Jean-Pierre Coulon wrote

> Is anybody aware of an engraving rule about horizontal spacing of
> notes according to their value (whole note, half note, etc.) ?

I didn't do a lot of study before deciding how PMX would do this, but the
two rules for space-vs-time I noticed most were square-root and logarithmic,
both of which give spacing that increases more slowly than linearly.  PMX
uses s = (const)*sqrt(t) as a basic rule.  However, if a system gets really
crowded, PMX will switch to a more complicated rule.  The rule kicks in when
the smallest inter-note space hits a lower bound (whose value can be
adjusted by the user).  The modified rule holds the smallest space at this
lower bound value and "flattens" the space-time relation so that as more
notes are squeezed in, the largest spaces get smaller but the smallest one
stays the same.  Of course this can only go on until all spaces have become
equal and hit the lower bound; then to add more notes you've either got to
reduce the minimum space or let it spill over.

There is another wrinkle in horizontal spacing in PMX that many people may
not have noticed; no one has ever commented on it. Suppose on two staves you
have

c44 c /
cd44 c8 /

These notes divide the bar into three spaces, with durations 1/4, 1/8, 1/8.
I think it looks better to make the middle space smaller than if it were an
1/8 note.  So I decided to base the size on the shortest SOUNDING note.
Except for the constant, the first space would be sqrt(1/4) and the last one
sqrt(1/8).  For the middle gap of 1/8, the shortest sounding note is 1/4, so
the gap is [sqrt(1/4)]*(1/8)/(1/4) which is a little smaller than sqrt(1/8).
I did this because it was the way I interpreted some of Werner's comments on
the subject.  I'm still not sure if this is what he meant, but I do like the
shorter spaces in these cases.

--Don Simons

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