Exploring Microtonal Matching

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Exploring Microtonal Matching

• Iman S. H. Suyoto and Alexandra L. Uitdenbogerd
• ISMIR 2004

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Outline

• Introduction
• Computer Representations ( MTRI )
• Retrieval Processes
• Analysis of Experiments
• Conclusions

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Introduction ( 1/2 )

• Examine music from western tradition.
• Ex. Separate an octave into 12 semitones.
• Different tuning systems.
• Ex. Chinese five-tone.

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Introduction ( 2/2 )

• Some have no corresponding pitches in other
  tuning systems.
• In one Eastern tuning system, the interval
  between two pitches is 240 cents. (Between 200
  and 300) ? microtonality
• Difficulties
• Represent music of alternative tuning systems.
• Find matches to queries from different tuning
  systems.

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Computer Representations (MTRI)

• Micro-Tonal Representation for Information
  Retrieval
• Support for non-twelve-tone systems.
• Support for polyphonic music.
• Each tune encoded by MTRI has two files
• MTP MTRI pitch specification file
• MTS MTRI score file

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Retrieval Processes

• Step1 Take one melody for two parts
• Pitch string
• Duration string
• Step2 Calculate the pitch similarity and the
  duration similarity individually of two melodies.
• Step3 Calculate the resultant similarity vector.

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Pitch Standardization (1/2)

• Express interval in cents.
• Represent a note by the interval between itself
  and its previous one.

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Pitch Standardization (2/2)
Melody1
P1
D1
Melody2
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Duration Standardization

• Represent a note by its duration relative to its
  previous one.
• R same
• L longer
• S shorter

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Polyphonic Music

• Treat each track or part of a polyphonic piece as
  a separate sequence of notes for matching.
• Calculate similarity score for each part.
• The best one is chosen as the representative
  score for the piece.

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Approximate Matching (1/6)

• Use local alignment matrix to calculate the
  similarity.
• Reward / penalty
• Applied a range of penalties, including zero.
  (grace notes / repetitive notes)
• Si, j max 0,
• Si-1, j-1 w Xi,
  Yj,
• S i , j-1 w -
  , Yj,
• Si-1, j w Xi,
  -

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Approximate Matching (2/6)

• We designed several scoring schemes for exact
  microtonal interval.
• Test various scoring schemes to find the better
  one. (small false matches)

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Approximate Matching (3/6)

• Formula to calculate reward/penalty scores
• the interval in cents
• the reward/penalty order
• Floor error ?

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Approximate Matching (4/6)

• Example we use T 25 , 1 , and
  insertion/deletion score of -25.
• P1 is 100 130 200 -50 and P2 is 100 100 -180

max0, 25.0022.51, 22.51-25, 25.00-25
47.51
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Approximate Matching (5/6)

• The duration similarity is obtained by the
  similar steps.
• Scoring matrix for note duration

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Approximate Matching (6/6)

• Calculate the resultant similarity vector
• pitch unit vector
• duration unit vector
• We model pitch and duration similarities as two
  orthogonal vectors.
• Ranking is based on

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Analysis of Experiments (1/2)

• MHFM (Mean Highest False Match)
• the mean similarity of the highest-ranked
  incorrect answer with respect to that of the
  correct answer.

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Analysis of Experiments (2/2)

• With duration similarity incorporated

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Conclusions

• The applicability of microtone-aware matching
  techniques to music of various tuning systems.
• Reward/penalty order ? MHFM ? the
  correctness of a retrieval system .
• However, needs a sufficiently larger collection
  and query set.