Why a bunch of kids playing out of tune with each other makes it impossible for anyone to hear intonation

Imagine the situation. You are a kid, in a group of kids who are all playing the same instrument, recorder for example.

Given this situation, is it possible to hear when you are playing in tune?

Have a play with the following tool. Can you find a pitch that makes what you are hearing sound good?

Now try to do the same thing again using the following tool. Again, can you make the result sound good?

What you will find is that the second tool it is easy to hear when the note you are controlling is in tune. The first tool by comparison sounds bad regardless of what you do.

So what is going on?

Why is it easy to hear correct intonation with the second tool, but not the first?

Why the second tool is easy to hear

The second tool plays two notes of a single frequency. We can visualise this as a graph as follows.

It is easy to hear when both are in tune as both the fixed pitch the tool is playing, and the one controlled by the slider are a single frequency, with a nice clean spike like above.

When they are in tune, the two spikes like up flawlessly, producing a nice clean sound.

Why the first tool always sounds awful

The first tool by comparison simulates a classroom of children playing the same instrument slightly out of tune from each other.

If you graph those pitches you'd have something like the following. A wide spike with a flat top:

When a single player is varying their own tuning, what they are hearing is the sharp spike of their own instrument, combined with the wide 'hill' all of the other players are creating.

In simple terms, when you have a large number of children playing the same instrument, yet slightly out of tune, it is impossible to hear intonation as there is no centre of pitch!

How to solve this problem?

There are two very easy ways to avoid this issue:

  1. Teach the children to match pitch with a reference one at a time.
  2. If the children are playing together, you must provide a pitch reference from an instrument with a different timbre.

Teaching one at a time allows the children to learn to hear intonation in the easiest possible situation.

An instrument with a different timbre allows intonation to be herd even when there are a lot of detuned notes, as such an instrument has different overtones. People can use these to base intonation, even if the fundamental frequency is unclear.