How do we measure musical intervals?

The notes of the major third C-E (C4 or middle C to E4) have these frequencies:

Note Frequency
C4 (middle C) 260 Hertz
E4 325 Hertz
Frequency measures the number of times per second a sound vibrates. Hertz is the unit of measure.

We may think that the difference in frequencies determines the size of the interval:

325 - 260 = 65

However, this is not correct. The same notes one octave lower, give a different result despite being the same interval:

Note Frequency
C3 130 Hertz
E3 162.5 Hertz

162.5 - 130 = 32.5

Therefore, there is another mathematical operation that we must use to measure musical intervals correctly.

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