Ki hou

Ma ka pō o Kepakemapa 23-24, ʻo Johann Franz Encke, ka mea i hoʻolauleʻa i kona lā hānau he 55, ua kikeke mau ʻia i ka hale. Ua kū ʻo Heinrich d'Arre, he haumāna pau ka hanu, ma ka puka. Ma hope o ke kamaʻilio ʻana i ʻelua mau huaʻōlelo me ka malihini, ua hoʻomākaukau koke ʻo Encke, a hele lāua ʻelua i ka Berlin Observatory i alakaʻi ʻia e Encke, kahi e kali pū ana kekahi Johann Galle e kali pū ana iā lāua ma kahi kokoke i ke kelepona hoʻohālike.

ʻO nā mākaʻikaʻi, kahi i hui pū ai ka meʻe o ka lā ma kēia ʻano, a hiki i ka hapalua hola ʻekolu o ka pō. No laila, i ka makahiki 1846, ua ʻike ʻia ka honua ʻewalu o ka ʻōnaehana solar, ʻo Neptune.

Akā ʻoi aku ka liʻiliʻi o ka ʻike i hana ʻia e kēia mau astronomers ma mua o ko mākou ʻike ʻana i ka honua a puni mākou.

Kumumanaʻo a me ka hana

ʻO ka nui o Neptune ma lalo o 3 mau kekona arc. No ka hoʻomaopopo ʻana i ke ʻano o kēia, e noʻonoʻo ʻoe e nānā ana ʻoe i kahi pōʻai mai kona kikowaena. E mahele i ka pōʻai i 360 mau ʻāpana (Fig. 1).

ʻO ka huina i loaʻa iā mākou ma kēia ʻano he 1° (hoʻokahi degere). ʻĀnō e hoʻokaʻawale i kēia ʻāpana lahilahi i nā ʻāpana ʻē aʻe 60 (ʻaʻole hiki ke hōʻike hou i kēia ma ke kiʻi). ʻO kēlā me kēia ʻāpana he 1 mau minuke arc. A ʻo ka hope, puʻunaue mākou i ka 60 a me kahi minuke arc - loaʻa iā mākou kahi arc kekona.

Pehea i ʻike ai ka poʻe kilo hōkū i kahi mea liʻiliʻi ma ka lewa, ʻoi aku ka liʻiliʻi ma mua o 3 mau kekona arc? ʻAʻole ʻo ka mana o ka telescope ka manaʻo, akā pehea e koho ai i ke kuhikuhi ma ka honua lani nui kahi e ʻimi ai i kahi honua hou.

He maʻalahi ka pane: ua haʻi ʻia nā mea nānā i kēia kuhikuhi. ʻO ka mea haʻi i kapa ʻia ʻo ka French mathematician Urbain Le Verrier, ʻo ia ka mea nāna, e nānā ana i nā anomalies i ke ʻano o Uranus, ua manaʻo ʻo ia he honua ʻē aʻe ma hope ona, ʻo ia ka mea e huki ai iā Uranus iā ia iho, e hoʻohuli iā ia mai ka "pololei. ” alahele. ʻAʻole wale ʻo Le Verrier i hana i kēlā manaʻo, akā hiki iā ia ke helu i kahi e pono ai kēia honua, ua kākau ʻo ia e pili ana iā Johann Galle, nona ka mea ma hope o ka ʻimi ʻana i ka liʻiliʻi loa.

No laila, ua lilo ʻo Neptune i ka honua mua i wānana mua ʻia e ke kumumanaʻo, a laila loaʻa i ka hana. Ua kapa ʻia kēlā ʻike ʻo "ka ʻike ma ka piko o ka peni", a ua hoʻololi mau loa ia i ka manaʻo i ka ʻepekema ʻepekema e like me ia. Ua pau ka hoʻomaopopo ʻana i ka ʻepekema ʻepekema he pāʻani wale nō o ka noʻonoʻo, ʻoi aku ka maikaʻi o ka wehewehe ʻana i "he aha"; Ua hōʻike maopopo ka ʻepekema ʻepekema i kona hiki ke wānana.

Ma o na hoku i ka poe mele

E hoʻi kāua i ke mele. E like me kāu e ʻike ai, he 12 mau memo i loko o ka octave. ʻEhia mau pū kani ʻekolu e hiki ke kūkulu ʻia mai ia mau mea? He maʻalahi ka helu - aia he 220 mau mele.

ʻO kēia, ʻoiaʻiʻo, ʻaʻole ia he helu astronomically nui, akā i loko o ia mau consonances he mea maʻalahi ke huikau.

ʻO ka mea pōmaikaʻi, loaʻa iā mākou kahi manaʻo ʻepekema o ke kuʻikahi, loaʻa iā mākou kahi "palapala ʻāina" - ke ākea o nā multiplicities (PC). Pehea i kūkulu ʻia ai kahi PC, ua noʻonoʻo mākou i kekahi o nā memo mua. Eia kekahi, ua ʻike mākou pehea e loaʻa ai nā kī maʻamau i ka PC - nui a me ka liʻiliʻi.

E hoʻokaʻawale hou aku kākou i kēlā mau loina e kau ana i nā kī kuʻuna.

ʻO kēia ke ʻano o ka nui a me ka liʻiliʻi i ka PC (fig. 2 a me ka fig. 3).

ʻO ke kumu waena o ia mau hana he kihi: me nā kukuna i kuhikuhi ʻia i luna - he triad nui, a i ʻole me nā kukuna i kuhikuhi ʻia i lalo - he triad liʻiliʻi (Fig. 4).

Hoʻokumu kēia mau kihi i kahi crosshair, e hiki ai iā ʻoe ke "centralize" i kekahi o nā kani, e hoʻolilo iā ia i "main". ʻO kēia ke ʻano o ka tonic.

A laila kope ʻia kēlā ʻano kihi i ka symmetrically, i nā leo kokoke loa. Hāʻawi kēia kope i ka subdominant a me ka mana.

Ua kapa ʻia ʻo Tonic (T), subdominant (S) a me dominant (D) i nā hana nui ma ke kī. ʻO nā memo i hoʻokomo ʻia i loko o kēia mau kihi ʻekolu e hana i ka unahi o ke kī pili.

Ma ke ala, ma waho aʻe o nā hana nui i ke kī, ʻike pinepine ʻia nā ʻaoʻao ʻaoʻao. Hiki iā mākou ke hōʻike iā lākou ma PC (Fig. 5).

Eia ʻo DD he ʻano mana pālua, ʻo iii ka hana o ke kolu o ka ʻanuʻu, ʻo VIb ke ono i hoʻemi ʻia, a pēlā aku. ʻIke mākou ʻo ia nā kihi nui a me nā kihi liʻiliʻi, aia ma kahi mamao loa mai ka tonic.

Hiki i kekahi memo ke hana ma ke ʻano he tonic, e kūkulu ʻia nā hana mai ia mea. ʻAʻole e loli ke ʻano - ke kūlana pili o nā kihi i ka PC - e neʻe wale ia i kahi ʻē aʻe.

ʻAe, ua loiloi mākou i ka hoʻonohonoho pono ʻana o nā tonali kuʻuna. E ʻike anei mākou, e nānā ana iā lākou, i ke ala e pono ai ke ʻimi i nā "planeta hou"?

Manaʻo wau e loaʻa iā mākou kekahi mau kino lani.

E nana kakou i ka fig. 4. Hōʻike ia pehea mākou i hoʻonohonoho pono ai i ke kani me ke kihi triad. I kekahi hihia, ua kuhikuhi ʻia nā kaola ʻelua i luna, i kekahi - i lalo.

Me he mea lā ua hala mākou i ʻelua mau koho hou aʻe, ʻaʻole ʻoi aku ka maikaʻi ma mua o ka hoʻonohonoho ʻana i ka memo. E kuhikuhi mākou i kekahi kukuna i luna a i lalo kekahi. A laila loaʻa iā mākou kēia mau kihi (Fig. 6).

Hoʻokumu kēia mau triad i ka memo, akā ma kahi ʻano maʻamau. Inā ʻoe e kūkulu iā lākou mai nā memo i, a laila ma ke koʻokoʻo e like lākou me kēia (Fig. 7).

E mālama mākou i nā loina hou aʻe o ke kūkulu ʻana i ka tonality ʻaʻole i loli: e hoʻohui mākou i ʻelua kihi like symmetrically i nā memo kokoke loa.

E loaʻa kī hou (Fig 8).

E kakau kakou i ko lakou mau unahi no ka akaka.

Ua hōʻike mākou i nā memo me nā koi, akā, ʻoiaʻiʻo, i kekahi mau mea e ʻoi aku ka maʻalahi o ke kākau hou ʻana iā lākou me nā papa enharmonic.

Hōʻike ʻia nā hana nui o kēia mau kī ma ka fig. 8, akā nalo nā ʻaoʻao e hoʻopau i ke kiʻi. Ma ka hoʻohālikelike me Fig. 5 hiki iā mākou ke huki iā lākou i kahi PC (Fig. 10).

E kākau kākou iā lākou ma ke koʻokoʻo mele (Fig. 11).

Hoʻohālikelike i ka gamma ma Fig. 9 a me nā inoa hana ma ka fig. 11, hiki iā ʻoe ke ʻike i ka hoʻopaʻa ʻana i nā ʻanuʻu ma aneʻi he mea ʻole ia, "haʻalele ʻia e ka hoʻoilina" mai nā kī kuʻuna. ʻO ka ʻoiaʻiʻo, hiki ke kūkulu ʻia ka hana o ka degere ʻekolu ʻaʻole loa mai ke kolu o ka memo ma ka pālākiō, ka hana o ke ono i hoʻemi ʻia - ʻaʻole loa mai ke ono i hoʻemi ʻia, a pēlā aku, he aha ke ʻano o kēia mau inoa? Hoʻoholo kēia mau inoa i ke ʻano hana o kahi triad. ʻO ia hoʻi, ʻo ka hana o ke kolu o ka ʻanuʻu i ke kī hou e hana like i ka hana o ke kolu o ka ʻanuʻu i hana ʻia ma ka nui a i ʻole ka liʻiliʻi, ʻoiai ʻo ia ka mea ʻokoʻa loa i ka hoʻolālā ʻana: hoʻohana ʻokoʻa ka triad a aia ia. ma kahi ʻokoʻa ma ka pālākiō.

Malia paha e hoʻokūpaʻa i nā nīnau manaʻo ʻelua

Hoʻopili ʻia ka mea mua me ke tonality o ka hapaha ʻelua. ʻIke mākou ma ka hoʻonohonoho maoli ʻana i ka memo paʻakai, Ua kūkulu ʻia kona kihi tonic mai i (i – ke kani haʻahaʻa ma kahi chord). Noi mai i hoʻomaka ka paona o kēia tonality. A ma ka laulā, ʻo ka tonality a mākou i hōʻike ai e kapa ʻia ʻo ia ka tonality o ka lua o ka hapaha i. He mea ʻē kēia i ka nānā mua ʻana. Eia naʻe, inā mākou e nānā i ka Fig. 3, e ʻike mākou ua hālāwai mua mākou i ka "hoʻololi" like i ka mea liʻiliʻi maʻamau. Ma kēia ʻano, ʻaʻohe mea kupaianaha i hana ʻia i ke kī o ka hapaha lua.

ʻO ka nīnau ʻelua: no ke aha i kapa ʻia ai kēlā inoa - nā kī o ka ʻāpana II a me IV?

Ma ka makemakika, e puunaue i na ko'i elua i ka mokulele i 4 mau hapaha, i helu pinepine ia ma ke kuekuka manawa (Fig. 12).

Nānā mākou i kahi e kuhikuhi ʻia ai nā kukuna o ke kihi e pili ana, a kāhea mākou i nā kī e like me kēia hapaha. I kēia hihia, ʻo ka mea nui ke kī o ka hapaha mua, ʻo ke keiki liʻiliʻi ke kolu o ka hapaha, a ʻo nā kī hou ʻelua, ʻo ia hoʻi, ʻo II a me IV.

Hoʻonohonoho i nā telescopes

Ma ke ʻano he ʻai ʻai, e hoʻolohe kākou i kahi haʻawina liʻiliʻi i kākau ʻia e ka haku mele ʻo Ivan Soshinsky ma ke kī o ka hapahā ʻehā.

"Etulle" I. Soshinsky

ʻO nā kī ʻehā wale nō i loaʻa iā mākou? ʻO ka ʻōlelo paʻa, ʻaʻole. ʻO ka ʻōlelo koʻikoʻi, ʻaʻole pono nā kūkulu tonal no ka hoʻokumu ʻana i nā ʻōnaehana mele, hiki iā mākou ke hoʻohana i nā loina ʻē aʻe i pili ʻole i ka centralization a i ʻole symmetry.

Akā e hoʻopaneʻe mākou i ka moʻolelo e pili ana i nā koho ʻē aʻe i kēia manawa.

Me he mea lā iaʻu he mea nui kekahi ʻaoʻao. ʻO nā hana manaʻo a pau ke kūpono wale nō ke hele lākou mai ka manaʻo i ka hana, i ka moʻomeheu. Pehea i hoʻopaʻa ʻia ai ka naʻau i ke mele ma hope o ke kākau ʻana o ka Well-Tempered Clavier e JS Bach a me nā ʻōnaehana ʻē aʻe e pili ana i ko lākou neʻe ʻana mai ka pepa a i nā helu, i nā keʻena ʻaha mele, a i ka hopena i ka ʻike mele o nā mea hoʻolohe.

ʻAe, e hoʻonohonoho i kā mākou telescopes a ʻike inā hiki i ka poʻe haku mele ke hōʻoia iā lākou iho he mau paionia a he poʻe colonizer o nā honua mele hou.

Mea kākau — Roman Oleinikov