Intervals, Pitch & Frequency (Page 4 of 5) in pdf

Intervals, Pitch & Frequency Page 4

5. Approximate to two decimal places

1. the frequency of pitch 72

4. the pitch of the lowest hearable frequency

2. the pitch of 1000 Hz

5. the pitch of the highest hearable frequency

3. the frequency of pitch 1

6. the pitch that is two ifths above 440 Hz

Intervals in pitch. We’ve de ined intervals such as octaves and ifths as being ratios of frequencies.

When we measure pitch, intervals are differences in pitch. For example, if a frequency corresponds to

pitch p, then the frequency an octave above it corresponds to pitch (12 + p). Let’s calculate the

difference in pitch between frequencies f and rf (think of r as the ratio):

(69 + 12 log

log

(rf /440))

(f /440)) = 12(log

(rf /440)

(f /440)).

To simplify this expression, we need to use the fact that if A and B are positive numbers,

log(A · B) = log A + log B and log(A/B) = log A

log B. Therefore,

The interval in pitch from frequency f to frequency rf is 12 log

(r).

For example, an octave, measured in pitch, is 12 log

(2) = 12. What is the pitch value of a ifth?

Intervals, Pitch & Frequency Page 4