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:

$f = 2^{(d - 69)/12} \cdot 440$

Despite this being taken from 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.

<<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

<<mtof.c>>=

#include <math.h>
#define SK_MTOF_PRIV
#include "mtof.h"
<<funcs>>

Function

The macro SK_MTOF performs the MIDI-to-frequency equation above.

<<macros>>=

#define SK_MTOF(f) (pow(2, (nn - 69.0) / 12.0) * 440.0);

mtof with caching

To save on some CPU cycles, a cached version of SK_MTOFhas been created.

State is stored in sk_mtof.

<<typedefs>>=

typedef struct sk_mtof sk_mtof;

<<structs>>=

struct sk_mtof {
   SKFLT freq;
   SKFLT nn;
};

Initialize with sk_mtof_init.

<<funcdefs>>=

void sk_mtof_init(sk_mtof *mf);

<<funcs>>=

void sk_mtof_init(sk_mtof *mf)
{
    mf->freq = -1;
    mf->nn = -1;
}

Compute with sk_mtof_tick:

<<funcdefs>>=

SKFLT sk_mtof_tick(sk_mtof *mf, SKFLT nn);

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

<<funcs>>=

SKFLT sk_mtof_tick(sk_mtof *mf, SKFLT nn)
{
    if (nn != mf->nn) {
        mf->nn = nn;
        mf->freq = SK_MTOF(nn);
    }
    return mf->freq;
}