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Detroit Stats City. Math Modeling Motown’s Music. Nicola Grissom Steve Mahler Becky Trisko. Objectives. To rate similarities between selected songs of Southeast Michigan’s homegrown artists

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Detroit stats city

Detroit Stats City

Math Modeling Motown’s Music

Nicola Grissom Steve Mahler Becky Trisko


Objectives

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

Artists and Songs

Madonna:

Express Yourself

Kid Rock:

American Badass


Artists and songs1

Artists and Songs

Iggy Pop:

Search & Destroy

Eminem:

Without Me


Artists and songs2

Artists and Songs

The White Stripes:

Hotel Yorba

The Supremes:

Stop in the

Name of Love


Artists and songs3

Artists and Songs

Aaliyah:

We Need a Resolution

Marvin Gaye:

Let’s Get it On


Artists and songs4

Artists and Songs

The Temptations:

Get Ready

Derrick May:

Strings of Life


Artists and songs5

Artists and Songs

Alice Cooper:

School’s Out

Forever

Ted Nugent:

Cat Scratch

Fever


Methods

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”


Methods1

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

0.215

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


Statistics presentation on detroit music

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


Indscal

.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


Dimensional

  • Dim 1Dim 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


    Dimensions

    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

    Madonna

    Aaliyah

    Supremes

    Marvin Gaye

    Temptations

    Eminem

    Derrick May

    Kid Rock

    Iggy Pop

    Alice Cooper

    Ted Nugent

    Tree Model

    Group 1

    Group 2


    Mean appeal to females in tree structure groups

    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


    Conclusion

    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.


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