Perception of sound
12 Frequency ratios and pitch perception
Piano keyboard
On the piano, keys are arranged in order of pitch, with the lowest frequencies at the far left of the keyboard. Look at the keyboard carefully, and you’ll notice a repeating pattern of twelve keys. Not surprisingly, musical notes are labeled using a cycle. The piano’s white keys are labeled A through G. To distinguish between different A’s, the lowest A on the piano is labeled A0, the next lowest A is labeled A1 and so on. The diagram of a small section of the piano keyboard below illustrates the idea.
The octave
Distances along the piano keyboard are called musical intervals- intervals, for short. The interval from one A to the next A (or one D to the next D) is called an octave. You’ve probably heard an octave before- both “Somewhere over the Rainbow” and “Chestnuts Roasting on an Open Fire” start with an octave jump. The octave is a really important interval for two reasons. First, an octave is especially easy on the ears- two notes an octave apart can be difficult to tell apart, especially when played together. Second, an octave corresponds to a factor of two in frequency. The note to which orchestras tune (A4) has a fundamental of 440 Hz- sometimes called A440. The note an octave higher (A5) has a fundamental of 880 Hz. The note an octave lower (A3) has a fundamental of 220 Hz.
Frequency ratios and pitch perception
The octave reveals something important about music and pitch perception: human perception of the “distance between two pitches” depends on the frequency ratio of the two notes- the bigger the ratio, the further apart the pitches seem. Two frequencies that are a factor of two apart always sound an octave apart, no matter whether the two frequencies are 500 Hz and 1000 Hz or 10,000 Hz note and 20,000 Hz. Frequency differences tell you almost nothing about perceived pitch differences.
Stop to thinks
- What is the frequency of the note two octaves above a note with a frequency of 300 Hz?
- One note is 200 Hz higher than another note. What is the musical interval between the notes?
- Which is a larger musical interval: from 1000 Hz to 2000 Hz, or from 2000 Hz to 3000 Hz?
Frequencies and the keyboard
The diagram below shows the frequencies of every note on the piano keyboard. The bars get taller as you go to the right. That’s not surprising- higher pitched notes are at the right end of the piano. What might be surprising is that the graph is not a line. That’s because musical intervals are based on multiplication- not addition. As you move one piano key to the right, the frequency does not increase by a specific number of Hertz. On the lowest note of the piano, moving one key to the right increases the frequency by less than 2 Hz. At the top end of the piano, moving over one key increases the frequency by over 200 Hz. What remains the same is the percent increase– as you move one key to the right, the new frequency is about 6 percent higher than the previous not