genfreqtab.c

// ---------------------------------------------------------------------------
// Generate tuning tables -- by Ivo van Poorten (C)2020 - License: 0BSD
// output RFC4180 CSV table with header
// build with gcc -o genfreqtab genfreqtab.c -lm 
// ---------------------------------------------------------------------------

#define TUNE_TO_A (440.0)   // floating point in Hertz

//#define PRINT_CSV
#define PRINT_MADS_DTA

// ---------------------------------------------------------------------------

#include "stdio.h"
#include "math.h"

// ---------------------------------------------------------------------------

#define NUMBER_OF_OCTAVES 10

// semitone offsets

#define C0  (-57)
#define C1  (-45)
#define C2  (-33)
#define C3  (-21)
#define C4  (-9)
#define C5  (3)
#define C6  (15)
#define C7  (27)
#define C8  (39)
#define C9  (53)
#define C10 (63)

// Atari XL main clocks

#define SYSCLOCK_PAL  1773447.0
#define SYSCLOCK_NTSC 1789790.0

// Well-tempered tuning
//
// Fn = F0 * a^n

#define F0 (TUNE_TO_A)
#define a_100cents (pow(2.0,(1.0/12.0)))

#define FORMULA(n) ((F0) * (pow(a_100cents,(n))))

// Pokey 16-bit value to frequency relation
//
// f = sysclock/(v+7)/2
//
// so
//
// v = sysclock/(2*f)-7

#define FREQ_TO_VALUE(sysclock, freq) ((sysclock/(2*freq))-7)
#define VALUE_TO_FREQ(sysclock, value) (sysclock/(value+7)/2)

#define SIZE (NUMBER_OF_OCTAVES*12)

double equal_tempered_frequencies[SIZE], pal_frequencies[SIZE], \
           ntsc_frequencies[SIZE];
int pal_values[SIZE], ntsc_values[SIZE];


int main(int argc, char **argv) {
    int i, j;
    double e;

#ifdef PRINT_CSV
    printf("n, equal_tempered_frequency, PAL_hex, NTSC_hex, "
           "PAL_frequency, NTSC_frequency\n");
#endif

    for (i=0; i<(NUMBER_OF_OCTAVES*12); i++) {
        e = equal_tempered_frequencies[i] = FORMULA(i+C0);

        pal_values[i]  = round(FREQ_TO_VALUE(SYSCLOCK_PAL,  e));
        ntsc_values[i] = round(FREQ_TO_VALUE(SYSCLOCK_NTSC, e));


        pal_frequencies[i]  = VALUE_TO_FREQ(SYSCLOCK_PAL,  pal_values[i]);
        ntsc_frequencies[i] = VALUE_TO_FREQ(SYSCLOCK_NTSC, ntsc_values[i]);

#ifdef PRINT_CSV
        printf("%i, %0.2f, %04x, %04x, %0.2f, %0.2f\n",
                i, equal_tempered_frequencies[i],
                pal_values[i], ntsc_values[i],
                pal_frequencies[i], ntsc_frequencies[i]);
#endif
    }

#ifdef PRINT_MADS_DTA

    printf("\npal_16bit_frequency_table\n");

    for (i=0; i<NUMBER_OF_OCTAVES; i++) {       // octaves
        printf("; Octave %i\n", i);
        printf(" dta a(");
        for (j=0; j<11; j++) {                  // notes
            printf("$%04x,", pal_values[i*12+j]);
        }
        printf("$%04x)\n", pal_values[i*12+j]);
    }

    // code duplication ;)

    printf("\nntsc_16bit_frequency_table\n");

    for (i=0; i<NUMBER_OF_OCTAVES; i++) {       // octaves
        printf("; Octave %i\n", i);
        printf(" dta a(");
        for (j=0; j<11; j++) {                  // notes
            printf("$%04x,", ntsc_values[i*12+j]);
        }
        printf("$%04x)\n", ntsc_values[i*12+j]);
    }

    printf("\n");
#endif
}