It is thought that because a doubling of frequency causes a response at equal distance on the basilar membrane, we hear octaves as related. Every doubling in Hz is perceived as an equivalent octave. Each successive octave is a doubling of the frequency of the previous one-1ƒ, 2ƒ, 4ƒ, 8ƒ, 16ƒ.

In general, we perceive pitch logarithmically in relation to frequency. In strict equal temperament, a perfect fifth, for example, has the same ratio wherever it is in the tuning system (1:1.498307), very close to the 2:3 ratio it would be in the just intonation system. With equal temperament then, the ratio between the same intervals are constant, regardless of their placement.

For larger intervals, the formula P ref * 2 n/12 where P ref is the initial reference frequency and n is the number of semitones above it you wish to calculate, so a minor 3rd above A440 would be computed as 440 * 2 3/12 (or 3/12√ 2). If you desire more accuracy, that would be 1:1.059463094359295Īs an example, to find the frequency of the A# semitone above A440, multiply 440 by 1.05946 to get ~466.163. The formula for successive equal temperament 12-notes-to-an-octave semitones (called 12 tet) is a frequency ratio of one to the twelfth root of two ( 12√ 2 or 2 1/12), which approximately equals ~1:1.05946. 12 tet Equal Temperament Successive Semitone Ratio

Midi note number to frequency formula