# How to calculate the resulting frequency of two tones played together?

I it possible to calculate the resulting frequency when you play two tones with a frequency of X and Y at the same time?

This question has simple answers only when one is talking about sinoidal signals of equal amplitude. Since the respective phase changes all of the time, one can answer this question by starting with both signals at phase 0, and then we have So basically you get a function with the mean frequency of the two, and it is beating with an envelope with a frequency of the difference of the two functions (formally, it is half the difference but since you cannot hear the difference between an envelope of cos(x) and |cos(x)| and the second has double the frequency of the first, the envelope frequency ends up as the difference itself).

The formula works for any value, but its interpretation as a tone with a beating envelope makes only sense when frequencies a and b are reasonably close.

This is the basic technique with which accordion "tremolo" registers work, and also organ "tremulant" registers.

• Thanks. Now I will be able to do my 12 tone tuning scale, that has the pitches 1, the resulting frequency of 1 and 2, the resulting frequency of 1, 2 and the last number I got, and this go on. With this scale being a octave one. Will problably sound really good. – knifre Nov 4 '14 at 12:14
• To be more accurate: if the two frequencies are close together, you can't hear the very low difference frequency, but you can usually hear the "beat" caused by amplitude changes at that low frequency. In fact, that's a good way to tune: when you stop hearing the "woooaaaoooww" beat, you're in tune. Oh, and you also get the sum frequency, which for e.g. "a" and "b" a fifth apart, generate the next octave of the lower note. – Carl Witthoft Nov 4 '14 at 12:57

You have to add both two frequencies and you will have the first new tone. then subtract the largest least the less and you´ll have the second. try it