#! /usr/bin/perl -w
# GENERATE THE FRACTIONS FOR PYTHAGOREAN TUNING (OR MEANTONEs )
# THIS IS JUST QUICK AND DIRTY CODE TO CACULATE THE THINGS THAT I WANT
use strict;
my( $num, $k, $n, $power3, $power2, %value2fraction, @ordered, $delta, $cents );
my( @noteNames, $sharps, %value2name, $p, $flats, $q, $action );
my( $tempered3rdHarm, %index2LogHarm, %index2LogRescaler, %index2PowerOf2,$count );
my( %index2Fraction, %index2NoteName, $flatString, $sharpString );
my( %index2value, $theta, $r, $factor,$theta_0, $r_0, $x, $pi );
my( $stretchForPicture );

#$num = 200;                       #NUMBER OF ITERATIONS -- NOW COMMAND LINE ARG
$tempered3rdHarm = 3;
#$tempered3rdHarm = 3 * (80/81)**(2/7);
#$tempered3rdHarm = 2**(19/12);


if( defined($ARGV[0] ) && defined( $ARGV[1] ) )
{
  $num    = $ARGV[0];
  $action = $ARGV[1];
}
else
{
  $action = "no args";
}
                                 #HERE WE ITERATIVELY GENERATE THE NOTE SEQUENCE
@noteNames = qw( F C G D A E B );  
$power2 = 2;  
$sharps = 0;                                                          #ASCENDING
for( $k = 1;  $k <= $num; $k++ )
{
  $power3            = $tempered3rdHarm**$k;
  $index2LogHarm{$k} = $k * log( $tempered3rdHarm );
  $count  = 1;
  $power2 = 2;
  until( $power3/$power2 < 2 )
  {
      $power2 = 2*$power2;
      $count++;
  }
  $index2LogRescaler{$k}             = -$count * log(2); 
  $index2PowerOf2{$k}                = -$count;
                                              #print "$k    $power3\/$power2\n";
  $index2value{ $k }                 = $power3/$power2;
  $value2fraction{ $power3/$power2 } = $power3." / ".$power2;
  $index2Fraction{ $k }              = $power3." / ".$power2;
  $value2name{     $power3/$power2 } = $noteNames[($k+1) % 7]; 
  if( ($k % 7) == 6 )
  {
      $sharps++;
  }
  $sharpString           = "";
  $index2NoteName{$k} = $value2name{$power3/$power2 };

  if( $sharps < 4 )
  {
    for( $p=1; $p <= $sharps; $p++ )
    {
      $value2name{$power3/$power2 }  = $value2name{$power3/$power2 }."#";
      $sharpString = $sharpString."#";
    }
  }
  else
  {
      $sharpString = $sharps."#";
  }
  #print "$k    $power3\/$power2  $value2name{$power3/$power2 }\n";
  $index2NoteName{$k}  = $index2NoteName{$k}."<sup>$sharpString</sup>";
}

$value2fraction{ 1 }  = "1";                                         # MIDDLE C
$value2name{1 }       = $noteNames[1]; 
$index2LogHarm{0}     = 0 * log( $tempered3rdHarm );
$index2LogRescaler{0} = 0;
$index2PowerOf2{0}    = 0;
$index2Fraction{0}    = "1";
$index2NoteName{0}    = "C";
$index2value{0}       = 1;

$power2 = 2;                                                         #DESCENDING
$flats  = 0;
for( $k = 1;  $k <= $num; $k++ )
{
  $power3             = $tempered3rdHarm**$k;
  $index2LogHarm{-$k} = -$k * log( $tempered3rdHarm );
  $count              = 1;
  $power2             = 2;     
  until( $power2/$power3 > 1 )
  {
      $power2 = $power2*2;
      $count++;
  } 
  $index2LogRescaler{-$k}            = $count * log(2); 
  $index2PowerOf2{-$k}               = $count;
                                             #print "-$k    $power2\/$power3\n";
  $index2value{ -$k }                 = $power2/$power3;
  $value2fraction{ $power2/$power3 } = $power2." / ".$power3;
  $index2Fraction{ -$k }             = $power2." / ".$power3;
  $q = $k%7;
  if( $q == 1 )
  {
    $value2name{$power2/$power3 } = $noteNames[0]; 
  }
  else
  {
    if( $q == 0)
    {
	$q = 7;
    }
    $value2name{$power2/$power3 } = $noteNames[8 - $q]; 
    if( (8 - $q) == 6 )                                     #WE'RE ON THE NOTE B
    {
	$flats++;
    }
  }
  $flatString           = "";                 #APPEND THE STRING OF FLAT SYMBOLS
  $index2NoteName{-$k} = $value2name{$power2/$power3 };
  if( $flats < 4 )
  {
    for( $p=1; $p <= $flats; $p++ )
    {
      $value2name{$power2/$power3 } = $value2name{$power2/$power3 }."b";
      $flatString = $flatString."b";
    }
  }
  else                                                        #JUST PUT A NUMBER
  {
      $flatString = $flats."b";
  }
  #print "$k    $power2\/$power3  $value2name{$power2/$power3 }\n";
  $index2NoteName{-$k} = $index2NoteName{-$k}."<sup>$flatString</sup>";
}
if( $action =~ /PLOT/ )      #- - - - - - - - - -- - - - - - - - - - - - - - - -
{                                  #THIS PLOTS THE LINES log(3^n) AND log(2^k(n))
  open( FFF2, ">-");
  open( FFF3, ">-");
  for( $k= -$num;  $k<=$num; $k++ )             # WRITE DATA FOR GNU-PLOT log(3)
  {
    write(FFF2);
  }
  print "\n";
  for( $k= -$num;  $k<=$num; $k++ )             # WRITE DATA FOR GNU-PLOT log(2)
  {
     write(FFF3);
  }
  close(FFF2);
  close(FFF3);
}
elsif( $action =~ /SPIRAL5THS/ )      #- - - - - - - - - -- - - - - - - - - - -- 
{                                              #STANDARD SPIRAL IN POLAR CO-ORDS
  open( POLARIS, ">-");
  $pi       = 3.141592653589793;
  $theta_0  = $pi / 2;
  $factor   = log(3) / ( (19/12) * log(2) ) * $pi/6;
  $stretchForPicture    = 1.01;
  $r_0      = 2;
  #write( POLARIS );
  for( $k = -$num;  $k <= $num;  $k++ )                # WRITE DATA FOR GNU-PLOT
  {
    $theta = $theta_0 - $k * $factor *$stretchForPicture;
    $r     = (0.2 / $pi) * ($theta - $theta_0) + $r_0;
    write(POLARIS);
  }
  print "\n";
  
  print "\n";
  #for( $k=-$num*10;  $k <= $num*10;  $k++ )       #DATA FOR SMOOTH SPIRAL CURVE
  #{
  #  $theta = $theta_0 - $k * $factor/10;
  #  $r     = (0.2 / 3.141592653589793) * ($theta - $theta_0) + $r_0;
  #  write(POLARIS);
  #}
  #print "\n";
  close(POLARIS);
}
elsif( $action =~ /MINORS/ )   #- - - - - - ----- - - -- - - - - - - - - - -
{
  &harmonicMatchingIntervals( $num, %index2NoteName );
}
elsif( $action =~ /CLOSING/ )    #- - - - - - - -- - - - - - - - - - - - - - - -
{
    &tableOfClosingValues( $num, $tempered3rdHarm, %index2value );
}
elsif( $action =~ /HTMLPOWERS/ ) #- - - - - - - -- - - - - - - - - - - - - - - -
{
  open(  POWERS_HEAD, ">-");
  write( POWERS_HEAD );
  for( $k= $num;  $k >= -$num; $k-- )              # WRITE HTML TABLES OF POWERS
  {
      &printPowers();
  }
  close(POWERS_HEAD);
  print "</TABLE>\n<\BODY>\n</HTML>\n";
}
elsif( $action =~ /TABLE/ ) #- - - - - - - - - - - - - - - - - - - - - - - - - -
{
  open( FFF_HEAD, ">-");
  open( FFF, ">-");
  write(FFF_HEAD);
  @ordered = sort( keys( %value2fraction ) );
  for( $k=0; $k <= $#ordered; $k++ )
  {
      #print "$value2fraction{$ordered[$k]}\n";
      if( $k < $#ordered )
      {
        $delta = $ordered[$k+1]/$ordered[$k];
        $cents = 1200*log( $delta ) / log (2);
        #print "                  $cents cents\n";
        write(FFF);
      }
      else
      {
	$cents = "*";
	write(FFF);
      }
  }
  close( FFF );
  close( FFF_HEAD );
}
else  #- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
{
    print "Unknown action: $action\n";
    print "Examples of correct useage:\n";
    print "perl -w genPythag.pl 50 CLOSING > table.html";
    print "the first argument is the number of iterations to do (here 50 so ";
    print "it goes from -50 to 50). The 2nd is the type of action\n";
    print "perl -w genPythag.pl 30 TABLE \n";
    print "perl -w genPythag.pl 30 HTLMPOWERS \n";
    print "perl -w genPythag.pl 30 PLOT \n";
    print "perl -w genPythag.pl 30 SPIRAL5THS \n";
}

# ==============================================================================
sub tableOfClosingValues()
{
  my( $num, $tempered3rdHarmonic, %index2value  ) = @_;
  my( %index2ClosestLowerIndexNeighbor, $n, $k,$d, $dmin, $d1min, $dOld );
  my( $count, $onlyPrintChanges );

  $onlyPrintChanges = "false";

  &printClosingTableHeader( $tempered3rdHarmonic );
  $dOld   = 204;
  $count  = 3;                                 #D WILL BE THE 4TH NOTE GENERATED
  for( $n = 2;  $n <= $num;  $n++ )  
  {
    $x    = $index2value{$n};                                  #POSITIVE ITERATE
    $count++;
    $dmin = 1200;
    for( $k = -($n-1);  $k <= ($n -1);  $k++ )
    {
      $d = &distInCents( $x, $index2value{$k} );  
      if( $d < $dmin )
      {
	  $dmin = $d;
          $index2ClosestLowerIndexNeighbor{$n} = $k;
      }
    }
    $d = &distInCents( $x, 2 );              #EXTRA CHECK FOR C AT TOP OF OCTAVE
    if( $d < $dmin )
    {
      $dmin = $d;
      $index2ClosestLowerIndexNeighbor{$n} = 0;
    }

    if( $dmin < $dOld - 0.000000001)
    {
      print "<TR  BGCOLOR=\"YELLOW\">\n";
      $dOld = $dmin;
      &printClosingTableRow( $count,  $n,  $index2PowerOf2{$n}, $index2NoteName{$n},
                             $index2ClosestLowerIndexNeighbor{$n},
                             $index2PowerOf2{ $index2ClosestLowerIndexNeighbor{$n} },
                             $index2NoteName{ $index2ClosestLowerIndexNeighbor{$n} },
			     $dmin );
    }
    elsif( $dmin > $dOld + 0.00000001 )
    {
      print "<TR BGCOLOR=\"RED\">\n";
      &printClosingTableRow( $count,  $n,  $index2PowerOf2{$n}, $index2NoteName{$n},
                             $index2ClosestLowerIndexNeighbor{$n},
                             $index2PowerOf2{ $index2ClosestLowerIndexNeighbor{$n} },
                             $index2NoteName{ $index2ClosestLowerIndexNeighbor{$n} },
			     $dmin );

    }
    else
    {
      if( $onlyPrintChanges eq "false" )
      {     
       print "<TR >\n";
       &printClosingTableRow( $count,  $n,  $index2PowerOf2{$n}, $index2NoteName{$n},
                             $index2ClosestLowerIndexNeighbor{$n},
                             $index2PowerOf2{ $index2ClosestLowerIndexNeighbor{$n} },
                             $index2NoteName{ $index2ClosestLowerIndexNeighbor{$n} },
      			     $dmin );
      }
    }

    $x     = $index2value{-$n};    #---------------CORRESPONDING NEGATIVE ITERATE
    $count++;
    $d1min = 1200;
    for( $k = -($n-1);  $k <= $n;  $k++ )
    {
      $d = &distInCents( $x, $index2value{$k} );        
      if( $d < $d1min )
      {
	  $d1min = $d;
          $index2ClosestLowerIndexNeighbor{-$n} = $k;
      }
    }
    $d = &distInCents( $x, 2 );              #EXTRA CHECK FOR C AT TOP OF OCTAVE
    if( $d < $d1min )
    {
      $d1min = $d;
      $index2ClosestLowerIndexNeighbor{-$n} = 0;
    }

    if( $d1min < $dOld - 0.0000001)
    {
      print "<TR  BGCOLOR=\"YELLOW\">\n";
      $dOld = $d1min;
      &printClosingTableRow( $count,  -$n,  $index2PowerOf2{-$n}, $index2NoteName{-$n},
                             $index2ClosestLowerIndexNeighbor{-$n},
                             $index2PowerOf2{ $index2ClosestLowerIndexNeighbor{-$n} },
                             $index2NoteName{ $index2ClosestLowerIndexNeighbor{-$n} },
			     $d1min );
    }
    elsif( $d1min > $dOld + 0.00000001)
    {
      print "<TR BGCOLOR=\"RED\">\n";
      &printClosingTableRow( $count,  -$n,  $index2PowerOf2{-$n}, $index2NoteName{-$n},
                             $index2ClosestLowerIndexNeighbor{-$n},
                             $index2PowerOf2{ $index2ClosestLowerIndexNeighbor{-$n} },
                             $index2NoteName{ $index2ClosestLowerIndexNeighbor{-$n} },
			     $d1min );
    }
    else
    {
      if( $onlyPrintChanges eq "false"  )
      {     
       print "<TR >\n";
       &printClosingTableRow( $count,  -$n,  $index2PowerOf2{-$n}, $index2NoteName{-$n},
                              $index2ClosestLowerIndexNeighbor{-$n},
                              $index2PowerOf2{ $index2ClosestLowerIndexNeighbor{-$n} },
                              $index2NoteName{ $index2ClosestLowerIndexNeighbor{-$n} },
      			      $d1min );
      }
    }
  }

  print "</TABLE>\n<\BODY>\n</HTML>\n";

}
# ==============================================================================
sub printClosingTableHeader()
{
  my( $tempered3rdHarmonic ) = @_;
  print "<html> \n";
  print "<head> \n";
  print "</head> \n";
  print "<body> \n";
  print "<TABLE border=2> \n";
  print "<CAPTION><b> Tempered 3rd Harmonic  = $tempered3rdHarmonic </b></CAPTION> \n";
  print "<tr> \n";
  print "<th>Count</th> \n";
  print "<th>New note name</th> \n";
  print "<th>New note value</th> \n";
  print "<th>Best match value</th> \n";
  print "<th>Best match Name</th> \n";
  print "<th>Distance in cents</th> \n";
}
# ==============================================================================
sub printClosingTableRow()
{
  my( $count, $pow3new,   $pow2new,   $newNote, 
              $pow3close, $pow2close, $closestNote,  $dist ) = @_;
  print "<TD> $count </TD>\n";
  print "<TD> $newNote </TD>\n";
  print "<TD> 3<sup>$pow3new</sup>   2<sup>$pow2new</sup>   </TD>\n";
  print "<TD> 3<sup>$pow3close</sup> 2<sup>$pow2close</sup> </TD>\n";
  print "<TD> $closestNote </TD>\n";
  print "<TD> $dist </TD>\n";
}
# ==============================================================================
sub printPowers()
{
  print "<TR align=\"center\">\n";
  print "<TD> $k </TD>\n";      
  print "<TD> 3<sup>$k</sup> </TD>\n";
  print "<TD> 2<sup>$index2PowerOf2{$k}</sup> </TD>\n";
  print "<TD> $index2Fraction{$k} </TD>\n";
  print "<TD> $index2NoteName{$k}  </TD>\n";
}
# ==============================================================================
sub harmonicMatchingIntervals()
{                                               # LEFT             RIGHT
                          # WE SEEK TO COMPUTE d( 2^p harm[i] 3^n, 2^q harm[j] )
  my( $max, %i2NoteName ) = @_;
  my( $n, @harmL, $indexL, @harmR, $indexR,  $pq, $d, $eta, $count, $alpha );
  $harmL[0] = 3;
  $harmL[1] = 5;
  $harmL[2] = 7;
  $harmL[3] = 9;

  $harmR[0] = 1;
  $harmR[1] = 3;
  $harmR[2] = 5;
  $harmR[3] = 7;
  $harmR[4] = 9;
  
  $count = 1;
  &printMinorTableHeader();
  for( $indexR = 0;  $indexR <= 4;  $indexR++ )
  {
    for( $n = -$max;   $n <= $max;   $n++ )
    {
      if( $n == 0 )
      {
	next;
      }
      for( $indexL = 0;  $indexL <= 3;  $indexL++ )
      {
        for( $pq = -10;  $pq <= 10;  $pq++ )                 # REALLY I WANT p - q
        {
	   $d = &signedDistInCents( 2**$pq * $harmL[$indexL] * 3**$n, 
                                    $harmR[$indexR]                   );
           if( abs($d) < 60 )
           {
	     $eta = ( $harmR[$indexR] / (2**$pq * $harmL[$indexL]))**(1/$n);
             $alpha = - log( $eta/3) / log( 81/80 );
	     &printMinorTableRow( $i2NoteName{$n}, $n, $pq, $harmL[$indexL], 
                                  $harmR[$indexR], $d, $eta, $count, $alpha );
             $count++;
	   }
        }
      }
    }
  }
  print "</TABLE> \n</BODY> \n</HTML>\n";
  
}
# ==============================================================================
sub printMinorTableHeader()
{
  print "<html> \n";
  print "<head> \n";
  print "</head> \n";
  print "<body> \n";
  print "<TABLE border=2> \n";
  print "<CAPTION> Landmarks for Minor Intervals </CAPTION>\n";
  print "<TR> \n";
  print "<TH> Num </TH>\n";
  print "<th> Note <br> name </th> \n";
  print "<th> Value </th> \n";
  print "<th> Harmonic </th> \n";
  print "<th> Octaves </th> \n";
  print "<th> Matched <br> Harmonic of <b>c</b> </th> \n";
  print "<th>Distance in cents</th> \n";
  print "<th> Factor &eta; </th> \n";
  print "<th> Factor &alpha; </th> \n";
  print "</TR>\n";
}
# ==============================================================================
sub printMinorTableRow()
{
  my( $noteName, $n, $pq, $harmL, $harmR, $dCents, $eta, $count, $alpha) = @_;
  print "<TR>\n";
  print "<TD> $count </TD>\n";
  print "<TD> $noteName </TD>\n";
  print "<TD ALIGN=CENTER> 3<sup>$n</sup> </TD>\n";
  print "<TD ALIGN=CENTER> $harmL </TD>\n";
  print "<TD ALIGN=CENTER> 2<sup>$pq</sup> </TD>\n";
  print "<TD ALIGN=CENTER> $harmR </TD>\n";
  print "<TD ALIGN=CENTER> $dCents </TD>\n";
  print "<TD ALIGN=CENTER> $eta </TD>\n";
  print "<TD ALIGN=CENTER> $alpha </TD>\n";
  print "</TR>\n";
}
# ==============================================================================
sub distInCents()
{
  my( $f0, $f1 ) = @_;
  my( $cents );
  $cents = (1200/log(2))*log( $f0/$f1 );
  return abs($cents);
}
# ==============================================================================
sub signedDistInCents()
{
  my( $f0, $f1 ) = @_;
  my( $cents );
  $cents = (1200/log(2))*log( $f0/$f1 );
  return $cents;
}
# ==============================================================================
format POLARIS = 
@<<<<<<<<  @<<<<<<<<<< 
$theta,  $r
.
# ==============================================================================
format FFF_HEAD =

FRACTION                           NOTE NAME  CENTS TO NEXT NOTE
-----------------------------      ---------  ------------------
.

format FFF =
@<<<<<<<<<<<<<<<<<<<<<<<<<<<<<     @<<<<<<<   @<<<<<<<<<
$value2fraction{$ordered[$k]}, $value2name{$ordered[$k]}, $cents;
.
# ==============================================================================
format FFF1 = 
@<<<<<<<<    3 @<<<<<<  2 @<<<<<<<     @<<<<<<<<<<<<<<<<<  @<<<<<<<<<<<<<<<<
$k,$k, $index2PowerOf2{$k},  $index2LogHarm{$k}, $index2LogRescaler{$k};
.
# ==============================================================================
format FFF2 = 
@<<<<<<<<  @<<<<<<<<<<
$k,  $index2LogHarm{$k};
.
# ==============================================================================
format FFF3 = 
@<<<<<<<<  @<<<<<<<<<<
$k, $index2LogRescaler{$k};
.
#===============================================================================
format POWERS_HEAD =
<html>
<head>
</head>
<body>
<TABLE border=2 >
<TR align="center">
<TH>Index</TH>
<TH>Three</TH>
<TH> Two </TH>
<TH>Fractional Value</TH>
<TH>Note Name</TH>
</TR>
.