Lesson Summary 

Analyze and compute the relationship between frequency and musical notes.


Frequency - The number of cycles per unit time.  The SI unit for frequency is hertz (Hz), named after the German physicist Heinrich Hertz; 1 Hz means that an event repeats once per second. Designated by a lowercase f.

Hertz - The unit used to represent frequency (Hz)

Pitch - A particular frequency of sound used in a musical context.
Note - A named pitch, in western musical notation we knows these as A, B, C, D, E, F, and G.
Semitone - The smallest audible change in western musical notation. 
A440 - the musical note A above middle C, serves as a general tuning standard for musical pitch and has a frequency of 440 Hz.
Logarithm -  the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 10 to the power 3 is 1000: 1000 = 10 × 10 × 10 = 10^3.
Equal Temperament - The system of tuning, in which every pair of adjacent notes (semitone) has an identical frequency ratio. Since pitch is perceived as the logarithm of frequency, this means that the "distance" from every note to its semitone is the same for every note.  Western musical notation uses twelve tone equal temperament.
Example: The fourth of an A note is D.  D is 5 semitones up from A so for A440 we can find our D frequency by multiplying 440 by 2 to the power of 5/12.  
MIDI (Musical Instrument Digital Interface) - A technical standard that allows a wide variety of electronic musical instruments, computers and other related devices to connect and communicate with one another.  A MIDI note is a single numerical value that digitally represents a frequency. 
where f  is defined as frequency and 440hz is in reference to concert pitch A440. 

Play the keyboard notes of the Werkstatt and modulate the FREQ knob to hear the relationship between frequency and musical pitch. 


Jumper Cables


 Begin by setting the Werkstatt to match the settings in Figure 1.


 Figure 1. VCO exercise settings


By playing the left most button followed by the right most button you will hear a pitch relationship known as the octave.  This means that the lowest note is doubled in frequency equaling the highest note.

As you change the FREQ knob you will hear the frequency increase in a non musical linear fashion.  Compare this change to the notes played by pressing the keyboard buttons.  The musicality of pressing the note buttons over playing the FREQ knob is because the frequency relationships are determined by the equal temperament formula.

The above formula is shown for a single semitone change.

Using twelve tone equal temperament determine the frequency and MIDI values for the following notes.

1. A two octaves above A440.

2. F same octave as A440.

3. G# one octave below A440.

4. C three octaves above A440.