Problem Set 3: Note Frequency

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Task Outline

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

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 Python 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:

Semitone notes

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:

frequency = ref * 2 ** (octa + (semi/12.0))

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

Description	File Size	File Name
`Python` Source Code for Note Frequency	1.3KB	pset03.zip

Contents of pset03.zip:

PSet03NoteFrequency/
├── notefrequency.py
└── testnotefrequency.py

Write a Python program in the file notefrequency.py 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(octave, 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

Run the file testnotefrequency.py to execute the PyUnit test bench. PyUnit indicates a successful test with an OK output, and an unsuccessful test with a FAIL output.