Detroit Stats City

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Detroit Stats City

• Math Modeling Motowns Music

Nicola Grissom Steve
Mahler Becky Trisko
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Objectives

• To rate similarities between selected songs of
  Southeast Michigans homegrown artists
• To develop a model accurately describing the main
  dimensions used by song raters in rating
  similarities between songs

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Artists and Songs
Madonna Express Yourself
Kid Rock American Badass
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Artists and Songs
Iggy Pop Search Destroy
Eminem Without Me
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Artists and Songs
The White Stripes Hotel Yorba
The Supremes Stop in the Name of Love
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Artists and Songs
Aaliyah We Need a Resolution
Marvin Gaye Lets Get it On
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Artists and Songs
The Temptations Get Ready
Derrick May Strings of Life
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Artists and Songs
Alice Cooper Schools Out Forever
Ted Nugent Cat Scratch Fever
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Methods

• Each Song was rated on a 21 point Likert scale on
  similarity with each other song
• Following ratings, subjects rated each song on
  the following factors (7 point Likert Scale)
• Danceability
• Singability
• Popularity When Released
• Appeal to Males
• Appeal to Females
• Appeal to You

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Methods

• In addition, the following objective indices were
  collected on the songs
• Sex of Performer
• Year Song was Released
• Top Billboard Chart Position
• Style of Music

• And on their raters
• Sex of Rater
• Age of Rater

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Scree Plot
Elbow
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MDS
Euclidean distance model
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INDSCAL
Derived Subject Weights
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Dimensional?

• If the songs were rated on continuous dimensions,
  the distance of a song from the origin on a
  dimension should correlate with an independent
  measure of that songs position on that
  dimension.

Correlations between MDS-Derived Dimension Scores
and Subject-Rated Dimensions
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Dimensions?

• None of the objective or subject-rated
  characteristics we measured accounted well for
  the dimensions mapped by MDS.
• In addition, ranking the songs based on these
  characteristics did not well describe the
  putative dimensions mapped by MDS.

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Tree Model
Group 1
Group 2
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Mean Appeal to Females in Tree Structure Groups
Appeal to Females
r .91
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Conclusion

• Although we originally hypothesized that the
  subjects would employ dimensions in rating
  similarity between songs, our data was more
  appropriately modeled by a hierarchical tree
  structure.
• Subjects seemed to categorize songs by genre and
  perhaps singability/appeal to females.