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Index › Programming Questions & Help › Sound,  Music Libraries › Round frequency to the nearest semitone
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Round frequency to the nearest semitone (Read 1085 times)
agargara
Round frequency to the nearest semitone
Apr 29th, 2009, 5:41pm  
Hello, I have been trying to figure out a way to round a frequency to the nearest semitone. For example, given the pitch 442Hz, it would round it to 440Hz to be a standard "A."

I'm thinking in equal temperament, but just intonation or quarter-tone scale ideas are welcome too...

EDIT:
Here's somewhat of a solution I came up with, but it's not very elegant and requires a lot of memory to work properly. There must be a better way...

Code:
// Convert to nearest midi note
float pitch = (round(69 + 12 * (log(myFreq/440.0) / log(2.0)))); 
pitch = 440*pow(2,(pitch-69)/12); // Convert back
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danielle
Re: Round frequency to the nearest semitone
Reply #1 - Apr 29th, 2009, 11:27pm  
In terms of generating the value math-wise each time anew, that seems right.

If avoiding the processing cost of computing those logs+exponent is really necessary, the old-school algorithm would probably be to make a lookup table of all the frequencies of equal tempered pitches, then use an optomized search algorithm (binary search, perhaps, since the array is already sorted: start in the middle, figure out which half it's in, move to that half, find which quarter it's in, etc) to find the closest existing value to a given input.

To really delve back into my college algorithms memory: for an array of N elements, finding the closest element with a binary search would take log2(N) comparisons. So if you stored 128 note values, it would take 7 comparisons to find the closest value, which is probably much faster than computing a logarithm and an exponent...but a bit more code

dan
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