topical media & game development
research directions -- musical similarity matching
An
altogether different approach at establishing melodic similarity
is proposed in
[Compare]. This approach has been followed
in the Meldex system
[Meldex], discussed in
section
[Web].
This is a rather technical section, that may be skipped on first reading.
The approach is different in that it relies on
a (computer science) theory of finite sequence comparison,
instead of musical considerations.
The general approach is, as explained in
[Compare],
to search for an optimal correspondence between elements
of two sequences, based on a distance metric or measure
of dissimilarity,
also known more informally as the
edit-distance,
which amounts to the (minimal) number of transformations that need to be applied
to the first sequence in order to obtain the second one.
Typical transformations include
deletion,
insertion and
replacement.
In the musical domain, we may also apply transformations
such as
consolidation (the replacement of several elements
by one element) and
fragmentation (which is the reverse of
consolidation).
The metric is even more generally applicable by associating a weight
with each of the transformations.
Elements of the musical sequences used in
[Compare] are
pitch-duration pairs, encoded in base-12 pitch information
and durations as multiples of 1/16th notes.
The actual algorithms for determining the dissimilarity
between two sequences uses dynamic programming techniques.
The algorithm has been generalized to look for matching phrases,
or subsequences, within a sequence.
The complexity of the algorithm is ,
provided that a limit is imposed on the number of notes
involved in consolidation and fragmentation.
Nevertheless, as indicated in experiments for the
Meldex database, the resulting complexity is still
forbidding when large databases are involved.
The Meldex system offers apart from the (approximate)
dynamic programming algorithm also a state matching algorithm
that is less flexible, but significantly faster.
The Meldex experiments involved a database
of 9400 songs, that were used to investigate six
musical search criteria:
(1) exact interval and rhythm,
(2) exact contour and rhythm,
(3) exact interval,
(4) exact contour,
(5) approximate interval and rhythm, and
(6) approximate contour and rhythm.
Their results indicate that the number of notes needed
to return a reasonable number of songs scales
logarithmically with database size [Meldex].
It must be noted that the Meldex database contained
a full (monophonic) transcription of the songs.
An obvious solution to manage the complexity of
searching over a large database would seem to be the storage
of prototypical themes or melodies instead of complete songs.
indexing and analysis
There are several tools available that may assist us in creating
a proper index of musical information.
One of these tools is the Humdrum system,
which offers facilities
for metric and harmonic analysis,
that have proven their worth in several musicological investigations [Humdrum].
Another tool that seems to be suitable for our purposes,
moreover since it uses a simple pitch-duration, or piano-roll,
encoding of musical material, is
the system for metric and harmonic analysis described in [Meter].
Their system derives a metrical structure, encoded
as hierarchical levels of equally spaced beats,
based on preference-rules which determine the overall
likelihood of the resulting metrical structure.
Harmonic analysis further results in (another level of)
chord spans labelled with roots,
which is also determined by preference rules that take
into account the previously derived metrical structure.
As we have observed before, metrical and harmonic analysis
may be used to eliminate confounding information
with regard to the 'prototypical' melodic structure.
(C) Æliens
04/09/2009
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