frequencyToNote.lua

local frequencyToNote = function (input) 
  
  local A4 = 440.0
  local A4_INDEX = 57

  local notes = {
    "C0","C#0","D0","D#0","E0","F0","F#0","G0","G#0","A0","A#0","B0",
    "C1","C#1","D1","D#1","E1","F1","F#1","G1","G#1","A1","A#1","B1",
    "C2","C#2","D2","D#2","E2","F2","F#2","G2","G#2","A2","A#2","B2",
    "C3","C#3","D3","D#3","E3","F3","F#3","G3","G#3","A3","A#3","B3",
    "C4","C#4","D4","D#4","E4","F4","F#4","G4","G#4","A4","A#4","B4",
    "C5","C#5","D5","D#5","E5","F5","F#5","G5","G#5","A5","A#5","B5",
    "C6","C#6","D6","D#6","E6","F6","F#6","G6","G#6","A6","A#6","B6",
    "C7","C#7","D7","D#7","E7","F7","F#7","G7","G#7","A7","A#7","B7",
    "C8","C#8","D8","D#8","E8","F8","F#8","G8","G#8","A8","A#8","B8",
    "C9","C#9","D9","D#9","E9","F9","F#9","G9","G#9","A9","A#9","B9" }

  local pow = function(a,b)
    return a ^ b
  end
  
  local MINUS = 0
  local PLUS = 1
  
  local frequency
  local r = pow(2.0, 1.0/12.0)
  local cent = pow(2.0, (1/1.27)/1200.0)
  local r_index = 1
  local cent_index = 0
  local side

  frequency = A4

  if(input >= frequency) then
    -- higher than, or equal to A4
    while(input >= r*frequency) do
      frequency = r*frequency
      r_index = r_index+1
    end
    while(input > cent*frequency) do
      frequency = cent*frequency
      cent_index = cent_index+1
    end
    if((cent*frequency - input) < (input - frequency)) then
      cent_index = cent_index+1
    end
    if(cent_index > 64) then
      r_index = r_index+1
      cent_index = 127-cent_index
      if(cent_index ~= 0) then
        side = MINUS
      else
        side = PLUS
      end
    else
      side = PLUS
    end

  else 
    -- lower than A4
    while(input <= frequency/r) do
      frequency = frequency/r
      r_index = r_index-1
    end
    while(input < frequency/cent) do
      frequency = frequency/cent;
      cent_index = cent_index+1
    end
    if((input - frequency/cent) < (frequency - input)) then
      cent_index = cent_index+1
    end
    if(cent_index >= 64) then
      r_index = r_index-1
      cent_index = 127 - cent_index
      side = PLUS
    else 
      if(cent_index ~= 0) then
        side = MINUS
      else
        side = PLUS
      end
    end
  end

 
  local result = notes[A4_INDEX + r_index]
  if(side == PLUS) then
    result = result .. " plus "
  else
    result = result .. " minus "
  end
  result = result .. cent_index .. " cents"
  
  
  return result
end



print(frequencyToNote(46.24930284))   -- 
--print(frequencyToNote(3222.4))   -- G#7
--print(frequencyToNote(440))   -- A-4
--print(frequencyToNote(415.3)) -- G#4
--print(frequencyToNote(30.868))  -- B-0