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Re: Beams not connecting

From: Hans Aberg
Subject: Re: Beams not connecting
Date: Sat, 13 Oct 2007 20:32:50 +0200

I asked about this issue in the Usenet newsgroup rec.music.theory, were particularly Steve Latham helped out. It turns out that there are more than one styles in play, and Finale even allows one to choose (the meter typesetting style 3_/8 defined below is called "in one").

In one style, one tries to bring out the metric accent as much as possible in the beaming; I indicate this here as k!, as in 3!/8. At the other extreme, one ignores the metric accents, which I write as k_, as in 3_/8 (mnemonic: a dash as an absence of indicated accents). Lilypond typesets an intermediate form, which I write here as k?. In addition, beaming is used to indicate musical relationships, such as slurs and phrases, and to otherwise bring out the rhythm (as in Hindemith, "Elementary Training", p. 78-82).

I will use brackets "[" and "]" to indicate beaming. So |[e8] [e8] [e8]| is a measure of three 1/8 notes with flags and no beams, and | [e8] [e8 e8]| means that the two last ones are beamed together. And | [[e16] [e16]] [[e16 e16] [e16 e16]]| means that the two first 1/16 notes have a single connecting beam with two flags, and the last four !/16 notes have a single beam, with an additional beam within the first and last pairs. This captures the beaming and subbeaming, except possibly the direction of lose flags in some cases.

So x = | e8. e16 e16 e16 |, is typeset as:
 (x1)  3!/8: | [e8. e16] [e16 e16] |
 (x2)  3?/8: | [[e8. e16] [e16 e16]] |
 (x3)  3_/8: | [e8. [e16 e16 e16]] |
One suggestion was that the form (x3) (which is what Issue 11 wanted) was used in CPP music typesetting for two reasons: the metric accents are always known (as CPP only admits a restricted set of meters), and it easier when drawing by hand to draw long beams than a series of broken ones or flags. So there is no reason to use form (x3), except for backwards compatibility with tradition: some are used to it, and it may therefore help reading. Steve felt that (x1) is the correct style, which is what Finale typesets if the "in one" switch is not set (and this "off", I think is the default).

Lilypond draws (x2) by default, it seems. Hindemith [loc.cit.] uses a similar beamings to bring out the rhythmic structure, so it seems me it isn't wrong, but should perhaps be used only when the user calls for it explicitly. This style could also be used with complex meters. Take for example 7/16, where 7 is decomposed as (2+1)+(2+2) (common Balkan meter), meaning primary accent on beat 1, subordinate accent on beat 4, and accents subordinate to that on beats 3, 6. Then one might typeset seven e16 as (if the user calls for it)
  | [[e16 e16] e16] [[e16 e16] [e16 e16]]|
(Actually, Hindemith's examples could also easily be typeset by the use of such matching braces "[" "]".)

Now, there some funny things happening:

Take the time reversed pattern y = | e16 e16 e16 e8. |. This gives the styles:
 (y1)  3!/8: | [e16 e16] [e16 e8.] |
 (y2)  3?/8: | [[e16 e16] [e16 e8.]] |
 (y3)  3_/8: | [[e16 e16 e16] e8.] |
Though this pattern is rare, even if one is using style 3_/8 ("in one"), it seems that one prefers the reversed form (y1), or even as
 (y4)        | [e16 e16] [e16] [e8.] |
(from Jørgen Jersild, "Lærebog i rytmelæsning", p. 21.)

So in the style 3_/8, one may depart from the unaccented pattern.

Also look at the PDF page 2 of:
In the first measure of the allegro (in 3_/8), the first 1/8 is drawn with separate flag, but in m. 5 and other places, they are all beamed together. The exception in m1. is perhaps due to it is a chord, or perhaps an emphasis of some sort. I am not sure this is a good example, but I think one might break up the unaccented beaming when it is so desired typographically or musically.

  Hans Åberg

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