Is there a formula that converts scientific note names to piano key numbers? As an example, given A4 it would output 49.

  • $\begingroup$ This doesn’t feel like the right place for this question. Anyone have a better spot? $\endgroup$ – Dan Szabo Dec 14 '19 at 10:27

The frequencies are on an exponential scale. You can use any note as your base value. On a Chromatic scale, each note is a twelfth step of an octave (doubling of frequency, same tone). So, a very common formula is to use the 440Hz A note. (Search on 432Hz to see a controversy about this.)

$$ f = 440 \cdot 2^{\frac{n}{12}} $$

Where $n$ is the semi-tone count from your base.

Here is a good reference: Note names, MIDI numbers and frequencies

Upon rereading, I didn't really answer your question. Because of the gaps in note names (black keys on the piano), this is more of a programming exercise than a simple formula.

In Python:

def NoteConverter( ArgNoteName ):

        theLetter = ArgNoteName[0:1]
        theNumber = int( ArgNoteName[1:] )

        theOrdinal = "C D EF G A B".find( theLetter )

        theMidiNumber = theNumber * 12 + theOrdinal + 12

        return theMidiNumber


This is for Midi numbering. Subtract 20 to get your piano key number (on most pianos).

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  • $\begingroup$ Note that the logarithmic computation is for an even-tempered scale, which is good enough for most work. But there are all sorts of temperings, each of which is a compromise of some sort. $\endgroup$ – TimWescott Dec 16 '19 at 16:15

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