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  1. Detroit Stats City Math Modeling Motown’s Music Nicola Grissom Steve Mahler Becky Trisko

  2. Objectives • To rate similarities between selected songs of Southeast Michigan’s homegrown artists • To develop a model accurately describing the main dimensions used by song raters in rating similarities between songs

  3. Artists and Songs Madonna: Express Yourself Kid Rock: American Badass

  4. Artists and Songs Iggy Pop: Search & Destroy Eminem: Without Me

  5. Artists and Songs The White Stripes: Hotel Yorba The Supremes: Stop in the Name of Love

  6. Artists and Songs Aaliyah: We Need a Resolution Marvin Gaye: Let’s Get it On

  7. Artists and Songs The Temptations: Get Ready Derrick May: Strings of Life

  8. Artists and Songs Alice Cooper: School’s Out Forever Ted Nugent: Cat Scratch Fever

  9. 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”

  10. 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

  11. 0.215 0.21 0.205 0.2 Stress 0.195 0.19 0.185 0.18 0.175 0.17 1 2 3 4 5 Dimensions Scree Plot Elbow

  12. 2.0 tkno 1.5 mnm 1.0 aaa mad .5 kr 0.0 spms ip tn ac tptns -.5 mg -1.0 ws -1.5 -1.5 -1.0 -.5 0.0 .5 1.0 1.5 2.0 Dimension 1 MDS Euclidean distance model

  13. .9 .8 .7 .6 4 5 .5 3 2 .4 1 .3 .3 .4 .5 .6 .7 .8 .9 Dimension 1 INDSCAL Derived Subject Weights

  14. Dim 1 Dim 2 • Danceability .06 -.18 • Singability .09 -.15 • Popularity When Released .08 -.15 • Appeal to Males .12 -.17 • Appeal to Females .09 -.24 • Appeal to You .08 -.18 • Year Song was Released -.23 .43 • Top Billboard Chart Position -.25 .27 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 song’s position on that dimension. Correlations between MDS-Derived Dimension Scores and Subject-Rated Dimensions

  15. 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.

  16. White Stripes Madonna Aaliyah Supremes Marvin Gaye Temptations Eminem Derrick May Kid Rock Iggy Pop Alice Cooper Ted Nugent Tree Model Group 1 Group 2

  17. Singability 6 5 4 Group 1 Group 2 3 2 t = 4.18, p < 0.005 1 0 t = 4.14, p < 0.005 Mean Appeal to Females in Tree Structure Groups Appeal to Females r = .91

  18. 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.