On 12/21/2018 11:54 AM, Aaron Hill wrote:
On 2018-12-21 5:14 am, Reggie wrote:
Hello. I see what you are saying thank you. I just feel that feather
beaming
is so confusing it all depends on so much, it's not simple like "select
these notes and change beam style to feather left or right". It's first,
math. Then, trial error. Then, settling. Then, Repeat. I now
understand how
to create the feather beams on paper, but the bar line check fails is
what
remains to be problemsome. [ . . .]
I apologize for the very long email following, although I would
appreciate you taking the time to read through it. You may need to
re-read it a few times, so find a good cup of coffee (or something
stronger if you are so-inclined).
==
Feathered beams, as far as the visual depiction goes, are as simple as
you describe. All you need to do is set Beam.grow-direction to #LEFT
or #RIGHT, and then any manually beamed notes delimited with [ and ]
will have the beams feathered. That's it. You're done. No math at all.
However, note that this is *only* the visual aspect of feathering.
Unless you use \featherDurations, all of the notes will keep their
straight timing; and MIDI output will not reflect the desired
ritardando or accelerando.
So when you do need to care about the timing of notes,
\featherDurations comes into play; and it does bring with it some
potentially confusing math. This math is somewhat complicated by the
fact that the documentation and implementation do not agree with one
another. Consider the following:
\featherDurations #(ly:make-moment 1/2) { c8[ d e f] }
[Side note: Harm made a slight mistake in his example usage. If you
want to feather a sequence of notes, you must put those notes in curly
braces. Omitting the braces in the example above will result in no
feathering, as only the first note will be passed to the function.]
The documentation says that \featherDurations will use the specified
moment to scale the last note relative to the first; however, in
practice you will see that this scaling is done between each
subsequent note. In the example above, we would expect that the 'f'
should last half as long as the 'c'. But instead, we find that the
'f' is half of the 'e'; the 'e', half of the 'd'; and the 'd', half of
the 'c'. The result is that the 'f' is one eighth the duration of the
'c'.
Given the current implementation, it would be necessary to use an
approximate rational like 50/63 as the moment in order to get 'f' to
be half of 'c'. Why that number? Well, it's a close approximation to
the irrational cube root of one half. We determine this exact value
by taking the desired ratio (1/2) and raising it to the reciprocal of
the number of scaling steps between the first and last notes (three,
in this case, which becomes the fraction 1/3). (1/2)^(1/3) is about
0.7937; and 50/63 is roughly 0.79365.
But before we get lost in the murky details of whether the implemented
behavior is right or the documentation is right, let us circle back
around to a key point that I feel has not been stressed enough.
\featherDurations will change the individual durations and timing of
the notes in the sequence provided; however it will *not* change the
overall duration of the sequence. If bar checks outside the range of
feathered notes are failing, then the issue is completely unrelated to
\featherDurations. Your problem is with the note sequence itself.
(If you are using bar checks *within* the sequence of notes being
feathered, then you are asking for trouble. We'll talk about this in
a bit.)
This means your score really should be bar check clean *before* you
ever use \featherDurations. And that task may involve arithmetic of
its own. Consider the following sequence:
r64 { c64 d32 e16 f8 g4 a2 } | b1
We have a manually-written ritardando of notes. Note the rest is
there to ensure the whole note aligns to its own measure, but we are
mainly interested in the sequence delimited by the braces.
Let us assume we would like to notate this as a simple group of six,
thirty-secondth notes with a feathered beam:
r64 { c32[ d e f g a] } | b1
This fails the bar check because our six notes are not long enough to
fill out the measure. We fix this by first noting the original
sequence is 63 * 64th notes long. We are using 6 * 32nd notes, which
is equivalent to 12 * 64th notes. Scaling by the fraction 63/12 will
get us to our desired goal. You can confirm this by noting the bar
check in the following passes:
r64 { c32*63/12[ d e f g a] } | b1
Now that we have the correct total duration, we can add in
feathering. Consider the following to confirm that we have indeed
achieved what we wanted:
<< { r64 \featherDurations #(ly:make-moment 2/1)
{ c32*63/12[ d e f g a] } | b1 }
{ r64 { c64 d32 e16 f8 g4 a2 } | b1 } >>
In this case, we used the moment of 2/1 because we wanted each note to
be twice the length of its preceding note, which is what our
manually-written ritardando did. If you change the moment to some
other fraction, you can see how it ultimately affects the individual
timing of the notes within the sequence by comparing it to the
original sequence.
At the end of the day, there is no real need to use any math for the
\featherDurations moment. Any positive rational less than one will
produce an accelerando, while fractions greater than one generate a
ritardando. The best thing to do is to listen to the MIDI output and
determine if it sounds right to your ear.
I said earlier we would talk about bar checks *within* the feathered
sequence of notes. Consider the following addition to our example:
<< { r64 \featherDurations #(ly:make-moment 2/1)
{ c32*127/14[ d e f g a | b] } }
{ r64 \featherDurations #(ly:make-moment 2/1)
{ c32*63/12[ d e f g a] } | b1 }
{ r64 { c64 d32 e16 f8 g4 a2 } | b1 } >>
You'll see that the 'b' is included within the beamed notes. Because
we now have seven notes covering the period of two measures less one
64th, we had to adjust our scaling fraction to 127/14. However, what
is most important is that \featherDurations fixes the timing of the
notes to allow the inside bar check to pass. Omit it, and you'll see
that the bar check fails. But also try changing the 2/1 moment to
anything else, and the bar check will also fail.
What we have here is a very fragile element in the score that can be
easily avoided by never requiring any note (apart from the first)
within a feathered sequence to align to anything else. The final 'b'
above should properly be outside the feathered sequence (or possibly
start a new sequence of its own). In this way, the math to ensure all
of the sequences have the right lengths can be done completely
independent of \featherDurations.
Hopefully some of this will be helpful.
-- Aaron Hill
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Aaron,
Thank you for such an incredibly educational and useful post! I
appreciate the time you took to do all that for us!
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