Learning to Tune Clean, Pure, and Beatless Unisons

Here is an email I sent to a subscriber explaining how to use Soundbeam, (See HERE) or any graphical FFT program, to help you tune clean unisons by ear. 

On Monday, August 3, 2015, Mark Cerisano <mark at how to tune pianos.com> wrote

Ok. So, when you play a string, multiple frequencies are generated. 

For example, playing 100Hz sets up 100Hz, 200Hz, 300Hz, etc. (See HERE)

(Because of inharmonicity, these numbers are not actually correct. Higher partials are sharper the predicted by simple theory)
When you play two strings, you set up partial pairs, pairs of frequencies that are close to each other. 

Frequencies that are close but not exact, set up beats. (See HERE)

You want to tune a unison so that all the upper partials are exact and have no beating. 

Playing 100hz and 101Hz together sets up these partial pairs:
100/101
200/202
300/303
Etc.
Which sets up these partial beats:
1
2
3
Etc. 

This shows that, for an out of tune unison, the higher partials beat faster. 

For this reason, when tuning unisons, the aural piano tuner focuses their hearing on the higher partials and tries to eliminate them. I suggest listening to the 3rd partial of a unison since it is a different note than the unison. It is found an octave and a fifth above the fundamental (the note you are playing)
Example: tuning A4 as a beatless unison, you would focus your ear on E6 and eliminate the beating there. 

Now, when using a FFT program that shows the volume of each partial in a sound, you should see bumps at each partial when playing a unison. 

If all these bumps start out high and then gradually decrease in height as the volume of the note decreases, then the unison is said to be beatless. 

More likely though is that you will see the bumps pulsating up and down. 
This is what the beat at the partial pair of an out of tune unison looks like when viewed through an FFT program. 

Changing the pitch of one string will speed up or slow down the speeds of the beats at the partial pair. 

Try to elliminate the pulsating as much as possible. 

Try to hear the speed you see at the 3rd partial while you are tuning.

The goal is to be able to zero in on the beating 3rd partial and eliminate it without using the FFT program. 

Good luck. 
Mark

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