Draft
Student Activity
Music Unit Review
I.
II.
For each of the following identify the type of note and tell how many
beats the note receives if the quarter note gets one beat. (Do not use
the decimal form of the answer.)
1.
___________________ 2.
___________________
3.
___________________ 4.
___________________
In each of the following time signatures tell which type of note gets
one beat and how beats there will be per measure. (Questions 5,6,
and 7)
Time Signature
Note that gets one Beats per Measure
beat
(Name and
symbol)
3
4
6
8
4
4
III.
Some of the following measures have the correct number of beats
and some do not. Decide which measures are correct and which are
not then, using fractions, show the mathematics that will confirm your
answers.
8.
4
4
10. 4
4
9.
4
4
11. 4
4
Mathematical Models with Applications, Fine Arts Module
Music Unit Review
118
Draft
Student Activity
12. 4
13. 3
14. 3
15. 3
16. 3
17. 3
4
4
4
4
4
4
IV. Prepare rhythmic number lines to show where the beats occur with the
following sets of rhythms are played together
18. 2-against-3 |--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|
19. 3-against-4 |--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|
20. 3-against-5 |--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|
21. 4-against-5 |--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|
Mathematical Models with Applications, Fine Arts Module
Music Unit Review
119
Draft
V.
Student Activity
(22) Using the grid drawn below, sketch variations of y = sin(x ) that will
have amplitudes of 0.5, 2, and 3.
VI. Using a graphing calculator, calculate the frequencies and wave lengths
for the following.
Window:
xmin 0
ymin –1.5
Equation
1st
x-value
xmax 0.02375
ymax 1.5
2nd
x-value
Wave Length
in seconds
xscl 0.005
yscl 1
Frequency
cycles/second
y = sin(2764.6x )
y = sin(691.15x )
y = sin(1845.4x )
Mathematical Models with Applications, Fine Arts Module
Music Unit Review
120
Draft
Student Activity
VII. Given that the open string on the monochord is 60 cm long, find the
length of the string that will produce the following tones. (Multiply by
1
the constant ratio 12 to find the lengths for each note moving up the
2
chromatic scale.)
Half-Steps
1
Major Scale
do
String Length
60 cm
2
3
re
4
5
mi
6
fa
7
8
sol
9
10
la
11
12
ti
13
do
Mathematical Models with Applications, Fine Arts Module
Music Unit Review
121
Draft
Student Activity
VIII. Fill in the following frequency chart calculating the frequencies for
each note. As with the length you can use the recursive feature on
the calculator. The frequencies change in the opposite direction from
the string lengths. As the string lengths get shorter, the frequencies get
larger. Move up the scale multiply by 2
1
12
and move down the scale
1
12
by dividing by 2 . Round your answers to one decimal place. To
avoid round-off errors, begin your calculations at A(4) 440 Hertz.
Note
Frequency (hertz)
A
27.5
A sharp B flat
B
C
C sharp D flat
D
D shart E flat
E
F
F sharp G flat
G
G sharp A flat
A(1)
55
A sharp B flat
B
C
C sharp D flat
D
D shart E flat
E
F
F sharp G flat
G
G shart A flat
A(2)
110
A sharp B flat
B
C
C sharp D flat
D
D shart E flat
E
F
F sharp G flat
G
G shart A flat
Note
Frequency (hertz)
A (3)
220
A sharp B flat
B
C
C sharp D flat
D
D shart E flat
E
F
F sharp G flat
G
G sharp A flat
A(4)
440
A sharp B flat
B
C
C sharp D flat
D
D shart E flat
E
F
F sharp G flat
G
G shart A flat
A(5)
880
A sharp B flat
B
C
C sharp D flat
D
D shart E flat
E
F
F sharp G flat
G
G shart A flat
Mathematical Models with Applications, Fine Arts Module
Music Unit Review
122
DRAFT
Student Activity Answers
Music Unit Review
Answers
I.
1.
half note, 2 beat
3.
eighth note,
1
beat
2
2.
quarter note, 1 beat
4.
dotted quarter note,
1
1 beats
2
II.
Time Signature
3
4
6
8
4
4
Note that gets one beat
(Name and symbol)
Beats per Measure
3
quarter note
6
eighth note
4
quarter note
III.
8.
4
4
9.
yes
10.
1 1 1 1 4
+ + + =
4 4 4 4 4
4
4
yes
11.
1 1  1 1 1 4
yes  +  + + + =
4 8 8 4 4 4
12.
4
4
no
4
4
no
13.
1 1 1 1 1 1 7 4
+ + + + + = ≠
4 8 8 8 8 8 8 4
4
4
3
4
yes
Mathematical Models with Applications, Fine Arts Module
Music Unit Review
1 1 1 1 1 1 4
+ + + + + =
4 8 8 4 8 8 4
1 1 1 1 1 5 4
+ + + + = ≠
4 4 4 4 4 4 4
1 1 1 3
+ + =
4 4 4 4
123
DRAFT
14.
Student Activity Answers
3
4
15.
1 1 1 1 3
+ + + =
4 4 8 8 4
yes
16.
3
4
1 1 1 1 4 3
+ + + = ≠
4 8 8 2 4 4
no
17.
1 1 3
+ =
2 4 4
yes
3
4
3
4
1 1 1 3
+ + =
2 8 8 4
yes
IV.
18. 2-against-3
2 beats per measure
•
•
1
2
3
4
<
<
3 beats per measure
•
5
<
6
1
<
•
2
3
<
•
4
5
<
6
1
<
2
3
<
19. 3-against-4
3 beats per measure
•
1
•
2
3
4
5
•
6
<
<
4 beats per measure
7
8
9
<
•
10
11
12
<
1
•
2
3
<
4
5
6
<
7
8
<
20. 3-against-5
3 beats per measure
•
1
2
3
4
5
<
<
5 beats per measure
•
6
•
7
<
8
9
10
11
•
12
<
Mathematical Models with Applications, Fine Arts Module
Music Unit Review
13
<
14
15
1
<
2
3
4
<
124
5
DRAFT
Student Activity Answers
21. 4-against-5
4 beats per measure
=
=
1
2
3
4
5
<
<
5 beats per measure
6
=
7
8
9
10
11
=
12
<
13
14
15
<
16
17
18
19
20
<
V.
VI.
Answers will vary because of measurement error
Equation
1st x-value 2nd x-value Wave Length Frequency
in seconds
cycles/second
y = sin (2764 .6x )
0.00227
440 Hz
y = sin (691.15x )
0.00909
110 Hz
y = sin (1845 .4 x )
0.00340
293.7 Hz
Mathematical Models with Applications, Fine Arts Module
Music Unit Review
125
DRAFT
Student Activity Answers
VII.
Half-Steps
Major Scale
String Length
1
do
60 cm
2
3
56.6 cm
re
4
53.5 cm
50.5 cm
5
mi
47.6 cm
6
fa
44.9 cm
7
8
42.4 cm
sol
9
10
40.0 cm
37.8 cm
la
11
35.7 cm
33.7 cm
12
ti
31.9 cm
13
do
30.0 cm
Mathematical Models with Applications, Fine Arts Module
Music Unit Review
126
DRAFT
Student Activity Answers
VIII.
Note
Frequency (hertz)
A
27.5
A sharp B flat
29.1
B
30.9
C
32.7
C sharp D flat
34.6
D
36.7
D shart E flat
38.9
E
41.2
F
43.7
F sharp G flat
46.2
G
49.0
G sharp A flat
51.9
A(1)
55
A sharp B flat
58.3
B
61.7
C
65.4
C sharp D flat
69.3
D
73.4
D shart E flat
77.8
E
82.4
F
87.3
F sharp G flat
92.5
G
98.0
G shart A flat
103.8
A(2)
110
A sharp B flat
116.5
B
123.5
C
130.8
C sharp D flat
138.6
D
146.8
D shart E flat
155.6
E
164.8
F
174.6
F sharp G flat
185.0
G
196.0
G shart A flat
207.7
A(3)
220
Note
Frequency (hertz)
A (3)
220
A sharp B flat
233.1
B
246.9
C
261.6
C sharp D flat
277.2
D
293.7
D shart E flat
311.1
E
329.6
F
349.2
F sharp G flat
370.0
G
392.0
G sharp A flat
415.3
A(4)
440
A sharp B flat
466.2
B
493.9
C
523.3
C sharp D flat
554.4
D
587.3
D shart E flat
622.3
E
659.3
F
698.5
F sharp G flat
740.0
G
784.0
G shart A flat
830.6
A(5)
880
A sharp B flat
932.3
B
987.8
C
1046.5
C sharp D flat
1108.7
D
1174.7
D shart E flat
1244.5
E
1318.5
F
1396.9
F sharp G flat
1480.0
G
1568.0
G shart A flat
1661.2
A(6)
1760
Mathematical Models with Applications, Fine Arts Module
Music Unit Review
127
Draft
Student Activity
Sample Music Unit Test
4
1.
In a time signature of 4 what type of note will receive one beat?
____________
2.
In 4 time how many beats will be in the measure?
3.
The following measures are supposed to be in 4 time. Do the
measures have the correct number of beats? Using fractions to
explain your answers.
4
____________
4
a.
b.
4.
Using a mixture of quarter notes and eighth notes set up a correct
measure in 34 time. Support your notes with fractions.
5.
Using the line provided below, draw a rhythm chart to illustrate where
the beats will occur when 2 beats per measure are played against 3
beats per measure. Draw at least two measures.
|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
6.
What does amplitude mean?
Mathematical Models with Applications, Fine Arts Module
Music Unit Test
128
DRAFT
7.
8.
Student Activity
y = sin(x ) is drawn below. On the same set of axes draw a sine
graph that will have an amplitude of 3.
If the wave length of a wave is 0.003 seconds, what is the frequency?
________________
9.
The equation for a particular sound is given by y = sin(1646x ) . Graph
the function on your calculator using the window given below.
xmin 0
a.
xmax 0.01 x-scl 0.001 ymin –1.5
ymax 1.5
y-scl 1
Calculate the length of the wave. Show your work
______________
b.
Calculate the frequency
10. What are the units for frequency?
_______________
________________
11. If the open string length on a instrument is 40 cm, how long is the
string that produces the sound one octave higher?
__________________
Mathematical Models with Applications, Fine Arts Module
Music Unit Test
129
DRAFT
Student Activity
12. Complete the following frequency chart. Remember that the multiplier
 1
 
 12 
is (2)
.
A
110
A
B
C
C
13. On the monochord you tuned different notes by changing the length
of the string. If the open string is 60 cm long how long will the strings
be for the next 4 half steps.
Remember that the multiplier is (0.5)
 1
 
 12 
1
60 cm
2
3
4
5
Points from questions during activities.
14. ______________ 15._________________ 16. ________________
Mathematical Models with Applications, Fine Arts Module
Music Unit Test
130
DRAFT
Student Activity Answers
Music Unit Test
Answers
1.
quarter note
2.
4
3.
The following measures are supposed to be in 44 time. Do the measures have the correct
number of beats? Using fractions to explain your answers.
a.
b.
4.
yes
1 1 1 1 4
+ + + =
4 8 8 2 4
no
1 1 1 1 5 4
+ + + = ≠
2 4 4 4 4 4
Answers will vary
1 1 1 1 3
+ + + =
4 8 4 8 4
sample answer
5.
2 beats per measure
•
1
2
3
<
<
3 beats per measure
6.
•
4
•
5
<
6
1
<
•
2
3
<
4
•
5
<
6
1
<
2
3
<
Sample response: Amplitude is half the height of a sound wave graph. It represents the
loudness (intensity) of sound.
Mathematical Models with Applications, Fine Arts Module
Music Unit Test – Teacher Edition
131
7.
8.
frequency =
9. a.
1
≈ 333.33...
0.003
answers will vary but should be approximately
b.
2
≈ 0.003817245 ...
1646
frequency ≈ 261.9690363 ...
10.
cycles per second
11.
20 cm
12.
A
A
110
116.541 Hz
B
123.471 Hz
C
130.813 Hz
C
138.591 Hz
Mathematical Models with Applications, Fine Arts Module
Music Unit Test – Teacher Edition
132
13.
1
60 cm
2
56.632 cm
3
53.454 cm
4
50.454 cm
5
47.622 cm
Mathematical Models with Applications, Fine Arts Module
Music Unit Test – Teacher Edition
133