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

9c42c4bc1d91c409d754da88c91cb2ef?s=47 kur0cky
June 26, 2020

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

9c42c4bc1d91c409d754da88c91cb2ef?s=128

kur0cky

June 26, 2020
Tweet

Transcript

  1. Իָཧ࿦ͱํ޲౷ܭֶͷॳา LVSDLZ

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

    ޷͖ͳԻָɿΫϥγοΫɼαΠέτϥϯεɼFUDʜ 2
  3. Իָ

  4. υϨϛϑΝιϥγυ

  5. υϨϛϑΝιϥγυϨϛϑΝιϥγ υϨϛϑΝιϥγυɾɾɾ

  6. ແݶϧʔϓ ʢ॥؀ʣ

  7. ֯౓ͷσʔλαΠΤϯε

  8. ํ޲౷ܭֶ

  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
  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
  11. ԁप্ͷهड़౷ܭ

  12. ฏۉํ޲͸Ͳͬͪʁ

  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
  14. ԁप্ͷ෼ࢄ 14 ෼ࢄେ ෼ࢄখ

  15. ԁप্ͷ෼ࢄ 15 ฏۉϕΫτϧͷ௕͞ʹண໨͢Ε͹ྑ͍ ෼ࢄɿV = 1 − R ඪ४ภࠩɿsd =

    −2 log(R) ඪ४ภࠩ͸ͪΐͬͱಛघ ෼ࢄେ ෼ࢄখ
  16. ԁप্ͷ֬཰෼෍

  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
  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
  19. ޒ౓ݍ

  20. ޒ౓ݍ DJSDMFPGUI w ԻఔͰ͸ͳ͘ɼௐ LFZ ͷྠ w ֎ଆ͕ϝδϟʔɼ಺ଆ͕ϚΠφʔ w ྡΓ߹͏ௐ͸ه߸

    ̅ ̆ ͕ͭҟͳΔ w Ұप͢Δͱ·ͨ໭ͬͯ͘Δ 20
  21. ޒ౓ݍͷར༻ w εϦʔίʔυ͕Θ͔Γ΍͍͢ w جຊͷίʔυ͔Β྆αΠυΛݟΕ͹ྑ͍ w ࠨճΓ͍ͯ͘͠ͱࣗવͳίʔυʹͳͬͯΔ w πʔϑΝΠϒϫϯ͕؆୯ʹͰ͖Δ w

    KB[[ͳͲͰڧ͍ 21
  22. DBTFTUVEZ ࡞ۂՈ͝ͱͷ࡞ۂ܏޲

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

  24. ༗໊ͳ࡞ۂՈΛൈਮɽ›͕$NBKPS

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

  26. .BSEJB8BUTPO8IFFMFSݕఆ w ԁप্ͷͭͷ෼෍͕ҟͳΔ͔ͷϊϯύϥϝτϦοΫݕఆ w 6ݕఆͷDJSDVMBS֦ு w ܈ͷσʔλΛࠞͥͯ౳ִؒʹฒ΂ΔɽؼແԾઆͷ΋ͱQ஋Λܭࢉ w ݁Ռ 26

    Q஋ ݁Ռ NP[BSUWTNFOEFMTTPIO  غ٫ DIPQJOWTMJTU[  غ٫Ͱ͖ͳ͍
  27. ·ͱΊ w Իָͱ૬ੑ͕ྑ͍ͱࢥΘΕΔํ޲౷ܭֶʹ͍ͭͯɼͦͷॳาͷ ॳาΛ঺հͨ͠ w ௐ߸ͷଆ໘͔Βɼ࡞ۂ܏޲Λ෼ੳͨ͠ɽಛʹɼϦετͱγϣύ ϯͷޒ౓ݍͷ෼෍͸ҟͳΔͱ͸ݴ͑ͳ͔ͬͨɽ 27

  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