# How To Tune An Instrument (Without A Tuner)

Written ByAudio Basics

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Have you ever heard this pulsating effect when tuning an instrument?

Do you hear how the combined sound of the two strings seem to interfere with one another?

In this video, you’ll learn why we hear these “beats” and the beautifully simple math behind them.

### What’s Actually Happening?

Let’s start with a more controlled demonstration with two sine tone generators…

This smartphone will play a 440 Hz tone (which is the musical note A)…

Meanwhile, this other tablet will play a slightly detuned 441 Hz tone…

They sound almost identical when played separately, but of course the 441 Hz tone is slightly higher-pitched. But listen to the beat that arises when I play both tones together…

As you can hear, when these two tones are played together, they interfere with each other acoustically and create a pattern of pulses. In acoustics, this is called a beat.

If you know why this is happening, leave a comment below with the answer… If you don’t know yet – that’s ok. Stick around, because I’m about to explain it.

First, let’s experiment with changing the frequency of the detuned tone… Instead of 441 Hz, let’s go to 442 Hz…

We still hear a beat caused by the interference between these two frequencies, but this time the beat is faster… Here’s 440 Hz with 441 Hz…

And here is 440 Hz with 442 Hz…

The 440 Hz waveform and the 441 Hz waveform line up pretty well at the beginning. The positive sections align and the negative sections align. This means the two waves will sum together to create a stronger wave.

But as we scroll forward in time, the two waveforms start to get more and more out of phase. Eventually, we reach a point where one wave is positive while the other is negative. At this point, the two waves will work against one another, which results in cancellation, where the combined result is almost total silence.

As we scroll a bit further, this pattern repeats itself – in phase, out of phase, in phase, out of phase, and so on.

I’ve mapped out these points with markers on the timeline. As you can see, they follow a very consistent cadence. Every half second, the waves will be either fully aligned (and in phase) or fully misaligned (and out of phase).

Stated in Hertz (or cycles per second), the beat that occurs when we combine 440 Hz and 441 Hz is 1 Hz. Let’s change the frequencies to see how the beat frequency changes.

Now, I’ve marked the beat created with 440 Hz and 442 Hz… And you’ll notice that they occur twice as frequently. Now the beat occurs twice per second.

This pattern continues. The difference (in Hertz) between the two tones equals the frequency of the beat. Actually, the beat frequency is twice the difference frequency.

When tuning an instrument like a guitar, you can excite the note A on two strings (such as the 12th fret of the A string and the 7th fret of the D string)

If you hear a beat between these frequencies, that’s an indication that the notes are close (but not exactly in tune).

As the notes become closer in pitch, the frequency of the beat will decrease until they totally align and the beat disappears.

This can be replicated by playing 440 Hz with the smartphone and slowly tuning up to that frequency on the tablet.

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