[Denemo-devel] Checking for wrong enharmonics (e.g C# for Db)

[Daniel Wilckens]

Hi Richard,

I've only had time to look at the mailing list every once in a while 
recently but I did see your post asking for an algorithm to check for 
misspelled enharmonics.  This could be tough, as e.g. dimished fourths 
would be rare but not forbidden.  Here are a few thoughts of mine on 
this, though you probably already considered something along these 
lines.  Unless you want to go with something really fancy AI-wise, I'd 
probably go with an interactive script that stepped through the score 
looking for unlikely interval spellings in consecutive notes  (that 
would be diminished fourths like D to A#, augmented seconds like C to 
D#, augmented thirds, diminished thirds, etc.) and ask you to decide 
whether you really meant it to be written that way or whether you want 
the script to fix it for you to the other spelling.

To sketch an algorithm for this, each pitch-spelling would be given an 
integer (which I'll call its index) representing its distance in number 
of perfect 5ths from C.  So, C would be 0, G would be 1, F would be -1, 
.. C# would be 7 and Db would be -5, etc...  Then the script would flag 
something as unlikely if the index of consecutive notes differed by more 
than 6 (6, being a tritone, could go either way: C to F# or C to Gflat 
are both OK).  This is a pretty feeble-minded AI but should catch most 
errors of the sort you'd encounter I would think.

For individual chords, you could check if the set of indices of the 
tones comprising the chord fit into a set of 6 consecutive integers, i.e.

| MinIndex-MaxIndex | <= 6.

So a D7 chord, D, F#, A , C, would translate as the indices 2, 6, 3, 0, 
which easily fits into the set 0, ... 6, so it's OK.  (This would 
wrongly flag augmented 6th chords, since Aflat to F# would be indices -4 
and 6, which is an interval of 10.  That's one reason to require the 
user to check each proposed fix.  Augmented chords would be flagged 
also, but probably the user can deal with each one since they're not all 
that common until later.)  Consecutive chords should be flagged as 
suspicious, I would say, if their combined set of pitches has  | Min - 
Max | of 9 or more, since a cadence in a minor key involve the third of 
the dominant and the third of the root which have an interval of 
diminished fourth.  These tolerances could be tweakable.

I can't even think of any plausible fancier algorithm.  Somehow you 
could take into consideration not just the current and preceding 
note/chord, but perhaps the next one also.  There are some methods out 
there that might be worth looking into if you were really gung-ho, like 
Hidden Markov Models which some people have tried to write automatic 
piano-fingering generators with, but they take a lot of tweaking and 
"learning".  Hope this helps!

-Dan