#+TITLE: mtof
* Overview
=mtof= stands for MIDI-to-frequency. It converts
something that's a MIDI note number to frequency.

For now, this page will be limited to just 12-tone
equal temperament. But, with some easy adjustments,
the equation could be changed to produce a wide range
of equal temperament scales.
* Equation
Here'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 about
if this is the *right* way.

Let's first ignore the woes of equal temperament. That's a
whole other thing.

This equation is calibrated so that MIDI note number 69 is
concert A. If you're from Roland, they'll be the ones
who insist it should be 57. Pay no attention to them.

This equation is tuned to concert A440. This is
standard, and it's a fine standard. In contemporary
orchestras, concert A is sometimes tuned sharp to A441,
A442, or - dare I say it? - A443! Orchestras that specialize
in period music and/or instruments tend to tune lower. I
believe it's around A435 or so?

Suffice it so say that pitch and tonality have a beautiful
elasticity to it that shouldn't be forgotten in the digital
domain. However, for most practical purpose, this equation
gets the job done.
* Tangled Files
Two 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
* Function
The macro =SK_MTOF= performs the MIDI-to-frequency equation
above.

#+NAME: macros
#+BEGIN_SRC c
#define SK_MTOF(f) (pow(2, (nn - 69.0) / 12.0) * 440.0);
#+END_SRC
* mtof with caching
To save on some CPU cycles, a cached version of =SK_MTOF=
has been created.

State is stored in =sk_mtof=.

#+NAME: typedefs
#+BEGIN_SRC c
typedef struct sk_mtof sk_mtof;
#+END_SRC

#+NAME: structs
#+BEGIN_SRC c
struct sk_mtof {
   SKFLT freq;
   SKFLT nn;
};
#+END_SRC

Initialize with =sk_mtof_init=.

#+NAME: funcdefs
#+BEGIN_SRC c
void sk_mtof_init(sk_mtof *mf);
#+END_SRC

#+NAME: funcs
#+BEGIN_SRC c
void sk_mtof_init(sk_mtof *mf)
{
    mf->freq = -1;
    mf->nn = -1;
}
#+END_SRC

Compute with =sk_mtof_tick=:

#+NAME: funcdefs
#+BEGIN_SRC c
SKFLT sk_mtof_tick(sk_mtof *mf, SKFLT nn);
#+END_SRC

The function will only call =SK_MTOF= when the note number
has changed.

#+NAME: funcs
#+BEGIN_SRC c
SKFLT 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