neeg tam sim no yuav xav txog qhov me me thib ob xws li lub sijhawm tsis sib haum xeeb, tshwj xeeb tshaj yog nyob rau hauv kev ua suab paj nruag. Tab sis tsuas yog ob thiab ib nrab txhiab xyoo dhau los nws yog li ntawd. Thiab lub triton nkag mus rau hauv kev xyaum suab paj nruag, ntau yam suab paj nruag tej hauj lwm, txawm nyob rau hauv nrov suab paj nruag, yog tsim los nrog lub loj tshaj plaws kev koom tes ntawm tritone.

Piv txwv li, muaj pes tsawg leeg pib nrog tritones Jimi Hendrix Ntshav Haze:

Maj mam, ntau thiab ntau dissonances txav mus rau hauv qeb ntawm "tsis yog li ntawd dissonances" los yog "yuav luag consonances". Nws tsis yog tias peb qhov kev hnov ​​​​lus tsis zoo, thiab peb tsis hnov ​​​​tias lub suab ntawm tej ntu thiab chords hnyav lossis ua phem. Qhov tseeb yog tias peb cov kev paub suab paj nruag loj hlob tuaj, thiab peb tuaj yeem pom cov txheej txheem ntau kauj ruam uas txawv txawv, txawv txawv thiab nthuav hauv lawv tus kheej txoj kev.

Muaj cov kws ntaus suab paj nruag rau tus hma thib tsib lossis commas uas tau nthuav tawm hauv tsab xov xwm no yuav tsis zoo li txaus ntshai, lawv yuav kho lawv raws li ib yam ntawm cov ntaub ntawv nyuaj uas koj tuaj yeem ua haujlwm nrog hauv kev tsim cov suab paj nruag sib npaug thiab qub.

Tus sau - Roman Oleinikov Cov ntaubntawv povthawj siv- Ivan Soshinsky