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```Audio Explorer
Introduction
Audio Explorer is a system to explore the mathematics and physics of music by examining
the frequency domain. The frequency domain is a transformation of the sound signal into its frequency components; since our ear perceives frequencies, examining the frequency domain is a
useful way to understand the properties of music (sound sequences that we perceive as interesting). The keyboard will allow you to create a sound signal. That signal is then transmitted to the
computer where it is transformed into the frequency domain and displayed on the screen. From
there, you can use the software tool to examine this signal further. Page 2 gives an introduction to
the features of the software.
This laboratory is divided into two projects. Project 1 asks you to explore the properties of
different instruments. Project 2 asks you to explore some of the properties of notes that are determined by mathematics. Along the way, you will be prompted to answer certain questions. In the
back of this document, you will find a glossary of musical terms; please use these terms to more
exactly answer these questions. All group members should agree and understand the answers
Group members:
1
Using the Software
The purple window on the left is the spectrum graph; it shows the instantaneous audio signal
in the frequency domain; the y-axis represents the frequency and the x-axis represents the magnitude. The large white window is the sonogram graph; it shows the audio signal in the frequency
domain over time; the y-axis represents the frequency, the x-axis represents time, and the darkness
represents the magnitude. The vertical red line indicates the time position on the sonogram; pressing the Reset button clears the sonogram graph and sets the time position to the start. Pressing the
Record/Pause button starts or stops the recording of the sound signal.
The Math On/Off button gives you some tools to analyze the sound signal; you will need to
use these tools for project 2, but not for project 1. When the math is on, a keyboard will appear
and the horizontal red line of the spectrum graph will extend across the sonogram graph. To the
right side of the horizontal line, the frequency value is displayed along with the mathematics
showing how that frequency may correspond to a key on a keyboard. The corresponding key on
the keyboard is highlighted in red. Pressing the mouse on the spectrum graph or the keyboard
2
Project 1: Exploring Different Instruments
In this project, you will investigate different instruments. Remember that the frequency
response is the basis for much of what makes an instrument unique. One way to investigate the
different instruments is to compare them to one another. Some interesting contrasts are violin versus piano, trumpet (brass instrument) versus recorder (woodwind), and harmonica versus pipe
organ. Particularly, the pipe organ is a unique instrument. One effective way of comparing the
instruments is to record a scale (for instance, major scale starting at middle C) up with one instrument, pause the recording, change the instrument, and play the scale backwards. Below, note at
least five differences and offer possible explanations. Also, please note any unique methods you
used to note these differences.
1.1.
1.2.
1.3.
1.4.
1.5.
1.6.
1.7.
3
Project 2: Exploring the Mathematics of Sound
In this project, you will investigate the mathematics that determine the properties of music.
Matching harmonics (or harmony) is a major property of music. Start by switching the tone to
something linear and sustained, such as a harmonica or oboe. Press the Math On button to turn on
the analysis functions. For part 1, record a chromatic (every note) scale from the left to the right
extremes of the keyboard. Below, note what you see and offer a possible explanation.
2.1.
For part 2, record the C notes in sequence from the left to the right extremes of the keyboard.
Use the analysis functions to examine the frequencies of the C notes. What is the relationship of
the fundamental frequencies of the C notes?
2.2.
For part 3, record a note somewhere in the middle of the keyboard (C, F, and G make good
choices). Then, try to match the overtones of this base note to notes on the keyboard. Mark the
keys that do match and the base note on the keyboard below along with what overtone it is.
2.3.
For part 4, see if you can come up with an explanation of why certain keys match fairly well
to the overtones of the base note (Hint: would it work the same if there were 13 notes per octave?).
This is a challenging and hopefully interesting problem.
2.4.
4
Glossary
Chromatic Scale: in the scale of equal temperament, a scale in which the interval between the
tones are all half-tones.
Complex Tone: a sound sensation characterized by more than one pitch.
Frequency: the number of recurrent waves or cycles which pass a certain observation point per
second. Frequency is measured in Hertz (shortened to Hz), meaning per second.
Fundamental Frequency: the frequency component of the lowest frequency in a complex sound.
Half-tone: the interval in pitch between two successive notes in the scale of equal temperament.
There are 12 half-tones in an octave. The frequency ratio between the two successive notes is
the twelfth root of 2.
Harmonic: an overtone whose frequency is an integral multiple of the fundamental frequency.
Octave: the interval in pitch between two successive notes of the same letter.
Overtone: a component of complex tone having a pitch higher than the fundamental. An overtone
is a physical component of a complex sound having a frequency higher than that of the fundamental tone.
Pitch: the attribute of auditory sensation in terms of which sounds may be ordered on a scale
extending from low to high, such as a musical scale. Pitch is primarily dependent upon the
frequency of the sound stimulus.
Scale of Equal Temperament: a musical scale that reduces the number of tones per octave by
slightly altering the frequency of the tones from the exact frequencies of just intonation.
Scale of Just Intonation: a musical scale employing frequency interval ratios of the small integers
of the harmonic series. The two principal scales of just intonation are the major and the
minor.
Simple Tone: a sound sensation characterized by its singleness of pitch.
Subharmonic: an integral submultiple of the fundamental frequency of the sound to which it is
related.
5
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