The Mathematical Ratio of Intervals

The mathematical operation we must use to determine the size of an interval is division. When we divide the frequencies, both thirds have the same size or mathematical ratio (1.25):

325 / 260 = 1.25

162.5 / 130 = 1.25

This number, or mathematical ratio, allows us to calculate major thirds based on any note. By multiplying we get an ascending major third and by dividing we get a descending major third. Starting from a 440, we get the upper C# and the lower F:

Note	Frequency	Ascending major third (C#5)	Descending major third (F4)
A4	440 Hertz	440 * 1.25 = 550	440 / 1.25 = 352

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