Natural tuning, sometimes called Just Tuning or Ptolemaic Tuning is something of an oddity in that it has some attributes which would commend it as the best possible tuning but its drawbacks are so great that it is never used in practice. It has academic significance, however, as a tuning against which other tunings should be compared. If we take Pythagorean Tuning with its perfect 5ths and detune the D-A so that it is 22 cents flat, we get a remarkable effect, Natural Tuning. Looking at the tuning key of C, there are perfect ratios for the minor 3rd (316), major 3rd (386), 4th (498), 5th (702), minor 6th (814) and major 6th (884). The table in the chapter on Ratios and Cents will confirm these ratios and pitches. In fact, every simple ratio is concordant and so this looks like a perfect contender for 'Tuning of the Millenium'.

Unfortunately, the first problem with Natural Tuning is obvious from the colours in the chart. Modulating to any key except the tuning key and its relative minor produces unacceptable intervals. In the major keys, there are 3rds which are 41 cents sharp (pretty well 4ths) and the minor keys are just as bad.

A second problem, which may be even more significant is that there are 2 different tone intervals. The interval between the 4th and 5th is 204 cents, but the interval between the 5th and the 6th is only 182 cents. Examining the chromatic scale shows that there are also 3 different sizes for semitones. This make Natural Tuning useless in practice, since as a melody progresses through a set of intervals, it will quickly reach a point where the notes do not correspond to the original notes of the scale, due to going up one size of tone and back down another. (It would make Schoenberg appear positively tuneful!)

In conclusion, Natural Tuning is an academic oddity, but it is very useful as a test of other tunings. Because it is perfectly concordant in its tuning key in the notes which modern music requires to be concordant, it will be a very useful test of other tunings and temperaments to see how much they differ from Natural Tuning. For this reason, there is a button on the Control Panel below which shows the selected tuning relative to Natural Tuning.