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## Re: hang --"going backwards in time; " "insane spring distance requested

 From: Trevor Bača Subject: Re: hang --"going backwards in time; " "insane spring distance requested" Date: Tue, 27 Nov 2007 10:33:59 -0600

On Nov 27, 2007 7:31 AM, Ed Ardzinski <address@hidden> wrote:

I did some playing last night and was surprised that you can have any denominator for a time signature, so my initial idea is wrong...not that I really understand what 5/9 time would really mean, but obviously LP interprets it.

OT but entertaining:

:-)

5/9 means a measure of 5 "ninth" notes, just as 5/8 means a measure of 5 "eighth" notes.

What is a ninth note?

A ninth note is a note that lasts exactly 1/9 of a whole note (just as an eighth note is a note that lasts exactly 1/8 of a whole note).

So in the figure ...

\times 8/9 { c'8 c'8 c'8 c'8 c'8 c'8 c'8 c'8 c'8 }

... each of the notes carry the (effective) duration of 1/9 of a whole note ... which makes each of the nine notes above "ninth" notes.

Now, an absolutely *remarkable* aspect of Lily's duration-handling is that the following constructions are all valid:

\times 8/9 { c'8 }  % a single "ninth" note
\times 8/9 { c'8 c'8 }  % a pair of ninth notes
\times 8/9 { c'8 c'8 c'8 } % three of them
\times 8/9 { c'8 c'8 c'8 c'8 } % four
\times 8/9 { c'8 c'8 c'8 c'8 c'8 } % five ninth notes

(Try it; this is one of the things that modern(ist) compers discover about Lily that works "out of the box" that absolutely amazes us; try doing this with Finale and Sibelius ... and then trying doing this with these things crossing *over* barlines ...)

So the meter 5/9 then stands for a measure of exactly five ninth notes:

\new Staff {
\time 5/9
\times 8/9 { c'8 [ c'8 c'8 c'8 c'8 ] }
|
\time 5/8
c'8 [ c'8 c'8 c'8 c'8 ]
}

(Notice that the bar check passes just fine showing that Lily's duration math is all caught up at the end of the first measure.)

Opinions differ as to whether the tuplet should draw over such figures; there seems, in general, to be a preference against drawing the tuplet:

\new Staff {
\time 5/9
\once \override TupletNumber #'transparent = ##t
\times 8/9 { c'8 [ c'8 c'8 c'8 c'8 ] }
|
\time 5/8
c'8 [ c'8 c'8 c'8 c'8 ]
}

So there's that

There's a separate question as to the use or desirability or whatever of these types of figure. As with most rhythmic innovations, folks seem to react violently at first and then get used to them. Maybe it helps to see such figures as exact tempo changes lasting for a single measure; or, alternately, as "broken" tuplets where only the first 5 out of 9 nontuplets appear, for example.

(What frustrates me is that there's appearantly no *name* for the class of time signatures of the form m/n where n is *not* an integer power of 2. In my notes I frequently call these things "nonbinary" meters ... which seems somehow unfortunate. If anybody has a good name for these meters, I would love to steal.)

--
Trevor Bača