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水谷哲也 講師
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研究内容
人工知能とプログラム理論の融合による知見を用いた音楽情報学の研究
音楽の構造的機能とそれに基づく演奏創造
楽曲の構造的分析と演奏表情との関係
楽曲演奏におけるオンセット情報の抽出など
単にコンピュータで音楽を演奏するのではありません．
音楽における人間の「知性」と「感性」，「知」と「思」を論理的・数理的に捉えてモデル化する研究を行います．
なお，特に希望がある場合は，プログラム理論に関する研究，特に実時間知的プログラムの検証，検証理論の構築
具体例(自動演奏システムなど)への適用・解析などを行うこともできます．
教員と相談の上，その他の興味を持ったテーマを選ぶことは差し支えありません．

演奏表情の自動生成演奏モデルの作成
どのようにして人間らしい表情豊かな演奏を生成するか
人間らしい演奏のモデルをどのように作成するか

楽曲構造分析
楽曲に内在する緊張，誘引などの抽出
演奏の解析(重回帰分析など統計的手法を用いる)

Musical Expression Analysis• Musical Expression• Constructed by• note value, pitch, harmony, musical symbols• chord progression, melodic motion, progression, etc.
• repetition of tension and relaxation structures• hierarchical tonal tension structures from musicalscores [Lerdahl01]• Creation of musical rendition models• Analyzed by hierarchical tonal tension rules• Accurate but very complicated[Lerdahl01] F. Lerdahl, Tonal Pitch Space, Oxford University Press, Oxford, 2001.

Hierarchical Tonal Tension Rules• Representing of the tension in music score hierarchically• Assigned value to each chord• Defined by the prolongational tree and the chord distance• The prolongational tree :• the hierarchical relationship among events• This is very complicated;• High level musical knowledge and deep understanding ofmusical theories are required• The chord distance: defined in the cycle of fifth of diatonic
scaleHierarchical Tonal Tension Rules• Representing of the tension in music score hierarchically• Assigned value to each chord• Defined by the prolongational tree and the chord distance• The prolongational tree :• the hierarchical relationship among events• This is very complicated;• High level musical knowledge and deep understanding ofmusical theories are required• The chord distance: defined in the cycle of fifth of diatonic
scaleHierarchical Tonal Tension Rules• Representing of the tension in music score hierarchically• Assigned value to each chord• Defined by the prolongational tree and the chord distance• The prolongational tree :• the hierarchical relationship among events• This is very complicated;• High level musical knowledge and deep understanding ofmusical theories are required• The chord distance: defined in the cycle of fifth of diatonicscale

Data Cleansing System
Input: Performance Data(WAV)

Input: Score Data(MusicXML)

Input: Prolongational
Reduction Tree

Input: Musical Symbols

list ofevents ofchordwith notevalue

TensionAttaction
Analysis

assignMusical
Structure
Analyzing
Component

Output:Event Data

Onset Extraction
Matching

Performance
Data Cleansing
Component

Expression Data
Extraction

Output:Expression Data

Multiple Regression Analysis

MAXIMUM FILTER Λద༻ͨ͠ SuperFlux ͱ͍͏୳஌ؔ਺ (detection function) Λఆ͍ٛͯ͠Δɽlibrosa Ͱ͸ WAV ‫ࣜܗ‬ͷԻָϑΝΠϧΛೖྗͱͯ͠Φϯηοτநग़͕ՄೳͰ͋ΔɽWAV ‫ܗ‬ࣜͷϑΥʔϚοτϑΝΠϧ͸‫Ͱࡏݱ‬΋޿͘ී‫͓ͯ͠ٴ‬Γ CD ΍ಈըαΠτͳͲ͔Β΋༰қʹखʹೖΕΔ͜ͱ͕Ͱ͖Δɽ͜ͷͨΊʹຊ‫ڀݚ‬ͷର৅Ͱ͋ΔΫϥγοΫͷಛʹϐΞϊ‫ۂ‬ͷָ‫ۂ‬σʔλΛ૿΍͢͜ͱ͕Ͱ͖Δͱ‫ظ‬଴͞ΕΔɽ

Onset Time Extraction

ਤ 4.2: Φϯηοτநग़

Matching Onset Times with Events࣍ʹϚονϯάʹ͍ͭͯઆ໌͢ΔɽϚονϯάͱ͸ָේσʔλͷΠϕϯτͱָ‫ۂ‬σʔλͷΠϕϯτΛϚονͤ͞Δ͜ͱͰ͋Δɽ௚‫ײ‬తͳਤ͸ਤ 4.4 ͷΑ͏ʹͳΓɼॳΊͷԻ (ࠨͷԻ) ͔ΒϚονϯάΛߦ͍ͬͯ͘ɽ

ਤ 4.4: ϚονϯάP ͸ָේσʔλͷ֤Πϕϯτʹ͓͚Δ࢛෼Իූ୯ҐͷԻՁͰ͋Δɽ͜ͷϚονϯά͸্ड़ͷ࢛෼Իූ୯ҐͷԻՁ৘ใͰߦ͏ɽָේσʔλͷ֤ΠϕϯτͷԻՁ৘ใ P ͸ music21 ʹΑΓಘΔ͜ͱ͕Ͱ͖Δɽ͜͜ͰϚονϯάࣦഊͷྫΛઆ໌͢Δɽਤ

Analysis of Actual Musical Performances
Musical Data
ComposerL. v. Beethoven

Music Title
Piano Sonata No. 8, Op. 13 in C minor, “Sonata Pathétique”

Nocturne, Op. 9, No. 2 in E-flat major
F.F. Chopin
Étude Op. 10, No. 3 in E major, “Tristesse”
Prelude, Op. 28, No. 15 in D-flat Major, “Raindrop”
R. A. Schumann

M.A. Mozart

Kinderscenen, Op. 15, No. 7 in F major, “Träumerei”

Piano Sonata No. 11, K. 331 in A major, Movement 1

PianistC.ArrauV. D. Ashkenazy
W. Backhaus† I. Nakamichi
V.D. Ashkenazy
S. S. Bunin
V. S. Horowitz
M. J. Pires† A. Yokouchi† V. Lisitsa
V. D. Ashkenazy† I. Nakamichi
V. D. Ashkenazy† J. Bolet
V. D. Ashkenazy
I. F. Hemming
V. S. Horowitz
C. Eschenbach
G. H. Gould
I. Haebler
L. KrausA. deLarrocha
H. Nakamura
M. J. Pires
N. Shimizu† O. Jegunova† D. Barenboim†: from YouTubeno mark: from CrestMusePEDB

Analysis Results
Correlation Coefficients vs Change of Tempo
Music
Nocturne
Tristesse
K.331

PianistAshkenazy
Pires
Ashkenazy
Eschenbach
Pires

vs. tension-0.253**-0.160-0.325**0.296*
0.039

vs. attraction
0.064-0.211**
0.189
0.091
0.274

“**” coefficient is meaningful under the significant level 0.05“*” coefficient is meaningful under the significant level 0.1

1.

Except for K. 331, each music is performed as its tempo tends
to faster if the corresponding tension increases.

2.
3.

There is no such feature about attraction values.
Every coefficient is rather small, i.e. there are only weakcorrelation.

Analysis Results
Top 5 Explanatory Variables of Partial Regression Coefficients for change of tempo.
rank1
23
4
5Pathétique

Nocturne

Tristesse

RaindropTräumerei

K. 331

piano_start_M
staccato_A
staccato_M
slur_start_M*
slur_end_M

cre_start_A*
decre_cont_M*
piano_start_M
decre_start_M*
decre_end_M*

rit_start
tenuto_M*
rit_endpiano_start_M
accent_M

graced_M
suc_grace_M
piano_start_M-

suc_grace_M
forte_start_M
piano_start_M
cre_end_M*
graced_M*

slur_count_M
sforzando_M
slur_M
piano_start_A
slur_start_M*

4.

Almost all music performances are affected by “piano” musical symbol,
which is to be played “softly”.
Though most amateur or unnamed pianists often play it as “quietly”,
top pianists play it as rather “slowly”.

5.

Musical symbols on a melody part affect stronger than that on an accompaniment part.
It means that pianists intend to let listeners listen and feel the change of tempo of themelody part rather than the accompaniment part.

Implication-Realization Model• A melody is divided into some segments by rests or significant
changes of consecutive note values.
• A segmented note sequence is abstracted in a sequence of
three notes so that one note overlaps with consecutive one andconverted into a sequence of symbols.
PIPIDP

Symbols of I-R Modelœœ œœScore

Score

Score

Symbol Name

Score

D (duplication)

Score

Description and Sample

Score& 34∑

Interval direction and pitches
do not change

Score

œ

œœ

œ

œ

Realization

œ

œœ
œ

Implication of Pitch

œœ Realizationœœ œ œ Denialœ
œ
Realization
œ
œ
œ
œ
œ
œ
œ
œ
Score5œœœ œ œ œœ œ3direction
œ3œ
∑∑Intervalissameœ
œœ
œ
∑
&œ&4
œ
P (process)Realization
œ small intervalœœ œœ œœ œ œœ Realization&4
œœ Smallœ intervalœ
and5533œ œ œ œœ œœ œœ œœœœ œ œ œœ œœ œœ∑∑œ
Interval
directionchangesœ&4∑&4∑œœœœœœIP (intervallic process)Realization
Denialœ&œ&œœ
Small interval and smallœœ œœœœ intervalœ5105
œ œ ∑œ œ œ ∑3œ œ œœis sameœ œ œ œ œœœ œ Denialœœ∑∑Interval
direction
œœœ
∑
&4&
œ&
VP
(registralprocess)Realizationœœ œ œLargeœ intervalœœœ intervalœ œ œ œœ œ&œ œœ œ and small
œ551010œœ œœœ œœ œœ œœœsameœ∑∑œœInterval
directionis&œ&œ∑∑∑∑ Realization ∑œ œœœ œ œœ œ œ œ Realization œIR (intervallic reversal)& œ œ Large&œœsmallœ intervalœ œ andœ œ œintervalœ
1051510œœœ œ∑ œ b œœœœ∑ œ œ∑ Denial∑
Interval
directionchanges∑œœœœ∑∑& &R (reversal)
Realization
œœœœ
œœ
œ
œ
œintervalœ œ œ&
œ
Largeandsmallintervalœ œ œ10œ œœ œ&œœœ
10
œ1515œœ∑∑∑∑ œb œ∑œ œDenial œœbœœœVR (registral &reversal)
direction
Denialœœ
œ&œ Intervalœ œ œand∑&∑œSmallœ œintervalœchangesœœœœœ&œœœlarge intervalœ
œœœœœœ
15
10 1520œœœ bœ&&œ œ ∑œœ œ œ & œ & œ∑∑ b œ ∑ œ œ œ œ∑œ œ œ œ ∑œ œ ∑ œ œ œ ∑ œ œ œ ∑œ
œ15
œ152020bœœbœœ œ ∑ œ œ œ œ ∑œœ& & ∑ &œœ∑ œ ∑œœ œ &œœ œ∑œ∑∑∑œœœœ∑œœœ
œ 20 25
15 20œœbœ
œœ∑∑∑∑∑œ∑∑∑œœœ∑&œ & ∑ œ œ&&œ ∑ œ œ œ ∑∑3&4ID (intervallic duplication)∑34&œ œImplication of IntervalInterval direction changes
First and last tone are sameG4œ∑œA4D5G4

Analysis
Musical Data from CrestMusePEDB [Crest]
ComposerL. v. Beethoven

R. A. Schuman

M.A. Mozart

Music Title

PianistPiano Sonata No. 8, Op. 13 in C minor,

C.Arrau“Sonata Pathétique

Etude Op. 10, No. 3 in E major Tristesse

W. Backhaus
V. D. Ashkenazy
V. D. Ashkenazy
I. F. Hemming
V. S. Horowitz
N. Shimizu
A. deLarrocha
C. Eschenbach
G. H. Gould
L. Haebler
L. KrausH. Nakamura
M. J. Pires
V. D. Aashkenazy
M. J. Pires
S. S. Bunin
V. S. Horrowitz
V. D. Aashkenazy

Prelude, Op, 28, No. 15 No.7 in F major Raindrop

V. D. Aashkenazy

Kinderscenen, Op. 15, No. 7 in F major, “Träumerei”

Piano Sonata No. 11, K. 331 in A major, Movement 1(K331)

Nocturne, Op. 9, No. 2 in E-flat major
F.F. Chopin[Crest] CrestMusePEDB. [Online] http://www.crestmuse.jp/pedb/

Multiple Regression Analysis• Objective variable:• Local tempo obtained from actual performance• Extracting the onset time from the actual performance;• Matching to the correcponding notes in the score;• Then calculating the local tempo of each event of chord• Explanatory variables:• Number of symbols of the I-R model
assigned to event of chord

IP
Piano Sonata No. 8,
Op. 13 in C minor,
Sonata Pathétiqueby L.v. Beethoven

BeginSymbols:

CenterEndID
IPExplanatory variables:
number of symbols inevents of chords

Event Number

Explanatory Variables

Onset Timing and Velocity by Arrau

The objective variable :the local tempo

Comparison of the Analysis with the Previous Study
Coefficient of Determination
Music Title

PianistPrevious Study

SonataPathétique
Träumerei

K331

Nocturne
Etude
Raindrop

Correlation Coefficient

Arrau
Backhaus
Ashkenazy
Ashkenazy
Hemming
Shimizu
deLarrocha
Eschenbach
Gould
Haebler
Kraus
Nakamura
Pires
Aashkenazy
Pires
Bunin
Horrowitz
Aashkenazy
Aashkenazy

0.0671
0.178
0.111
0.515
0.415
-0.0360
0.382
0.297-0.08150.667
0.357-0.0687
0.180
0.594
0.240
0.208
0.113
0.198
0.594

This Analysis

0.17160.13010.1207-0.006342-0.2440.23870.035460.03569
0.13570.17980.19880.179
0.099490.115
0.0548-0.008-0.0136-0.03735
0.115

Previous Study

This Analysis

0.376
0.510
0.429
0.816
0.547
0.398
0.557
0.655
0.419
0.560
0.622
0.362
0.443
0.689
0.656
0.548
0.505
0.861
0.521

0.570
0.539
0.532
0.615
0.480
0.677
0.559
0.560
0.620
0.645
0.655
0.644
0.599
0.315
0.423
0.353
0.346
0.474
0.348

来年度の予定(希望)現在の研究のさらなる発展
演奏モデル・演奏ルールの確立
prolongational structureを用いない楽曲・演奏分析方法の確立
演奏データと楽譜情報とのマッチング(特に演奏が不正確のとき)

楽曲演奏におけるオンセット情報の抽出

ゼミの内容，時間など

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および教員の助言・指導が中心です．
曜日・時間は教官および学生の予定を考慮して定めます．
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