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 a sound oscillates per second. Hertz is the unit of measurement.

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

325 - 260 = 65

This is not correct. The same notes an octave lower will give a different result, even though the interval is the same:

Note Frequency
C3 130 Hertz
E3 162.5 Hertz

162.5 - 130 = 32.5

Therefore, to measure musical intervals correctly, we need to use another mathematical operation.

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