Unit3_VirtualLabMusic_wLSQ_fixed
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Lansing Community College *
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Mathematics
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Apr 3, 2024
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Mathematics of Music Lab
Introduction:
The musical scale used in western music originated with the ancient Greeks. Originally there were seven primary notes to a scale. This is called a diatonic
scale and even non-musicians are familiar with it as do-re-me-fa-so-la-ti-do. This scale can be played with the white keys on a piano keyboard, starting with C
. As you go though a diatonic scale it is eight steps from do
back to do
again. For this reason, this range of notes is called an octave
.
Over time, five more notes were added to the western musical scale. This 12-note scale is called a chromatic
scale. For a scale starting with C
, the five extra notes are played on a piano keyboard by pressing the black keys.
Musical scales are tied closely to mathematics. You will use a computer-interfaced Microphone to record the waveform of the sound that is produced. The computer will also perform a mathematical analysis of the waveform called an FFT to determine the fundamental frequency of the sound. Your challenge is to measure the frequencies of all the notes of a chromatic scale and then to determine a mathematical pattern.
The frequencies of two notes played at the same time that sound good to our ears usually have a special mathematical relationship. In this lab, you will investigate the mathematics behind intervals that are commonly used in music.
For this version of the lab the instructor will be following the procedure below in a recorded video of the lab. Students will record the data in the tables below from the experiment in the video and answer questions about the lab before completing a Lab Submission Quiz about this lab.
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Figure 1
Objectives:
Determine the fundamental frequencies of musical notes.
Determine how overtones or harmonics influence the quality of a musical note.
Materials (used by instructor):
Power Macintosh or Windows PC
Vernier Microphone
LabPro or Universal Lab Interface
Logger Pro
electronic keyboard or other musical instrument
Pre-Lab:
Preliminary Questions
If you cannot find the answers below in your text, please refer to the following website for additional information: Physics Classroom Sound Link http://www.physicsclassroom.com/Class/sound/
1.
How are musical sounds produced?
2.
To what physical quantity is the pitch of a note related?
3.
To what physical quantity is the loudness of a note related?
4.
Upon what is the quality (timbre) of an instrument dependent?
5.
What is a fundamental frequency?
6.
What is an overtone? 7.
What are harmonics? 8.
What is an octave?
Procedure (conducted by instructor, data recorded in tables by student):
1.
The instructor used a Vernier Microphone and LoggerPro to record notes from various instruments. The student must view the recorded lab and record the frequencies obtained in the tables below before answering some questions and completing the Lab Submission Quiz.
2.
Please fill the information in the tables below from the video recorded lab: PHYS120 Music Lab https://youtu.be/5BdXtR0fB2E
Data:
Table 1: Glockenspiel (xylophone)
Note
Or
Frequency,
given
Fundamental
Frequency
from
computer
(lowest) (Hz)
Pitch
compared to
previous
note
Other Frequencies Low G
A
B
C
D
E
F
High G
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Table 2: Boom Shaker Tubes
Note
Or
Frequency,
given
Fundamental
Frequency
from
computer
(lowest) (Hz)
Pitch
compared to
previous
note
Other Frequencies Low C
D
E
F
G
A
B
High C
Table 3: Guitar
String
(thinnest to
thickest)
Fundamental
Frequency
from
computer
(lowest) (Hz)
Pitch
compared to
previous
note
Other Frequencies 1
2
3
4
5
6
Table 4: Human Voice
Trial
Fundamental
Frequency
from
computer
(lowest) (Hz)
Pitch
compared to
previous
note
Other Frequencies 1
2
3
Table 5: Recorder
Note
Or
Frequency,
given
Fundamental
Frequency
from
computer
(lowest) (Hz)
Pitch
compared to
previous
note
Other Frequencies C
D
E
F
G
Table 6: Measurements from a piano
Key #
Note
Or
Frequency,
given
Fundamental
Frequency
from
computer
(lowest) (Hz)
Pitch
compared to
previous note
(higher or
lower)
Other Frequencies 1
“Below
Middle C”
C
4
5
E
4
8
G
4
13
“Middle C”
C
5
17
E
5
20
G
5
25
“Above
Middle C”
C
6
29
E
6
32
G
6
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Analysis:
1.
What is the relationship between a fundamental frequency and its harmonics?
2.
What is the relationship between frequencies of different octaves of the same note, for instance, as you go up the keyboard hitting all the “C”s what is the relationship of their frequencies?
3.
Which instruments exhibited the most harmonics in their notes? 4.
Which instruments showed the fewest harmonics in their notes?
5.
The image below shows the same “C” note from four different sources: Boom shaker tube, human voice, recorder, and piano. What is different about them and what is the same?
Conclusion:
What conclusions can you draw about musical notes, instruments and the human voice? Explain.
Lab Submission:
Upon completion of this lab be sure to also complete the Lab Submission Quiz for this lab experiment as well.