I'm in the process of reverse engineering a music file format from an old computer game. It uses numbers from 0 to 127 to represent note frequencies, however I need to convert these numbers to a different unit (in this case millihertz) in order to use them.
Unfortunately because of various technical reasons, the output frequency values I am working with are a little inaccurate due to rounding issues. I am not sure how to take this into account when trying to find a formula to fit the sequence, as most explanations I can understand assume the values are precise.
Could someone please help me find a formula to fit this sequence? Here are some values. The first column is the input note number, and the second column is the output frequency in millihertz.
0 16262 1 17258 2 18301 3 19391 4 20529 5 21762 6 23042 24 51774 50 146410 80 520403 98 1171287 127 1796378
I am reasonably certain the formula to calculate these is quite simple (given the game would not want to waste too much processing power on the music), but I'm being thwarted by the inaccuracies in the above list of numbers.
Here's some more values after some of the discussion below:
73 439232 89 878465 126 1772103
Here are some more values as requested. It looks like values are indeed invalid where the lower four bits of the note number are >= 12.
7 24417 8 25887 9 27452 10 29064 11 30818 12 13654 // possible invalid note 15 56136 // possible invalid note 16 32525