When I was a young musician the most difficult concept for me to grasp was playing "in tune." My musical talent was sufficient for me to play reasonably well in tune most of the time, but I didn't understand what I was doing and because of that I became confused at times. Of course all of my fellow students and many of the teachers were confused too, which didn't help! As I grew older I realized that neither my fellow students nor the teachers understood it any more than I did, as if we were all groping for an answer. The best explanation teachers could give was for us to listen for "beats" while supplying the "correct" pitch as an absolute by repeatedly striking a note on the piano. We were expected to first match a pitch from the piano then remember and play it later with precision. THAT was playing "in tune." It was like some sort of mystical ritual where one consulted an oracle (a tuning fork or piano) and repeated the ritual incessantly in the hopes of attaining the rapture of playing in tune. Understanding, if any, was gained through brute force and intuition. It wasn't until my early twenties that I learned two lessons about playing in tune that opened my eyes.
The first thing I learned was that intervals, not absolute pitches, are the primary tools for playing in tune. Learning to hear them is elementary for most people, since the the human ear is really good at reading them. Why? Because the human ear (and brain) can discern the existence of simple mathematical relationships between two frequencies. Since western tonal harmony uses intervals that are simple ratios between frequencies, these intervals are intuitive for most people. The problem is that so few of us are exposed to simple-ratio intervals at all, especially in a musical context. Because of this we may not even recognize them or know how important they are. When most people finally do hear them some of these intervals can sound wrong to them because they are different from what they have heard all their lives. In fact, some of the intervals that are actually in tune may require serious adjustment in perceptions at first, since they are quite different from those of the equally tempered scale, the dominant musical tuning system in use today.
This was the second thing I learned: Aside from the octave, the intervals of the equally-tempered scale (used to tune pianos) are NOT simple-ratio intervals and the human ear must be trained in a different way to discern them accurately. Frankly, the equally-tempered scale is a lousy way to learn to play in tune. It is non-intuitive and is an important reason why we don't teach our young music students intervals as tools for playing in tune. Instead, we teach them to tune a single note on their instrument (Concert A or B-flat) by playing it in unison with a piano or some other equally-tempered, absolute-pitch reference. Once that is accomplished they are to consult the piano (the oracle?) if there is a question. Worse, we now have digital tuners (little high-tech oracles) we can set on a music stand or clip to our instruments to give us tuning advice in real time! This is not only wrong, but it actually trains musicians to IGNORE what their ears tell them in deference to this little device. "Just have faith in the oracle and all will be well." Sorry, but it isn't that way. In fact it should actually be much easier than that.
It is obvious that the widespread use of the equally tempered scale has had a detrimental effect on both the knowledge and practice of playing in tune. This is not to say the equally tempered scale is a Bad Thing. Without it composers might not have developed the cool harmonic colors and progressions we enjoy today, and it is quite possible (and a good practice) to effectively use good intonation in an equally tempered context. But this inherent weakness in the equally tempered scale has been ignored for too long. The time has come to recover some of the public consciousness of this subject that has been lost over the past 150 years or so. Adults can learn to play in tune with intervals. I did in my twenties and I know many musicians who do without ever recognizing exactly what the process is. But our society needs to become aware enough of this to cause a sea-change in music education that will start young children down the musical road with intervals that will stimulate rather than confuse them.
That is the purpose of my effort here. Just intonation is well understood by composers and theorists, who have been present on the World Wide Web since its inception in the early 1990s, and on the internet before that. But the study of intonation for students and performers has been lacking. It is my dream that one day music teachers will be taught tuning by intervals as a normal practice and pass it on to their students. An added benefit, and possibly even a compelling reason to once again make music a central pillar of education, is that teaching intervals and intonation provides a tactile way for students to understand mathematics. In this way the arts inform and complement the practical side of education (again).