Detroit Stats City

Math Modeling Motown’s MusicNicola Grissom Steve Mahler Becky Trisko

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

Artists and Songs

Kid Rock:American Badass

Madonna:Express Yourself

Artists and Songs

Iggy Pop:Search & Destroy

Eminem:Without Me

Artists and SongsThe White Stripes:

Hotel Yorba

The Supremes:Stop in the Name of Love

Artists and Songs

Aaliyah:We Need a Resolution

Marvin Gaye:Let’s Get it On

Artists and SongsThe Temptations:

Get Ready

Derrick May:Strings of Life

Artists and Songs

Alice Cooper:School’s OutForever

Ted Nugent:Cat Scratch Fever

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)

1.“Danceability” 2. “Singability”3.“Popularity When Released”4.“Appeal to Males”5.“Appeal to Females”6.“Appeal to You”

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

Scree Plot

0.17

0.175

0.18

0.185

0.19

0.195

0.2

0.205

0.21

0.215

1 2 3 4 5

Str

ess

Dimensions

Elbow

MDSEuclidean distance model

Dimension 1

2.01.51.0.50.0-.5-1.0-1.5

2.0

1.5

1.0

.5

0.0

-.5

-1.0

-1.5

tnac

tkno

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spms

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INDSCALDerived Subject Weights

Dimension 1

.9.8.7.6.5.4.3

.9

.8

.7

.6

.5

.4

.3

5

4

3

2

1

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

Dim 1Dim 2

Danceability .06

-.18Singability

.09-.15

Popularity When Released.08 -.15

Appeal to Males.12 -.17

Appeal to Females.09 -.24

Appeal to You.08

-.18Year Song was Released -.23 .43Top Billboard Chart Position -.25 .27

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.

Tree Model

White Stripes

Ted Nugent

Alice Cooper

Iggy Pop

Kid Rock

Derrick May

Eminem

Temptations

Marvin Gaye

Supremes

Aaliyah

Madonna

Mean Appeal to Females in Tree Structure Groups

Appeal to Females

Group 1

Group 2

0

1

2

3

4

5

6

t = 4.14, p < 0.005

Singability

t = 4.18, p < 0.005

r = .91

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.