ISE599: Computational Modeling of Expressive Performance
Generative Rules for Music
Performance:
March 8, 2006
Anders Friberg
-PhD-
quantitative rule system for musical performance
- Master in Applied Physics at KTH
- Diploma in Performance at Berklee College of Music, Boston
A Formal Description of a
Rule System
Author: Andres Friberg
Leila Vaziri
Review
p
p
p
p
p
composer to the listener
A rule system is described that translates an
input score file to a musical performance.
Interpretation is one of the most important
aspects of music performance.
Analysis-by-synthesis: This means that we start
with a hypothesized principle, realize it in terms
of a synthetic performance, and evaluate it by
listening.
The rules appear to convey information which
helps the listener to process the musical signal
flow.
project started in 1977 when the analog singing
machine MUSSE constructed
Friberg: Generative Rules for Expressive Performance
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
Johan Sundberg
ß -born in 1936
ß
ß
ß
- Ph.D. in musicology Uppsala University 1966, doctor honoris causae 1996
University of York, UK
- Has a personal chair in Music Acoustics at the department of speech,
music and hearing
At KTH-- Royal Institute of Technology
Lars Fryden
Two different tone articulation models
p
First : Uses off-time duration (DRO)
Friberg: Generative Rules for Expressive Performance
March 8, 2006
Generative Rules
Purpose of the rules
p Implementing in LISP programming
language
p The resulting deviation from the rules are
additive.
p Order of the rules
p Exception for Synchronization rules and
amplitude rules should apply last.
p Mixed intonation rule should apply after
other intonation rules.
p
Two different tone articulation models
p
Second model :more complete , uses four-point
envelope (T1-T4, L1-L4) to shape each tone
individually.
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
Parameters for the Rules:
p
p
p
p
p
p
p
p
p
p
p
DR
Total duration of one tone
DRO Off-Time duration
_DR Deviation of the duration from the no rule
case, msec or percent
L
Level in dB
_L
Relative level deviation from L, in dB
VA
Vibrato amplitude in percent
_VA Relative vibrato amplitude deviation from VA,
in percent
VF
Vibrato frequency in Hz
_F
Relative frequency deviation in cents
T1-T4 Time breakpoints in the level envelope
L1-L4 Level breakpoints in the level envelope
March 8, 2006
Rules:
Single Parameter Rules
p Multiple Parameter Rules
p Intonation Rules
p Amplitude Envelope Rules
p Synchronization Rules
p
Parameter K
Single Parameter Rules:
Most of the rules include the quantity
parameter K.
p K used to alter the Quantity of the
manipulation induced by rule
p Always const value in the rule
p Default value K=1
p Different value for K, to generate different
performances for the same melody.
p
p
Friberg: Generative Rules for Expressive Performance
Rule
p Rule
p Rule
p Rule
p Rule
p Rule
p Rule
p Rule
DPC 1B.High Loud
DDC 2B.Double Duration
GMI 1A.Leap Articulation
GMI 1B.Leap Tone Duration
GMI 1C.Faster Uphill
GMI 3.Inegalles
GMI 4.Articulation of Repetition
GMA 3.Final Ritard
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
Rule DPC 1B.High Loud
p
The sound level of tones raised by dB/octave:
March 8, 2006
Rule DDC 2B.Double Duration
p
p
p
p
N is the semitone number, N=60 for note C4.
This rule increases the loudness in proportion
to the pitch height
p
p
A tone of duration less than 1 sec and half as
long as the preceding tone is increased by 12
percent if the following tone is longer.
For two notes having the duration ratio 2:1,
the short note will be lengthened and the long
note shortened
The preceding tone is shortened by the same
amount of msec.
Index n refers to the short tone.The index n-1
preceding one of double duration.
Rule GMI 1A.Leap Articulation
Alternative to rule GMI 1A
p A micropause inserted between the two
tone in the leap.
p Duration of micropause; leap distance and
duration of the first tone
p This rule does not apply to subphrase
borders,nor if DR_ ≥100 msec.
p
Friberg: Generative Rules for Expressive Performance
p
p
p
Let the first tone have index n
_N leap interval in semitones
Upper and lower limits:
The tone initiating the leap:
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
J.S. Bach: Bourree from suite C major
for cello solo
p
Micropauses in terms of DRO parameter values
induced by rule GMI 1A(leap articulation)
March 8, 2006
Rule GMI 1B.Leap Tone Duration
p
p
p
p
p
J.S. Bach: Bourree from suite C major
for cello solo
p
The Durational deviations resulting from rule GMI
1B( leap tone duration)
Rule GMI 1C.Faster Uphill
p
p
Friberg: Generative Rules for Expressive Performance
Modifies the duration of tones in singular leaps.
Applied if the leap preceded by repetition or
stepwise movement along the scale.
Let the first tone have index n ,_N leap interval in
semitones. The target tone index n+1.
Singular ascending leap
Singular descending leap
The durations in an ascending melodic line are
shortened
Duration of tone is shortened by 2.k msec
If preceding tone is lower and following tone is
higher.
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
Rule GMI 3.Inegalles
p
p
p
Optional rule
All eighth notes appearing on a strong beat will be
lengthened and all eighth notes appearing on a
weak beat will be shortened.
Sequences of paired tones of equal duration, the
duration of the tones appearing in metrically
stressed positions increase by 22% of their
duration, and the following tone shortened by
same amount.
Rule GMA 3.Final Ritard
p
p
p
p
p
Optional rule.
T running time form the beginning of ritard to the
current tone, indexed n
And T total be the total length of the ritard.
The tempo at the end of the piece is decreased
according to a square-root function of nominal
time
The change in duration for the notes in the ritard
will be :
Friberg: Generative Rules for Expressive Performance
March 8, 2006
Rule GMI 4.Articulation of Repetition
p
The off-time duration of the first tone in a
repetition is :
DRO= 35.k [msec]
Multiple Parameter Rules:
Rule
p Rule
p Rule
p Rule
p Rule
p
DDC 1.Durational Contrast
DPC 2A.Melodic Charge
GMA 1.Phrase
GMA 2A.Harmonic Charge
GMA 2B.Chromatic Charge
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
Rule DDC 1.Durational Contrast
p
p
p
Notes with duration between 30 and 600 msecs
are shortened and decreased in amplitude.
This rule makes short notes shorter and softer .
Depending on their durations according to two
breakpoint functions with values:
J.S. Bach: Kyrie I ,B minor mass
p
p
Minus sign represents a minor triad.
Example of the amplitude deviations induced
by rule DPC 2A ( melodic charge)
Friberg: Generative Rules for Expressive Performance
March 8, 2006
Rule DPC 2A.Melodic Charge
p
p
This rule accounts for the "remarkableness" of the
tones in relation to the underlying harmony
Melodic charge in a C major:
Rule GMA 1.Phrase
p
Phrases consists of subphrases.
Input notation by hand.
Tempo curves in form of arches with an initial
accelerando and a final ritardando are applied to
the phrase structure as defined in the score.
For the last tone of phrase:
p
For the last tone of subphrase:
p
For the last tone of piece:
p
p
p
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
Rule GMA 1.Phrase
p
Phrases and subphrases makers induced by
rule GMA 1(phrase)
March 8, 2006
Rule GMA 2A.Harmonic Charge
p
p
Rule GMA 2A.Harmonic Charge
p
F.Schubert`s Symphony in B minor( unfinished)
Rule GMA 2B.Chromatic Charge
p
Chromatic charge is defined as:
p
Disregarding rests.
This rule increases the sound level and duration in
areas where the intervals between the notes are
small
Smoothed by averaging over five tones.
Resulting mean: middle tone of the five
Amplitude and duration added:
p
p
p
p
Friberg: Generative Rules for Expressive Performance
“remarkableness” of chord measured by its
harmonic charge.
Computed from the melodic charge of the chord
tones as related to the root of the tonic:
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
Rule GMA 2B.Chromatic Charge
p
p
Melody generated by random function
Example of amplitude deviation produced by rule:
Chromatic charge
Rule DPC 1A.High Sharp
p
In one-voice music, pitch is sharpened by 4
cents/octave to equal temperament.
March 8, 2006
Intonation Rules:
Rule DPC 1A.High Sharp
p Rule DPC 2B.Melodic Intonation
p Rule ENS 1.Mixed Intonation for Ensemble
Music
p
Rule DPC 2B.Melodic Intonation
p
p
This rule can be used in monophonic contexts.
The fine tuning of the scale tones is adjusted
according to :
IC =number of semitones above the root of the
chord
_F =added deviation for that tone
Friberg: Generative Rules for Expressive Performance
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
Rule DPC 2B.Melodic Intonation
p
Frequency deviation according to melody
intonation expressed as function of melodic
charge
March 8, 2006
J.S. Bach suite, c minor, for cello solo
p
Frequency deviations from equal-tempered tuning
of melodic intonation rule
in a theme from the Sarabande
Rule ENS 1.Mixed Intonation for
Ensemble Music
Rule ENS 1.Mixed Intonation for
Ensemble Music
Harmonically acceptable but melodically
unacceptable when played according to
just intonation
p Melodically acceptable but harmonically
unacceptable when played with Rule DPC
2B( Melodic Intonation )
p The rule applied to a one-voice music
p
p
Friberg: Generative Rules for Expressive Performance
To produce negligible beating against the root of
the current chord the rule uses:
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
Rule ENS 1.Mixed Intonation for
Ensemble Music
p
Example of the time function for the adjustment
of tuning :
Rule DDC
2A.Accents(TentativeFormulation)
Accents are distributed to notes involved
in durational contrast in three cases:
1.Notes surrounded by longer notes
2.First of several equally short notes
followed by a longer tone.
3.The first long tone following a tone
provided with an accent according to
cases (a) or (b).
p
Friberg: Generative Rules for Expressive Performance
March 8, 2006
Amplitude Envelope Rules
Rule DDC 2A.Accents(Tentative
Formulation)
p Rule GMI 1A.Leap Articulation (Alternative
Tentative Formulation)
p Rule GMI 2.Amplitude Smoothing
p Rule GMI 4.Repetition Articulation
(Tentative Formulation)
p
Sound-level envelope
p
Sound-level envelope of each tone: interpolation between
four points specified by time and level values.
DR
L
W
D
= duration of the tone
= tonal sound level
= accent weight
= dip value
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
March 8, 2006
(A) Short notes surrounded by longer
notes
(B) First of several equally short notes
following a longer one.
(C)The first long tone after one or more
equally short tones.
Rule GMI 1A.Leap Articulation
(Alternative Tentative Formulation)
p
p
p
p
Friberg: Generative Rules for Expressive Performance
This rule should not be applied over phrases or sub
phrases borders or if the previous rule was applied.
The target tone of the leap have the index n+1
First tone of the leap the index n
Upper and lower limit:
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
Rule GMI 1A.Leap Articulation
(Alternative Tentative Formulation)
p
The dip value D :
Ascending leap:
p
Descending leap:
p
The envelope of target
tone calculated.
p
Rule GMI 4.Repetition Articulation
(Tentative Formulation)
p
p
The first tone in pair wise grouped repetitions
have the index n-1 and the second the index n.
Following applies to the first tone in repetition:
Friberg: Generative Rules for Expressive Performance
March 8, 2006
Rule GMI 2.Amplitude Smoothing
p
p
This rule eliminates steps in sound level.
It is not applied across phrase or sub-phrase
boundaries, or at repetitions.
Rule GMI 4.Repetition Articulation
(Tentative Formulation)
p
Following applies to the second tone in repetition:
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
March 8, 2006
Synchronization Rules
Rule ENS 2.Melody Synchronization
Rule ENS 2.Melody Synchronization
p Rule ENS 3.Bar Synchronization
p
p
p
p
p
p
Rule ENS 2.Melody Synchronization
After application of rules affecting the tone
durations, the timing of several voices will differ.
Strategy for synchronizing such voices
All no durational rules are applied to all voices.
This rule is important in polyphonic music where
the voices have the same importance.
Not apply to the accompaniment of a solo part,
where the solo is often leading over the
accompaniment.
Illustration of the strategy used for
synchronization in ensemble music
A new voice constructed that consists of
the shortest tone played by any of the
voices at any time.
p All durational rules applied to this new
synchronization voice.
p The timing information from this
synchronization voice used to synchronize
all the original voices.
p
Friberg: Generative Rules for Expressive Performance
Presented by L. Vaziri
ISE599: Computational Modeling of Expressive Performance
Rule ENS 3.Bar Synchronization
This rule may occasionally replace ENS 2
in rhythmically very complicated bars.
p For each bar: select the voice which has
the greatest number of notes, adjust the
other voices proportionally , their bardurations will equal that of the first
mentioned voice.
p This rule synchronizes the onset times for
the first note in each bar.
p
Friberg: Generative Rules for Expressive Performance
March 8, 2006
Conclusion
p
p
The purpose of the rules is to convert the written score,
complemented with chord symbols and phrase markers, to a
musically acceptable performance.
Questions?
Presented by L. Vaziri