kur0cky
June 26, 2020
1.5k

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

June 26, 2020

## 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