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Fuzzy Information Retrieval for Musical Scores

Project description

Fuzzy Information Retrieval for Musical Scores (Firms)

Firms is an IR system designed for performing fuzzy searches against a
corpus of musical scores. Users provide snippets of a musical work using
a common digital music representation (e.g. MusicXML) and Firms compares
it against a corpus of pre-indexed musical scores to efficiently rank
and return results. The retrieval process is "fuzzy" because Firms is
designed to be resilient against several common sources of transcription
error, from simple typos, to aural rythmic ambiguity and key


Firms is hosted on the Python Package Index (Pypi) and can be installed
along with all required dependencies with the ``pip`` command:

``pip install firms``


Firms can be used as either a library (by importing modules from the
``firms`` namespace) or through a command line interface (CLI). The CLI
is defined in ```` and can be run interactively to explore
available commands and options:


This will display a list of available commands. To see more detail about
a particular command or group of commands, append ``--help`` to the
command. For example, to see more detail about initializing a Firms
index, run

``firms create --help``

or for different options for adding pieces to the index:

``firms add --help``

Many commands have subcommands supporting related operations. For
instance, to add all MusicXML pieces from a directory, use the
``add dir`` subcommand:

``firms add dir /path/to/directory``

At a broad level, the CLI offers the following features:

#. Create a Firms index
#. Add pieces to the index by specifying a composer, a path to a valid
MusicXML file, or by adding all pieces in the music21 corpus
#. Show general information about the stored data
#. Query for a piece by providing an example via MusicXML or in
#. Show a piece as MusicXML
#. Output the midi version of a piece
#. Evaluate the system by randomly selecting sections from the music21
corpus and probabilistically introducing various types of errors


The ``./examples`` directory contains a number of example music scores
that can be added to the system for demo purposes. Each of these pieces
is in the public domain and are available at
`OpenMusicScore <>`__. To add these pieces to
the index, run

``firms add dir "examples"``

Each piece can be queried using the CLI method:

``firms query tiny <tiny-query>``

Replace ``<tiny-query>`` in the command above with the query
corresponding to the piece in the table below. This query format is a
simple ASCII-based notation for representing small snippets of music
using standard western notation.

More information on tinynotation can be found `in the music21
documentation <>`__.

============================== =====================================================================================================================
Piece Query
============================== =====================================================================================================================
Amazing Grace tinynotation: g8 c'2 e'8 c' e'2 d'4 c'2 a4 g2 g4 c'2 e'8 c' e'2 d'4 g'2.~ g'2 e'4 g'4.~ e'8 g' e' c'2 g4 a4. c'8 c' a
Entertainer tinynotation: d''16 e'' c'' a' a' b' g'8 d'16 e' c' a a b g8 d16 e c A A B A A- G8
March of the Wooden Soldiers tinynotation: d'8 r d' r b8. a#16 b8 r16 c'#16 d'8 r d' r b8. a#16 b8 r16 c'#16
Ode to Joy tinynotation: b b c' d' d' c' b a g g a b b4. a8 a2
Deck the Halls tinynotation: d'4. c'8 b4 a g a b g a8 b c' a b4. a8 g4 f# g2
============================== =====================================================================================================================

For example, to run the query for *Entertainer* from the table above,

``firms query tiny "tinynotation: d''16 e'' c'' a' a' b' g'8 d'16 e' c' a a b g8 d16 e c A A B A A- G8"``

In addition, an XML sample of "Ode to Joy" is provided in the
``examples`` directory, and can be used like so:

``firms query xml examples/ode-to-joy.query.xml``

Examples with Errors

The table below contains versions of the sample queries above with a
different type of musical error included.

============================== =============================================================================== ===========
Piece Query Error Type
============================== =============================================================================== ===========
Amazing Grace tinynotation: g8 c'2 e'8 c' e'2 d'4 c'2 a4 g2 g4 g4 c'2 e'8 c' e'2 d'4 g'2. g'2 Extra Note
Entertainer tinynotation: d''16 e'' c'' a' a' b' g' d' e' c' a a b g8 d16 e c A A B A A- G8" Wrong Note
March of the Wooden Soldiers tinynotation: d'8 r d' b8. a#16 b8 r16 c'#16 d'8 r d' r b8. a#16 b8 r16 c'#16 Missing Note
Ode to Joy tinynotation: d' d' e'- f' f' e'- d' c' b- b- c' d' d'4. c'8 c'2 Transposed
Deck the Halls tinynotation: d'2. c'4 b2 a g a b g a4 b c' a b2. a4 g2 f# g1 Stretched Rhythm
============================== =============================================================================== ===========

FIRMs is designed to be accomodate some level of error in the user

Repeated sections

Failing to trace through repeated sections of music causes issues for
songs with a heavily repetative structure. The performance of Firms is
highly dependent on how these types of songs are notated. Explicitly
writing out repeated sections in a flat format greatly improves the
performance. This can be seen in the *Amazing Grace* query in the
"Examples" section above. This example contains the main theme of the
song, but the BM25 method fails to score it highly because the repeated
sections are ignored from the original score. The "Amazing Grace with
Drums Explicit Repeat" example is an alternate engraving of the "Amazing
Grace with Drums" score with repeated sections written out linearly, as
they would be heard by an audience. This example scores *higher* than
the original version because the repeats are effectively captured.

Firms can automatically expand repeated sections during the indexing
process. The various ``add`` commands take a boolean flag to enable the

``firms add dir ./examples --explicit_repeats True``

Note that this process can slow down ingest time significantly. If a
piece does not contain any repeated sections, or the repeated sections
are malformed in some way, the following error message will be shown,
and the ingestion process will continue with the original unexpanded

Unable to expand piece. Continuing with original


In addition to the examples shown above, the FIRMs CLI includes a
command for performing random probabilistic evaluation by sampling the
pieces included in the index.

To run an evaluation, first add some pieces to the corpus. Note, this
command may take some time (~5 minutes on my laptop) as it adds over 400
pieces to the index.

``firms add composer bach --filetype xml``

Then run an evaluation, specifying the number of samples to take. Note,
this may take some time to complete (~15 minutes for my laptop). Try
``--n 10`` for a faster result (~1.5 min).

``firms exaluate --n 100 --noprint True``

This will take 100 samples of various lengths from the pieces available
in the FIRMs index, perform a search based on the sample, and collect
statistics on the average rank of the correct result. The
``--noprint True`` option skips printing the individual query results
tables, while still printing the aggregate true-positive ranking
statistic. For exmaple, the results on my run were as follows:


Statistics for BM25
nobs: 100
minmax: (0, 7)
mean: 0.19
variance: 0.882727272727
skewness: 6.297878668097064
kurtosis: 40.1179051948864
Statistics for LogWeightedSumGrader
nobs: 100
minmax: (0, 26)
mean: 0.42
variance: 6.85212121212
skewness: 9.47574350344239
kurtosis: 90.04614836416702

This shows statistics on the ranks of true-positive results, broken down
by the grading methods used. The field ``nobs`` represents the total
number of observations. The ``minmax`` field shows the minimum and
maximum ranks for true-positive results. The ``mean``, ``variance``,
``skewness``, and ``kurtosis`` fields are statistics calculated based on
the the ranks.

While this is interesting, it is not overly representative of realistic
queries. First, these snippets are randomly selected, whereas users are
more likely to enter memorable melodic lines and themes. Second, users
are likely to include errors in their entries, either due to
transcription or due to ambiguities in how a particular piece is

Tackling the first issue is beyond the scope of this project, but the
``evaluate`` method includes a number of parameters for
probabilistically introducing errors into the sample queries.

``firms evaluate --n 100 --erate .2``

The ``--erate .2`` parameter gives each snippet a 20% chance of
including an error. The type of error chosen is controlled by the
parameters ``--transposition_error``, ``--replace_note_error``,
``--remove_note_error``, and ``--add_note_error``. These are decimal
values between [0, 1) and should add up to 1, thus representing a
probability distribution. By default, they are each set to ``.25`` to
present an equal probability.

Often we're more concerned with whether the true-positive result is
within the top K results returned, such as the first page of a search
engine. To quantify this, we can configure the evaluation scorer to
treat all results below K as a 0, while maintaining the rank of results
beyond that.

``firms evaluate --n 100 --topk 10``

This allows the system to be a little more flexible defining what it
considers to be a correct result.


At a fundamental level, Firms operates primarily on the concept of
*stemming*. Each piece is broken into a number of small sections called
*snippets*. These snippets are passed through several stemmers, each of
which produces one or more *stems* capturing a particular dimension of
the snippet. For example, a stem may capture the pitches, rhythms, or
contour of notes within snippet. These stems are persisted in an index
for efficient lookup.

When a user enters a query, the query is passed through the same
process, first breaking it up into snippets, then passing each snippet
through the same stemmers. The resulting stems are looked up in the
pre-constructed index, returning a list of locations within each piece
that match the given snippet. From there, the results may be aggregated
using one of several scoring mechanisms.

The implementation provides two built-in scoring mechanisms. The first
is a log weighted sum of counts. The matching stems for each stemmer
type are aggregated by taking the natural logarithm of the count, then
multiplied by a per-stemmer weight value, and finally summed together to
form the final grade. The second is a standard Okapi BM25 implementation
without document length normalization. Two potential measures of
document length which may improve the accuracy of this method are the
total number of measures for a piece or the total number of snippets in
a piece. A measure based approach ignores the density of notes within a
measure: a measure with a single whole note would be weighted the same
as a measure with a melodic line of sixteenth notes. The snippet count
approach would disproportionally impact pieces with many parts or
voices, as each part and voice acts as a multiplier for the number of
snippets contained in a piece. For these reasons, document length
normalization was not inlcuded for this project.

This particular implementation uses a local SQLite database to store the
pre-computed snippets, stems, and other information as a flat-file
relational structure. Each stemmer type is an instance of the abstract
``FirmIndex`` class, which hides the details of the storage mechanism
used. This allows the underlying SQLite implementation to be swapped out
for a more efficient storage mechanism without impacting the rest of the

Scaling and Improvements

One interesting side-effect of the chosen architecture is that the
applciation may be trivially scaled by hosting multiple instances behind
a load balancer. On insert, an arbitrary instance could be chosen to
store the piece. On query, a scatter-gather approach could pass the
query to each instance, and the final results streamed back to the load
balancer for aggregation. This approach would enable parallel persistent
storage IO on each instance. With some further modification, each
instance could be configured to locally aggregate results before passing
them on for final aggregation.

There are many musical aspects not captured by the current
implementation, including:

- Unpitched notes, e.g. percussion
- Tied notes
- Non-traditional western music notation


Configure .pypirc file with:


index-servers =



Then to create a new version:

#. ``git commit``
#. Update ``version`` and ``download_url``
#. ``git tag <version-number>`` and ``git push --tags``
#. ``python sdist upload -r pypitest``
#. ``pip install --upgrade firms --no-cache-dir``

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