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

Transcript

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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