This might sound crazy and even a little depressing but it’s true and a topic worth discussing. You would think having a tuner come in and tune your piano would be enough, it should be in tune right? But is it really?

The short answer is no, your piano will never be perfectly in tune. If you look back in history and at other instruments this concept is easier to understand. When it comes to singing, pitches come completely from your head, just like when a violinist plays there are no frets for them to make the exact notes and the pitches are constantly changing; this is even true of guitars where a string can bend to affect the pitch of note.

There was a period in time in when keyboards were tuned to specific keys. So, if the keyboard was tuned to D major, it was perfectly in tune in D major. It would sound O.K. in A major and possibly G major, but would sound atrocious in A-flat major or D-flat major. Eventually tuners created a system in which all the half steps are equal so that all keys are equally out of tune!

When a piano tuner tunes your piano the first thing they do is set the temperament. The temperament is taking an octave and making all the half steps equal. This means that when you play any interval other than an octave on the piano, they are all equally out of tune. So if you play a perfect 4th, 3rd, or any other pair of notes, they will all be perfectly out of tune with each other. We have gotten so used to tempered tuning that we don’t even notice it’s out of tune. However, if a string player tries to match pitch with a piano they will have to make adjustments to play in tune.

Believe it or not this gets even more complex. Stretch octaves are something that goes beyond the idea of tempered tuning. Our ears actually hear flat in the high register so to compensate for this a tuner will stretch the tuning a bit higher in the high register so it sounds right to our ears even though it is not mathematically perfect.

To keep it simple, always remember that when your piano is tuned, the tuner is striving for the perfect compromise. It’s a crazy concept but it’s true. Thanks again for joining me Robert Estrin Robert@LivingPianos.com (949) 244-3729

## 8 thoughts on “Why a Piano is Never in Tune”

The mathematically perfect tuning comes from the way strings (and air columns, etc.) vibrate: They divide up into equal parts. Each integer they divide by produces an overtone. If you take the lid off a grand and have someone play and hold the key for one of the big bass strings, you can touch that string exactly in the middle with a pencil eraser. That damps out the fundamental, and you hear the first overtone, which is an octave higher. Try it again, only now touch with two erasers to divide the string in thirds, and you get the second overtone, which is an octave and a fifth above the fundamental.

So, the perfect fifth is a ratio of 3:2, or 1.5:1 exactly.

Equal temperament divides the octave into twelve equal semitones, equal in the sense that the ratio from any note to the one a semitone higher is always the same. To get the 2:1 ratio of the octave from those twelve steps, each one has to be the twelfth root of two.

Now here’s the point of all this, the piece of really good but not quite perfect luck, that makes equal temperament work:

The fifth in equal temperament is seven of those twelfth root of two steps, so its ratio is the twelfth root of two multiplied by itself seven times. That ratio turns out to be 1.4983:1, while the perfect fifth is 1.5000:1.

When a traditional tuner works by ear, they go around the circle of fifths and fourths to set up the temperament in the octave that they’ll use to extend to the whole piano. They narrow the fifths and widen the fourths by counting the beat frequencies, to get that little cheat from 1.5000 to 1.4983.

— J.S.

The reason for stretch tuning has nothing to do with how ears perceive pitch. If it was due to that, then pipe organs would also be tuned with stretch, but they are not. Pianos are tuned with stretch because of something called inharmonicity, which is the fact that harmonics of piano notes are not perfect harmonics, but are a little sharper than perfect harmonics. So when listening to an octave, the sharp harmonic of the lower note would have a beat with the upper note. To remove this beat it is necessary to tune the fundamental pitches to more than a 2:1 ratio. That is stretch.

So, how many years of study are required to understand this gibberish? Nice though it is, it’s still gibberish.

So! When my top half of the piano goes flat after about 9 months and I am prepared to give the tuner a call… Chances are its actually closer to being in tune… and I am paying someone to put it back out of tune? 😛 BRILL!

Hi Robert

The piano has harmonic distortion due to the string diameter. So the partials are compressed in relation to a theoretical exact intersection point of the node. In order to achieve the correct pitch as one goes up in the scale, the tuner must increase the pitch to match the corresponding partial from the lower octave note. Example: the second partial of let’s say the middle C is equal to the fundamental of the next upper C in theory. The intersecting point of the wave is infinitely small.

But do to the string diameter. The partial length is now reduced. What happens when at constant string tension the length is reduced.? The pitch goes up. So the tuner has to stretch the higher octave note to match the now diminished length and higher pitch 2nd partial of the lower octave note. This applies to all partials.including third and 4th partials which are octave and a 5th and the double octave respectively. The best way to visualize this phenomena is to draw the intersecting nodes on a piece of paper then give them a diameter. This pattern is called the Von Helmoltz effect in physics. So this is why the scale is stretched. The shorter the piano the thicker the strings an the more harmonic compression or distortion. This is why a concert grand sounds so much better than a baby grand.

Best regards

Bill

Bill

Different tuners tune differently so when you find the tuner who makes the piano sound right to you, you should stick with that tuner. I think my tuner is more towards sharp which is what I like. He just rebuilt my 1983 Baldwin grand and it sounds like a new piano! It is so wonderful

Years ago I played with Case Western Reserve University’s early music groups. The head of the program, Ross Duffin, is a world-class researcher in the field of early music. We played on superb custom-designed SATB recorders and spent LOTS of time getting mean-tone temperament exactly right. Our modern ears wanted to hear equal temperament as being ‘right’. It was very cool to arrive at a point (after weeks of rehearsal) where the mean-tone tuning came to feel right. Amazing too to find how much more ‘playable’ these great instruments became in their more natural ‘mean-tone’ state.

I haven’t actually tried this in person, but I’ve heard that some of the high end digital keyboards can be switched from equal temperament to mean tone and many other alternative temperaments.

— J.S.