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For time immortal, musicians have been trying every possible scheme they can conceive to create a musical scale that is more harmonious and more perfect than existing scales.
Literally, thousands of musical scales have been invented. They range from 5 note scales in China to scales with 56 or more notes per octave in India.
The Diatonic Scale
The Diatonic scale simply uses the white keys, or major notes of the scale. This scale has also been broken into 7 Greek modes, each with different properties and a different "sound." Some of the Greek modes are popular, while others are almost never used.
We know very little about the penta scale except that it consists of five notes and is used mainly in China.
Indian music, or Indian Raga, varies in one distinct way. Most music contains a drone note, or constant tone, that plays in the background and creates an interval with every note played.
It has been said that Indian musicians don't "tune" their instruments before playing, they tune themselves and the space they will play in.
The various Western scales have received the vast majority of invention.
The Just Diatonic Scale
The Just Scale, or Scale of Ptolemy, c 130 A.D. is based on the ratios of the major triad, or tonic chord. In the note of C, this chord would be a C, E, and G. The chord is built from applying the ratios that make up the major triad, a major 3rd (5/4), minor 3rd (6/5), 4th (4/3), and perfect 5th (6/4) to a starting point (A = 440 Hz) to determine the tuning for the whole scale.
Equal Tempered Scale
The Equal Tempered scale is actually a relatively new scale. It is interesting in that it is theoretically based completely on mathematics.
Essentially, with the advent of the piano forte in the 1700's, it became possible to play music in any key. Only most keys, like the one above, are harmonic only when played in certain keys. Playing music in another key will sound audibly disharmonious because the Pythagorean Comma error appears in the music.
In the equal tempered scale, the Pythagorean Comma error is equally divided among the twelve notes. This, as we said, was a boon, because now music could be played in any key. Unfortunately, however, this makes all the music played disharmonious.
In actual fact, a good piano tuner will tune in such a way that the common keys are more harmonious and will not stick strictly to exact octave tuning in the highest and lowest octaves.
The ratio from one note to another is 100 Cents or the 12th root of 2. The actual math is detailed on our page discussing Musical Mathematical Terminology.
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