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Re: Increment with '#' and decrement with 'b'

Cross-posted to 2 groups.

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Quoth Henry Law <news@lawshouse.org>:
> 
[ representing musical notes as A=>0, A#=>1, Bb=>1, B=>2, &c.]
>
> Actually in this project I'm using a notation that already exists, for 
> better or worse; it's the one in the vast number of chord charts that I 
> have which need transposing for different singers!  I need to be able to 
> transpose C Am7 Dm7 G7#5b9 to, say, Eb Cm7 Fm7 Bb7#5b9 (and without it 
> coming out as A#7#5b9 either).  And so on.

I don't think you can do that with this representation. Consider
transposing

    C   F   G   C   =>  3   8   10  3

into B major

    2   7   9   2   =>  B   E   F#  B

and Db major

    4   9   11  4   =>  Db  Gb  Ab  Db

The enharmonic information you need to distinguish between F# and Gb is
exactly what you've just thrown away.

I would do a transposing job like this with a circle-of-fifths
representation, perhaps something like

    my %sharps  = qw( F 0  C 1  G 2  D 3  A 4  E 5  B 6 );
    my %acc     = qw( # +7  b -7  x +14  ## +14  bb -14 );
    my ($accs)  = map qr/$_/, join "|", keys %acc;
    $acc{""}    = 0;

    my ($note, $acc, $mods) = /([A-G])($accs)(.*)/i
        or die "not a valid chord symbol: '$_'\n";

    my $chord = $sharps{uc $note} + $acc{lc $acc};
    # transpose $chord

    my %base    = reverse %sharps;
    my %offset  = reverse %acc;
    $offset{14} = "x";              # or ## if you prefer
    
    my $base    = $chord % 7;
    my $offset  = $chord - $base;

    $offset > 14    and die "triple-sharp required\n";
    $offset < -14   and die "triple-flat required\n";

    my $symbol  = "$base{$base}$offset{$offset}$mods";

I don't really like starting with F, but it seems to be the easiest way
to make it work: otherwise you end up with code like

    my $base = $chord % 7;
    $base == 6 and $base = -1;

which is just ugly when it can easily be avoided.

Ben

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Thread

Re: Increment with '#' and decrement with 'b' Ivan Shmakov <oneingray@gmail.com> - 2012-03-18 22:30 +0700
  Re: Increment with '#' and decrement with 'b' Henry Law <news@lawshouse.org> - 2012-03-18 16:55 +0000
    Re: Increment with '#' and decrement with 'b' Ben Morrow <ben@morrow.me.uk> - 2012-03-20 15:12 +0000

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