0.1 [ mini-project ] musical intervals and the equal-tempered scale

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In this mini-project you will learn about musical intervals, and discover the reason behind the choice of frequencies for the tuning system called "equal temperament."
 This module refers to LabVIEW, a software development environment that features a graphical programming language. Please see the LabVIEW QuickStart Guide module for tutorials and documentation that will help you: •Apply LabVIEW to Audio Signal Processing •Get started with LabVIEW •Obtain a fully-functional evaluation edition of LabVIEW

Overview

In this mini-project you will learn about musical intervals, and also discover the reason behind the choice of frequencies for the equal-tempered musical scale.

Spend some time familiarizing yourself with the piano keyboard below. Enter the pitch (letter) and its octave number to display the corresponding frequency. For example, middle C is C4, and C2 is two octaves below middle C. The frequency 440 Hz is an international standard frequency called concert A , and is denoted A4. Concert A is exactly 440 cycles per second, by definition.

The black keys are called sharps and are signified by the hash symbol # . For example, G#1 indicates the sharp of G1, and is located to the right of G1.

Try the following exercises to make sure that you can properly interpret the keyboard:

What is the frequency of the leftmost black key?

29.14 Hz

What is the name and frequency of the white key to the immediate left of C7?

B6, 1976 Hz

What is the name of the key that has a frequency of 370.0 Hz?

F#4

Part 1

One aspect of the design of any scale is to allow a melody to be transposed to different keys (e.g., made higher or lower in pitch) while still sounding "the same." For example, you can sing the song "Twinkle, Twinkle Little Star" using many different starting pitches (or frequencies), but everyone can recognize that the melody is the same.

Download and run tone_player.vi , a that VI accepts a vector of frequencies (in Hz) and plays them as a sequence of notes, each with a duration that you can adjust. Listen to the five-note sequence given by the frequencies 400, 450, 500, 533, and 600 Hz (it should sound like the first five notes of "Do-Re-Mi").

Now, transpose this melody to a lower initial pitch by subtracting a constant 200 Hz from each pitch; write the frequencies on your mini-project worksheet :

Modify tone_player.vi by inserting an additional front-panel control so that you can add a constant offset to the array of frequencies. Be sure that you keep the "Actual Frequencies" indicator so that you always know to which frequencies you are listening.

Set the offset to -200Hz, and listen to the transposed melody. How does the transposed version compare to the original? Does it sound like the same melody? Enter your response on the worksheet:

Transpose the original melody to a higher initial pitch by adding 200 Hz to each pitch; write the frequencies on your worksheet:

Set the offset to 200Hz, and listen to the transposed melody. How does the transposed version compare to the original? How does it compare to the version that was transposed to a lower frequency? Enter your response on the worksheet:

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