Comparing intervals using the mathematical ratio

We will use the mathematical ratio to compare two major thirds. For the first third we will use Pythagorean tuning and for the other we will use just intonation (see this article for information on the different tuning systems). In the following table we see the frequencies of the notes and calculate the mathematical ratio of each interval:

Temperament	C4	E4	Mathematical ratio
Major third Pitagorean tuning	260	329.06	329.06 / 260 = 1.2656153846
Major third Just intonation	260	325	325 / 260 = 1.25

The major third of the just intonation is smaller than that of the Pythagorean tuning (1.25 is smaller than 1.2656153846). However, the numbers do not help us to understand the difference in size. How large or small is the difference? How noticeable is the difference? Using cents will make the comparison easier.

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