Nā ʻano hoʻokani pila

Ua maʻa mākou a pau i ka ʻoiaʻiʻo he 12 mau memo ma kahi octave: 7 mau kī keʻokeʻo a me 5 mau ʻeleʻele. A ʻo nā mele a pau a mākou e lohe ai, mai ka papa mele a hiki i ka pōhaku paʻakikī, ʻo ia nā memo 12.

Ua like anei me keia? Ua kani anei ke mele i ka manawa o Bach, i ka Middle Ages a i ka Antiquity?

Huina hoʻokaʻawale

ʻElua mau mea nui:

• ua hana ʻia nā leo kani mua ma ka mōʻaukala i ka hapa lua o ke kenekulia XNUMX;
• a hiki i ka hoʻomaka ʻana o ke kenekulia XNUMX, ʻo ka wikiwiki wikiwiki i hiki ke hoʻouna ʻia ka ʻike i ka wikiwiki o ka lio.

I kēia manawa, e holo wikiwiki kākou i kekahi mau keneturia i hala.

Manaʻo ka ʻAbbot o kekahi monastery (e kapa iā ia ʻo Dominic) i manaʻo ʻia he pono ke hīmeni i nā oli a hana i nā canons ma nā wahi āpau a me ke ʻano like. Akā ʻaʻole hiki iā ia ke kāhea aku i ka monastery e pili ana a hīmeni i kāna memo "A" iā lākou e hoʻokani ai i kā lākou. A laila hana lākou i nā kaikunāne holoʻokoʻa i kahi kani kani, e hoʻopuka pololei i kā lākou leka "la". Ke kono nei ʻo Dominic i ka novice kaulana loa i kona wahi. E noho ana kekahi kanaka novice me ka pahu kani ma ka ʻeke hope o kāna kākini ma luna o ka lio a no ʻelua mau lā a me ʻelua pō, e hoʻolohe ana i ke kani ʻana o ka makani a me ke kani ʻana o nā māiʻuʻu, e holo ana i kahi monastery kokoke e hoʻohui i kā lākou hana mele. ʻOiaʻiʻo, ua pio ka pahu kani mai ka lele ʻana, a hāʻawi i ka memo "la" me ka pololei ʻole, a ʻo ka novice iā ia iho, ma hope o kahi huakaʻi lōʻihi, ʻaʻole hoʻomanaʻo maikaʻi inā kani nā memo a me nā manawa i loko o kāna monastery maoli.

ʻO ka hopena, i loko o ʻelua mau monasteries e pili ana, ʻokoʻa nā hoʻonohonoho o nā mea kani a me nā leo mele.

Inā wikiwiki mākou i ka XNUMXth-XNUMXth century, e ʻike mākou ʻaʻole i loaʻa ka notation i kēlā manawa, ʻo ia hoʻi, ʻaʻohe ʻano noʻonoʻo ma ka pepa e hiki ai i kekahi ke hoʻoholo pololei i ka mea e hīmeni ai a pāʻani paha. ʻAʻole noʻonoʻo ka noʻonoʻo o ia au, ʻo ka neʻe ʻana o ke mele i hōʻike ʻia ma kahi kokoke. A laila, inā paha i hoʻouna aku kā mākou Dominic maikaʻi ʻole i kahi mele holoʻokoʻa i kahi monastery e pili ana i kahi symposium e pili ana i ka hoʻololi ʻana i ka ʻike mele, ʻaʻole hiki ke hoʻopaʻa i kēia ʻike, a ma hope o kekahi manawa e hoʻololi nā harmonies a pau i kekahi ʻaoʻao a i ʻole.

Hiki paha, me ia huikau, ke kamaʻilio e pili ana i nā hale mele i kēlā au? Oddly enough, hiki.

Pūnaehana Pythagorean

I ka hoʻomaka ʻana o ka poʻe e hoʻohana i nā mea kani kaula mua, ua ʻike lākou i nā hiʻohiʻona hoihoi.

Inā ʻoe e puʻunaue i ka lōʻihi o ke kaula i ka hapalua, a laila hui pū ʻia ke kani e hana ai me ke kani o ke kaula holoʻokoʻa. Ma hope loa, ua kapa ʻia kēia wā (ka hui ʻana o ʻelua mau leo ​​like). octave (kiʻi 1).

Manaʻo ka poʻe he nui ka lima o ka hui like ʻana. Akā, ʻaʻole kēia ka hihia ma ka mōʻaukala. ʻOi aku ka maʻalahi o ka loaʻa ʻana o kahi hui harmonious ʻē aʻe. No ka hanaʻana i kēia, ponoʻoe e māhele i ke kaulaʻaʻole i 2, akā i 3 mau'āpana (Fig. 2).

Ua ʻike ʻia kēia ratio iā mākou i kēia manawa duodecima  (composite interval).

ʻAʻole i loaʻa iā mākou ʻelua mau leo ​​hou - octave a me duodecimal - i kēia manawa ʻelua ala e loaʻa ai nā leo hou hou aʻe. E puunaue ana i ka 2 a me 3.

Hiki iā mākou ke lawe, no ka laʻana, i kahi kani duodecimal (ʻo ia hoʻi 1/3 o ke kaula) a māhele i kēia ʻāpana o ke kaula. Inā mākou e puʻunaue iā 2 (loaʻa iā mākou ka 1/6 o ke kaula kumu), a laila e loaʻa kahi kani i ʻoi aku ka octave ma mua o ka duodecimal. Inā mākou e puʻunaue i ka 3, loaʻa iā mākou kahi leo duodecimal mai duodecimal.

ʻAʻole hiki iā ʻoe ke hoʻokaʻawale i ke kaula wale nō, akā hele pū kekahi i ka ʻaoʻao ʻē aʻe. Inā hoʻonui ʻia ka lōʻihi o ke kaula i 2 mau manawa, a laila loaʻa iā mākou ke kani i kahi octave haʻahaʻa; inā hoʻonui ʻoe i 3 mau manawa, a laila emi ka duodecima.

Ma ke ala, inā hoʻohaʻahaʻa ʻia ke kani duodecimal e hoʻokahi octave, ʻo ia hoʻi. e hoʻonui i ka lōʻihi i nā manawa 2 (loaʻa iā mākou ka 2/3 o ka lōʻihi o ke kaula kumu), a laila e loaʻa iā mākou ka lima like (Fig. 3).

E like me kāu e ʻike ai, ʻo ka hapalima ka wā i loaʻa mai kahi octave a me kahi duodecim.

ʻO ka mea maʻamau, ʻo ka mea mua i manaʻo e hoʻohana i nā ʻanuʻu o ka puʻunaue ʻana me 2 a me 3 e kūkulu i nā memo i kapa ʻia ʻo Pythagoras. He paʻakikī loa ka ʻōlelo ʻana inā ʻo ia ka hihia. A ʻo Pythagoras ʻo ia iho he kanaka ʻaneʻane moʻolelo. ʻO nā moʻolelo kākau mua loa o kāna hana a mākou i ʻike ai ua kākau ʻia ma 200 mau makahiki ma hope o kona make ʻana. ʻAe, a hiki ke manaʻo ʻia ʻo nā mea mele ma mua o ka hoʻohana ʻana o Pythagoras i kēia mau loina, ʻaʻole i hoʻokumu (a ʻaʻole kākau) iā lākou. ʻO kēia mau loina ma ke ao holoʻokoʻa, i kuhikuhi ʻia e nā kānāwai o ke ʻano, a inā e hoʻoikaika ka poʻe mele o nā kenekulia mua i ka lokahi, ʻaʻole hiki iā lākou ke kāpae iā lākou.

E ʻike kākou i ke ʻano o nā memo e loaʻa iā mākou ma ka hele ʻana ʻelua a ʻekolu paha.

Inā mākou e puʻunaue (a hoʻonui paha) i ka lōʻihi o kahi kaula me ka 2, a laila e loaʻa mau iā mākou kahi leka he octave ke kiʻekiʻe (a i ʻole ka haʻahaʻa). Ua kapa ʻia nā memo i ʻokoʻa e ka octave, hiki iā mākou ke ʻōlelo ʻaʻole e loaʻa iā mākou nā memo "hou" ma kēia ʻano.

He ʻokoʻa loa ke kūlana me ka mahele ʻana i ka 3. E lawe kāua i ka "hana" ma ke ʻano he memo mua a ʻike i kahi e alakaʻi ai nā ʻanuʻu o nā triplets iā mākou.

Hoʻokomo mākou ma ke axis duodecim no ka duodecimo (fig. 4).

Hiki iā ʻoe ke heluhelu hou aku e pili ana i nā inoa Latin o nā memo ma aneʻi. ʻO ka index π ma lalo o ka memo, ʻo ia nā memo o ka unahi Pythagorean, no laila e maʻalahi iā mākou ke hoʻokaʻawale iā lākou mai nā memo o nā unahi ʻē aʻe.

E like me kāu e ʻike ai, aia ma ka ʻōnaehana Pythagorean i ʻike ʻia nā prototypes o nā memo āpau a mākou e hoʻohana nei i kēia lā. ʻAʻole wale ke mele.

Inā lawe mākou i nā memo 5 kokoke loa i "do" (mai "fa" a "la"), loaʻa iā mākou ka mea i kapa ʻia. pentatonika - ka ʻōnaehana waena, i hoʻohana nui ʻia a hiki i kēia lā. ʻO nā memo 7 e hiki mai ana (mai "fa" a "si") e hāʻawi diatonic. ʻO ia kēia mau memo i kēia manawa ma nā kī keʻokeʻo o ka piano.

ʻOi aku ka paʻakikī o ke kūlana me nā kī ʻeleʻele. I kēia manawa, hoʻokahi wale nō kī ma waena o "do" a me "re", a ma muli o ke kūlana, ua kapa ʻia ʻo C-sharp a i ʻole D-flat. Ma ka ʻōnaehana Pythagorean, ʻelua mau memo like ʻole ʻo C-sharp a me D-flat a ʻaʻole hiki ke kau ʻia ma ke kī hoʻokahi.

hoʻokani maoli

He aha ka mea i hoʻololi ai nā kānaka i ka ʻōnaehana Pythagorean i kūlohelohe? ʻO ka mea kupanaha, ʻo ke kolu.

I ka hoʻokani Pythagorean, ʻo ka hapakolu nui (no ka laʻana, ka interval do-mi) ʻaʻohe dissonant. Ma ka Fig. 4, ʻike mākou no ka loaʻa ʻana mai ka memo "hana" i ka memo "mi", pono mākou e lawe i 4 mau ʻanuʻu duodecimal, e puʻunaue i ka lōʻihi o ke kaula me 4 3 manawa. ʻAʻole ia he mea kupanaha ka liʻiliʻi o nā leo like ʻelua, liʻiliʻi consonance, ʻo ia hoʻi, consonance.

Akā kokoke loa i ke kolu Pythagorean aia kahi hapakolu kūlohelohe, ʻoi aku ka leo o ka consonant.

Pythagorean kolu

Kūlohelohe kolu

ʻO ka poʻe mele mele, i ka wā i puka mai ai kēia wā, ua lawe ʻia ke kolu maoli o ka consonant.

No ka loaʻa ʻana o kahi hapakolu maoli ma kahi kaula, pono ʻoe e puʻunaue i kona lōʻihi me 5, a laila e hoʻohaʻahaʻa i ke kani i ka hopena ma 2 octaves, no laila ʻo 4/5 ka lōʻihi o ke kaula (Fig. 5).

E like me kāu e ʻike ai, ʻike ʻia ka māhele o ke kaula i 5 mau ʻāpana, ʻaʻole i loko o ka ʻōnaehana Pythagorean. ʻO ia ke kumu i hiki ʻole ai ke kolu kūlohelohe i ka ʻōnaehana Pythagorean.

ʻO ia ʻano hoʻololi maʻalahi i alakaʻi i kahi hoʻoponopono o ka ʻōnaehana holoʻokoʻa. Ma hope o ke kolu, ua hoʻololi nā leo āpau koe ka prima, kekona, ʻehā a me ka lima. Hoʻokumu ʻia maoli (i kekahi manawa kapa ʻia maemae) hale. Ua lilo ia i ʻoi aku ka consonantal ma mua o Pythagorean, akā ʻaʻole ʻo ia wale nō ka mea.

ʻO ka mea nui i hiki mai i ke mele me ke kani kūlohelohe ʻo ia ka tonality. ʻO ka mea nui a me ka liʻiliʻi (ma ke ʻano o nā chord a me nā kī) i hiki ke hoʻokani wale ʻia. ʻO ia hoʻi, ma ke ʻano, hiki ke hōʻuluʻulu ʻia kahi triad nui mai nā memo o ka ʻōnaehana Pythagorean, akā ʻaʻole ia e loaʻa ka maikaʻi e hiki ai iā ʻoe ke hoʻonohonoho i ka tonality i ka ʻōnaehana Pythagorean. ʻAʻole ia he coincidence i ka mele kahiko ka hale waihona waiwai monody. ʻAʻole ʻo Monody wale nō ke mele monophonic, ma ke ʻano hiki ke ʻōlelo ʻia he monophony, ka mea e hōʻole ʻole i ka hiki ke hoʻokani harmonic.

ʻAʻohe kumu o ka wehewehe ʻana i ke ʻano o ka mea nui a me ka liʻiliʻi i ka poʻe mele.

No nā mea hoʻokani mele ʻole, hiki ke ʻōlelo ʻia kēia hoʻokolohua. E hoʻokomo i kekahi ʻāpana kahiko mai ka Viennese classics a i ka waenakonu o ke kenekulia 95. Me ka manaʻo o 99,9% e lilo ia i ka mea nui a i ʻole ka mea liʻiliʻi. E ho'ā i nā mele kaulana o kēia wā. Aia ia i loko o kahi mea nui a i ʻole liʻiliʻi me ka nui o XNUMX%.

Pālākiō wela

Nui nā hoʻāʻo ʻana i ke ʻano. ʻO ka ʻōlelo maʻamau, ʻo ke ʻano he ʻokoʻa o kahi wā mai ka maʻemaʻe (kūlohelohe a i ʻole Pythagorean).

ʻO ka koho kūleʻa loa ʻo ia ke ʻano like (RTS), i ka wā i hoʻokaʻawale ʻia ai ka octave i 12 mau "kaulike". Hoʻomaopopo ʻia ka "kaulike" ma ʻaneʻi penei: ʻo kēlā me kēia memo aʻe ka helu like o nā manawa kiʻekiʻe ma mua o ka mea ma mua. A i ka hoʻokiʻekiʻe ʻana i ka memo 12 mau manawa, pono mākou e hele i kahi octave maʻemaʻe.

Ke hoʻopau nei i kēlā pilikia, loaʻa iā mākou kahi 12-note ʻano like ʻole (a i ʻole RTS-12).

Akā, no ke aha i makemake nui ʻia ai ka naʻau?

ʻO ka mea ʻoiaʻiʻo inā inā i loko o kahi kani kūlohelohe (ʻo ia hoʻi, ua hoʻololi ʻia e kahi mea i hoʻohālikelike ʻia) e hoʻololi i ka tonic - ʻo ke kani kahi a mākou e "helu ai" i ke tonality - no ka laʻana, mai ka memo "hana" i ka memo " re", a laila e uhaki ʻia nā pilina āpau āpau. ʻO kēia ka kuʻekuʻe wāwae o Achilles o nā kani maʻemaʻe a pau, a ʻo ke ala wale nō e hoʻoponopono ai i kēia, ʻo ia ka hoʻokaʻawale ʻana i nā manawa āpau, akā like kekahi me kekahi. A laila ke neʻe ʻoe i kahi kī ʻokoʻa, ʻoiaʻiʻo, ʻaʻohe mea e loli.

He mau pono ʻē aʻe ka ʻōnaehana tempered. No ka laʻana, hiki iā ia ke pāʻani i ke mele, i kākau ʻia no ka unahi maoli, a no ka Pythagorean.

ʻO nā mea liʻiliʻi, ʻo ka mea maopopo loa he wahaheʻe nā manawa āpau koe ka octave i kēia ʻōnaehana. ʻOiaʻiʻo, ʻaʻole pono ka pepeiao o ke kanaka. Inā he microscopic ka wahaheʻe, a laila ʻaʻole hiki iā mākou ke ʻike. Akā, ʻo ke kolu o ka huhū like, mamao loa ia mai ka mea maoli.

Kūlohelohe kolu

ʻEkolu huhū

Aia kekahi mau ala i waho o kēia kūlana? Hiki ke hoʻomaikaʻi ʻia kēia ʻōnaehana?

He aha e hiki mai ana?

E hoʻi kāua i ko mākou Dominica mua. Hiki iā mākou ke ʻōlelo i ka wā ma mua o ka hoʻopaʻa leo ʻana aia kekahi mau mele mele paʻa?

Hōʻike kā mākou noʻonoʻo ʻoiai inā e neʻe ka memo "la", a laila e mau nā kūkulu āpau (e hoʻokaʻawale i ke kaula i 2, 3 a me 5 mau ʻāpana). ʻO ia ke ʻano o nā ʻōnaehana e lilo i mea like. ʻOiaʻiʻo, hiki i kekahi monastery ke hoʻohana i ka Pythagorean kolu i kāna hana, a ʻo ka lua - ʻo ke ʻano maoli, akā ma ka hoʻoholo ʻana i ke ʻano o kona kūkulu ʻana, e hiki iā mākou ke hoʻoholo pono i ke ʻano mele, a no laila nā mea hiki i nā monasteries like ʻole. loaʻa mele.

No laila he aha ka hope? Hōʻike ka ʻike o ke kenekulia 12 ʻaʻole i pau ka ʻimi i ka RTS-12. Ma ke ʻano maʻamau, hana ʻia ka hana ʻana o nā tunings hou ma ka hoʻokaʻawale ʻana i ka octave ʻaʻole i 24, akā i loko o ka nui o nā ʻāpana, no ka laʻana, i 36 a i ʻole XNUMX. ʻO kēia ʻano hana mechanistic loa a ʻaʻole hua. Ua ʻike mākou i ka hoʻomaka ʻana o nā kūkulu ʻana ma kahi o ka mahele maʻalahi o ke kaula, ʻo ia hoʻi, pili lākou me nā kānāwai o ka physics, me nā haʻalulu o kēia kaula like. Ma ka hopena wale nō o ke kūkulu ʻana, ua hoʻololi ʻia nā memo i loaʻa me nā mea ʻoluʻolu. Inā mākou e huhū ma mua o ke kūkulu ʻana i kahi mea ma nā ʻāpana maʻalahi, a laila e kū mai ka nīnau: he aha kā mākou e hoʻomāhuahua nei, mai hea nā memo e haʻalele ai mākou?

Akā, aia kekahi nūhou maikaʻi. Inā no ke kūkulu hou ʻana i ke kino mai ka memo "hana" a i ka memo "re", pono ʻoe e wili i nā haneli haneli a me nā paipu, i kēia manawa, e kūkulu hou i ka synthesizer, e kaomi wale i hoʻokahi pihi. ʻO ia ke ʻano, ʻaʻole pono mākou e pāʻani ma waho o ke kani kani, hiki iā mākou ke hoʻohana i nā ratio maʻemaʻe a hoʻololi iā lākou i ka lua o ka pono.

Akā pehea inā makemake mākou e pāʻani ʻaʻole ma nā mea kani uila, akā ma nā "analog"? Hiki paha ke kūkulu i nā ʻōnaehana harmonic hou, e hoʻohana i kekahi kumu ʻē aʻe, ma kahi o ka māhele mechanistic o ka octave?

ʻOiaʻiʻo, hiki iā ʻoe, akā paʻa loa kēia kumuhana e hoʻi mākou i kekahi manawa.

Mea kākau – Roman Oleinikov

Hoʻopuka ka mea kākau i kona mahalo i ka haku mele ʻo Ivan Soshinsky no nā mea leo i hāʻawi ʻia