ᢿ⠇ㄆ㆑䞉ㄪᛶㄆ㆑䠄ᩥ⊩➼䠅
ᤵᴗ㈨ᩱ䠄䠒䠅䠄11/25䡚䠅
• ᚋ⸨┿Ꮥ䠖䛂ᢿ⠇ㄆ㆑䠄䝡䞊䝖䝖䝷䝑䜻䞁䜾䠅䛃䚸
bit ู෉䛂䝁䞁䝢䝳䞊䝍䛸㡢ᴦ䛾ୡ⏺䛃䚸3.3 ⠇
• Longuet-Higgins 䛾䜰䝹䝂䝸䝈䝮䛻䛴䛔䛶
ᒸ⏣㢧ᏹ䚸㜿㒊⣧୍䠖 䛂䝯䝻䝕䜱䛾ㄆ㆑䠖 ᢿ⠇ゎ㔘䛸
ㄪᛶゎ㔘䜢⤫ྜ䛧䛯ィ⟬䝰䝕䝹䛃䚸
bit ู෉䛂䝁䞁䝢䝳䞊䝍䛸㡢ᴦ䛾ୡ⏺䛃䚸4.4 ⠇
• 㡢ᴦ᝟ሗ⛉Ꮫ䛻䛴䛔䛶䠄⥆䛝䠖䛂⫈䛟ഃ䛃䛾ฎ⌮䠅
• ᢿ⠇ㄆ㆑䚸䝡䞊䝖䝖䝷䝑䜻䞁䜾䠄⿵㊊䠅
• ㄪᛶㄆ㆑
• ࿴ኌゎᯒ
• ᵓ㐀ゎᯒ
• 䝕䝰䝡䝕䜸䠖 ᚋ⸨┿Ꮥ Cindy ௚
• ᐇ㘓㡢䛛䜙䛾䝡䞊䝖ᢳฟ
• ᴦჾ㡢䠄≉䛻ᡴᴦჾ㡢䠅䛾≉ᚩᢳฟ䛸䚸ᢿ⠇䝰䝕
䝹䜈䛾䛒䛶䛿䜑
• 䠐ᢿᏊ᭤䛜ᑐ㇟
• ⮬ື₇ዌ䞉కዌ䞉ྜዌ
1
䠆䛂⫈䛟ഃ䛃
㡢ᴦ䛾䛂㧗ḟ䛃ᵓ㐀
• 㡢㡪ಙྕゎᯒ
䞉㡢➢ྠᐃ
䞉㡢※㆑ู
䞉ኌ㒊ศ㞳
• ᢿ⠇ㄆ㆑ 䞉ㄪᛶㄆ㆑
• ⮬ື᥇㆕ 䞉䠄ᴦ㆕ㄆ㆑䠅
• ᴦ᭤඲య䜢䜂䛸䜎䛸䜎䜚䛾䜒䛾䛸䛧䛶⤫ྜ䛧䚸≉ᚩ䛵䛡䜛
䜘䛖䛺ᒓᛶ䚸㛵ಀᛶ䚸ᵓ⠏せᅉ➼䚻䚹
• ᴦ㆕䛺䛹䛾㡢ᴦ⾲グ䛻㢧ᅾ໬䛧䛺䛔䛜䚸₇ዌ䜔⫈ྲྀ䛻
䛒䛯䛳䛶䠄ព㆑ⓗ䛻䛫䜘↓ព㆑ⓗ䛻䛫䜘䠅ㄆ㆑䛥䜜䜛䚹
• ᵓ㐀ศᯒ䞉ᴦ᭤ゎ㔘
䞉䜾䝹䞊䝥໬
䞉᪕ᚊศᯒ
䞉࿴ኌゎᯒ
䞉㝵ᒙⓗᵓ㐀
䞉㢮ఝᛶ䛾↷ྜ䞉᳨⣴
• 䛹䛾䜘䛖䛺㡢ᴦᵓ㐀䛜䛒䜛䛛䚸ఱ䜢䜒䛳䛶㡢ᴦᵓ㐀䛸䛩
䜛䛛䛿䚸䜎䛰䜎䛰ᮍ☜ᐃ䞉◊✲㏵ୖ䚹
э ᐃᘧ໬䞉㐩ᡂ䛩䜉䛝┠ᶆ⮬య䛜୙᫂☜
䛹䛾䜘䛖䛺ᵓ㐀䜢⪃䛘䜛䛛䠄タᐃ䛩䜛䛛䠅⮬య䛜
◊✲䛾୍㒊
• ឤᛶ᝟ሗฎ⌮
䞉᝟ື䚸 ዲ䜏䚸 ⱁ⾡ᛶ
3
4
㡢ᴦᵓ㐀䛾ศ㢮
㡢ᴦᵓ㐀䛾౛
• [bit ู෉䛂䝁䞁䝢䝳䞊䝍䛸㡢ᴦ䛃4.1 ⠇]
•
•
•
•
•
•
•
•
•
䛂ᯟᵓ㐀䛃䠄ᢿ⠇䚸ㄪᛶ䠅
࿴ኌᵓ㐀
䠄ᴦᘧⓗ䛺ᵓ㐀䠖 ືᶵ䚸ᴦ⠇䚸ᴦ᭤ᙧᘧ➼䠅
䜾䝹䞊䝥䚸䜾䝹䞊䝥໬
㝵ᒙᵓ㐀
• ⡆⣙໬ (Reduction)
• 䝥䝻䝉䝇䚸䜽䝻䞊䝆䝱
• 䝟䝍䞊䞁䛸䛭䛾↷ྜ
ศ๭䛸䛧䛶䛾ᵓ㐀
ไ⣙䛸䛧䛶䛾ᵓ㐀
ᢳ㇟໬䛸䛧䛶䛾ᵓ㐀
䝟䝍䞊䞁䛸䛧䛶䛾ᵓ㐀
• [West, Howell & Cross]
• Structure as subdivision
• Structure as constraint
2
5
6
㡢ᴦᏛ䞉㡢ᴦ⌮ㄽ
㡢ᴦᏛ䞉㡢ᴦ⌮ㄽ(⥆䠅
• ศ㔝䞉㡿ᇦ
• ࿴ኌᏛ
• ᑐ఩ἲ
• ᴦᘧㄽ
• 䛭䛾௚䠄ᴦ඾䚸స᭤⌮ㄽ䚸䜸䞊䜿䝇䝖䝺䞊䝅䝵䞁➼䠅
• 㡢ᴦศᯒ䠄ᴦ᭤ศᯒ䠅
• ୺䛸䛧䛶䛂స䜛ഃ䛃䛾⌮ㄽ䞉Ꮫၥ
• ཝᐦ䛺ᐃᘧ໬䚸ᙧᘧ໬䛜⾜䜟䜜䛶䛔䛺䛔
э⫼ᬒ▱㆑䜔ಶูุ᩿䛻㢗䜛㠃䛜኱䛝䛔
Expertise 䛾ୡ⏺
• ప䝺䝧䝹䛾ㄆ▱䞉ศᯒ㐣⛬䛿ど㔝䛻ධ䜙䛺䛔䚹
cf. 㡢ᴦᚰ⌮Ꮫ
• 䛭䛾䜎䜎䛷䛿䝁䞁䝢䝳䞊䝍ฎ⌮䜈䛾ᛂ⏝䛜ᅔ㞴
7
8
䠆䛂⫈䛟ഃ䛃
௚䛾ㄆ▱䝰䝎䝸䝔䜱䛸䛾㛵㐃
"Syntax tree" by Aaron Rotenberg - Own work.
Licensed under Public Domain via Wiki Commons
• 䠄どぬ䚸㡢ኌ䚸ゝㄒ➼䠅
• ゝㄒᩥἲ䠄ᩘ⌮ⓗ䞉ᙧᘧᩥἲ䠅
ἲ䠅
• Chomsky 䠄1957䡚䠅
• 㡢㡪ಙྕゎᯒ
䞉㡢➢ྠᐃ
䞉㡢※㆑ู
䞉ኌ㒊ศ㞳
• ᢿ⠇ㄆ㆑ 䞉ㄪᛶㄆ㆑
• ⮬ື᥇㆕ 䞉䠄ᴦ㆕ㄆ㆑䠅
• ᵓ㐀ศᯒ䞉ᴦ᭤ゎ㔘
䞉䜾䝹䞊䝥໬
• 㡢ᴦ䜈䛾ᛂ⏝
• ࿴ኌᩥἲ䠄Winograd, etc.䠅
c.䠅
• L.Bernstein (Unanswered Question)
• F. Lerdahl & R. Jackendoff (GTTM)
䞉࿴ኌゎᯒ
䞉᪕ᚊศᯒ
䞉㝵ᒙⓗᵓ㐀
䞉㢮ఝᛶ䛾↷ྜ䞉᳨⣴
• ឤᛶ᝟ሗฎ⌮
䞉᝟ື䚸 ዲ䜏䚸 ⱁ⾡ᛶ
9
10
䠆࿴ኌゎᯒ
࿴ኌ䛾ᵓ㐀
• ࿴ኌ⌮ㄽ䛸䛧䛶ᩚഛ䛥䜜䛶䛔䜛䛯䜑䚸
グྕฎ⌮ⓗ䛺ᢅ䛔䛜䛧䜔䛩䛔䚹
• ᪤Ꮡ䛾ゎᯒᡭἲ䠄ᙧᘧᩥἲ䚸䝹䞊䝹䝧䞊䝇䝅䝇
䝔䝮➼䠅䛷ᢅ䛘䜛䚹
• ⌧ᅾ䛾࿴ኌ⌮ㄽ䛿䚸䝸䞊䝬䞁䜙䛻䜘䜛䛂ᶵ⬟࿴
ኌ䛃䛻ᇶ䛵䛔䛶䛔䜛䚹䠏࿴㡢䝧䞊䝇䚸ᶵ⬟䛸䛧䛶䠖
• グྕⓗ䛺ᯟ⤌䜢㞳䜜䜛㒊ศ䠄࿴㡢䛾ྠᐃ䚸㠀࿴
ኌ㡢䛾ฎ⌮䛺䛹䠅䛷䛿ㄪᛶㄆ㆑䛺䛹䛾ሙྜ䛸ྠ
䛨䜘䛖䛺ၥ㢟䛜⏕䛨䜛䚹
• 䜹䝕䞁䝒䠄䜿䞊䝕䞁䝇䠖 Kadenz, Cadence䠅
• T (tonic: I, VI)
• D (dominant: V, VII)
• S (subdominant: IV, II)
• T-D-T
• T-S-T
• T-S-D-T 䛺䛹䚹
11
12
䠆࿴ኌゎᯒ䝅䝇䝔䝮 (Winograd 1968)
࿴ኌᩥἲ
ධຊ䝕䞊䝍
• ࿴ኌ䛿ᙧᘧᩥἲ䛾ᯟ⤌䛷ᢅ䛘䜛䚹
ᩥ⬦⮬⏤ᩥἲ䚸Systemic grammar, HPSG,
Production system, etc.
• ฎ⌮䛾ᡂྰ䜒ุ᩿䛧䜔䛩䛔 ĺ䛂࿴ኌㄢ㢟䛃
ゎᯒ⤖ᯝ
(Bach: Chorale 57)
(䝞䝇ㄢ㢟䚸䝋䝥䝷䝜ㄢ㢟䚸➼䚻䠅
• 䛧䛛䛧ཝᐦ䛺ᙧᘧ໬䞉㧗ᗘ䛺ฎ⌮䜢ᐇ⌧䛩䜛䛾
䛿ᅔ㞴
• ᙧᘧ໬䛷䛝䜛䛣䛸䛻䜘䜚䚸䛛䛘䛳䛶ே㛫䛾䛂⪺䛣
䛘䛃䛸䛾㛵ಀ䛜୙᫂☜䛻䛺䜛䚹
13
14
䠆࿴ኌゎᯒ䝅䝇䝔䝮 䠄ෆ㒊⾲⌧䠅
㡢ᴦᵓ㐀䛾౛
ධຊ䝕䞊䝍
䠄㡢➢ิ䠅
䛂ᯟᵓ㐀䛃䠄ᢿ⠇䚸ㄪᛶ䠅
࿴ኌᵓ㐀
䠄ᴦᘧⓗ䛺ᵓ㐀䠖 ືᶵ䚸ᴦ⠇䚸ᴦ᭤ᙧᘧ➼䠅
䜾䝹䞊䝥䚸䜾䝹䞊䝥໬
㝵ᒙᵓ㐀
• ⡆⣙໬ (Reduction)
• 䝥䝻䝉䝇䚸䜽䝻䞊䝆䝱
• 䝟䝍䞊䞁䛸䛭䛾↷ྜ
•
•
•
•
•
ゎᯒ⤖ᯝ
䠄䝁䞊䝗ิ䠅
15
䠆ㄆ▱ⓗ㡢ᴦ⌮ㄽ
16
GTTM
• 䠐✀䛾㡢ᴦᵓ㐀
• Grouping Structure
• Metrical Structure
• Time-Span Reduction
• Prolongational Reduction
• F. Lerdahl & R. Jackendoff: GTTM
(Generative Theory of Tonal Music)
• E. Narmour (< L. Meyer): IRM
(Implication-Realization Model)
• 䛂⌮᝿ⓗ䛺⫈ྲྀ⪅䛃䛜⫈ྲྀ䛩䜛㡢ᴦᵓ㐀䛾䝰䝕䝸
䞁䜾
• Well-formedness rules, Preference Rules 䛻䜘䜚ᵓ
ᡂ䛥䜜䜛䚹
• ᮧᑿ䚸ಖ⛉
17
18
⫼ᬒ䠖⡆⣙໬ (1)
ᩥ⊩
• F. Lerdahl & R. Jackendoff: A Generative Theory
of Tonal Music, MIT Press 1983.
• ➉ෆዲᏹ䠖䛂㡢ᴦ䛾ᵓ㐀ゎᯒ䛸䛭䛾ᛂ⏝䛃䚸
bit ู෉䛂䝁䞁䝢䝳䞊䝍䛸㡢ᴦ䛾ୡ⏺䛃4.6 ⠇䚸
pp.224-240.
• ὾୰㞞ಇẶ䛾䝩䞊䝮䝨䞊䝆 䠄⌧ᅾ୙㏻䠅
http://music.iit.tsukuba.ac.jp/gttmjp.html
• ∦ᐤᬕᘯẶ䛾ᤵᴗ㈨ᩱ䠄PPT/PDF䠅
http://ist.ksc.kwansei.ac.jp/~katayose/lecture/10M
IP.pdf
• ᖹ⏣௚䠖䛂㐨䛧䜛䜉䠖 䛄ィ⟬䛾どⅬ䛛䜙㡢ᴦ䛾ᵓ
㐀䜢═䜑䛶䜏䜛䛸䛅䛃 䚸᝟ሗฎ⌮Ꮫ఍ㄅ 2008ᖺ
7-11᭶
⡆⣙໬ (2)
19
(Mozart: Var. Ah! Vous dirai-je Maman)
20
⡆⣙໬ (3)
(var.1)
(var.3)
cf. ኱ᾆ䠖⡆⣙㡢ิἲ
21
22
GTTM 䛻䜘䜛ゎᯒ䠄䠍䠅
GTTM 䛻䜘䜛ゎᯒ䠄䠎䠅
• Time-span reduction tree
• Grouping structure, Metrical structure
23
24
GTTM: Time-Span Reduction (2)
Implication-Realization Model
• L. B. Meyer 䛻䜘䛳䛶๰ጞ䛥䜜䚸E. Narmour 䛻
䜘䛳䛶኱つᶍ䛻Ⓨᒎ䠄⪃䛘䜘䛖䛻䜘䛳䛶䛿ኚ⠇䠅䛥
䜜䛯㡢ᴦ⌮ㄽ䚹
• ୺䛸䛧䛶᪕ᚊ䛾㐠ື䛾≉ᚩ䛵䛡䞉ศ㢮䜢┠ᣦ䛩䚹
• ₇ዌ䛥䜜䛯᩿∦䛻䜘䛳䛶䛂ᬯព䛃(implication) 䛥
䜜䛯㐍⾜䞉ゎỴ䛸䚸䛭䛾䛂ᐇ⌧䛃(realization) 䛸䛾
㛵ಀ䜢ᢅ䛖䚹
• ᬯព䛿ᮇᚅ䠄ண 䠅㏻䜚䛻ᐇ⌧䛥䜜䜛䛣䛸䜒䛒䜜
䜀䚸䛭䛖䛷䛺䛔ሙྜ䜒䛒䜛䚹
25
26
Implication-Realization Model (1)
ᩥ⊩
• L.B. Meyer (Univ. of Chicago Press)
• Emotion and Meaning in Music (1956)
• Explaining Music (1973)
• Eugene Narmour (Univ. of Chicago Press)
• Beyond Schenkerism (1977)
• The Analysis and Cognition of Basic Melodic Structures
(1990)
• The Analysis and Cognition of Melodic Complexity
(1992)
• ᮧᑿᛅᘅ䠖䛂ᴦ᭤ศᯒ䛻䛚䛡䜛ㄆ▱䛃䚸
Ἴከ㔝⦅䠖䛄㡢ᴦ䛸ㄆ▱䛅➨䠍❶䚸ᮾ኱ฟ∧఍ 1987
27
Implication-Realization Model (2)
28
㑄⛣㐣⛬䛸䛧䛶䛾㡢ᴦᵓ㐀
• 䛒䜛㡢䠄㡢⛬䚸㡢ิ䚸䠊䠊䠊䠅䛾୪䜃䛿୍ᐃ䛾つ๎
ᛶ䛻䛧䛯䛜䛖䛸⪃䛘䜛䚹э䠍ḟඖⓗ䛺㑄⛣㐣⛬
• 㑄⛣䛾ྍ⬟ᛶ䜢☜⋡ⓗ䛻⪃䛘䜜䜀䚸☜⋡㐣⛬䛸
䛧䛶ᢅ䛘䜛䚹
• ☜⋡ศᕸ䠖⤫ィⓗ䝕䞊䝍䛺䛹䛻䜘䜛
• 㐍⾜ண 䠖䝬䝹䝁䝣㐣⛬䛸䛧䛶䛸䜙䛘䜛
• ၥ㢟Ⅼ䠖 ᩥ⬦䞉኱ᇦⓗᵓ㐀䛜ᢅ䛘䛺䛔䚹
29
30
䠄ᴦ᭤䝔䞊䝬㎡඾⣴ᘬ䠅
(Mozart: Rondo in D, K.485)
• 䛂䝋䝣䜯䝭䝺䝗䛃(AGF#ED)䛷䛿ぢ䛴䛛䜙䛺䛔䚹
31
32
㡢ᴦ᝟ሗ᳨⣴
• 䝛䝑䝖䝽䞊䜽ୖ䛷䛾䝕䜱䝆䝍䝹㡢ᴦ᝟ሗ㓄ಙ䛺䛹䛻క䛔䚸
◊✲㠃䛷䜒䛣䛣ᩘᖺ䚸⬮ග䜢ᾎ䜃䛶䛝䛶䛔䜛䚹䠄ISMIR ➼䠅
• ᐇ㝿䛾◊✲䛿䚸ᩥ⊩᝟ሗ᳨⣴䚸⏬ീㄆ㆑䞉᳨⣴䛺䛹䛷㛤
Ⓨ䛥䜜䛯ᡭἲ䛾ᛂ⏝䛜ከ䛔䚹
• ᑐ㇟䝕䞊䝍
• 㡢㡪䝕䞊䝍䠄WAV 䝣䜯䜲䝹➼䠅
• グྕ໬䝕䞊䝍䠄MIDI 䝣䜯䜲䝹➼䠅
• 䛂ឤᛶ䛃䝟䝷䝯䝍
• ฎ⌮䛾ຠ⋡
• ⣴ᘬ䛾᭷↓
• ↷ྜ䜰䝹䝂䝸䝈䝮䛾ฎ⌮ຠ⋡
33
34
䠆䝟䝍䞊䞁䞉㢮ఝᛶ
㢮ఝᛶㄆ㆑䛾どⅬ
• ᯟᵓ㐀䛺䛹䛾ඹ㏻せᅉ䜢ྲྀ䜚㝖䛔䛯䚸᭤䛾≉ᚩ䞉
ಶᛶ䜢⾲䛩䜒䛾䚹
• 㡢ᆺ (contour)䚸㦵᱁䚸signature
• 䝟䝍䞊䞁䛾✀㢮䠄䛸䜙䛘᪉䠅
• 䝟䝍䞊䞁✵㛫䠄≉ᚩ䝟䝷䝯䝍✵㛫䠅
ᩘ್ⓗ䛺䝟䝍䞊䞁㊥㞳䛻䜘䜛↷ྜ
• グྕิ
DP (Dynamic Programming) 䛺䛹䛻䜘䜛↷ྜ
• ᵓ㐀ⓗ䝟䝍䞊䞁 䠄ᢳ㇟໬䞉㝵ᒙ໬䠅
ᢳ㇟໬䛻䜘䜛୍⮴䠄ඹ᭷ᒓᛶ䛻䜘䜛↷ྜ䠅
• 䝕䞊䝍䛾✀㢮
• 䝟䝍䞊䞁䝕䞊䝍䠄᫬㛫❆༊ษ䜚䠅
• グྕ໬䝕䞊䝍
• ᵓ㐀໬䝕䞊䝍
• 䛂ᴫᛕ௜䛡䛃
• ㏆ఝ䠄㢮ఝ䠅䛸䛧䛶䛾㢮ఝᛶ
• 䛂୍⮴䛃䛸䛧䛶䛾㢮ఝᛶ эᢳ㇟໬䚸㒊ศᵓ㐀
• ௜㝶ⓗ䞉䠎ḟⓗ䛺ฎ⌮䛛䚸᰿※ⓗ䛺ฎ⌮䛛
35
36
㢮ఝᛶ䜢ᢅ䛖ୖ䛷䛾ၥ㢟Ⅼ
↷ྜ䜰䝹䝂䝸䝈䝮
• 䛹䛾䜘䛖䛺ほⅬ䛾ୖ䛷୍⮴䠋㢮ఝ䜢ぢ䜛䛛
• ㏆ఝ䠄㢮ఝ䠅䛸䛧䛶䛾㢮ఝᛶ
• 䛂୍⮴䛃䛸䛧䛶䛾㢮ఝᛶ эᢳ㇟໬䚸㒊ศᵓ㐀
• 䝧䜽䝖䝹↷ྜ
• ≉ᚩᢳฟ䚸䝟䝍䞊䞁✵㛫ෆ䛾᳨⣴
• グྕⓗ↷ྜ
LCS (Longest Common Subsequence) ᢳฟ䛾
DP 䝬䝑䝏䞁䜾➼
• ᵓ㐀↷ྜ
• グྕᩘ䠄㡢➢ᩘ䠅䛜␗䛺䜛ሙྜ䚸
᫬㛫ⓗ䛺㛗䛥䛜␗䛺䜛ሙྜ䛻䛹䛖↷ྜ䜢⾜䛖䛛
• ఱ䜢䜒䛳䛶୍⮴䞉㢮ఝ䛧䛶䛔䜛䛸⪃䛘䜛䛛䚹
䛂䝜䜲䝈䛃䛜ධ䜚㎸䜐వᆅ䛿䛹䜜䛠䜙䛔䛒䜛䛛䚹
37
Hanon ⦎⩦᭤
• 㡢㡪ಙྕᑐ㇟䛾ሙྜ
• ヲ⣽䛺ゎᯒ䞉↷ྜ䛿ᘬ䛝ྜ䜟䛺䛔䛾䛷䚸኱㞧ᢕ䛺
≉ᚩ㔞ᢳฟ䛻䜘䜛↷ྜ䛜୰ᚰ
• ౛䠖 SmartKiosk 䠄ᚋ⸨䠅
38
ୖ⾜ᙧ
• ྠ䛨䝟䝍䞊䞁䠄㡢ᆺ䠅䛾
⧞䜚㏉䛧䠛
• ༙㡢༢఩䛷ぢ䜛䛸䛭䛖
䛷䛿䛺䛔䚹
39
ୗ⾜ᙧ
40
Hanon ⦎⩦᭤
• ྠ䛨䝟䝍䞊䞁䠄㡢ᆺ䠅䛾
⧞䜚㏉䛧䠛
• ༙㡢༢఩䛷ぢ䜛䛸䛭䛖
䛷䛿䛺䛔䚹
• 䛷䛿༙㡢䝟䝍䞊䞁䜢୍
⮴䛥䛫䜛䛸䠛
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42
⾲⌧䛾ᢳ㇟໬䠄㡢㧗䞉㡢㝵䠅
• CEG 䛾࿴㡢䠖
• ༙㡢㝵䠖 [0 4 7] C+{+4 +3}
• ඲㡢㝵䠖 [0 2 4] C+{+2 +2}
• ࿴㡢 䠖 [0 1 2] C+{+1 +1}
• 䜰䝹䝧䝹䝔䜱䞉䝞䝇 CGEG CAFA BGDG ...
• ࿴㡢䝺䝧䝹䛷䛿 {+2 ̺1 +1} 䛸䛔䛖
ྠ୍䝟䝍䞊䞁
chromatic [0 2
4
5
7]
[0 2 3
5
7]
{* +2 +2 +1 +2} {* +2 +1 +2 +2}
diatonic [0 1 2 3 4]
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44
䝧䜽䝖䝹↷ྜ
DP 䝬䝑䝏䞁䜾
• ༙㡢ิ
[ 0 2 4 5 7]
ᕪ䝧䜽䝖䝹䠖 [0 0 1 0 0]
[ 0 2 3 5 7]
• ㄪ䛜㐪䛖䛸䠛
[ 0 2 4 5 7]
ᕪ䝧䜽䝖䝹䠖 [-2 -2 -1 -2 -2]
[ 2 4 5 7 9]
• 㡢⛬ิ䠄༙㡢䠅
{* +2 +2 +1 +2} ᕪ䝧䜽䝖䝹䠖 {* 0 +1 -1 0}
{* +2 +1 +2 +2}
• ᭱㛗୍⮴㒊ศิ䠄LCS䠅
[0 2 4 5 7] 䛸 >@ĺ>@
୙୍⮴Ⅼ䠖 4я3
• DP 䝬䝑䝏䞁䜾䠖
DP (Dynamic Programming) 䛾ᡭἲ䛻䜘䜚䚸ຠ⋡
ⓗ䛻グྕิ↷ྜ䜢⾜䛖䜰䝹䝂䝸䝈䝮
45
㡢ิ䛾⡆⣙໬䞉ኚᙧ
46
㡢ᴦ᝟ሗ᳨⣴䠖ఱ䜢᥈䛩䛛
• 䠄᭩ㄅⓗ᝟ሗ䠖 䝍䜲䝖䝹䚸䜰䞊䝔䜱䝇䝖➼䠅
я 䝁䞁䝔䞁䝒᳨⣴
• 䛂୺㢟䛃䛸䛂ኚዌ䛃
• ᪕ᚊ䛻䛿୰᰾䛸䛺䜛䛂ᵓ㐀㡢䛃䛸䚸๪ḟⓗ䞉⿦㣭
ⓗ䛺㡢䛸䛜䛒䜛䚹
• ᵓ㐀㡢䠖 ᪕ᚊ䛾㦵᱁䜢ᐃ䜑䜛䚹
• ⿦㣭㡢䠖 ≉ᐃ䛾䝟䝍䞊䞁䛻䛧䛯䛜䛖䚹
• ≉ᐃ䛾ᴦ᭤䠄䛂ཝᐦᆺ㡢ᴦ᝟ሗ᳨⣴䛃䠅
᳨⣴䜻䞊
• ᐇ㝿䛾ᴦ᭤䝕䞊䝍䠄䛂㡢ᴦㄆ㆑䝅䝇䝔䝮䛃䠅
• 䝴䞊䝄⏕ᡂ䠄䝝䝭䞁䜾᳨⣴➼䠅
• ୚䛘䛯᮲௳䜢‶䛯䛩䠄䛂᭕᫕ᆺ㡢ᴦ᝟ሗ᳨⣴䛃䠅
• ឤᛶ᝟ሗ䠄ឤᛶ⾲⌧ㄒ➼䠅
• 䝴䞊䝄䛾Ⴔዲ➼
• 䝟䝍䞊䞁䛾ཎᆺ䛿䚸ᵝ䚻䛺ᐃᆺⓗ䛺᪉ἲ䛷ኚᙧ
䛥䜜䛶䛔䛟䚹
47
Cf: ᕹ㊊௚䠖ᴦ᭤㓄ಙ䝃䞊䝡䝇䜢ᨭ䛘䜛㡢ᴦ᝟ሗฎ⌮ᢏ⾡
48
ᩥ⊩ 䠄㡢ᴦ᳨⣴䚸㡢ᴦ䝕䞊䝍⾲⌧䠅
㡢ᴦ᝟ሗ᳨⣴䠖 ᑐ㇟䝕䞊䝍
• ISMIR (International Society for Music Information Retrieval)
http://www.ismir.net/
• SMDL / Music XML Languages
http://xml.coverpages.org/xmlMusic.html
• MIREX
http://www.music-ir.org/mirex/wiki/MIREX_HOME
• W. B. Hewlett & E. Selfridge-Field:
Melodic Similarity: Concepts, Procedures and Applications,
MIT Press (1998) BN 0-262-58175-2
• 䝕䞊䝍䛾✀㢮䞉ᒓᛶ
•
•
•
•
㡢㡪䝕䞊䝍䠄WAV 䝣䜯䜲䝹➼䠅
グྕ໬䝕䞊䝍䠄MIDI 䝣䜯䜲䝹➼䠅
䛂ឤᛶ䛃䝟䝷䝯䝍
䝍䜾䛾᭷↓
• ฎ⌮䛾ᡭἲ䞉ຠ⋡
• ⣴ᘬ䛾᭷↓
• Ꮫ⩦䛻䜘䜛䝟䝷䝯䝍䛾⮬ືྲྀᚓ
• ↷ྜ䜰䝹䝂䝸䝈䝮䛾ฎ⌮ຠ⋡
• ᕹ㊊௚䠖䛂ᴦ᭤㓄ಙ䝃䞊䝡䝇䜢ᨭ䛘䜛㡢ᴦ᝟ሗ᳨⣴ᢏ⾡䛃䚸
㟁Ꮚ᝟ሗ㏻ಙᏛ఍ㄅ䠄ᤵᴗ䝨䞊䝆ཧ↷䠅,
49
MIREX䠄㡢ᴦ᝟ሗ᳨⣴䝁䞁䝔䝇䝖䠅
• The Music Information Retrieval Evaluation
eXchange (MIREX) 2005䡚
• http://www.music-ir.org/
http://www.music-ir.org/mirex/wiki/MIREX_HOME
• 㡢ᴦ᝟ሗ᳨⣴䛻㛵䜟䜛ᵝ䚻䛺䝆䝱䞁䝹䛾䝁䞁䝔䝇䝖
• 䝆䝱䞁䝹䚸స᭤ᐙ䚸ឤᛶ᝟ሗ➼䛾㆑ู
• ᵓ㐀ゎᯒ䠄᭤ศ๭䚸䝯䝻䝕䜱ᢳฟ➼䚻䠅
• ྛ✀䛾᭤᳨⣴
• “Ground truth”: ே㛫䛜୚䛘䛯䛂ṇゎ䝕䞊䝍䛃
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50

本日の概要（10/14） 音楽の記号的側面 ＊音楽データの形態 音楽データ

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