Consonance yog dab tsi?

Hauv daim ntawv dhau los, peb pom tias lub suab ua haujlwm li cas. Cia peb rov qab ua cov qauv no:

SOUND = GROUND TONE + TXHUA YAM NTAWM NTAU

Tsis tas li ntawd, raws li cov neeg Nyij Pooj qhuas cov paj ntoo, peb kuj tseem yuav qhuas cov lus teb ntau zaus - qhov amplitude-frequency yam ntxwv ntawm lub suab (Daim duab 1):

Nco qab tias kab rov tav axis sawv cev rau lub suab (oscillation zaus), thiab ntsug axis sawv cev rau lub suab nrov (amplitude).

Txhua kab ntsug yog ib qho kev sib haum xeeb, thawj qhov kev sib haum xeeb feem ntau hu ua qhov tseem ceeb. Harmonics yog teem raws li nram no: qhov thib ob harmonic yog 2 lub sij hawm siab tshaj lub suab nrov, qhov thib peb yog peb, plaub yog plaub, thiab hais txog.

Rau lub hom phiaj ntawm brevity, es tsis txhob "frequency nth harmonic" peb tsuas hais tias "nth harmonic", thiab es tsis txhob "frequency" - "suab zaus".

Yog li, saib cov lus teb zaus, nws yuav tsis nyuaj rau peb los teb cov lus nug, dab tsi yog consonance.

Yuav suav li cas rau infinity?

Consonance txhais tau tias "co-sounding", sib koom ua suab. Yuav ua li cas ob lub suab sib txawv ua ke?

Cia peb kos lawv rau ntawm daim ntawv qhia hauv qab ib leeg (Daim duab 2):

Nov yog cov lus teb: qee qhov kev sib haum xeeb tuaj yeem sib koom ua ke ntau zaus. Nws yog qhov tsim nyog los xav tias qhov sib txuam ntau zaus, ntau lub suab "feem ntau" muaj, thiab, yog li ntawd, qhov ntau consonance nyob rau hauv lub suab ntawm xws li ib ntus. Yuav kom meej meej, nws yog ib qho tseem ceeb tsis yog tsuas yog tus naj npawb ntawm kev sib haum xeeb, tab sis qhov kev faib ua feem ntawm tag nrho cov suab sib haum xeeb sib tw, uas yog, qhov sib piv ntawm tus naj npawb ntawm qhov sib piv rau tag nrho cov suab sib haum xeeb.

Peb tau txais cov qauv yooj yim tshaj plaws rau kev suav consonance:

qhov twg N_{sovp ua} yog tus naj npawb ntawm kev sib haum xeeb,  N_ntau yog tag nrho cov suab nrov harmonics (tus naj npawb ntawm cov suab nrov sib txawv), thiab cons thiab yog peb lub siab xav. Yuav kom ua lej kom raug, nws yog qhov zoo dua los hu rau kom muaj nuj nqis ib qho kev ntsuas ntawm zaus consonance.

Zoo, qhov teeb meem me me: koj yuav tsum xam N_{sovp ua} и N_ntau, faib ib qho los ntawm lwm tus, thiab tau txais cov txiaj ntsig xav tau.

Qhov teeb meem nkaus xwb yog tias tag nrho cov naj npawb ntawm cov harmonics thiab txawm tias tus naj npawb ntawm kev sib haum xeeb yog infinite.

Yuav ua li cas yog peb faib infinity los ntawm infinity?

Cia peb hloov qhov ntsuas ntawm daim duab dhau los, "tshem tawm" ntawm nws (Daim duab 3)

Peb pom tias kev sib haum xeeb tshwm sim dua thiab dua. Daim duab rov qab (Fig. 4).

Qhov kev rov ua dua no yuav pab peb.

Nws yog txaus rau peb xam qhov ratio (1) nyob rau hauv ib tug ntawm cov dotted duab plaub (piv txwv li, nyob rau hauv thawj ib tug), ces, vim hais tias ntawm repetitions thiab tag nrho cov kab, qhov ratio yuav nyob twj ywm tib yam.

Rau kev yooj yim, qhov zaus ntawm lub suab nrov ntawm thawj (qis) lub suab yuav suav tias yog sib npaug ntawm kev sib koom ua ke, thiab qhov zaus ntawm lub suab nrov ntawm lub suab thib ob yuav raug sau ua ib feem tsis txaus ntseeg.  .

Cia peb nco ntsoov nyob rau hauv kab lus hais tias nyob rau hauv lub suab paj nruag tshuab, raws li txoj cai, nws yog precisely suab uas siv, qhov piv ntawm frequencies uas yog qhia los ntawm ib co feem.  . Piv txwv li, lub ncua sij hawm ntawm ib tug thib tsib yog qhov piv  , quart-  , triton —   thiab lwm yam

Cia peb xam piv (1) hauv thawj daim duab plaub (Fig. 4).

Nws yog ib qho yooj yim kom suav cov naj npawb ntawm kev sib haum xeeb. Raws li txoj cai, muaj ob ntawm lawv, ib tug belongs rau lub suab qis, qhov thib ob - mus rau sab sauv, hauv daim duab 4 lawv tau cim liab. Tab sis ob qho tib si ntawm cov harmonics suab ntawm tib zaus, raws li, yog tias peb suav cov naj npawb ntawm cov zaus sib xws, ces tsuas muaj ib zaus xwb.

Dab tsi yog tag nrho cov suab nrov zaus?

Wb sib cav li no.

Tag nrho cov harmonics ntawm lub suab qis yog teem rau tag nrho cov lej (1, 2, 3, thiab lwm yam). Sai li txhua qhov kev sib haum xeeb ntawm lub suab sab saum toj yog qhov sib npaug, nws yuav sib koom nrog ib qho ntawm cov kev sib haum xeeb ntawm hauv qab. Tag nrho cov harmonics ntawm lub suab sab sauv yog ntau ntawm cov suab nrov , yog li qhov zaus n-th harmonic yuav muab sib npaug rau:

uas yog, nws yuav yog integer (txij li m yog integer). Qhov no txhais tau hais tias lub suab sab sauv hauv daim duab plaub muaj kev sib haum xeeb los ntawm thawj (tsim suab nrov) mus rau n-Auj, yog li ntawd, suab n zaus.

Txij li tag nrho cov kev sib haum xeeb ntawm lub suab qis yog nyob rau hauv cov lej, thiab raws li (3), thawj qhov sib txawv tshwm sim ntawm qhov zaus. m, nws hloov tawm tias lub suab qis hauv lub duab plaub yuav muab m suab nrov zaus.

Nws yuav tsum tau muab sau tseg tias coinciding zaus m peb rov suav dua ob zaug: thaum peb suav cov zaus ntawm lub suab sab saud thiab thaum peb suav cov zaus ntawm lub suab qis. Tab sis qhov tseeb, qhov zaus yog ib qho, thiab rau cov lus teb kom raug, peb yuav tsum tau rho tawm ib qho "ntxiv" zaus.

Tag nrho ntawm tag nrho cov suab nrov zaus hauv lub duab plaub yuav yog:

Hloov (2) thiab (4) rau hauv cov qauv (1), peb tau txais ib qho yooj yim qhia rau xam tus consonance:

Txhawm rau hais txog lub consonance ntawm lub suab uas peb suav, koj tuaj yeem qhia cov suab no hauv cov cim cons:

Siv cov qauv no yooj yim, koj tuaj yeem suav cov consonance ntawm txhua lub sijhawm.

Thiab tam sim no cia peb xav txog qee yam khoom ntawm zaus consonance thiab piv txwv ntawm nws cov kev suav.

Khoom thiab piv txwv

Ua ntej, cia peb suav cov consonances rau lub sijhawm yooj yim tshaj plaws thiab xyuas kom meej tias cov mis (6) "ua haujlwm".

Lub sijhawm twg yog qhov yooj yim tshaj plaws?

Tiag tiag prima. Ob daim ntawv suab hauv unison. Ntawm daim duab nws yuav zoo li no:

Peb pom tias tag nrho cov suab nrov frequencies coincide. Yog li ntawd, lub consonance yuav tsum sib npaug rau:

Tam sim no cia peb hloov qhov piv rau lub unison  rau hauv formula (6), peb tau txais:

Kev suav ua ke nrog cov lus teb "intuitive", uas yuav tsum tau ua.

Cia peb ua lwm yam piv txwv uas cov lus teb intuitive tsuas yog pom tseeb - lub octave.

Nyob rau hauv ib qho octave, lub suab sab saud yog 2 lub sij hawm siab dua qhov qis dua (raws li qhov zaus ntawm lub suab nrov), feem, ntawm daim duab nws yuav zoo li no:

Nws tuaj yeem pom los ntawm daim duab uas txhua qhov kev sib haum xeeb thib ob sib koom ua ke, thiab cov lus teb intuitive yog: lub consonance yog 50%.

Cia peb suav nws los ntawm cov mis (6):

Thiab dua, tus nqi suav yog sib npaug rau "intuitive".

Yog peb coj daim ntawv raws li lub suab qis rau thiab teeb tsa tus nqi consonance rau txhua lub sijhawm nyob rau hauv lub octave ntawm daim duab (yooj yim lub sij hawm), peb tau txais cov duab hauv qab no:

Qhov ntsuas siab tshaj plaws ntawm consonance yog nyob rau hauv lub octave, tsib thiab plaub. Lawv keeb kwm xa mus rau "zoo meej" consonances. Cov me thiab loj thib peb, thiab cov me thiab loj thib rau yog qis me ntsis, cov ntu no suav tias yog "tsis zoo" consonances. Cov seem ntawm cov ntu muaj qis dua ntawm consonance, kev lig kev cai lawv koom nrog pawg ntawm dissonances.

Tam sim no peb sau qee yam khoom ntawm kev ntsuas ntawm zaus consonance, uas yog los ntawm cov qauv rau nws cov kev suav:

1. Qhov ntau qhov sib piv  (tus lej ntau m и n), qhov tsawg consonant lub caij.

И m и n nyob rau hauv cov mis (6) yog nyob rau hauv denominator, yog li ntawd, raws li cov lej no nce, qhov ntsuas ntawm consonance txo.

2. Lub upward consonance ntawm lub ncua sij hawm yog sib npaug zos rau downward consonance ntawm lub interval.

Txhawm rau kom tau txais qhov luv luv es tsis txhob nce lub sijhawm, peb xav tau hauv qhov piv   sib puav m и n. Tab sis nyob rau hauv formula (6), kiag li tsis muaj dab tsi yuav hloov los ntawm xws li ib tug hloov.

3. Qhov ntsuas ntawm zaus consonance ntawm ib ntus tsis nyob ntawm seb peb tab tom tsim nws los ntawm.

Yog tias koj hloov ob daim ntawv los ntawm tib lub sijhawm nce lossis nqis (piv txwv li, tsim qhov thib tsib tsis yog los ntawm daim ntawv rau, tab sis los ntawm daim ntawv ре), ces tus ratio  nruab nrab ntawm cov ntawv yuav tsis hloov, thiab yog li ntawd, qhov ntsuas ntawm zaus consonance yuav nyob twj ywm tib yam.

Peb tuaj yeem muab lwm yam khoom ntawm consonance, tab sis tam sim no peb yuav txwv peb tus kheej rau cov no.

Physics thiab lyrics

Daim duab 7 muab peb lub tswv yim ntawm kev ua haujlwm zoo li cas. Tab sis qhov no yog li cas peb yeej perceive lub consonance ntawm intervals? Puas muaj cov neeg uas tsis nyiam kev sib raug zoo zoo tag nrho, tab sis cov kev sib raug zoo tsis sib haum xeeb zoo li qab ntxiag?

Yog lawm, cov neeg zoo li no yeej muaj nyob. Thiab txhawm rau piav qhia qhov no, ob lub tswv yim yuav tsum paub qhov txawv: lub cev consonance и pom consonance.

Txhua yam uas peb tau txiav txim siab hauv kab lus no tau ua nrog lub cev consonance. Txhawm rau xam nws, koj yuav tsum paub tias lub suab ua haujlwm li cas, thiab qhov sib txawv vibrations ntxiv li cas. Lub cev consonance muab cov prerequisites rau perceived consonance, tab sis tsis txiav txim siab nws 100%.

Perceived consonance yog txiav txim yooj yim heev. Ib tug neeg raug nug seb nws puas nyiam qhov kev sib raug zoo no. Yog hais tias muaj, ces rau nws nws yog consonance; yog tsis yog, nws yog dissonance. Yog tias nws muab ob lub sijhawm sib piv, peb tuaj yeem hais tias ib qho ntawm lawv yuav zoo li tus neeg tam sim no ntau tus lej, qhov tsawg dua.

Puas pom tau tias consonance suav tau? Txawm hais tias peb xav tias nws muaj peev xwm, ces qhov kev suav no yuav ua rau muaj kev puas tsuaj loj, nws yuav suav nrog ib qho ntxiv infinity - infinity ntawm tus neeg: nws qhov kev paub, hnov ​​​​tus yam ntxwv thiab lub hlwb muaj peev xwm. Qhov no infinity tsis yog li ntawd yooj yim mus nrog.

Txawm li cas los xij, kev tshawb fawb hauv cheeb tsam no tseem tab tom ua. Tshwj xeeb, tus kws sau paj huam Ivan Soshinsky, uas ua siab zoo muab cov ntaub ntawv suab rau cov ntawv sau no, tau tsim ib qho kev pab cuam uas koj tuaj yeem tsim ib tus kheej daim ntawv qhia txog kev nkag siab ntawm consonances rau txhua tus neeg. Lub vev xaib mu-theory.info tam sim no tab tom tsim, qhov twg leej twg tuaj yeem raug sim thiab paub cov yam ntxwv ntawm lawv lub rooj sib hais.

Thiab tseem, yog hais tias muaj ib tug perceived consonance, thiab nws txawv ntawm lub cev, dab tsi yog lub ntsiab lus nyob rau hauv xam lub tom kawg? Peb tuaj yeem hloov kho cov lus nug no hauv txoj kev tsim kho ntxiv: ob lub ntsiab lus no cuam tshuam li cas?

Cov kev tshawb fawb qhia tau hais tias kev sib raug zoo ntawm qhov nruab nrab pom kev pom zoo thiab lub cev consonance yog nyob ntawm qhov kev txiav txim ntawm 80%. Qhov no txhais tau hais tias txhua tus neeg yuav muaj lawv tus kheej tus yam ntxwv, tab sis lub physics ntawm lub suab ua rau muaj kev cuam tshuam loj heev rau lub ntsiab lus ntawm consonance.

Tau kawg, kev tshawb fawb txog kev tshawb fawb hauv cheeb tsam no tseem yog qhov pib. Thiab raws li lub suab qauv, peb tau coj tus qauv yooj yim ntawm ntau yam kev sib haum xeeb, thiab kev suav ntawm consonance tau siv qhov yooj yim tshaj plaws - zaus, thiab tsis suav nrog qhov peculiarities ntawm lub hlwb kev ua haujlwm hauv kev ua suab paj nruag. Tab sis qhov tseeb hais tias txawm nyob rau hauv lub moj khaum ntawm xws simplifications ib tug high degree ntawm correlation ntawm txoj kev xav thiab kev sim tau txais yog heev txhawb thiab txhawb kev tshawb fawb ntxiv.

Daim ntawv thov ntawm txoj kev tshawb fawb hauv kev ua suab paj nruag kev sib haum xeeb tsis txwv rau kev suav ntawm consonance, nws kuj tau txais txiaj ntsig zoo dua.

Piv txwv li, nrog kev pab los ntawm txoj kev tshawb fawb, suab paj nruag kev sib haum xeeb tuaj yeem ua rau pom graphically, pom. Peb yuav tham txog yuav ua li cas rau lwm zaus.

Tus sau - Roman Oleinikov