Chidzidzo 1
Music Theory

Chidzidzo 1

Kuti tinzwisise zvakakosha zvedzidziso yemimhanzi uye kugona kuverenga kwemimhanzi, tinoda kunzwisisa kuti ruzha chii. Chaizvoizvo, ruzha ndirwo hwaro hwemimhanzi, pasina iyo mimhanzi haigoneke.

Chinangwa chechidzidzo: nzwisisa hunhu hweruzha, nzwisisa kuti ruzha rwemumhanzi rwakasiyana sei kubva kune chero humwe, uye dzidza akati wandei ane hukama mazwi emimhanzi.

Uye zvakare, iwe unofanirwa kuwana zano nezve iyo note-octave system. Izvi zvese zvine chekuita nehunhu hwezwi.

Sezvauri kuona, muchidzidzo chekutanga tine chirongwa chakakura chakatimirira, uye tine chokwadi chekuti uchararama nazvo! Saka ngatitangei.

Muviri zvimiro zvezwi

Kutanga, ngatidzidzei zvimiro zvezwi kubva pakuona kwefizikisi:

rira -Ichi chiitiko chemuviri, chinova mechanical wave vibration inopararira mune imwe svikiro, kazhinji mumhepo.

Ruzha rune zvimiro zvemuviri: nzwi, simba (ruzha), ruzha spectrum (timbre).

Basic physical properties yeruzha:

urefu inotemerwa nehuwandu hweoscillation uye inoratidzwa mu hertz (Hz).
inzwi simba (kukwidza) kunotarwa neamplitude yevibrations uye inoratidzwa mumadecibels (dB).
Sound spectrum (timbre) zvinoenderana nekuwedzera masaisai ekudengenyeka kana overtones ayo anoumbwa panguva imwe chete neiyo huru vibrations. Izvi zvinonzwika zvakanaka mumimhanzi nekuimba.

Izwi rekuti "overtone" rinobva pamazwi maviri echiRungu: pamusoro - "pamusoro", toni - "tone". Kubva pakuwedzera kwavo, izwi rekuti overtone kana "overtone" rinowanikwa. Kunzwa kwevanhu kunokwanisa kuona manzwi ane frequency ye16-20 hertz (Hz) uye vhoriyamu ye000-10 dB.

Kuita kuti zvive nyore kufamba, ngatitii 10 dB kurira, uye 130 dB ruzha rwendege iri kusimuka, kana ukainzwa padhuze. 120-130 dB ndiyo nhanho yemarwadzo echikumbaridzo, apo inenge yatove isina kugadzikana kuti nzeve yemunhu inzwe inzwi.

Panyaya yehurefu, huwandu kubva pa30 Hz kusvika pa4000 Hz inoonekwa seyakasununguka. Tichadzokera kunyaya iyi patinotaura nezve hurongwa hwemimhanzi uye chiyero. Zvino zvakakosha kuyeuka kuti kukwirira kwenzwi uye kurira kweruzha zvinhu zvakasiyana zvakanyanya. Panguva ino, ngatitaure pamusoro pezvinhu zvemimhanzi.

Music Sound Properties

Ruzha rwenziyo rwakasiyana sei nemamwe ose? Iri inzwi rine zvakafanana uye zvakafanana kudzokorora (kureva periodic) masaisai oscillations. Ruzha rusina-periodic, kureva kusaenzana uye kusaenzana kudzokorora mavhitaminzi, hausi wemumhanzi. Aya ndiwo ruzha, muridzo, kuungudza, kurira, kudzvova, kushinyira nemamwe manzwi akawanda.

Nemamwe mashoko, ruzha rwemumhanzi rune zvese zvakafanana sezvimwe, kureva kuti ine mutsindo, mutsindo, timbre, asi musanganiswa wakati wezvinhu izvi unotibvumira kuisa ruzha semumhanzi. Chii chimwe, kunze kweperiodicity, zvine chekuita nekurira kwemimhanzi?

Chekutanga, kwete iyo yese inonzwika renji inoonekwa semimhanzi, yatichakurukura zvakadzama gare gare. Chechipiri, kune ruzha rwemimhanzi, nguva yaro yakakosha. Izvi kana kuti nguva inonzwika pane imwe nzvimbo yakakwirira inokubvumira kusimbisa mimhanzi kana, zvakasiyana, siya ruzha rwakatsetseka. Inzwi pfupi pamagumo inokubvumira kuisa pfungwa inonzwisisika muchidimbu chemimhanzi, uye yakareba - kusiya manzwiro ekuderera muvateereri.

Chaizvoizvo kureba kwekurira kunoenderana nenguva yemasaisai oscillations. Kana masaisai achiwedzera kurebesa, ruzha rwacho runonzwika kurebesa. Kuti unzwisise hukama huri pakati penguva yerwiyo rwemimhanzi uye mamwe maitiro ayo, zvakakosha kuti ugare pane chakadai sepanotangira ruzha rwemimhanzi.

Mabviro enziyo dzenziyo

Kana ruzha ruchigadzirwa nechiridzwa chemimhanzi, maitiro ayo chaiwo haatsamiri munzira ipi neipi paurefu hwekurira. Ruzha panzwi raunoda runoenda chaizvo sekureba iwe wakabata pasi kiyi yaunoda ye synthesizer. Ruzha pavhoriyamu yakatarwa inoenderera kusvika iwe wadzikira kana kuwedzera vhoriyamu pane synthesizer kana yemagetsi gitare ruzha combo amplifier.

Kana isu tichitaura nezve izwi rekuimba, saka zvimiro zvemumhanzi zvinopindirana zvakanyanya kuoma. Ndepapi zviri nyore kuchengetedza ruzha paurefu hwakakodzera pasina kurasikirwa nesimba rayo? Zvino, kana iwe uchikwevera ruzha kwenguva yakareba kana iwe paunoda kuipa chaiko kwesekondi? Kudhirowa ruzha rwemumhanzi kwenguva yakareba pasina kurasikirwa neruzha rwemhando, kureba kwayo uye simba inyanzvi yakakosha. Kana iwe uchida kutsvaga inzwi rakanaka uye kudzidza kuimba, tinokurudzira kuti udzidze yedu yepamhepo kosi "Voice and Speech Development".

Mimhanzi system uye chiyero

Kuti tinzwisise zvakadzama zvimiro zveruzha rwemimhanzi, tinoda mamwe mashoma epfungwa. Kunyanya, senge mimhanzi system uye chiyero:

Music system - seti yemanzwi anoshandiswa mumhanzi wehumwe hurefu.
Kutevedzana kwenzwi - Aya ndiwo manzwi emumhanzi system, inofamba ichikwira kana kudzika.

Mimhanzi yemazuva ano inosanganisira 88 ruzha rwehurefu hwakasiyana. Vanogona kuurayiwa mukukwira kana kudzika. Chiratidziro chakajeka chehukama pakati pemhanzi system uye chiyero ndiyo kiibhodhi yepiyano.

Iwo makumi masere nemasere makiyi epiyano (88 nhema uye 36 chena - isu tichatsanangura nei gare gare) inovhara manzwi kubva pa52 Hz kusvika 27,5 Hz. Acoustic masimba akadaro anokwana kuita chero rwiyo rwunonakira nzeve yemunhu. Ruzha rwuri kunze kwerudzi urwu harushandiswe mumimhanzi yemazuva ano.

Chikero chinovakwa pane dzimwe nguva. Mitsindo ine mafambiro anosiyana nekaviri (2 times kumusoro kana pasi) inonzwisiswa nenzeve seyakafanana. Kuita kuti zvive nyore kufamba, pfungwa dzakadai sematanho, octave, toni uye semitone zvinounzwa mudzidziso yemimhanzi.

Chikero nhanho, octave, toni uye semitone

Ruzha rwemumhanzi rwese rwechiyero runonzi nhanho. Nhambwe iri pakati pemanzwi akafanana (matanho echikero) anosiyana pakureba nekaviri inonzi octave. Nhambwe iri pakati pemanzwi ari pedyo (matanho) isemitone. Semitones mukati meoctave yakaenzana (rangarira, izvi zvakakosha). Masemitone maviri anoumba toni.

Mazita akagoverwa kumatanho makuru echiyero. Aya anoti “do”, “re”, “mi”, “fa”, “sol”, “la”, “si”. Sezvaunonzwisisa, aya ndiwo manotsi manomwe atakaziva kubva paudiki. Pakiibhodhi yepiyano, vanogona kuwanikwa nekudzvanya makiyi machena:

Chidzidzo 1

Usatarise manhamba uye mavara echiLatin parizvino. Tarisa pane keyboard uye matanho akasainwa echiyero, iwowo manotsi. Iwe unogona kuona kuti kune 52 machena makiyi, uye 7 chete mazita ematanho. Izvi zvinonyatsokonzerwa nekuti matanho ane ruzha rwakafanana nekuda kwekusiyana kwehurefu ne2 nguva dzakapihwa mazita mamwe chete.

Kana tikadzvanya makiyi epiyano manomwe mumutsara, kiyi yechisere inopihwa zita chairo seriya ratakatanga kudzvanya. Uye, maererano, kuburitsa ruzha rwakafanana, asi pakukwirira kaviri kana kushoma, zvichienderana nekuti isu taifamba sei. Iwo chaiwo tuning frequency epiyano anogona kuwanikwa mune yakakosha tafura.

Imwezve kujekeswa kwemazwi kunodiwa pano. Octave haingorevi chinhambwe chiri pakati pemanzwi akafanana (matanho echikero), ayo anosiyana pakureba nekaviri, asiwo gumi nemaviri semitones kubva painoti "kusvika".

Unogona kuwana dzimwe tsananguro dzezwi rekuti "octave" rinoshandiswa mumhanzi dzidziso. Asi, nekuti chinangwa chekosi yedu ndechekupa izvo zvekutanga zvemumhanzi kuverenga, isu hatisi kuzopinda mukati medzidziso, asi tichazvimisa pachedu kune ruzivo runoshanda rwaunoda kudzidza mimhanzi uye mazwi.

Nekujeka uye tsananguro yezvinoreva zvinoshandiswa zvetemu, isu tichashandisa zvakare piano keyboard uye kuona kuti octave makiyi manomwe machena uye mashanu makiyi matema.

Sei uchida makiyi matema papiyano

Pano isu, sezvakavimbiswa kare, tichatsanangura kuti sei piyano ine 52 makiyi machena uye makumi matatu nematanhatu chete matema. Izvi zvichakubatsira iwe kunzwisisa zviri nani matanho echiyero uye semitones. Icho chokwadi ndechekuti madaro mumasemitone pakati pematanho makuru echiyero anosiyana. Semuenzaniso, pakati pematanho (notsi) “ku” na “re”, “re” na “mi” tinoona semitone 36, kureva kiyi nhema pakati pemakiyi maviri machena, uye pakati “mi” na“fa” panongova ne2 chete. semitone, kureva makiyi machena anotevedzana. Saizvozvo, pane chete semitone imwe pakati pe "si" uye "ita" nhanho.

Pakazara, nhanho 5 (notsi) dzine madaro e2 semitones, uye nhanho mbiri (notsi) dzine chinhambwe che1 semitone. Zvinobuda arithmetic inotevera:

Saka takawana 12 semitones mune octave. Kiibhodhi yepiyano inobata 7 octaves akazara uye 4 mamwe semitones: 3 kuruboshwe (apo painonzwika yakaderera) uye 1 kurudyi (yakakwirira ruzha). Tinoverenga zvose semitones nemakiyimutoro kwavari:

Saka takawana nhamba yese yemakiyi epiyano. Tinonzwisisa zvimwe. Takatodzidza kuti mune 7 makiyi machena uye 5 makiyi matema muoctave yega yega. Kupfuura maoctave manomwe akazara, tine mamwe matatu machena uye 7 makiyi matema. Tinoverenga kutanga makiyi machena:

Zvino tinoverenga black keys:

Heano makiyi edu makumi matatu nenhanhatu matema nemakiyi makumi mashanu neshanu machena.

Saka, makiyi matema anodiwa kuparadzanisa nhanho huru dzechiyero nemasemitone pazvinenge zvichidikanwa.

Zvinoita sekunge wafunga matanho echiyero, octaves, toni uye semitones. Rangarira ruzivo urwu, sezvo ruchabatsira muchidzidzo chinotevera, kana taenda kuongororo yakadzama yezvinyorwa zvemimhanzi. Uye ruzivo urwu ruchadiwa muchidzidzo chekupedzisira, patinodzidza kuridza piyano.

Ngatijekese imwe pfungwa. Mamiriro ekuvaka chiyero akafanana kune ese mimhanzi inonzwika, ingave inotorwa uchishandisa piyano, gitare kana kuimba kuimba. Takashandisa kiibhodhi yepiyano kutsanangura zvinyorwa chete nekuda kwekujeka kukuru.

Nenzira imwecheteyo, isu tichashandisa piyano kuti tinzwisise iyo note-octave system mune zvakadzama. Izvi zvinoda kuitwa muchidzidzo chanhasi, nekuti. pane inotevera tichaenda kumimhanzi notation uye notation yezvinyorwa padanda.

Note-octave system

Kazhinji, huwandu hwemanzwi anogona kunzwika kunzeve yemunhu hunovhara anenge gumi nerimwe octave. Nekuda kwekuti kosi yedu yakatsaurirwa kukuverenga nziyo, isu tinongofarira kurira kwemimhanzi, kureva nezve11 octaves. Kuti zvive nyore kurangarira maoctave nemanzwi anoenderana nawo, tinokurudzira kuenda kubva kumusoro kusvika pasi, kureva kubva kumusoro kweruzha kusvika pasi. Chimiro muhertz che octave yega yega chinozoratidzwa mubinary system kuitira nyore kurangarira.

Octaves (mazita) uye mitsara:

Hazvina musoro kufunga mamwe maoctave mumamiriro ekurira kwemimhanzi. Saka, chinyorwa chepamusoro chevarume ndiF chakapinza che5th octave (5989 Hz), uye rekodhi iyi yakaiswa naAmirhossein Molai munaChikunguru 31, 2019 muTehran (Iran) [Guinness World Records, 2019]. Muimbi Dimash anobva kuKazakhstan anosvika painoti "re" mu5th octave (4698 Hz). Uye mitsindo ine hurefu huri pasi pe16 Hz haigone kunzwisiswa nenzeve yemunhu. Unogona kudzidza tafura yakazara yetsamba yezvinyorwa kune mafrequency uye octaves pa mufananidzo unotevera:

Chidzidzo 1

Mucherechedzo wekutanga we octave yekutanga inojekeswa nepepuru, kureva kuti "do", uye yegirini - nyora "la" yekutanga octave. Yakanga iri paari, kureva frequency ye1 Hz, nekusarudzika ese matuner ekuyera gomo anofanoiswa.

Notes mu octave: sarudzo dzemazita

Nhasi, nzira dzakasiyana dzinoshandiswa kuratidza kuve kwenoti (pitch) kune akasiyana octave. Nzira iri nyore ndeyekunyora pasi mazita ezvinyorwa sezvaari: “do”, “re”, “mi”, “fa”, “sol”, “la”, “si”.

Yechipiri sarudzo ndiyo inonzi "Helmholtz notation". Iyi nzira inosanganisira kusarudzwa kwezvinyorwa mumabhii echiLatini, uye yeOctave - muhuwandu. Ngatitange nemanotsi.

Helmholtz sheet music:

Zvakakoshawo kuziva kuti chinyorwa "si" dzimwe nguva chinogona kumiririrwa kwete nebhii B, asi netsamba H. Tsamba H ndeyetsika yemimhanzi yeklasiki, asi tsamba B inoonekwa sechisarudzo chemazuva ano. Mukosi yedu, iwe unowana misiyano yese, saka yeuka kuti ese B naH anomiririra "si".

Iye zvino kune octaves. Zvinyorwa muoctave yekutanga kusvika yechishanu zvakanyorwa nemavara maduku echiLatin uye anoratidzwa nenhamba kubva pa1 kusvika ku5. Zvinyorwa zve octave duku zviri mumabhii maduku echiLatin asina nhamba. Rangarira kushamwaridzana: diki octave - mavara madiki. Manotsi e octave hombe akanyorwa nemavara makuru echiLatin. Rangarira: hombe octave - mavara makuru. Zvinyorwa zve contra-octave uye sub-contra-octave zvakanyorwa mumabhii makuru uye nhamba 1 uye 2, zvichiteerana.

Zvinyorwa mu octaves maererano neHelmholtz:

Kana paine munhu anoshamisika kuti nei chinyorwa chekutanga che octave chisina kuratidzwa netsamba yekutanga yealfabheti yechiLatin, isu tichakuudza kuti pane imwe nguva kuverenga kwakatanga nenoti "la", kumashure uko zita rekuti A rakagadziriswa. Zvisinei, vakabva vasarudza kutanga nhamba ye octave kubva pachinyorwa "kusvika" , iyo yakatove yakagoverwa zita C. Kuti tidzivise kuvhiringidzika muzvinyorwa zvemimhanzi, takasarudza kuchengeta mavara ezvinyorwa zvezvinyorwa sezvazviri.

Unogona kuwana rumwe ruzivo nezve notation yaHelmholtz uye mamwe mazano mubasa rake, rinowanikwa muchiRussian pasi pemusoro wekuti "Dzidziso yekunzwa kwekunzwa senge hwaro hwehupenyu hwedzidziso yemimhanzi" [G. Helmholtz, 2013].

Uye pakupedzisira, iyo sainzi notation, iyo yakagadzirwa neAmerican Acoustic Society muna 1939 uye iyo yakakosha kusvika nhasi. Manotsi anoratidzwa nemavara makuru echiLatin, uye ari eiyo octave - nenhamba kubva ku0 kusvika ku8.

Scientific notation:

Ndokumbira utarise kuti nhamba hadzienderane nemazita emaoctave kubva kune yekutanga kusvika yechishanu. Mamiriro ezvinhu aya anowanzorasisa kunyange vagadziri vezvirongwa zvevaimbi. Naizvozvo, kana paine kusahadzika, gara uchitarisa ruzha uye kukwirira kwenoti netuner. Kuti uite izvi, dhawunirodha nharembozha yePano Tuner uye uibvumire kuwana maikorofoni.

Zvinoramba zvichiwedzera kuti kekutanga hurongwa hwesainzi notation yakabudiswa muChikunguru chinyorwa cheChinyorwa cheAcoustical Society of America (Journal yeAcoustical Society of America) [Chinyorwa cheAcoustical Society of America, 1939] .

Zvino ngatipfupikisai ese arizvino anogamuchirwa notation masisitimu eoctave yega yega. Kuti tiite izvi, isu tichadzokorora zvakare mufananidzo watove wajaira kwauri nepiyano keyboard uye nematanho ematanho echiyero (manotsi), asi nekurudziro yekuteerera. nhamba nearufabheti mazita:

Chidzidzo 1

Uye, pakupedzisira, kuti tinzwisise zvizere ruzivo rwekutanga rwemhanzi dzidziso, tinofanira kunzwisisa mhando dzematoni uye semitones.

Mhando dzematoni uye semitones

Ngatitii pakarepo kuti kubva pakuona kwakashandiswa, ruzivo urwu haruzonyanya kubatsira kwauri kuridza zviridzwa zvemimhanzi kana kudzidzisa mazwi. Nekudaro, mazwi anoreva marudzi ematoni uye semitones anogona kuwanikwa mumabhuku akasarudzika. Naizvozvo, iwe unofanirwa kuve neruzivo pamusoro pavo kuitira kuti usarambe uchifunga nguva dzisinganzwisisike paunenge uchiverenga mabhuku kana kudzidza kwakadzama kwezvinhu zvemimhanzi.

Inzwi (mhando):

Halftone (mhando):

Sezvaunogona kuona, mazita anodzokororwa, saka hazvizove zvakaoma kuyeuka. Saka, ngationei!

Diatonic semitone (mhando):

Mimwe mienzaniso yaunogona kuona pamufananidzo:

Chidzidzo 1

Chromatic semitone (mhando):

Chidzidzo 1

Diatonic toni (mhando):

Chidzidzo 1

Chromatic toni (mhando):

Chidzidzo 1

Ngatijekese kuti mienzaniso inotorwa kubva mubhuku raVarfolomey Vakhromeev "Elementary Theory of Music" uye inoratidzwa paibhodhi yepiyano kujekesa, nokuti. isu tichadzidza mudonzvo chete muchidzidzo chinotevera, uye isu tinoda pfungwa dze toni uye semitone ikozvino [V. Vakhromeev, 1961]. Kazhinji, isu tichadzokorora kutaura nezvemabasa eiyi mudzidzisi mukuru weRussia uye nyanzvi yemimhanzi mukosi yedu yese.

Nenzira, muna 1984, mwedzi mishomanana asati afa, Varfolomey Vakhromeev akapiwa Order of the Holy Equal-to-the-Apostles Prince Vladimir we 2nd degree ye "Textbook of Church Singing" yaakanyora kuzvikoro zvebhaibheri. yeChechi yeOrthodox yeRussia. Bhuku racho rakapfuura nekudhindwa kwakati wandei mushure mekufa kwake [V. Vakhromeev, 2013].

Imwezve ruzivo rwakakosha rwatinoda tisati taenda kune zvemimhanzi notation. Takatosangana nemafungiro ekusimudza nekudzikisa dhigirii guru rechiyero. Saka, kuwedzera kwenhanho kunoratidzwa neshoko uye chiratidzo chakapinza (♯‎), uye kuderera kunoratidzwa neshoko uye chiratidzo chakatsetseka (♭).

Kuwedzera kwe2 semitones kunoratidzwa nekaviri inopinza kana kaviri inopinza, kuderera kwe2 semitones kunoratidzwa nekaviri flat kana kaviri flat. Kune kaviri inopinza pane yakakosha icon, yakafanana nemuchinjikwa, asi, nokuti zvakaoma kuitora pa keyboard, notation ♯♯ kana zviratidzo zviviri zvepaundi ## zvinogona kushandiswa. Zviri nyore nemafurati maviri, vanonyora zvingave 2 ♭♭ zviratidzo kana mavara echiLatin bb.

Uye pakupedzisira, chinhu chekupedzisira chaunofanira kutaura pamusoro pe "Properties of sound" ndiyo anharmonicity yemanzwi. Iwe wakadzidza kare kuti semitones mukati meoctave akaenzana. Naizvozvo, ruzha rwakadzikiswa ne<em>semitone maererano nedanho guru rinenge rakaenzana nenzwi nenzwi rinosimudzwa ne<em>semitone maererano nedanho riri masemitone maviri kudzika.

Zvichitaurwa zviri nyore, A-flat (A♭) uye G-yakapinza (G♯) yeimwechete octave inonzwika zvakafanana. Saizvozvo, mukati meoctave, G-flat (G♭) uye F-inopinza (F♯), E-flat (E♭) uye D-inopinza (D♯), D-flat (D♭) uye kusvika -sharp (С♯‎), etc. Chiitiko kana manzwi ehurefu hwakafanana aine mazita akasiyana uye achiratidzwa nezviratidzo zvakasiyana anodaidzwa kunzi anharmonicity of sounds.

Kuti tive nyore kunzwisisa, takaratidza chiitiko ichi pamuenzaniso wematanho (notsi), pakati pawo pane 2 semitones. Mune zvimwe zviitiko, kana paine semitone 1 chete pakati pematanho makuru, izvi hazvisi pachena. Semuenzaniso, F-flat (F♭) ndeye E (E), uye E-yakapinza (E♯‎) ndeye F (F). Zvakangodaro, muzvinyorwa zvakakosha zvedzidziso yemimhanzi, mazita akadai saF-flat (F♭) uye E-inopinza (E♯) anogona kuwanikwa zvakare. Wava kuziva zvavanoreva.

Nhasi iwe wakadzidza zvakakosha zvemuviri zvimiro zvezwi zvakazara uye zvimiro zvemumhanzi ruzha kunyanya. Iwe wakabata nehurongwa hwemimhanzi uye chiyero, chiyero nhanho, octave, toni uye semitones. Iwe zvakare wakanzwisisa iyo note-octave system uye ikozvino wakagadzirira kutora bvunzo pane izvo zvechidzidzo, umo isu takabatanidza iyo inonyanya kukosha mibvunzo kubva kune inoshanda maonero.

Chidzidzo bvunzo yekunzwisisa

Kana iwe uchida kuyedza ruzivo rwako pamusoro pechidzidzo ichi, unogona kutora bvunzo pfupi ine mibvunzo yakati wandei. Imwe chete sarudzo inogona kuve yakarurama pamubvunzo wega wega. Mushure mekusarudza imwe yesarudzo, sisitimu yacho inoenderera ichienda kumubvunzo unotevera. Mapoinzi aunogamuchira anokanganiswa nekurongeka kwemhinduro dzako uye nenguva yaunopedza uchipfuura. Ndapota cherechedza kuti mibvunzo yakasiyana nguva imwe neimwe, uye sarudzo dzinosanganiswa.

Uye zvino tinotendeukira kune kuongororwa kwemimhanzi notation.

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