Fundamentals of Music ProcessingChapter 5: Chord Recognition খྛ ᕣՏεϥΠυʹؚ·ΕΔਤFundamentals of Music ProcessingΑΓҾ༻
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Chapter 5: Chord RecognitionChord(Ի)• 3ͭҎ্ͷҟͳΔԻූ͔Βߏ͞ΕΔԻͷ͜ͱHarmony()• ෳͷԻ͔ΒͳΔܥྻɺԻਐߦFM7 G7 Em7 AmHarmony
Chapter 5: Chord RecognitionChord Recognition(Իೝࣝ)• Ի͔ΒԻਐߦΛೝࣝ͢Δٕज़ԻָϑΝΠϧ͔ΒίʔυේΛࣗಈͰ࡞ग़དྷΔԻೝ͕ࣝ͏·͍͘͘ͱ…
Chapter 5.3: HMM-Based Chord RecognitionChapter 5.1~5.2• ಛྔ͔ΒԻΛ͋Δఔਪఆग़དྷΔ͔͠͠ɺ͜ΕԻҰͭҰ͔ͭ͠ݟ͍ͯͳ͍Α͘ग़ΔԻܨ͕Γͷڧ͍Իʹண͍ͨ͠ྫ: I–IV–V–Iਐߦ• FGසग़͠ɺ͍͖ͳΓFmʹߦ͘͜ͱ΄΅ແ͍HMM(ӅΕϚϧίϑϞσϧ)Λར༻ͯ͠ԻਪఆΛߦ͏
Chapter 5.3: HMM-Based Chord RecognitionԻ: , ঢ়ଶ: (for ) ͱͨ͠ͱ͖ɺϚϧίϑੑΛԾఆ͢Δͱ Ͱ͋Δ֬A := {α1, α2, ⋯, αI} s i ∈ [1 : I]sn+1= αjP[sn+1= αj|sn= αi, sn−1= αk, ⋯] = P[sn+1= αj|P[sn+1= αj|sn]͜͜Ͱ ΛҎԼͷΑ͏ʹఆٛ͢Δɻ(for )aiji, j ∈ [1 : I]͜Εঢ়ଶ͕ ͔Β ʹભҠ͢Δ֬ͱߟ͑Δ͜ͱ͕ग़དྷΔαiαjaij:= P[sn+1= αj|sn= αi] ∈ [0,1]·ͣɺϚϧίϑ࿈Λར༻ͨ͠Ի༧ଌʹ͍ͭͯઆ໌͢Δ
Chapter 5.3: HMM-Based Chord Recognition۩ମྫ; , ͷͱ͖I = 3 A := {α1= C, α2= G, α3= F}·ͨ࠷ॳͷঢ়ଶ͕ Ͱ͋Δ֬ΛҎԼͷΑ͏ʹఆٛ͢Δαici:= P[s1= αi] ∈ [0,1]
Chapter 5.3: HMM-Based Chord Recognition, ,ͷͱ͖ঢ়ଶܥྻ: ʹ͍ͭͯߟ͑ΔI = 3 A := {α1= C, α2= G, α3= F}C = (c1, c2, c3)T = (0.6,0.2,0.3)TS = (C, C, C, G, G, F, F, C, C)࠷ॳͷঢ়ଶ͕ Ͱ͋Δ֬ΛҎԼͷΑ͏ʹఆٛ͠ɺαici:= P[s1= αi] ∈ [0,1]۩ମྫ
Chapter 5.3: HMM-Based Chord RecognitionભҠ͕֬ҎԼͷͱ͖ͷΑ͏ͳԻਐߦ͕ى͖Δ֬SS = (C, C, C, G, G, F, F, C, C)= c1⋅ a11⋅ a11⋅ a12⋅ a22⋅ a23⋅ a33⋅ a31⋅ a11≈ 1.29 ⋅ 10−4
Chapter 5.3: HMM-Based Chord Recognitionઌఔঢ়ଶܥྻ Λ༻͍ͯɺԻਐߦͷ֬Λܭࢉ͕ͨ͠ ࣮ੈքͰऔΓ͏Δͯ͢ͷ ʹ͍ͭͯܭࢉෆՄೳ SSྫ: 10छྨͷԻɺ20͔ͭΒߏ͞ΕΔۂͷ߹ ύλʔϯͷ֬Λܭࢉ͢Δඞཁ͕͋Δ1020ͦ͜Ͱ෦ͷঢ়ଶͰͳ͘ɺಛϕΫτϧΛ༻͍ͯ ԻਐߦΛٻΊΔํ๏ͱͯ͠HMMΛར༻͢Δɻ
Chapter 5.3: HMM-Based Chord Recognition
Chapter 5.3: HMM-Based Chord RecognitionInput:Իσʔλ͔Β؍ଌͨ͠ܥྻ ͔Β ϞσϧΛར༻͠ɺ؍ଌܥྻ Λ࡞ɻO = (o1, ⋯, oN)B = (β1, ⋯, βN)؍ଌܥྻ ؍ଌγϯϘϧ ͔Βߏ͞ΕΔB = (β1, ⋯, βN)ℬ = {β1, ⋯, βk} (for k ∈ [1 : K])
Chapter 5.3: HMM-Based Chord RecognitionViterbi:؍ଌܥྻ ͱ ॳظঢ়ଶͷ֬ ੜ֬ͱભҠ͔֬Β༗άϥϑΛ࡞B = (β1, ⋯, βN)C = (c1, c2, c3)T = (0.6,0.2,0.3)Tੜ֬ભҠ֬
Chapter 5.3: HMM-Based Chord Recognitionੜ֬ભҠ֬ ॳظঢ়ଶͷ֬ੜ͞Εͨ༗άϥϑ
Chapter 5.3: HMM-Based Chord RecognitionViterbiΞϧΰϦζϜʹΑͬͯ ࠷Β͍͠ܦ࿏ʹ͍ͭͯܭࢉΛߦ͏
Chapter 5.3: HMM-Based Chord Recognitionੜ͞Εͨ༗άϥϑViterbiΞϧΰϦζϜͰ֤ҐஔͰɺ ֤ԻʹͨͲΓண͘·Ͱͷ࠷దίετͱ ͦͷલʹࢸΔ·ͰͷϙΠϯλΛ֮͑ͳ͕ΒܭࢉΛߦ͏
Chapter 5.3: HMM-Based Chord Recognition࠷ޙʹɺͦͷϙΠϯλΛḷΓ࠷Β͍͠ԻਐߦΛ ٻΊΔA := {α1= C, α2= G, α3= F} ͷͱ͖̂S = (C, C, C, G, G, F)