Guest, Leeina said, "When I started going to workshops with professional teachers, they taught us to play a chord, hold it, and listen to it. Basically, you ask yourself, "Does this sound good?" There is an inner sense which tells us whether that chord is right or not, and it was magical the way the group could alter its playing to produce better harmony." I'm sorry to tell you that this is not something magical, in the sense that it can be explained rationally. However, it is still wondrous. What you and the others sensed, when you played a chord with all the notes in tune, was overtones, and you heard them, although you weren't aware of them.

The easiest overtunes to hear are created by playing octaves. It's not much harder to hear fifths. By a strange coincidence (-: the violin is tuned in fifths. That's why it's relatively easy to learn to tune a violin by ear.

Jeri, I'm impressed with your ability to sing and hear notes that are tempered or not. That's real talent. The violin, which has no frets, is generally played in a tempered scale so it will sound "in tune" with everybody else. I have read that most violinists play some notes just a tiny bit "off scale" because their instincts show the way to playing a "natural," rather than a tempered, scale. This means that violinists would tend to play an F# a tiny bit high when the note is leading into a G. I've read this but I haven't heard it. It could be tested experimentally and that would be fun.