Link
Embed
Share
Beginning
This slide
Copy link URL
Copy link URL
Copy iframe embed code
Copy iframe embed code
Copy javascript embed code
Copy javascript embed code
Share
Tweet
Share
Tweet
Slide 1
Slide 1 text
Fundamentals of Music Processing Chapter 5: Chord Recognition খྛ ᕣՏ εϥΠυʹؚ·ΕΔਤFundamentals of Music ProcessingΑΓҾ༻
Slide 2
Slide 2 text
Chapter 5: Chord Recognition Chord(Ի) • 3ͭҎ্ͷҟͳΔԻූ͔Βߏ͞ΕΔԻͷ͜ͱ Harmony() • ෳͷԻ͔ΒͳΔܥྻɺԻਐߦ FM7 G7 Em7 Am Harmony
Slide 3
Slide 3 text
Chapter 5: Chord Recognition Chord Recognition(Իೝࣝ) • Ի͔ΒԻਐߦΛೝࣝ͢Δٕज़ ԻָϑΝΠϧ͔ΒίʔυේΛࣗಈͰ࡞ग़དྷΔ Իೝ͕ࣝ͏·͍͘͘ͱ…
Slide 4
Slide 4 text
Chapter 5.3: HMM-Based Chord Recognition Chapter 5.1~5.2 • ಛྔ͔ΒԻΛ͋Δఔਪఆग़དྷΔ ͔͠͠ɺ͜ΕԻҰͭҰ͔ͭ͠ݟ͍ͯͳ͍ Α͘ग़ΔԻܨ͕Γͷڧ͍Իʹண͍ͨ͠ ྫ: I–IV–V–Iਐߦ • FGසग़͠ɺ͍͖ͳΓFmʹߦ͘͜ͱ΄΅ແ͍ HMM(ӅΕϚϧίϑϞσϧ)Λར༻ͯ͠ԻਪఆΛߦ͏
Slide 5
Slide 5 text
Chapter 5.3: HMM-Based Chord Recognition Ի: , ঢ়ଶ: (for ) ͱͨ͠ͱ͖ɺϚϧίϑੑΛԾఆ͢Δͱ Ͱ͋Δ֬ A := {α1 , α2 , ⋯, αI } s i ∈ [1 : I] sn+1 = αj P[sn+1 = αj |sn = αi , sn−1 = αk , ⋯] = P[sn+1 = αj |P[sn+1 = αj |sn ] ͜͜Ͱ ΛҎԼͷΑ͏ʹఆٛ͢Δɻ(for ) aij i, j ∈ [1 : I] ͜Εঢ়ଶ͕ ͔Β ʹભҠ͢Δ֬ͱߟ͑Δ͜ͱ͕ग़དྷΔ αi αj aij := P[sn+1 = αj |sn = αi ] ∈ [0,1] ·ͣɺϚϧίϑ࿈Λར༻ͨ͠Ի༧ଌʹ͍ͭͯઆ໌͢Δ
Slide 6
Slide 6 text
Chapter 5.3: HMM-Based Chord Recognition ۩ମྫ; , ͷͱ͖ I = 3 A := {α1 = C, α2 = G, α3 = F} ·ͨ࠷ॳͷঢ়ଶ͕ Ͱ͋Δ֬ΛҎԼͷΑ͏ʹఆٛ͢Δ αi ci := P[s1 = αi ] ∈ [0,1]
Slide 7
Slide 7 text
Chapter 5.3: HMM-Based Chord Recognition , , ͷͱ͖ ঢ়ଶܥྻ: ʹ͍ͭͯߟ͑Δ I = 3 A := {α1 = C, α2 = G, α3 = F} C = (c1 , c2 , c3 )T = (0.6,0.2,0.3)T S = (C, C, C, G, G, F, F, C, C) ࠷ॳͷঢ়ଶ͕ Ͱ͋Δ֬ΛҎԼͷΑ͏ʹఆٛ͠ɺ αi ci := P[s1 = αi ] ∈ [0,1] ۩ମྫ
Slide 8
Slide 8 text
Chapter 5.3: HMM-Based Chord Recognition ભҠ͕֬ҎԼͷͱ͖ ͷΑ͏ͳԻਐߦ͕ى͖Δ֬ S S = (C, C, C, G, G, F, F, C, C) = c1 ⋅ a11 ⋅ a11 ⋅ a12 ⋅ a22 ⋅ a23 ⋅ a33 ⋅ a31 ⋅ a11 ≈ 1.29 ⋅ 10−4
Slide 9
Slide 9 text
Chapter 5.3: HMM-Based Chord Recognition ઌఔঢ়ଶܥྻ Λ༻͍ͯɺԻਐߦͷ֬Λܭࢉ͕ͨ͠ ࣮ੈքͰऔΓ͏Δͯ͢ͷ ʹ͍ͭͯܭࢉෆՄೳ S S ྫ: 10छྨͷԻɺ20͔ͭΒߏ͞ΕΔۂͷ߹ ύλʔϯͷ֬Λܭࢉ͢Δඞཁ͕͋Δ 1020 ͦ͜Ͱ෦ͷঢ়ଶͰͳ͘ɺಛϕΫτϧΛ༻͍ͯ ԻਐߦΛٻΊΔํ๏ͱͯ͠HMMΛར༻͢Δɻ
Slide 10
Slide 10 text
Chapter 5.3: HMM-Based Chord Recognition
Slide 11
Slide 11 text
Chapter 5.3: HMM-Based Chord Recognition
Slide 12
Slide 12 text
Chapter 5.3: HMM-Based Chord Recognition Input: Իσʔλ͔Β؍ଌͨ͠ܥྻ ͔Β ϞσϧΛར༻͠ɺ؍ଌܥྻ Λ࡞ɻ O = (o1 , ⋯, oN ) B = (β1 , ⋯, βN ) ؍ଌܥྻ ؍ଌγϯϘϧ ͔Βߏ͞ΕΔ B = (β1 , ⋯, βN ) ℬ = {β1 , ⋯, βk } (for k ∈ [1 : K])
Slide 13
Slide 13 text
Chapter 5.3: HMM-Based Chord Recognition
Slide 14
Slide 14 text
Chapter 5.3: HMM-Based Chord Recognition Viterbi: ؍ଌܥྻ ͱ ॳظঢ়ଶͷ֬ ੜ֬ͱભҠ͔֬Β༗άϥϑΛ࡞ B = (β1 , ⋯, βN ) C = (c1 , c2 , c3 )T = (0.6,0.2,0.3)T ੜ֬ ભҠ֬
Slide 15
Slide 15 text
Chapter 5.3: HMM-Based Chord Recognition ੜ֬ ભҠ֬ ॳظঢ়ଶͷ֬ ੜ͞Εͨ༗άϥϑ
Slide 16
Slide 16 text
Chapter 5.3: HMM-Based Chord Recognition ViterbiΞϧΰϦζϜʹΑͬͯ ࠷Β͍͠ܦ࿏ʹ͍ͭͯܭࢉΛߦ͏
Slide 17
Slide 17 text
Chapter 5.3: HMM-Based Chord Recognition ੜ͞Εͨ༗άϥϑ ViterbiΞϧΰϦζϜͰ֤ҐஔͰɺ ֤ԻʹͨͲΓண͘·Ͱͷ࠷దίετͱ ͦͷલʹࢸΔ·ͰͷϙΠϯλΛ֮͑ͳ͕ΒܭࢉΛߦ͏
Slide 18
Slide 18 text
Chapter 5.3: HMM-Based Chord Recognition ੜ͞Εͨ༗άϥϑ ViterbiΞϧΰϦζϜͰ֤ҐஔͰɺ ֤ԻʹͨͲΓண͘·Ͱͷ࠷దίετͱ ͦͷલʹࢸΔ·ͰͷϙΠϯλΛ֮͑ͳ͕ΒܭࢉΛߦ͏
Slide 19
Slide 19 text
Chapter 5.3: HMM-Based Chord Recognition ੜ͞Εͨ༗άϥϑ ViterbiΞϧΰϦζϜͰ֤ҐஔͰɺ ֤ԻʹͨͲΓண͘·Ͱͷ࠷దίετͱ ͦͷલʹࢸΔ·ͰͷϙΠϯλΛ֮͑ͳ͕ΒܭࢉΛߦ͏
Slide 20
Slide 20 text
Chapter 5.3: HMM-Based Chord Recognition ੜ͞Εͨ༗άϥϑ ViterbiΞϧΰϦζϜͰ֤ҐஔͰɺ ֤ԻʹͨͲΓண͘·Ͱͷ࠷దίετͱ ͦͷલʹࢸΔ·ͰͷϙΠϯλΛ֮͑ͳ͕ΒܭࢉΛߦ͏
Slide 21
Slide 21 text
Chapter 5.3: HMM-Based Chord Recognition ੜ͞Εͨ༗άϥϑ ViterbiΞϧΰϦζϜͰ֤ҐஔͰɺ ֤ԻʹͨͲΓண͘·Ͱͷ࠷దίετͱ ͦͷલʹࢸΔ·ͰͷϙΠϯλΛ֮͑ͳ͕ΒܭࢉΛߦ͏
Slide 22
Slide 22 text
Chapter 5.3: HMM-Based Chord Recognition ੜ͞Εͨ༗άϥϑ ViterbiΞϧΰϦζϜͰ֤ҐஔͰɺ ֤ԻʹͨͲΓண͘·Ͱͷ࠷దίετͱ ͦͷલʹࢸΔ·ͰͷϙΠϯλΛ֮͑ͳ͕ΒܭࢉΛߦ͏
Slide 23
Slide 23 text
Chapter 5.3: HMM-Based Chord Recognition ࠷ޙʹɺͦͷϙΠϯλΛḷΓ࠷Β͍͠ԻਐߦΛ ٻΊΔ A := {α1 = C, α2 = G, α3 = F} ͷͱ͖ ̂ S = (C, C, C, G, G, F)