# Musical Notes

A musical octave spans a factor of two in frequency and there are twelve notes per octave. Notes are separated by the factor 2 1/12 or 1.059463. (1.059463 x 1.059463 x 1.059463...continued for a total of twelve = 2; try it!)

 Notes Frequency (octaves) A 55.00 110.00 220.00 440.00 880.00 A# 58.27 116.54 233.08 466.16 932.32 B 61.74 123.48 246.96 493.92 987.84 C 65.41 130.82 261.64 523.28 1046.56 C# 69.30 138.60 277.20 554.40 1108.80 D 73.42 146.84 293.68 587.36 1174.72 D# 77.78 155.56 311.12 622.24 1244.48 E 82.41 164.82 329.64 659.28 1318.56 F 87.31 174.62 349.24 698.48 1396.96 F# 92.50 185.00 370.00 740.00 1480.00 G 98.00 196.00 392.00 784.00 1568.00 A♭ 103.83 207.66 415.32 830.64 1661.28

Starting at any note the frequency to other notes may be calculated from its frequency by:

Freq = note x 2 N/12,

where N is the number of notes away from the starting note. N may be positive, negative or zero.

For example, starting at D (146.84 Hz), the frequency to the next higher F is:

146.84 x 2 3/12 = 174.62,

since F is three notes above. The frequency of A in the next lower octave is:

146.84 x 2 -17/12 = 55,

since there are 17 notes from D down to the lower A.

The equation will work starting at any frequency but remember that the N value for the starting frequency is zero.