Download Introduction Local Boundary Detection Model Study of Expressive Timing (LBDM)

Introduction
The Local Boundary Detection Model
(LBDM) and its Application in the
Study of Expressive Timing
z
z
z
z
z
z
Expressive performance of a musical work relies on the
underlying musical structure.
Both traditional music theory and modern computational
analysis find a strong link between musical structure and
expression.
Learning rules of melodic expression by computational
means is significantly improved when structural aspects of
the music are taken into account.
Introduction
Local Boundary Detection Model
It is commonly hypothesized that the ending of a musical
phrase is marked by a slowing down of tempo.
The Local Boundary Detection Model (LBDM)
calculates boundary strength values for each interval
of a melodic surface according to the strength of
local discontinuities; peaks in the resulting sequence
of boundary strengths are taken to be potential local
boundaries.
Interonset Interval (IOI) = the time between the start of a
note and the start of the note immediately after it
For small melodic gestures of just a few notes it is
commonly assumed that the final note IOI is lengthened and
a small micro pause inserted.
Rules
LBDM Algorithm
Change Rule (CR): Boundary strengths proportional to
the degree of change between two consecutive
intervals are introduced on either of the two intervals.
Proximity Rule (PR): If two consecutive intervals are
different, the boundary introduced on the larger
interval is proportionally stronger.
Evaluation of LBDM
z
z
z
Friberg et al (1998) developed a set of punctuation rules
called the Punctuation Rule System.
The system marks low-level structural boundaries in a
melody. (i.e. comma for a pause)
These rules were tested against an expert performer's
punctuation and the LBDM.
Conclusion of Evaluation
z
z
The LBDM is not a complete model for melodic
grouping.
LBDM needs to be extended to include other
components, such as harmonic and melodic
similarity
Experiment 1
Expressive Timing Deviations at Local Boundaries
z
It is often theorized that the last note of a musical
phrase is lengthened and a micro pause inserted.
z
The Punctuation Rule System uses this theory.
z
The LBDM was used to test this theory.
z
z
z
z
Conclusions of Experiment 1
z
z
z
z
There were twice as many lengthened strong boundaries than
shortened ones.
Weak boundary values are lengthened and shortened equally.
Notes with stronger LBDM boundary values tend to be
lengthened in terms of the IOI.
The theory that all or most notes at the end of musical phrases
are lengthened is wrong.
Seven complete Mozart Sonatas were performed by
a professional musician and monitored by computer.
The LBDM and timing deviation curves were
computed.
LBDM boundaries were split into Strong and Weak.
Timing deviations were classified as Longer,
Shorter, or Same.
Experiment 2
z
z
z
The first 20 bars of Chopin’s Etude Op10, No3. was
played by 22 professional musicians.
Performances were monitored by computer
LBDM was applied and the IOI deviation curve was
computed.
Conclusion of Experiment 2
z
z
z
z
Reinforces results of Experiment 1.
There were more lengthened strong boundaries than shortened
ones.
Weak boundaries are lengthened and shortened almost
equally.
Conclusions of Experiment 2
z
z
z
The second-to-last note almost always has an increased IOI.
The second-to-last note is lengthened or the last note is
delayed.
In most of these cases, a series of short notes is followed by a
longer one.
Notes with stronger LBDM values tend to be lengthened in
terms of IOI.
Chopin’s Etude Op10, No3.
Final Conclusions
z
z
z
The LBDM's performance was shown to be comparable to the
Punctuation Rule System.
The hypothesis that the final note of a phrase is always
lengthened is not always valid.
The end of a melodic phrase is more often marked by the
lengthening of the second-to-last note or delaying the last
note.