Problem Set 3: Note Frequency

Task Outline

• Due Date: Monday, September 23, 2019
• Total Points: 10
• Implement a Java program that calculates the frequency of a particular music note, given its octave and pitch class.

Background Theory

• One of the oldest problems in music theory is how to map the notes of a musical piece to a set of audio frequencies. Your task is to write a Java program that performs a particular kind of mapping.
• First, we must define a form of musical note notation. One common way of accomplishing this is to use the octave pitch notation. This notation represents each note as a number pair, where the first number indicates which octave the note belongs to, and the second number indicates which semitone the pitch corresponds to.
• There are 12 semitone notes within each octave on the keyboard, as in the following diagram:

• octave pitch representations are written in decimal format. For example, the 5th octave and 9th semitone(corresponding to note A) would be written as: 5.9
• In order to map a sound frequency to this octave pitch representation, we must begin by selecting a reference note. In the Western musical scale, we assign the frequency 440Hz to the octave pitch reference note of 4.9. This corresponds to the 4th octave, 9th semitone, which is note A.
• Our mapping must ensure that the same note in the next higher octave has double the frequency. In other words, 5.9 corresponds to 880Hz, and 3.9 corresponds to 220Hz. This mapping system assumes that each of the semitones within an octave is equally spaced, and this is known as a tempered scale.
• The formula we use to calculate the frequency from a given octave pitch note is as follows:

• In Java, this formula would be implemented as:

frequency = ref * Math.pow(2, (octa + (semi/12.0)));

• double frequency: The result of the calculation, in Hertz.
• int ref: The frequency of the reference note, which is: 440 Hertz.
• int octa: The octave note minus the reference note, which is: octave - 4
• int semi: The pitch semitone minus the reference semitone, which is: pitch - 9

Code Distribution

Description	File Size	File Name
Java Source Code for Note Frequency	4.8KB	pset03.zip

Contents of pset03.zip:

PSet03NoteFrequency/
├── NoteFrequency.class
├── NoteFrequency.ctxt
├── NoteFrequency.java
├── NoteFrequencyJUnitTest.class
├── NoteFrequencyJUnitTest.ctxt
├── NoteFrequencyJUnitTest.java
├── package.bluej
└── README.TXT

Specification

• Write a Java program in the file NoteFrequency.java that calculates the frequency of a particular musical note, given its octave and pitch class.
• You will write your solution in a function called temperedScale(int octave, int pitch) right below the place where it says: YOUR CODE HERE
• When the function call temperedScale(0, 0) is executed, the output of the program should be: 16.351597831287414

Testing

• Click on the Run Tests button to execute the JUnit test bench. JUnit indicates a successful test with a green bar, and an unsuccessful test with a red bar.

Submission

• Upload the file NoteFrequency.java to the Web-CAT automated grading platform.