Intervals, Pitch & Frequency (Page 2 of 5) in pdf

Intervals, Pitch & Frequency Page 2

1. Find m and n and calculate the following frequencies:

1. Two octaves plus three ifths above 440 Hz.

5. Seven octaves above 100 Hz.

2. Two octaves plus three ifths below 440 Hz.

6. Twelve ifths minus seven octaves above 100 Hz

(to two decimal places). What would you hear if

you played this frequency and 100 Hz

3. One octave minus one ifth above 440 Hz.

simultaneously?

4. Twelve ifths above 100 Hz.

Pitch Our ears don’t judge distance in the same way that we measure frequency. For example, we hear

the distance between any two notes an octave apart as the same—so we hear the distance from 110 Hz

to 220 Hz as being the same as the distance from 440 Hz to 880 Hz. Therefore, we use the system of

pitch to measure frequency in a way that corresponds to human perception. Twelve units of pitch

equals one octave. There are two ways to notate pitch: either using a note name (a letter from A-G) and

a number to indicate the octave, or using MIDI notation, in which each key on the piano corresponds to

a whole number from 21 to 108.

Here is a picture of a piano keyboard with the frequencies and pitches labeled. In addition, two MIDI

numbers are shown: 69 (A4) and 60 (C4, or “middle C”).

2. Circle all the piano keys producing pitches that are a whole number of octaves above or below

440 Hz. This pitch is called “A4.” Write the note names of the pitches you circled. (Each note name is a letter plus a

number.)

3. Find the MIDI numbers of the piano keys you circled.

4. Find the frequencies that are one or two ifths above or below 440 Hz. Locate their best

approximations on the keyboard and put an ”X” on these keys.

Intervals, Pitch & Frequency Page 2