Beat Rates     back to rollingball home

As aural tuners, most of us learned to listen to the beat rates of the major thirds in the temperament octave, which is usually F3-F4. When I was a pup, my mentor set up a pendulum with a length of one meter, which therefore swings with a period of one second; and while watching the pendulum swing, I learned to recite "From Chicago to New York" so that the seven syllables filled the second... therefore the speed of the syllables was 7 per second, which was also the desired beat rate of the F3-A3 third. And so on with "From Mississippi to New York" and other such phrases.

The beat rates of these major thirds are formed by the simultaneous sounding of the fifth partial of the lower note with the fourth partial of the upper note. This page illustrates these frequencies, and the resulting beats, as they occur in a typical Steinway D as sampled with TuneLab.

The 4-second sound files are created using the shareware program Audacity, and emphasize the beating frequencies plus only a whiff of the fundamentals of the two piano tones comprising the major third.

Major Third 5th partial
of the lower note
4th partial
of the higher note
Beats per
second
A2-C#3 
549.932 554.370 4.4
A#2-D3 
582.706 587.402 4.7
B2-D#3 
617.437 622.406 5.0
C3-E3 
654.242 659.501 5.3
C#3-F3 
693.247 698.814 5.6
D3-F#3 
734.585 740.478 5.9
D#3-G3 
778.397 784.636 6.2
E3-G#3 
824.832 831.439 6.6
F3-A3 
874.051 881.046 7.0
F#3-A#3 
926.221 933.601 7.4
G3-B3 
981.525 989.304 7.8
G#3-C4 
1040.152 1048.347 8.2
A3-C#4 
1102.307 1110.93 8.6
A#3-D4 
1168.151 1177.271 9.1
B3-D#4 
1237.954 1247.598 9.6
C4-E4 
1311.957 1322.154 10.2
C#4-F4 
1390.416 1401.198 10.8