Sonification - 6. Chromatic Scale

Sonification of Complex Data Sets: An Example from Basketball

Frances L. Van Scoy

Chromatic Scale for Simple Functions

Simple functions of a single variable can be represented by selected notes of the chromatic scale. For example the function f(t) = t can be represented by the chromatic scale.

Figure 2 Graph of f(t) = t

Music 3 Musical representation of f(t) = t

A semicircle eliminates some notes of the chromatic scale and repeats others. We show this in the following table in which we compute the value of sqrt(144-t²) for 0 <= t <=12 as we determine how to represent a quarter circle.

x

0

1

2

3

4

5

6

7

8

9

10

11

12

x²

0

1

4

9

16

25

36

49

64

81

100

121

144

144-x²

144

143

140

135

128

119

108

95

80

63

44

23

0

sqrt( 144 - x²)

12.00

11.96

11.83

11.62

11.31

10.91

10.39

9.75

8.94

7.94

6.63

4.80

0.00

rounded

12

12

12

12

11

11

11

10

9

8

7

5

0

note

C

C

C

C

B

B

B

Bb

A

Ab

G

F

C

A semicircle, then can be represented by the notes

C F G G# A A# B B B C C C C C C C B B B Bb A Ab G F C.

Figure 3 Graph of f(t) = sqrt(k² -t²)

Music 4 Musical representation of f(t) = sqrt(k² -t²)

x	0	1	2	3	4	5	6	7	8	9	10	11	12
x²	0	1	4	9	16	25	36	49	64	81	100	121	144
144-x²	144	143	140	135	128	119	108	95	80	63	44	23	0
sqrt( 144 - x²)	12.00	11.96	11.83	11.62	11.31	10.91	10.39	9.75	8.94	7.94	6.63	4.80	0.00
rounded	12	12	12	12	11	11	11	10	9	8	7	5	0
note	C	C	C	C	B	B	B	Bb	A	Ab	G	F	C