https://www.ethanhein.com/wp/2024/the-bottom-number-in-time-signatures-has-always-confused-me/#more-29476
Explaining time signatures is hardly easy and why the bottom number is what it is is does seem stranger than the top number. If you have a measure of 7/4 then you can say there are 7 beats and that they are quarter notes. That's simple, but Ethan Hein points out that no one easily explains why that bottom number is what it is. I could say that the bottom number indicates, often, the foundational metrical unit that establishes pulse but the reason that becomes circular quickly is because there are so many ways to notate musical passages it's not a given that notation itself tells you what meter you're in.
Explaining time signatures is hardly easy and why the bottom number is what it is is does seem stranger than the top number. If you have a measure of 7/4 then you can say there are 7 beats and that they are quarter notes. That's simple, but Ethan Hein points out that no one easily explains why that bottom number is what it is. I could say that the bottom number indicates, often, the foundational metrical unit that establishes pulse but the reason that becomes circular quickly is because there are so many ways to notate musical passages it's not a given that notation itself tells you what meter you're in.
Danuta Mirka, in her book Metric Manipulations In Haydn and Mozart : Chamber Music For Strings, 1787-1791, points out that in the 18th century composers would stick with the established meter no matter how many times or in what ways they actually changed meters in a written work. In other words, you cannot assume that a composer won't shift out of 4/4 into 5/8 or 6/8 or 3/4 or even potentially 11/16 and 13/16 in a work just because they stay resolutely in 4/4 on the written page. Thanks to accent marks and other articulations, as well as notational conventions, it was possible to create metrical changes in a work despite never changing the written meter. Music in the 18th century was resolutely monometric in notation even though metrical changes and outright changes of meter happened in practice. I'm still early into the book enough I can't share examples cited beyond the fact that she works with two of the biggest usual suspects in the history of music theory, Haydn and Mozart.
I had to go with a Theodore Front link because the Oxford University Press link kept having issues
https://global.oup.com/academic/product/metric-manipulations-in-haydn-and-mozart-9780195384925
Speaking from personal experience the other thing about notating meter is that not all composers feel it's worth it to notate something in, say, 11/4. Shostakovich didn't always write out grooves in 5/4 or when he could switch back and forth between 2/4 and 3/4 as he does in the third movement of his Third String Quartet.
Or you could have a passage where a cello barrels along in 2/4 while other strings in Bartok's String Quartet No. 4 shift into 3/4 before the music moves from meters like 2/4 and 3/4 (at the same time) to 5/8. This part of Bartok's Third String Quartet has a killer pizzicato cello solo.
But you can see, if you read along with Bartok's score, he'll have whiplash meter shifts between 3/8 and 2/4. My memory may be fuzzy here but I vaguely recall the composer Paul Creston, in his book Principles of Rhythm, complained that there were huge spans of music in Bartok's string quartets where he could have notated things in 4/4 and used judicious accent marks rather than endlessly changing meters in every stave for every instrument. Good luck finding a copy of the Creston! If I hadn't read it decades ago I couldn't even just allude to it now. Creston's point stands, there are all kinds of ways you can notate a single passage and some composers go for the hard bordering on inscrutable way to write out a score and others stay four-on-the-floor in their scores even if they introduce meter changes.
That the bottom number in a meter conveyed tempo information would generally true right up to about the 20th century but from probably 1930 onward all bets are off. For instance, take 3/2. I know from my experience in choral singing, the Alice Parker arrangement of "Hark! I hear the harps eternal", which is scored in 3/2 but does not feel all that slow, at least for a choral work. You can see the score in the link below.
The arrangement has a light, airy element to it yet it doesn't sound slow, and it sure doesn't feel slow if you try singing it.
Parker packs in contrapuntally dense call and response passages just barely over a minute into an already short arrangement. There's such a thing as going with the larger numeric value (the half note) because you don't want to scare your sight-reading singers to death with needlessly small note values. And if you want the music performed with swing (whether or not that happens varies from ensemble to ensemble and conductor to conductor and Parker's arrangement withstands either approach because she's that great a choral arranger), then going with the larger note value lets you gauge how much you want (or even can) swing in the arrangement depending on the exigences of how good your singers are.
For 5/8, I know he's hardly beloved even among fans of classical music but one of the more memorable entries in 5/8 I've heard is the Fuga in G from Paul Hindemith's Ludus Tonalis.
But don't think he was the first or only composer to write a 5/8 fugue because Anton Reicha's Op. 36, No. 20 Fugue in A major predates Hindemith by more than a century.
Reicha's fugues were so weird Beethoven reportedly said "the fugue is no longer a fugue". Reicha also advocated the use of quarter-tones to embellish melodies in his Treatise on Melody in 1814
For 11/8 I recommend a few pieces by contemporary Bulgarian guitarist composer Atanas Ourkouzounov, who has a Youtube channel that features his music, in some cases with read-along scores. So if you want 11/8 here's a Chaconne.
hear also ...
hear also Asymmetrical Improvisations where the first movement is in 11/8 and the second is in 7/8
But the thing about 11 anything is you could also go 4+3+4 over 8 or 3+3+3+2 over 8 or you could notate it as 4/4 and 3/4 and 4/4 or three measures of 3/4 followed by a measure of 2/4. Because asymmetrical meters break down into smaller units (i.e. Brubeck going 2+2+2+3 within 9/8) some composers just don't use the less conventional meters when they can (they hope) inspire players to play their music by staying with simpler meters for the sake of reading. It's possible to cram 3/8, 6/8, 5/8, 13/16 and 11/16 into a work that's officially 4/4 for most of its run.
It's that reality, and examples I have semi-randomly grabbed from the classical repertoire that I think helps explain why the bottom number in a meter can seem so ambiguous. Maybe back in the day when people used the concept of tactus it was possible to talk about a stable undergirding rhythm without attempting to use notated music to confine performers to what we call measure but the horse left the barn a long time ago on that front.
3 comments:
Thanks for the thoughtful response as always, many of these examples are new to me!
I guess anything in 4/4 could be changed to 4/2 and it would use less ink!
It has always felt wrong to me that the shorter a note is, the more ink or black pixels are needed to represent it.
Ethan, glad to be able to share examples that are new to you.
Eric, I have never had a reason to go beyond 32nd notes. I can't help but think people came up with the idea of tempo changes because at some point a person asked why anyone was even using a sixty-fourth note.
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