Is there a formula that converts scientific note names to piano key numbers? As an example, given A4 it would output 49.
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$\begingroup$ 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
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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).
answered Dec 14 '19 at 13:18
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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
