As a piano tuner who, in my early years, took a lot of voice lessons, I have long been intrigued by the difference between piano intonation and vocal intonation. Since the piano must be able to function in all keys, it is tuned in what we call equal temperament. That is, all twelve pitches of the octave are equally spaced. In other words, the pitch difference between a C and a D is the same as that between a D and an E. The voice, on the other hand, is not so restricted. If that D wants to resolve up to the E, we can shade the pitch upward a bit, leading the ear toward the E. This will make the distance between C and D wider than the distance between D and E, all in the name of musical expression. Other musical instruments are capable of this pitch shading, but the piano, restricted as it is to the keyboard, cannot shade pitches in that way so must use other methods of phrasing.
What this means, though, is that the experience of making music on the piano is different than what we do with our voice. For many years of singing, I was not aware of this and believed that all my vocal pitches had to be the same as the piano’s pitches or it was “out of tune”. And this is, for the most part, true. When singing with any instrument (keyboard or non) we must agree on the pitches and be in tune with each other. It’s just that the piano is much more “iron fisted” about its intonation. It seems to be saying, “My way or the hi-way, kid.” So we comply with our totalitarian accompaniment, and we sing “in tune”.
But did you know that the piano is tuned out of tune with the actual physical vibration pattern of its strings? Yes, it’s that equal temperament thing again. You see, any pitch source sounds the tone that gives it its name (the fundamental), as well as many more weaker tones that we call partials. These partials are multiples of the basic pitch. In other words, in any string, there is a partial that is twice as fast as the basic note, one that is three times as fast, one that is four times, etc. If you go to this youtube video you will see an excellent visual representation of this phenomenon.
Now if you were to construct a scale from those partials (Do, Re, Mi, etc.), the resultant notes (termed “just” intonation) would not work in any other key. For example, if you wanted the Mi of the key of C to serve as the Fa in the key of B, it wouldn’t sound in tune. Therefore, the piano’s notes are “tempered” so that they sound equally out of tune in every key. I believe that this idiosyncrasy is one of the elements that gives the piano its unique tonal character and adds to the beauty of its sound.
The voice, on the other hand (when not in the company of a piano) is not so encumbered and is free to create pure (just) intervals, shade leading tones or even throw in a blues note when it seems appropriate. When I came to that realization, a Capella (unaccompanied) singing took on a whole new meaning for me. Where before, I worried about getting all the notes exactly where the piano said they needed to be, now I can take delight in the sheer joy of a pure sixth. Ah, such liberation.