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

See Intervals in the Tutorial section.

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José Rodríguez Alvira.