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Beyond Error Tolerance:
Finding Thematic Similarities in Music Digital Libraries
Tamar Berman
J. Stephen Downie
Bart Berman
GSLIS
University of Illinois
at Urbana-Champaign
GSLIS
University of Illinois
at Urbana-Champaign
Independent Researcher
www.notesonfranzschubert.com
INTRODUCTION
 The objective: given a theme description, retrieve relevant phrases
from a music database. These phrases will be thematically similar to
each other
 The inspiration: Barlow and Morgenstern’s Dictionary of Musical
Themes
 The challenge: the relevant phrases may be quite different from each
other in musical details such as melody and rhythm. They may not
have identical harmonies
 The solution:
1. Describe the theme as a sequence of melody and harmony
events that must be presented in a given order and completed
within a given time frame
2. Create an index for the music database which describes changes
in harmony over time. Use this index to perform the retrieval
EXAMPLE
 First theme in Allegro of Mozart’s Clarinet Concerto in A, K622
 Taken from the Barlow and Morgenstern dictionary
 A later presentation of the theme (measures 32-33)
 Would have been retrieved only by harmony events
METHOD OF INDEXING
 Possible search keys:
1. Melody sequence: {E C# D F# E D C# C# D B D B A G#}
2. Transposed melody sequence, as in B&M: GEFAGFEEFDFDCB
3. Rhythm: {Half, Dotted Quarter, Eighth, Eighth, Eighth, Eighth, Eighth,
Quarter}
4. Exact harmony: {I I IV I ii ii I V7}
5. Harmony events:
First event: A, C#, E with E as top voice
Second event: A, C# with C# as top voice
Third event: A, C#
 The music in the database in transformed into an equally-spaced
time series of 12-dimensional vectors. This time series serves as
an index to the database, and is used by the retrieval queries
 Each element in the time series, called a harmonic window, describes
the pitch content of the time interval contained within the window
 For example, a harmonic window which starts 5 seconds into the piece
and ends 6 seconds into the piece describes, for each pitch class, its role
within that time frame: top voice, bass, middle or absent
 The series is constructed on the basis of two parameters:
1. Window length: size (in seconds) of the time interval
described by each harmonic window
2. Onset interval: time (in seconds) between window onsets
(“sampling rate”)
TESTING AND PERFORMANCE
 The method was tested on midi sequences of music by Mozart
 Simple query retrieval achieved up to 88% precision
 Complex query retrieval achieved up to 100% precision
 First presentation of the theme (measures 1-4)
 Would have been successfully retrieved by any of the search keys
Special Thanks to: The Andrew W. Mellon Foundation
and the National Science Foundation