What it sounds like is you want your tuner to think A = 415.30 which is really an Ab. The Eb a diminished 5th above A 440 is 622.26 We can also obtain the same frequency by using a D#, 4th octave, with a microtonal adjustment of (94-100) = -6 cents. We will have to insert a D, 4th octave, with a microtonal adjustment of 94 cents. The result is 93.72, rounded to M = 94 cents The note to insert is a D (1=C#, 2=D, 3=D#). Semitone S = integer part of 293.72 / 100 = 2. You get M, the microtonal adjustment value in cents.įor example, if we need a frequency Z of 310 Hz: The integer part of this result is S, the semitone number within the octave (0=C, 1=C#, 2=D, 3=D#, 4=E.11=B) Calculate Y' by subtracting 1200 x N from Y. The integer part of this result is the octave number N for the note to play. (using ^ as power symbol): 440 x 1.00057778950655 ^ 50 = 452.89 Hz.īy reversing the math above, knowing a frequency Z in Hertz, it is possible to calculate all values for the note:ġ200 x log(F/16.3515978312876)/log(2)= total number of cents from C0.

1.00057778950655.įor example, if you insert an A4 (440 Hz) with a microtonal adjustment of +50 cents (a quarter tone), the resulting frequency for this note will be 440 Hz multiplied by the 50th power of the cents multiplier, i.e. Increasing the note frequency by 1 cent means multiplying its frequency by the 1200th root of 2, i.e. It means each semitone is logarithmically splitted into 100 parts. The value you set in the microtonal adjustment of Melody/Harmony is a value in hundredths of semitone (cent). In the same way, A flat (or G sharp) of octave 4 will be 440 / 1.059463094359 = 415.3 Hz Thanks to this, we can calculate all the frequencies for each semitone in the fourth octave (and by extension, in every octave, because we just have to multiply or divide these frequencies by 2 to get the values for adjacent octaves): This means that A sharp (or B flat) of octave 4 will be 440 x 1.059463094359 = 466.16 Hz For example, A5 will be 880 Hz.ĭue to this, splitting one octave into 12 logarithmic, equally-spaced intervals means that each note frequency is equal to the frequency of the previous (lower) semitone multiplied by the 12th root of 2, i.e. Traditionally, the A4 (A, 4th octave) is 440 Hz.Ī physical law says that the frequency for the same note played one octave up will be doubled.

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