#+TITLE: mtof* Overview=mtof= stands for MIDI-to-frequency. It convertssomething that's a MIDI note number to frequency. For now, this page will be limited to just 12-toneequal temperament. But, with some easy adjustments,the equation could be changed to produce a wide rangeof equal temperament scales.* EquationHere's the mathematical equation that will be used for=mtof=, and it's inevitably going to make some people upset: @!(fig "mtof_eqn" ``f = 2^{(d - 69)/12} \cdot 440``)!@ Despite this being taken from [[https://en.wikipedia.org/wiki/MIDI_tuning_standard][wikipedia]],there is still controversy in the music industry aboutif this is the *right* way. Let's first ignore the woes of equal temperament. That's awhole other thing. This equation is calibrated so that MIDI note number 69 isconcert A. If you're from Roland, they'll be the oneswho insist it should be 57. Pay no attention to them. This equation is tuned to concert A440. This isstandard, and it's a fine standard. In contemporaryorchestras, concert A is sometimes tuned sharp to A441,A442, or - dare I say it? - A443! Orchestras that specializein period music and/or instruments tend to tune lower. Ibelieve it's around A435 or so? Suffice it so say that pitch and tonality have a beautifulelasticity to it that shouldn't be forgotten in the digitaldomain. However, for most practical purpose, this equationgets the job done.* Tangled FilesTwo files as usual: =mtof.c= and =mtof.h=. #+NAME: mtof.h#+BEGIN_SRC c :tangle mtof.h#ifndef SK_MTOF_H#define SK_MTOF_H#ifndef SKFLT#define SKFLT float#endif <<typedefs>><<funcdefs>><<macros>>#ifdef SK_MTOF_PRIV<<structs>>#endif #endif#+END_SRC #+NAME: mtof.c#+BEGIN_SRC c :tangle mtof.c#include <math.h>#define SK_MTOF_PRIV#include "mtof.h"<<funcs>>#+END_SRC* FunctionThe macro =SK_MTOF= performs the MIDI-to-frequency equationabove. #+NAME: macros#+BEGIN_SRC c#define SK_MTOF(f) (pow(2, (nn - 69.0) / 12.0) * 440.0);#+END_SRC* mtof with cachingTo save on some CPU cycles, a cached version of =SK_MTOF=has been created. State is stored in =sk_mtof=. #+NAME: typedefs#+BEGIN_SRC ctypedef struct sk_mtof sk_mtof;#+END_SRC #+NAME: structs#+BEGIN_SRC cstruct sk_mtof {   SKFLT freq;   SKFLT nn;};#+END_SRC Initialize with =sk_mtof_init=. #+NAME: funcdefs#+BEGIN_SRC cvoid sk_mtof_init(sk_mtof *mf);#+END_SRC #+NAME: funcs#+BEGIN_SRC cvoid sk_mtof_init(sk_mtof *mf){    mf->freq = -1;    mf->nn = -1;}#+END_SRC Compute with =sk_mtof_tick=: #+NAME: funcdefs#+BEGIN_SRC cSKFLT sk_mtof_tick(sk_mtof *mf, SKFLT nn);#+END_SRC The function will only call =SK_MTOF= when the note numberhas changed. #+NAME: funcs#+BEGIN_SRC cSKFLT sk_mtof_tick(sk_mtof *mf, SKFLT nn){    if (nn != mf->nn) {        mf->nn = nn;        mf->freq = SK_MTOF(nn);    }    return mf->freq;}#+END_SRC