He aha ka consonance?

Ma ka memo mua, ua ʻike mākou i ka hana ʻana o ke kani. E hana hou kākou i kēia ʻano hana:

KA LEO = KA LEO GROUND + NUI A PAU

Eia kekahi, i ka mahalo ʻana o ka poʻe Kepanī i nā pua cherry, e mahalo pū mākou i ka pakuhi pane alapine - ke ʻano amplitude-frequency o ke kani (Fig. 1):

E hoʻomanaʻo ʻo ke koʻi ākea e hōʻike ana i ka pitch (frequency oscillation), a ʻo ke axis vertical e hōʻike ana i ka leo nui (amplitude).

ʻO kēlā me kēia laina kuʻuna he harmonic, ʻo ka harmonic mua i kapa ʻia ʻo ke kumu. Hoʻonohonoho ʻia nā Harmonics penei: ʻo ka lua o ka harmonic he 2 mau manawa kiʻekiʻe ma mua o ka leo kumu, ʻo ke kolu ʻekolu, ʻo ka hā ʻehā, a pēlā aku.

No ka pōkole, ma kahi o "frequency nth harmonic" e ʻōlelo wale mākou "nth harmonic", a ma kahi o ka "frequency kumu" - "frequency leo".

No laila, ke nānā nei i ka pane pinepine, ʻaʻole paʻakikī iā mākou ke pane i ka nīnau, he aha ka consonance.

Pehea e helu ai i ka palena ʻole?

ʻO ke ʻano o ka consonance ʻo ia ka "co-sounding", ka leo hui. He aha ke kani like ʻana o nā leo like ʻole?

E kahakiʻi iā lākou ma ka pakuhi like ma lalo o kekahi (Fig. 2):

Eia ka pane: hiki i kekahi o nā harmonics ke kūlike i ka pinepine. Maikaʻi ka manaʻo e ʻoi aku ka nui o nā alapine like, ʻoi aku ka nui o nā leo "maʻamau", a no laila, ʻoi aku ka nui o ka consonance i ke kani o ia manawa. No ka pololei loa, ʻaʻole pono wale ka helu o nā harmonics like, akā he aha ka hapa o nā harmonics kani a pau e pili ana, ʻo ia hoʻi, ka ratio o ka helu o ka hoʻohālikelike ʻana i ka huina o nā harmonics kani.

Loaʻa iā mākou ke kumu maʻalahi loa no ka helu ʻana i ka consonance:

kahi N_sovp ʻo ia ka helu o nā harmonic like,  N_{ka mea maʻamau} ʻo ia ka huina o nā mea kani kani (ka helu o nā alapine kani like ʻole), a hooluolu mai a ʻo kā mākou consonance makemake ʻia. No ka pololei makemakika, ʻoi aku ka maikaʻi o ke kāhea ʻana i ka nui he ana o ka pinepine consonance.

ʻAe, liʻiliʻi ka mea: pono ʻoe e helu N_sovp и N_{ka mea maʻamau}, e puunaue i kekahi i kekahi, a loaa ka hopena i makemakeia.

ʻO ka pilikia wale nō ka pau ʻole o ka huina o nā harmonics a me ka helu o nā harmonics like.

He aha ka hopena inā e puʻunaue kākou i ka infinity me ka infinity?

E hoʻololi i ka pālākiō o ka pakuhi mua, "neʻe" mai ia mea (Fig. 3)

ʻIke mākou i ke ʻano o nā harmonic like ʻole. Hoʻopili hou ʻia ke kiʻi (Fig. 4).

E kōkua kēia hana hou iā mākou.

Ua lawa iā mākou ke helu i ka ratio (1) ma kekahi o nā ʻāpana kikoʻī (e like me ka mea mua), a laila, ma muli o ka hana hou ʻana a ma ka laina holoʻokoʻa, e mau kēia ratio.

No ka maʻalahi, e noʻonoʻo ʻia ke alapine o ka leo kumu o ka leo mua (lalo) e like me ka lokahi, a e kākau ʻia ke alapine o ka leo kumu o ka leo lua ma ke ʻano he hakina hiki ʻole ke hoʻemi ʻia.  .

E hoʻomaopopo kākou i loko o nā pale i loko o nā ʻōnaehana mele, ma ke ʻano he kānāwai, ʻo ia nā leo i hoʻohana ʻia, ʻo ka ratio o nā alapine i hōʻike ʻia e kekahi hapa.  . No ka laʻana, ʻo ka waena o ka hapalima ka ratio  , hapahā –  , triton —   etc.

E helu kākou i ka lākiō (1) i loko o ka huinahā mua (Fig. 4).

He mea maʻalahi ka helu ʻana i ka helu o nā harmonic like. ʻO ka maʻamau, ʻelua o lākou, ʻo kekahi no ka leo haʻahaʻa, ʻo ka lua - i luna, ma ka Fig. 4 ua kaha ʻia lākou i ka ʻulaʻula. Akā ʻo kēia mau harmonics ʻelua kani i ka alapine like, i kēlā me kēia, inā mākou e helu i ka helu o nā alapine kūpono, a laila hoʻokahi wale nō ia alapine.

He aha ka huina o na alapine kani?

E paio kaua penei.

Hoʻonohonoho ʻia nā harmonics a pau o ka leo haʻahaʻa i nā helu holoʻokoʻa (1, 2, 3, etc.). I ka manawa he integer kekahi harmonic o ka leo luna, e hui pū ia me kekahi o nā harmonic o lalo. ʻO nā harmonic a pau o ka leo luna he mau helu o ka leo kumu , pela ka pinepine n-e like ka harmonic me:

ʻo ia hoʻi, e lilo ia i integer (mai m he helu helu). 'O ia ho'i, 'o ka leo o luna o ka 'aha'ae like 'ole mai ka mua (leo kumu) a i n-o, nolaila, kani n nā alapine

No ka mea, aia nā harmonics a pau o ka leo haʻahaʻa i nā helu integer, a e like me (3), hiki i ka coincidence mua ma ke alapine. m, e hāʻawi ana ke kani haʻahaʻa i loko o ka ʻaoʻao m nā alapine kani.

Pono e hoʻomaopopo i ka pinepine coinciding m helu hou mākou i ʻelua: i ka helu ʻana i nā alapine o ke kani luna a i ka helu ʻana i nā alapine o ka leo haʻahaʻa. Akā ʻo ka ʻoiaʻiʻo, hoʻokahi ka alapine, a no ka pane pololei, pono mākou e unuhi i hoʻokahi alapine "keu".

ʻO ka huina o nā alapine kani a pau i loko o ka ʻāpana ʻehā:

Ke hoʻololi nei i ka (2) a me (4) i ke kumu (1), loaʻa iā mākou kahi ʻōlelo maʻalahi no ka helu ʻana i ka consonance:

No ka hoʻoikaika ʻana i ka consonance o nā kani a mākou i helu ai, hiki iā ʻoe ke kuhikuhi i kēia mau kani i nā bracket hooluolu mai:

Ke hoʻohana nei i kahi ʻano maʻalahi, hiki iā ʻoe ke helu i ka consonance o kekahi manawa.

A e noʻonoʻo kākou i kekahi mau waiwai o ka consonance frequency a me nā hiʻohiʻona o kāna helu ʻana.

Nā waiwai a me nā laʻana

ʻO ka mua, e helu kākou i nā consonances no nā wā maʻalahi loa a e hōʻoia i ka hana (6) "hana".

He aha ka wā maʻalahi?

ʻOiaʻiʻo prima. ʻElua mau leo ​​kani i ka lokahi. Ma ka pakuhi e like me kēia:

ʻIke mākou ua kū like nā alapine kani a pau. No laila, pono e like ka consonance me:

I kēia manawa e hoʻololi kākou i ka ratio no ka unison  i ke kumu (6), loaʻa iā mākou:

Kūlike ka helu ʻana me ka pane "intuitive", ka mea e manaʻo ʻia.

E lawe i kekahi laʻana e like me ka maopopo o ka pane intuitive - ka octave.

I ka octave, ʻo ka leo luna he 2 mau manawa kiʻekiʻe ma mua o ka haʻahaʻa (e like me ke alapine o ka leo kumu), i kēlā me kēia, ma ka pakuhi e like me kēia:

Hiki ke ʻike ʻia mai ka pakuhi e hui like kēlā me kēia harmonic kekona, a ʻo ka pane intuitive: ʻo ka consonance he 50%.

E helu kākou ma ke kumu (6):

A eia hou, ua like ka waiwai i helu ʻia me ka "intuitive".

Inā mākou e lawe i ka memo e like me ke kani haʻahaʻa i a e kuhi i ka waiwai consonance no nā wā āpau i loko o ka octave ma ka pakuhi (nā wā maʻalahi), loaʻa iā mākou kēia kiʻi:

ʻO nā ana kiʻekiʻe loa o ka consonance aia ma ka octave, ka ʻelima a me ka ʻehā. Ua ʻōlelo mua lākou i nā consonances "kūpono". ʻO ka hapakolu liʻiliʻi a me ka hapa nui, a ʻo ka hapa liʻiliʻi a me ke ono nui he haʻahaʻa haʻahaʻa, ua manaʻo ʻia kēia mau manawa he consonances "ʻaʻole kūpono". ʻO ke koena o nā kikowaena he haʻahaʻa haʻahaʻa o ka consonance, ma ke ʻano maʻamau, pili lākou i ka hui o dissonances.

I kēia manawa, papa inoa mākou i kekahi mau waiwai o ke ana o ka consonance alapine, i loaʻa mai ke kumu no kāna helu ʻana:

1. ʻOi aku ka paʻakikī o ka ratio  (ʻo ka nui o ka helu m и n), ʻo ka liʻiliʻi o ka consonant ka wā.

И m и n ma ka helu (6) aia i ka denominator, no laila, i ka hoʻonui ʻana o kēia mau helu, e emi ana ke ana o ka consonance.

2. Ua like ka consonance o luna o ka manawa me ka consonance iho o ka manawa.

No ka loaʻa ʻana o kahi manawa haʻahaʻa ma kahi o kahi wā i luna, pono mākou i ka ratio   swap m и n. Akā ma ke ʻano (6), ʻaʻohe mea e hoʻololi i kēlā ʻano pani.

3. ʻAʻole hilinaʻi ke ana o ka consonance frequency o kahi wā i ka memo a mākou e kūkulu ai.

Inā hoʻololi ʻoe i nā memo ʻelua ma ka manawa like i luna a i lalo (e laʻana, kūkulu i ka hapalima ʻaʻole mai kahi memo i, aka, mai ka palapala re), a laila ka ratio  ʻAʻole e loli ma waena o nā memo, a no laila, e mau ke ana o ka consonance pinepine.

Hiki iā mākou ke hāʻawi i nā waiwai ʻē aʻe o ka consonance, akā i kēia manawa e kaupalena mākou iā mākou iho i kēia.

Pilikino a me nā mele

Hāʻawi ka Figure 7 iā mākou i ka manaʻo o ka hana ʻana o ka consonance. Akā ʻo kēia ke ʻano o kā mākou ʻike maoli ʻana i ka consonance o nā wā? Aia kekahi poʻe makemake ʻole i nā consonances kūpono, akā ʻoluʻolu nā harmonies dissonant?

ʻAe, aia nō kēlā mau kānaka. A no ka wehewehe ʻana i kēia, pono e hoʻokaʻawale ʻia nā manaʻo ʻelua: consonance kino и ʻike ʻia ka consonance.

ʻO nā mea a pau a mākou i noʻonoʻo ai i kēia ʻatikala e pili ana i ka consonance kino. No ka helu ʻana, pono ʻoe e ʻike i ka hana ʻana o ke kani, a me ka hoʻohui ʻana o nā haʻalulu like ʻole. Hāʻawi ka consonance kino i nā mea e pono ai no ka consonance i ʻike ʻia, akā ʻaʻole ia e hoʻoholo i ka 100%.

Hoʻoholo maʻalahi ka consonance i ʻike ʻia. Nīnau ʻia ke kanaka inā makemake ʻo ia i kēia consonance. Ina he oiaio, nona ka consonance; ina aole, he dissonance. Inā hāʻawi ʻia ʻo ia i ʻelua mau manawa no ka hoʻohālikelike ʻana, a laila hiki iā mākou ke ʻōlelo e ʻike ʻia kekahi o ia mau mea i ke kanaka i kēia manawa i ʻoi aku ka consonant, a ʻoi aku ka liʻiliʻi.

Hiki ke helu ʻia ka consonance i ʻike ʻia? ʻOiai ke manaʻo nei mākou he hiki, a laila e paʻakikī kēia helu ʻana, e komo pū kekahi i ka palena ʻole - ka palena ʻole o ke kanaka: kona ʻike, nā ʻano lohe a me nā hiki o ka lolo. ʻAʻole maʻalahi kēia infinity e hana.

Eia naʻe, ke hoʻomau nei ka noiʻi ʻana ma kēia wahi. ʻO ka mea nui, ʻo ka mea haku mele ʻo Ivan Soshinsky, nāna i hāʻawi lokomaikaʻi i nā mea leo no kēia mau memo, ua hoʻomohala i kahi papahana e hiki ai iā ʻoe ke kūkulu i kahi palapala ʻāina o ka ʻike o nā consonances no kēlā me kēia kanaka. Ke kūkulu ʻia nei ka pūnaewele mu-theory.info, kahi e hoʻāʻo ʻia ai kekahi a ʻike i nā hiʻohiʻona o kā lākou lohe.

Eia naʻe, inā he consonance i ʻike ʻia, a ʻokoʻa ia mai ke kino, he aha ke kumu o ka helu ʻana i ka hope? Hiki iā mākou ke hoʻoponopono hou i kēia nīnau ma kahi ala ʻoi aku ka maikaʻi: pehea e pili ai kēia mau manaʻo ʻelua?

Hōʻike nā haʻawina e pili ana ka pilina ma waena o ka consonance i ʻike ʻia a me ka consonance kino ma ke kauoha o 80%. 'O ia ho'i, loa'a i kēlā me kēia kanaka ko lākou mau hi'ohi'ona pono'ī, akā, ke hā'awi nui nei ka physics o ke kani i ka wehewehe 'ana i ka consonance.

ʻOiaʻiʻo, aia nō ka noiʻi ʻepekema ma kēia wahi i ka hoʻomaka. A ma ke ʻano he ʻano leo, ua lawe mākou i kahi kumu hoʻohālike maʻalahi o nā harmonics lehulehu, a ua hoʻohana ʻia ka helu ʻana o ka consonance i ka mea maʻalahi - pinepine, a ʻaʻole i noʻonoʻo i nā ʻano o ka hana o ka lolo i ka hana ʻana i ka hōʻailona kani. Akā ʻo ka ʻoiaʻiʻo i loko o ke ʻano o ia mau hoʻomaʻamaʻa ʻana i loaʻa kahi kiʻekiʻe kiʻekiʻe o ka correlation ma waena o ka manaʻo a me ka hoʻokolohua i loaʻa i ka paipai a hoʻoulu hou i ka noiʻi.

ʻAʻole i kaupalena ʻia ka hoʻohana ʻana i ke ʻano ʻepekema ma ke kahua o ka lokahi mele i ka helu ʻana o ka consonance, e hāʻawi pū ana i nā hopena hoihoi.

No ka laʻana, me ke kōkua o ke ʻano ʻepekema, hiki ke hōʻike ʻia ka lokahi mele mele ma ke kiʻi, ʻike ʻia. E kamaʻilio mākou pehea e hana ai i kēia manawa aʻe.

Mea kākau – Roman Oleinikov