Oscilloscope Piano Tuning 101

fft on scope

[Todd Harrison] recently wrote in to tip us off on his submission to the Tektronix oscilloscope contest – using a scope to tune a piano. In his video he demonstrates how a Fast Fourier Transform can be used to determine the fundamental frequency of the note being played. This is a quick and easy way to determine if that key is in tune, and if not, how far off it is from the desired frequency and in which direction.

He goes on to explain that a scope can only be used as a starting reference point since “mathematically correct” tuning on a piano doesn’t sound right to the human ear. It turns out that when struck, the stretched wires in the piano behave less than ideally. In the case of a piano, the overtones (the other peaks shown on the scope higher in frequency than the fundamental) are actually slightly sharper (higher in frequency) than the expected harmonic whole-number multiple of the fundamental frequency.  As a result, the frequency ranges of each octave must be “stretched” in order to accommodate this and sound correct when multiple notes are played together across octaves.

Typically, only the A4 key is actually tuned to its correct frequency of 440Hz and all of the other keys are manually tuned off of this baseline. The amount of necessary stretch applied to each octave increases as you get further away from this initial reference point in either direction and is unique to each and every individual instrument – thus there is no universal device capable of perfect tuning. Although [Todd] admits that he won’t attempt to tune the entire piano himself using this technique, he finds it a convenient way to keep the most heavily played center sections of the piano closer to true between professional tunings.

If you have any interesting or unique uses for your Techtronix scope, you can enter the contest here. Just don’t forget to tip us off too!  Thanks [Todd]!

Comments

  1. therian says:

    you telling me I can see frequencies on oscilloscope, wow what a discovery

  2. Jason Komp says:

    I’m sure this isn’t a shocking revelation to everyone reading this post, but I wouldn’t have thought to pull out my scope for something like this (if I actually owned a piano that is).

  3. Nic says:

    So… now you can calibrate tuning forks too, right?

  4. I really enjoyed it.. I own a piano and have a pretty good ear, but not “absolute pitch”.. So this will help!

    I agree it’s not an outstanding discovery, it is pratical and it can help the understanding of the nature of sound.

    To add more information on this, you can calculate the frequency of the notes using this formula:

    Table of frequencies:

    http://www.phy.mtu.edu/~suits/notefreqs.html

    Explanation on how to calculate it: http://www.phy.mtu.edu/~suits/NoteFreqCalcs.html

    Diatonic Scale Plot:

    http://en.wikipedia.org/wiki/File:Music_frequency_diatonic_scale-3.svg

  5. ZetaPhi says:

    Can anyone suggest any good sites to read up on why a piano shouldn’t be tuned using “mathematically correct” tuning? I’ve always thought that was interesting.

  6. ss says:

    What about using Lissajous and the oscilloscope in X-Y format?

  7. Merlin Zener says:

    I used to do this years ago, not only on my own piano [I had a Yamaha CP-70 electric grand which I toured with] but also later on when working as a roadie for other musicians.

    I would just run the output of a Boss tuner into the cro, and view the lissajous pattern.

    The OP is correct as far as pianos go – you can’t really tune the whole piano just using the electronics, but it speeds up the process – you get it close, then finish it off by ear.

    It works better for guitars and basses.

  8. steve says:

    even when tuning a guitar or bass its best to just tune the 1 string (low e) with a tuner and tune the rest relative to eachother. this is cool but id rather use a tuning fork then lug around my scope (though my 72 sencore is about the size of a microwave.)

  9. Viadd says:

    The googlon for why the harmonics aren’t harmonic is ‘inharmonicity’, which when combined with ‘piano’ brings up a bunch of links.

    Basically, a ‘theoretical’ string will simultaneously vibrate at 1,2,3… times its fundamental frequency, because the restoring force is purely due to tension trying to pull the string straight.

    The main difference of a real string is that the string has stiffness, and that additional force trying to make it straight has a different force law, so vibrations are not strictly proportional to n in frequency.

    Anyway, the A above middle C string vibrates at 440 Hz, and at a frequency that is not quite 880 Hz, call it 881. When you tune the A above that, if you tuned it to 880 Hz, it would be discordant with the A440 string’s harmonics and it would sound awful, so you tune it to 881 Hz.

    Wiki of course:

    http://en.wikipedia.org/wiki/Piano_acoustics

    http://en.wikipedia.org/wiki/Inharmonicity

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