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This should be the formula to get a half step:
- Measure the frequencies of two notes an octave apart. In this example, 440 and 880.
- Average F1 (440) with F2 (880). You get F3 (660), or 6 half steps.
- Average F1 with F3. You get F4, 550. That's 3 half steps.
- That's close enough; you could go on forever and not get it.
Look! Let's use easier numbers as an example: In this example (E1), F1 will be 200 and we will try to find a half step up. We do the above proceedure (referred to from now on as HSP). F4 is 75. The difference between F1 and F4 is 75.
In E2, F1 is 200 and we will go down an octave. Do HSP, except go down instead of up. F4 ends up being 187.5. The difference between F1 and F4 is not 75, like before! It is 13.5, a totally unrelated number!