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音楽理論と方向統計学の初歩/introduction of circular statistics and musicology

kur0cky
June 26, 2020

音楽理論と方向統計学の初歩/introduction of circular statistics and musicology

kur0cky

June 26, 2020
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  1. Իָཧ࿦ͱํ޲౷ܭֶͷॳา
    LVSDLZ

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  2. ࣗݾ঺հ
    w 5XJUUFSɿ!LVSDLZ@Z
    w "HFɿ
    w ձࣾɿ໊ࢗ؅ཧͷ๭๭ೖࣾϲ݄
    w ԋ૗ɿόΠΦϦϯɼυϥϜ
    w ޷͖ͳԻָɿΫϥγοΫɼαΠέτϥϯεɼFUDʜ
    2

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  3. Իָ

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  4. υϨϛϑΝιϥγυ

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  5. υϨϛϑΝιϥγυϨϛϑΝιϥγ
    υϨϛϑΝιϥγυɾɾɾ

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  6. ແݶϧʔϓ
    ʢ॥؀ʣ

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  7. ֯౓ͷσʔλαΠΤϯε

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  8. ํ޲౷ܭֶ

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  9. ༷ʑͳ॥؀͢Δσʔλ
    w ԁप্ɿ֯౓
    w σΟεΫ্ɿ֯౓ºεΧϥʔ
    w ٿ໘্ɿ֯౓º֯౓
    w γϦϯμʔ্ɿ֯౓ºεΧϥʔ
    w τʔϥε্ɿ֯౓º֯౓
    (0 < r < R)
    (0 < θ < π)
    (0 < r)
    9
    ࠓճ͸ԁप্͚ͩΛߟ͑Δ

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  10. ํ޲౷ܭֶ
    w ֯౓΍࣌ؒͳͲɼ॥؀͢Δ஋ʹରͯ͠΋֬཰෼෍Λߟ͍͑ͨ
    w هड़౷ܭɼ෼෍ɼݕఆɼϞσϦϯάɼFUD
    w LVSDLZ͕ձ࿩Ͱൃ͠΍͍͢Ի͸ʁ
    w ͋Δ஍఺ͷ෩޲ͷ࣌ܥྻߏ଄͸Ͳ͏ͳͬͯΔʁ
    w Ԡ༻෼໺
    w ಈ෺ͷӡಈํ޲ɼ෩΍ਫྲྀɼ࣌ؒɼ෼ࢠͷೋ໘֯ɼFUD
    10

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  11. ԁप্ͷهड़౷ܭ

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  12. ฏۉํ޲͸Ͳͬͪʁ

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  13. ฏۉํ޲

    ϕΫτϧͷฏۉͰߟ͑Δ
    (
    1
    4
    π +
    7
    4
    π)/2 = π
    13
    º

    ΦΠϥʔͷެࣜΑΓɼReiθ =
    1
    N ∑
    j
    eiθj
    (Rcos¯
    θ, Rsin¯
    θ) =
    1
    N ∑
    j
    cosθj
    ,
    1
    N ∑
    j
    sinθj

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  14. ԁप্ͷ෼ࢄ
    14
    ෼ࢄେ ෼ࢄখ

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  15. ԁप্ͷ෼ࢄ
    15
    ฏۉϕΫτϧͷ௕͞ʹண໨͢Ε͹ྑ͍
    ෼ࢄɿV = 1 − R
    ඪ४ภࠩɿsd = −2 log(R)
    ඪ४ภࠩ͸ͪΐͬͱಛघ
    ෼ࢄେ ෼ࢄখ

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  16. ԁप্ͷ֬཰෼෍

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  17. ෼෍ͷ࡞Γํ
    w ר͖ࠐΈ๏ɿ֬཰ີ౓ؔ਺Λԁप্ʹר͖ࠐΉ
    w XSBQQFE$BVDIZ෼෍͕༗໊
    w ࣹӨ๏ɹɹɿมྔ֬཰ϕΫτϧΛݪ఺͔Βͷڑ཭ͰׂΔ
    w ৚݅෇͖๏ɿมྔཱ֬ϕΫτϧΛۃ࠲ඪม׵͠ɼ֯౓ΛಘΔ
    w ਖ਼ن෼෍ˠWPONJTFT෼෍
    w ౤Ө๏ɹɹɿ ͱͯ֯͠౓ΛಘΔɽ
    x = tan(θ/2)
    17

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  18. WPONJTFT෼෍
    w ผ໊ʮԁप্ͷਖ਼ن෼෍ʯ
    w ର৅͔ͭ୯ๆ
    w ࢦ਺ܕ෼෍଒
    w ݫີʹ͸࿨ͷ࠶ੜੑ͕ෆ੒ཱ
    w
    w ɿਖ਼نԽఆ਺
    w ɿฏۉํ޲ύϥϝʔλ
    w ɿूத౓ύϥϝʔλ
    f(θ; μ, κ) = Ceκ cos(θ−μ)
    C
    μ
    κ
    18

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  19. ޒ౓ݍ

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  20. ޒ౓ݍ DJSDMFPGUI

    w ԻఔͰ͸ͳ͘ɼௐ LFZ
    ͷྠ
    w ֎ଆ͕ϝδϟʔɼ಺ଆ͕ϚΠφʔ
    w ྡΓ߹͏ௐ͸ه߸ ̅ ̆
    ͕ͭҟͳΔ
    w Ұप͢Δͱ·ͨ໭ͬͯ͘Δ
    20

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  21. ޒ౓ݍͷར༻
    w εϦʔίʔυ͕Θ͔Γ΍͍͢
    w جຊͷίʔυ͔Β྆αΠυΛݟΕ͹ྑ͍
    w ࠨճΓ͍ͯ͘͠ͱࣗવͳίʔυʹͳͬͯΔ
    w πʔϑΝΠϒϫϯ͕؆୯ʹͰ͖Δ
    w KB[[ͳͲͰڧ͍
    21

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  22. DBTFTUVEZ
    ࡞ۂՈ͝ͱͷ࡞ۂ܏޲

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  23. σʔλ֓ཁ
    23
    w ༗໊࡞ۂՈͷۂ৘ใϦετ
    w ࡞඼൪߸ɼλΠτϧɼௐɼ࡞ۂ೥ɼδϟϯϧɼฤ੒
    w ιʔεɿແྉָේͷϥΠϒϥϦʔ*.4-1͔ΒεΫϨΠϐϯά
    ໘ന͍σʔληοτʹͳΓͦ͏ͳͷͰɼγΣΞͯ͠෼ੳ͠·ͤΜ͔ʁস
    https://imslp.org/wiki/Main_Page

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  24. ༗໊ͳ࡞ۂՈΛൈਮɽ›͕$NBKPS

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  25. ϝϯσϧεκʔϯ͸ϞʔπΝϧτͷӨڹΛଟ෼ʹड͚͍ͯΔΒ͍͠
    ٕ޼ܥϐΞϊ࡞ۂՈ͸ࣗ༝౓͕ߴͦ͏ɽࣅͯΔ

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  26. .BSEJB8BUTPO8IFFMFSݕఆ
    w ԁप্ͷͭͷ෼෍͕ҟͳΔ͔ͷϊϯύϥϝτϦοΫݕఆ
    w 6ݕఆͷDJSDVMBS֦ு
    w ܈ͷσʔλΛࠞͥͯ౳ִؒʹฒ΂ΔɽؼແԾઆͷ΋ͱQ஋Λܭࢉ
    w ݁Ռ
    26
    Q஋ ݁Ռ
    NP[BSUWTNFOEFMTTPIO غ٫
    DIPQJOWTMJTU[ غ٫Ͱ͖ͳ͍

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  27. ·ͱΊ
    w Իָͱ૬ੑ͕ྑ͍ͱࢥΘΕΔํ޲౷ܭֶʹ͍ͭͯɼͦͷॳาͷ
    ॳาΛ঺հͨ͠
    w ௐ߸ͷଆ໘͔Βɼ࡞ۂ܏޲Λ෼ੳͨ͠ɽಛʹɼϦετͱγϣύ
    ϯͷޒ౓ݍͷ෼෍͸ҟͳΔͱ͸ݴ͑ͳ͔ͬͨɽ
    27

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  28. ͓͢͢Ίจݙ
    w +BNNBMBNBEBLB 43 4FOHVQUB "
    5PQJDTJODJSDVMBS
    TUBUJTUJDT 7PM
    XPSMETDJFOUJpD
    w όΠϒϧతͳɼํ޲౷ܭͷ௒༗໊ςΩετ
    w ਗ਼ਫ๜෉
    ʰ֯౓σʔλͷϞσϦϯά *4.γϦʔζਐԽ͢Δ౷ܭ਺ཧ
    ʱ ۙ
    ୅Պֶࣾ
    w ํ޲౷ܭͰ͸௝͍͠࿨ॻ
    w 7BMEF[ %/
    45"5*45*$4*/.64*$0-0(:
    w Իָº౷ܭͷຊ
    28

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