Being about as musical as a brick, I can't comment about how you transpose the notes. I do think you'd be better off setting up the array first and then deriving the hash from it rather than the other way around; it saves you having to sort. The no warnings qw{ qw }; is to silence warnings where Perl thinks we are trying to put comments inside a qw{ ... } list.

knoppix@Microknoppix:~$ perl -Mstrict -MData::Dumper -wE '
> my @notesArr  = do {
>    no warnings qw{ qw };
>    qw{ A A# B C C# D D# E F F# G G# };
>    };
> my $value     = 0;
> my %notesHash = map { $_ => $value ++ } @notesArr;
> print Data::Dumper->Dumpxs(
>    [ \ @notesArr, \ %notesHash ],
>    [ qw{ *notesArr *notesHash } ]
>    );'
@notesArr = (
              'A',
              'A#',
              'B',
              'C',
              'C#',
              'D',
              'D#',
              'E',
              'F',
              'F#',
              'G',
              'G#'
            );
%notesHash = (
               'F' => 8,
               'A' => 0,
               'A#' => 1,
               'C#' => 4,
               'E' => 7,
               'B' => 2,
               'D#' => 6,
               'C' => 3,
               'D' => 5,
               'G#' => 11,
               'F#' => 9,
               'G' => 10
             );
knoppix@Microknoppix:~$
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I hope this is of interest.