The need for temperament can be explained by the fact that you can't fit twelve
 perfect fifths into seven octaves. The span of seven octaves is 2^7 = 128 but
 the span of twelve perfect fifths is 1.5^12 = 129.75. This extra amount is called
 the ditonic comma. Some or all of the fifths must be slightly detuned or tempered
 some fraction of the comma. For any temperament, all the fractions of comma must
 add up to negative one. A temperament is typically described by listing the fraction
 of comma added to or taken away from each fifth. An interval with zero comma would
 be a perfect fifth. The following is the equation to calculate the frequency ratio
 for the interval of a fifth given its amount of comma:

f (x) = (128 / 1.5^(12 + 1 / x))^(-1 * x)

For example, to calculate the interval of a fifth
minus 1/4 comma, us -0.25 for the value of x. This
gives a frequency ratio of 1.49493. Here's a table
of frequency ratios for the different fractions
of comma. Using this table, you can easily 
calculate the frequencies for any temperament.

Here is an example of how to calculate
the frequencies for the Valotti 
temperament. The Valotti temperament
 has six perfect fifth intervals and 
six intervals with –1/6 comma. The 
perfect fifths are B-F#, F#-C#, C#-G#,
 G#-Eb, Eb-Bb and Bb-F. The –1/6 
comma fifths are C-G, G-D, D-A, A-E,
 E-B and F-C. The frequency ratio 
for a perfect fifth is 1.5 and for 
a –1/6 comma is 1.49662. The 
following table shows the series of
calculations. Several times there 
will be division by two to keep the
frequencies in the same octave. Start
 on A = 440 Hz and use the
frequency ratios to go around the
 circle of fifths.