There are many different tuning systems around the world. China’s may be different from ours and from India’s. The main three tuning systems are Pythagorean's system, well temperament and equal temperament, the ones we are used to today. These three are connected to each other.
    Tuning is a serious thing if instruments have to play together at the same time. Have you ever been to a little kid’s school concert when they are playing different instruments and they have only practiced for two weeks? It’s not that pretty, but it’s cute. Well, some of the problem is that the instruments are out of tune or they are playing notes that clash.
    The music that we are use to today is called Western music. This music goes with the Western tuning system called equal temperament. This tuning system replaced fairly popular tuning systems in Europe and other places. The tuning of instruments in different temperaments also depends on the history of their music tradition. The octave is something recognized by all the music traditions. When one note has a frequency that is two times higher then the second note, the second note is an octave lower than the first note. Confusing? Yeah, but just hang in there, it gets simpler.
    The best mathematical way to show this relationship in with the ratio 2:1. These two notes that we have been talking about when played together sound really pretty. This is when the sound “in tune”, but if you play two notes that have too close of a frequency, the notes will sound really horrible together. It is actually quite painful. Have you ever heard your music teacher have two different parts of music being sung at the same time and in some spots the notes sound "out of tune" or they "clash"?
     Now Pythagorean system. It was discovered by no one else but Pythagoras himself. Pythagoras and his followers or club members believed that numbers were the ruling principle of the universe. The ways their model of the universe was set up was actually pretty cool because when it moves it created a kind of harmony and that harmony is the same arithmetical relationships as musical harmony.
    Intervals with very simple frequency ratios found in the harmonic series are called Pure intervals. In the Pythagorean system all tuning is based on the interval of the pure fifth. These have the frequency ratio of exactly 3:2. If you use a series of perfect fifths you can fill a chromatic scale-with the notes in different octaves, of course. In the Pythagorean system the series of perfect fifth will never take you back the original note that you started with. This is the main weakness in this system. Perfect fifths would go something like this: C, G, D, A, E, B, F sharp, C sharp, G sharp, D sharp, A sharp, E sharp, and B sharp. In equal temperament though, the last note in that series would take you back to a C, just seven octaves higher than the original.
    In order for instruments that used Pythagorean system to keep pure octaves they had to use eleven pure fifths and one smaller fifth. Usually this pure fifth did not sound so great. It was actually called the Wolf fifth because it sounded so horrible. In most instruments this note sounded fine but if it was played on a piano or harpsichord it would cause problems.
     Well temperament. Well temperament was replaced with equal temperament, but was very popular in the 18th and 19th centuries when they were trying to keep a balance between staying close to pure intervals and avoiding wolf intervals. Well temperament has several pure fifths and several fifths that are smaller than a pure fifth-kind of like Wolf fifths, but they weren’t quite that small. In this system the tuning would be very noticeably different in each key, but it would still be pleasant to the ear. That is why equal temperament was welcome by players of hard to tune instruments, like the piano. What was really cool about well temperament was that every key represented a color or a feeling. The keys were even a different color. You know how we listen to different types of music when we are having a bad day or a good day. This is kind of the same thing only every key represented an emotion.
   The order is written in the time line below.