The A above the middle C normally has a frequency of 440 cycles per second, or Hertz. This means it vibrates 440 times per second. An A one octave higher has a frequency of 880 Hz, or exactly twice as many vibrations per second. The mathematical expression for this ratio is 880:440, or 2:1. The following table shows the mathematical relationship of several intervals (using just intonation), ordered from consonant to dissonant.

Relation	Interval
2:1	Octave
3:2	Fifth
4:3	Fourth
5:4	Major Third
6:5	Minor Third
9:8	Major Second
16:15	Minor Second