Re: [proposal] easy triplets and tuplets - Draft 3

[David Kastrup]

Francisco Vila <address@hidden> writes:

> 2012/10/9 David Kastrup <address@hidden>:
>> Francisco Vila <address@hidden> writes:
>>
>>> 2012/10/9 Keith OHara <address@hidden>:
>>>> Currently, everyone who thinks of a triplet as a 3:2 ratio, 3 notes in the
>>>> usual time for 2, suffers similar confusion when trying to remember \times
>>>> 2/3.  Triplets are usually written with a simple 3, but 4-note-tuplets are
>>>> often designated 4:3 for clarity, while LilyPond requires the reversed
>>>> fraction in \times 3/4 {}
>>>
>>> Here come Spanish students again.
>>> I can think in \times <fraction> {} as a mathematical expression and
>>> it has sense, because "times" means multiply,
>>
>> How does a mathematician explain the difference between \times 2/3 and
>> \times 4/6 ?
>
> There is no difference BUT tuplets have a printed number, and in
> lilypond this number is taken from the denominator for your
> convenience.
>
> When I learned how to read music, triplets were taught to me as
> "always shrinking" groups and you see a "3" but there is an implicit
> "2" so we have 3:2. Only the numerator is printed by convention.
>
> Thus, if you write
>
>   \times 2/3 { b16 b b b b b }
>
> or
>
>   \times 4/6 { b8 b b }
>
> this is mathematically perfect but the number you are asking to be
> printed is a confusing "3" and a confusing "6" respectively.

The concept used for printing/grouping tuplets is different than the
concept used for scaling the time.  That's what makes \times such a
confusing interface.

The pure scaling alone is available as \scaleDurations.  I have no beef
with it using 2/3 as input, and I would have trouble coming up with a
justification of using 3/2 here, actually seeing little point in doing
so.  One could use something like \compressMusic 3/2 but I don't see
much of a motivation for that.

But with tuplets, the concept is not really "scale duration by x" but
rather "n to m notes" including all the necessary visual changes, and
\times, including its argument style, expresses this concept poorly.

I don't really think that people consider \times and \scaleDurations as
closely related (and their naming choice is also totally different), so
I don't think that there will be much of an opportunity confusing the
behavior of \scaleDurations with \tuplet.

-- 
David Kastrup