There are two factors that will mess up your mathematics and may be the cause of your unexplained readings. 1 Equal Temperament. In my simple understanding, this is the mathematical averaging of the pitch gaps between the notes. Prior to the use of equal temperament, keyboards were tuned accurately to play in particular keys only (called "just tunings"). During the Baroque period (incl. JS Bach) and before there was a strong desire for a tuning which would enable modulations between keys and a more adventurous approach to composition and harmony. Bach's "The Well Tempered Clavier" was a series of pieces demonstrating the validity of using equal temperament. It was discovered that if musicians were able to live with some little pitch compromises, it was possible, and slight approximations were made to the tuning of certain degrees in the scale. If you want to test it out, try these fun things; (a) Using a digital keyboard, play middle C and the C above it. The notes will be very in tune and there will be no "beats" - those little vibrations that are not actually part of the notes but are the product of the two. ( Do the same with C and G, then with C and F. They will also be perfectly in tune. © Now the fun begins, Try it with C and E. You will hear a very subtle vibration or beat being created. Same if you play a C and A. This is a result of the notes being slightly out of tune- equal temperament at work. Obviously this affects the math too. By the way, unaccompanied choirs are not so affected by equal temperament as the singers tune to each other on a chord by chord basis. They can have a very pure sound with regard to pitch. Also, horn players when playing in a band play their notes a little differently depending on which key they are in. Vibrato helps you to not go crazy at this point. Kind of fuzzying the lines. Once you hear the out of tune-ness of equal temperament, you will either relax a little about pitch, or possible go stark raving mad trying to fix the world of music. I hope you choose the former 2 The Slant. In order for our ears to perceive very low notes or very high notes as being in tune, the pitch needs to be "bent". High notes need to be tuned sharp, and low notes need to be tuned flat. All piano tuners use this knowledge to a lesser or greater degree depending on what sounds best to them and you would be surprised how far the actual bend can be. It can be in the range of 20 cents at the extremes. Pianos tolerate the slant (also called the stretch) at the treble end well as the high notes have very little sustain. If you want to test this one, find a keyboard with a string sound or pure lead sound and play middle C and the highest C on the keyboard. Sometimes the high C will sound flat because the slant is not sufficently extreme. If you check it with a tuner it will measure as being in tune but it will sound wrong. This is simply a function of how we humans hear. By contrast, some keyboards will sound right but if you measure them the high note will appear to be sharp. Of the keyboards I have owned, the Rolands tended to sound more slanted than the Yamaha's but that was just a casual observation. (Of course the Casio's are perfect!) I don't know if either of these two phenomenons are the cause of what you observed but at least it may help you to feel that the world is less crazy than you suspect.