Opinions on tuplet number formatting defaults?

[Trevor Bača]

Hi,

There are some rules about the interpretation of tuplet numbers that
Lily doesn't seem to know about yet.

Consider how players interpret these lone numbers inside a tuplet bracket:

3 interprets as 3:2

5 interprets as 5:4
6 interprets as 6:4
7 interprets as 7:4 (though there was confusion about the one in the
50s and 60s)

9 interprets as 9:8
10 interprets as 10:8
11 interprets as 11:8
12 interprets as 12:8
13 interprets as 13:8
14 interprets as 14:8
15 interprets as 15:8 (and likewise some confusion about this one)

17 interprets as 17:16
etc.

The general rule is that a lone number n in brackets interprets as an
abbreviation for the ratio n:d, with d equal to "the greatest integer
power of 2 less than n".

(The confusion in the 50s and 60s about 7 and 15 possibly standing for
7:8 and 15:16 instead of 7:4 and 15:8 shows that there was, for a
couple of decades, a competing rule on the interpretation of lone
tuplet numbers. The competing rule was something like "n interprets as
n:d, with d equal to "the integer power of 2 *closest to* n". This
eventually got scrapped because the "closest to" version of the rule
has real problems with the interpretation of 6 -- should it stand for
6:4 or 6:8 given that 6 is equally close to both 4 and 8?)

All sorts of other ratios as possible -- like 3:4 or 3:5 -- but if d
is not an integer power of 2, then the ratio needs to be fully written
out as n:d rather than simply abbreviating as n.

So what does this mean for Lily's tuplet numbers? It means that Lily
might ought to format "nonbinary" tuplets (to coin a kinda ugly term
... meaning those tuplets in which d is not an integer power of 2)  by
default as fractions instead of lone numbers. For example:

 \times 5/3 { c'8 c'8 c'8 }

should by default render as 5:3. In today's Lily, that tuplet number
renders simply as 5, which is incorrect because players will interpret
a lone 5 as abbreviating 5:4, as in the table above.

Anyone else see the sense in changing Lily's default formatting of
TupletNumber text? Or much ado about nothing?

(The point hardly matters for music of the common practice since the
common practice tuplets are almost always triplets. Primary benefit
would be for contemporary music.)

[One arcane sidenote: in music of the common practice written in
ternary meter, the interpretation of lone tuplet numbers changes. In
6/8 time, for example, four eighth notes bracketted together under a
lone "4" will interpret as 4:3. But the point almost never arises in
contemporary music. Anything with lot of 7:5 flying around is probably
not going to be interpreted as being in "ternary meter".]


--
Trevor Bača
address@hidden