Submitted by Christopher Heckman:
When midi2ly is run, it will print fractions with large numerators
and denominators, like
r4361/120 e429/120 r431/120 e459/120 r4361/120 e429/120
when the actual durations are more likely to be
r2. e41/4 r41/4 e41/2 r2. e41/4 r41/4 e41/2 r2. e4*1/4
I have written a patch to fix this.
--
Fixes to midi2ly.py: better note lengths, now supports meter changes
(1) Note lengths currently are fractions like 61/120. If the numerator
can be changed by 1 to get a better fraction, it is done. Quarter
notes are also replaced with eighths/sixteenths if appropriate.
For example: a duration of 461/120 is changed to 41/2 and then
to 8. (2) Current version of midi2ly does not support meter changes.
Patch does.
Christopher's explanation of his work:
This will reduce the fractions (n-1)/d, n/d, and (n+1)/d (where the
original fraction is n/d). If (n-1)/d or (n+1)/d reduces more, its
reduction replaces n/d, except in one technical case. For instance,
the fraction 29/120 is considered to be rounded off after some error
has been added. The possible values to be checked are 28/120 (7/30 in
lowest terms), 29/120 (which does not reduce), and 30/120 (1/4). Since
30/120 reduces to the smallest denominator, 29/120 gets replaced with
1/4.
Now the technical case: If n/d is in lowest terms, n is odd, and d is
even but not divisible by 2, then n/d won't reduce, but you will be
able to cancel a factor of 2 from (n-1)/d and (n+1)/d. Since there is
no way to break this tie, the original value n/d is kept. (Note this
is the only case where (n-1)/d and (n+1)/d will be reduced by the same
denominator. I've proven this.)
Note that this will not make changes like 4*1/4 into 16; that might
be in a future version. This would turn the example output into
r2. e16 r16 e8 r2. e16 r16 e8 r2. e16
Also, fractions which don't reduce but have large denominators might
be replaced with approximations with small denominators. (Continued
fractions allow you to calculate these.)
Fixes to midi2ly.py: better note lengths, now supports meter changes
(1) Note lengths currently are fractions like 61/120. If the numerator
can be changed by 1 to get a better fraction, it is done. Quarter
notes are also replaced with eighths/sixteenths if appropriate.
For example: a duration of 461/120 is changed to 41/2 and then
to 8. (2) Current version of midi2ly does not support meter changes.
Patch does.
Resolves: #5119
http://codereview.appspot.com/325800043
Diff:
This fails a basic 'make' when applied to current master.
Also Christopher, if and when you submit a new patch, can you clean up the whitespace errors that are also reported ('git apply' squelches some, but I can see that you are using tabs in the diff on Rietveld and this will cause comments by other devs). Also see:
http://lilypond.org/doc/v2.19/Documentation/contributor-big-page#policy-decisions-_0028finished_0029
Diff: