Tuning by beats
When two notes differ in frequency, the loudness pulses at the rate of that difference. That pulse is a beat. Where the pulse disappears is where you are in tune. A needle cannot tell you this. Here the beats are counted from the actual sound.
Why the needle cannot tell you
A tuner needle is built on equal temperament. But the position the ear wants when several notes sound together is not the equal-tempered one. The equal-tempered major third sits 14 cents above the just third, the minor third 16 cents below, and the seventh of a dominant seventh chord 31 cents above. A chord in which everyone has centred the needle is muddy by exactly that much.
Distance from just intonation
| Interval | Ratio | Offset from equal | Beats when played in equal temperament, lower note A=440 |
|---|---|---|---|
| Perfect fifth | 3:2 | +2 | 1.5 /s |
| Perfect fourth | 4:3 | -2 | 2.0 /s |
| Major third | 5:4 | -14 | 17.5 /s |
| Minor third | 6:5 | +16 | 23.7 /s |
| Major sixth | 5:3 | -16 | 20.0 /s |
| Minor sixth | 8:5 | +14 | 27.7 /s |
| Seventh of a dominant seventh | 7:4 | -31 | 56.0 /s |
The beat rate is not the difference between the two fundamentals. It is the difference between the harmonics that coincide. In a perfect fifth the third harmonic of the lower note meets the second of the upper, giving 1.5 beats per second, slow enough to count. In a major third the fifth harmonic meets the fourth, giving 17.5 per second, which is heard as roughness rather than as beating. That is why thirds are the hardest interval in an ensemble. You cannot count them, so you have to remove them by ear.
How to do it
- Sustain the same interval, with another player or as a double stop
- Hold it straight. Vibrato cannot be told apart from a beat
- Watch how many beats per second appear on the screen
- Move in the direction that reduces the count. When it disappears, you are in tune
Who needs this
String players working on double stops, wind bands and brass bands holding chords, barbershop and choral singing, early music ensembles. All of them are taught to get rid of the beats, and none of them had a way to see whether the beats were gone.
What this does not do
It cannot tell you who is sharp. It does not separate individual players out of a large ensemble, and it does not grade anyone. The reading is dependable for roughly two to eight players.
KUON TUNER