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MIDI note/frequency conversion

Type : -
References : Posted by tobybear[AT]web[DOT]de

Notes :
I get often asked about simple things like MIDI note/frequency conversion, so I thought I could as well post some source code about this.
The following is Pascal/Delphi syntax, but it shouldn't be a problem to convert it to almost any language in no time.

Uses for this code are mainly for initializing oscillators to the right frequency based upon a given MIDI note, but you might also check what MIDI note is closest to a given frequency for pitch detection etc.
In realtime applications it might be a good idea to get rid of the power and log2 calculations and generate a lookup table on initialization.

A full Pascal/Delphi unit with these functions (including lookup table generation) and a simple demo application can be downloaded here:
http://tobybear.phreque.com/dsp_conv.zip

If you have any comments/suggestions, please send them to: tobybear@web.de


Code :
// MIDI NOTE/FREQUENCY CONVERSIONS

const notes:array[0..11] of string= ('C ','C#','D ','D#','E ','F ','F#','G ','G#','A ','A#','B ');
const base_a4=440; // set A4=440Hz

// converts from MIDI note number to frequency
// example: NoteToFrequency(12)=32.703
function NoteToFrequency(n:integer):double;
begin
if (n>=0)and(n<=119) then
result:=base_a4*power(2,(n-57)/12)
else result:=-1;
end;

// converts from MIDI note number to string
// example: NoteToName(12)='C 1'
function NoteToName(n:integer):string;
begin
if (n>=0)and(n<=119) then
result:=notes[n mod 12]+inttostr(n div 12)
else result:='---';
end;

// converts from frequency to closest MIDI note
// example: FrequencyToNote(443)=57 (A 4)
function FrequencyToNote(f:double):integer;
begin
result:=round(12*log2(f/base_a4))+57;
end;

// converts from string to MIDI note
// example: NameToNote('A4')=57
function NameToNote(s:string):integer;
var c,i:integer;
begin
if length(s)=2 then s:=s[1]+' '+s[2];
if length(s)<>3 then begin result:=-1;exit end;
s:=uppercase(s);
c:=-1;
for i:=0 to 11 do
if notes[i]=copy(s,1,2) then
begin
c:=i;
break
end;
try
i:=strtoint(s[3]);
result:=i*12+c;
except
result:=-1;
end;
if c<0 then result:=-1;
end;



Comments


Added on : 29/11/02 by tobybear[ AT ]web[ DOT ]de
Comment :
For the sake of completeness, here is octave fraction notation and pitch class notation:

// converts from MIDI note to octave fraction notation
// the integer part of the result is the octave number, where
// 8 is the octave starting with middle C. The fractional part
// is the note within the octave, where 1/12 represents a semitone.
// example: NoteToOct(57)=7.75
function NoteToOct(i:integer):double;
begin
result:=3+(i div 12)+(i mod 12)/12;
end;

// converts from MIDI note to pitch class notation
// the integer part of the number is the octave number, where
// 8 is the octave starting with middle C. The
fractional part
// is the note within the octave, where a 0.01 increment is a
// semitone.
// example: NoteToPch(57)=7.09
function NoteToPch(i:integer):double;
begin
result:=3+(i div 12)+(i mod 12)*0.01;
end;




Added on : 03/12/02 by kaleja[ AT ]estarcion[ DOT ]com
Comment :
I thought most sources gave A-440Hz = MIDI note 69. MIDI 60 = middle C = ~262Hz, A-440 = "A above middle C". Not so?



Added on : 13/05/03 by DFL
Comment :
Kaleja is correct. Here is some C code:

  double MIDItoFreq( char keynum ) {
    return 440.0 * pow( 2.0, ((double)keynum - 69.0) / 12.0 );
  }

you can double-check the table here:
http://tomscarff.tripod.com/midi_analyser/midi_note_frequency.htm




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