Triangulated Counterpoint

As I started working on adding a third voice to facilitate the contrapuntal combination of two different national anthems (see previous two posts), I had an emerging sense/memory that I had done something like this before. I could just almost see three staves in which a newly written bass line interacts with two distinct melodies, and I could feel the sense of satisfaction in having completed an unlikely trio. I even remembered writing a blog post about this process as a kind of compositional triangulation. I searched my blog and came up with...nothing. 

Finally, after a day of being taunted by this déjà vu, I shut the radio off while driving, did a deep memory search, started to have a vague idea that it had to do with writing for church, and at last the story below came back to me.  I had indeed started a blog post, but never finished it and thus never published it. Here's what I had so far:

As my interest in various kinds of mashups has grown, I'm drawn again and again to the idea that mashups are a kind of counterpoint  -  or, seen from a different vantage point, counterpoint is a kind of mashup. (Yeah, yeah, this could extend to saying all music is a mashup, but that's less interesting.) Mashups and contrapuntal works both draw on the kind of stimulation/pleasure the brain gets from following multiple musical strands simultaneously. Of course, coordination (of a beat, of harmonies, of voice-leading, etc.) certainly plays a role in making mashups and counterpoint effective, and this raises an interesting question. For any two given musical works, is there always some kind of coordination that can be applied to make them function effectively together? My best guess is: yeah, probably, though I'm not in a hurry to fuse together "The Hoedown Throwdown" with a Telemann flute sonata. (I really don't like Telemann.)

But an interesting sub-set of that question might be this: for two works which fit together in terms of time-scale, is there some third-party musical work (pre-existing or not) which can serve to bring the first two together in a more satisfying way than if they're simply heard mashing against each other? The idea is that the third party music sort of triangulates between the features of the first two musics, accentuating where they already work well against each other and building bridges in places where the differences (or similarities) are ineffective.

OK, I didn't just come up with this question out of the blue. It arose when I was preparing music for the church's children's choir to sing on All Saints Day (Nov. 1). We'd already decided that they'd sing the delightful, slightly batty* "I sing a song of the saints of God," (hear here) although some of the children didn't seem that enthusiastic since they'd also sung it the year before under a different music director. It's a great little choir, and though the age-span of the children and our limited rehearsal time mean things can't get too complex, I thought it would make things more interesting to add a descant. So I began experimenting. For some reason that I don't remember (the muse is amusing that way), the tune of "Jesus loves me" came to mind and I had the idea that it might kind of fit with the Grand Isle tune we'd be singing. ("Jesus loves me" probably has a privileged place in my mashup memory bank because of the beautiful way it's used by Ives in his 4th violin sonata.)

Like thousands of other hymn tunes, each has a 4-4-4-4 phrase structure in common time, so it was just matter of what happens when they go together....

To pick up from that unfinished post, here's what happens when they are paired with my then-newly composed bass line:

They go together remarkably well for two tunes that have nothing to do with each other. From a contrapuntal perspective, the most vexing problem is a few instances of parallel unisons (m.11, m.13-14, and, going into the final cadence), though only the last one really bothers me. (There are also parallel octaves between tune #2 and my bass line going into m.7 and probably several other sins, but Jesus still loves me. I actually like the parallel 5ths heading into m.4.) In the Glenn Gould national anthem mashup I mentioned a couple of posts back, he also complains about how his little discovery is partly spoiled by concluding parallel octaves. Nonetheless, I feel like I successfully completed the triangle.

As it happened, we didn't have time to have the children split into two parts, but for the final verse of the hymn (after I'd dazzled everyone with my musical depiction of "a fierce, wild beast" in verse 2), I had a flutist play "Jesus loves me" above this new harmonization, and the effect was lovely. Hopefully it will return for All Saints Day this year, and I'll try to get a live field recording.

I've heard it said that any given artwork is, in some respects, a discovery of a work that already exists in some kind of infinite web of theoretical works. I'm not sure how useful such an idea is broadly speaking, but in the case of the "composition" above, it feels close to being true. It's not at all difficult to imagine someone else coming up with the same basic idea, though the mediating bass line would likely be different in some ways - but maybe not that different. I've definitely had enough experience now with various kinds of mashing things together to be not so surprised when surprising intersections appear.

For example, it's surprising that a person I don't know on Twitter, whose timeline I only saw because he'd tweeted out a perversely hysterical video (no longer available, alas) of an Olympic swimming announcer miscalling a race, led me to the same Twitterer's suggestion about playing national anthems simultaneously in the case of a tie, which led to me bringing the U.S. and Canada together, which led to me remembering to finish a blog post I'd forgotten about from almost a year ago. Perhaps if I go check my Twitter feed now, I'll end up writing Beethoven's thirteenth symphony...

See also: My Jesus, Joy of Man's Desiring

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* I don't necessarily mean "slightly batty" as a bad thing. One of MY FAVORITE PIECES OF MUSIC EVER is Britten's "Rejoice in the Lamb," a setting of words by Christopher Smart that leave the slightly part of "slightly batty" way behind.

Rhythmic Mediation at the Border

After I posted yesterday's musing about putting the American and Canadian anthems together (in spite of one being in triple meter and the other duple), a Facebook friend (thanks, Paul!) asked about the possibility of putting both tunes in 6 and using tied dotted notes to keep the original rhythmic values intact, while also aligning the barlines. That seemed like a lot of trouble until I remembered that Lilypond, the quirky but powerful notation software I prefer, makes it incredibly easy (assuming you've gotten used to Lilypond) to notate polymetric music. I'd never had a chance to try this out, so this was the perfect opportunity.

Essentially, this makes it possible to combine the tunes in the most basic (but also complex!) way, with the phrases lining up perfectly. All the downbeats arrive together, but within each measure the beats clash, sometimes as simple cross-accents and sometimes as if the two parts have nothing to do with each other. Because The Star-Spangled Banner is a bit longer in terms of phrases, I decided to expand the final phrase of O Canada to make the ends meet, but otherwise this is less composition than simple overlay.

When I first listened to the output, it sounded pretty hopelessly garbled, even with very different instrumental colors assigned to the separate voices:

Then it occurred to me that I could soften the effect by using the gentle, more pointillistic sounds of plucked guitars. The result is less jarring, though still pretty disorganized:



In the previous post, I proposed the idea of a third contrapuntal voice as a kind of mediator, but as the big problem here is a rhythmic one, I decided to toss a drum kit loop into the mix instead. It turns out that rhythmic mediation makes a big difference, even if it mainly just serves to affirm where the downbeats are. For me at least, what had seemed relatively random sounding now had acquired a cool veneer that makes the points of rhythmic contention come across more as intricate detail than mindless mashup.



Your mileage may vary, of course, but as "found composition," I think this is pretty charming. It allows, as good counterpoint and good mashups do, the opportunity for one's musical perception to enjoy multiple points-of-view at once.

I still have a more successful example of combining two independent melodies to share, but that will have to wait until tomorrow. Stay tuned!

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See also:

• Brahms Mixed Meter Mashup, blogged about here
• Playlist of "Border Anthems" here.

Border Counterpoint

The Summer Olympics are in full swing now, and though they continue NOT to offer medals in piano (what is a Ligeti étude if not a type of rhythmic gymnastics?), there have been some musical concerns raised. First, the New York Times had a hard-hitting piece on the unusually mellow harmonization of the U.S. national anthem being used at the medal ceremonies. (It's also just bad. Hear at 3:15 here.) Then, not long after swimmers from the U.S. and Canada tied in the women's 100 meter freestyle swimming event, a Twitterer proposed the following solution to a real problem:

For a gold medal tie they should play BOTH national anthems simultaneously at the podium #Rio2016

— Bryan (@NachoHelmet) August 12, 2016

Well, of course, I love mashing things up, so NachoHelmet's idea proved too tempting to resist. Although I could have just put two existing performances together and let them fight it out (which I'm sure could've been satisfying), I decided to try to "compose" something. The most fundamental problems are that 1) the U.S. tune is in triple meter while Canada's is in duple, 2) the phrase structures don't really match up at all, and 3) I'm pretty lazy.

Although there are surely more sophisticated ways to bend the tunes towards each other, I first decided it would be fun to see what happens if each is simply allowed to go its own way. I "discovered" that by 1) starting the tunes together, 2) simply adding one extra beat after the very first "O, Canada," and 3) leaving out the first of the two concluding "O Canada we stand on guard for thee" phrases, the tunes could end at the same time and kind of amble along without hurting each other too much. (They don't clash too badly.) The unsynced meters make them seem quite independent so that it's not that easy to follow both at once, but I like that kind of funhouse effect.



The trick is to find/create a third part which can, in theory, bring the two melodies together. However, I didn't spend much time creating the bass line above, and it shows. I described this "walking bass" on  Facebook as "more like a drunk guy trying to play Pokemon Go with a 1990s flip-phone, a broken compass, and combat boots." As mediator, with those two melodies each going their separate ways, the bass sounds like it's purposelessly going back and forth from one to the other, trying to create accord, but mostly just going in circles. A true diplomat!

The other basic option for composing these tunes together is to align their phrases more naturally by changing one of the meters. In this case I showed my national bias, leaving my country alone and stretching the Canadian anthem into a lazy triple meter by doubling the length of the stressed beats.*  This meant I didn't have room for the whole tune, so it cuts from the middle to the end abruptly, but it works for this stars and stripes guy. The mediator in this case, working alongside two tunes that are at least trying to play nice, has a much stronger sense of direction, although an attempt to hide some consecutive 2nds from m.13 into m.14 resulted in an odd bit of harmonic disturbance.



I'm sure the voice-leading could be better, but I wasn't aiming for perfection. Just exploration.

I do have a better example of this kind of mashup counterpoint which I'm saving for later this week (teaser!), but I'll close here with a video I just found while looking for piano versions of The Star-Spangled Banner. I was going to do a little footnote bit about how gold-medal winning pianists could play their own national anthems when I ran across this remarkable studio audio in which the great Canadian pianist Glenn Gould boasts of having discovered a way to blend two anthems - not including his own! What I love about this is his sense not so much of having composed something, but rather having discovered a secret link:



If I only I had Gould here to help me now...

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* Alternatively, I could've stretched The Star-Spangled Banner into a duple meter as Renee Fleming does here - but I really didn't like that performance. She lost me at "hailed."

Chopin in 7/8

Some day I need to write about the curious, sometimes uneven, but very impressive and increasingly essential Boston Musical Intelligencer, a locally based site which provides exponentially more reviews of area concerts than the Boston Globe ever did (at least in my 20+ years in Boston), even before the Globe started cutting arts coverage in the recent past.

But today, I'd just like to respond, in typical MMmusing fashion, to a line from a review of a young pianist who finished an impressive recital with the Chopin B Minor Sonata. The reviewer, David Moran, concludes by saying:

To my ear it all felt 7/8-baked, the last finishing touches not yet settled. And again his hands and fingers were not perfectly clean or always together in attacks and at measure starts. The effect was slightly hesitant, at best probing, but at worst causing small starts and fits—noty, almost static, unurgent. That said, I admired it more than enjoyed it, and it was so unusual I would like to study a recording.

The review appeared last week, but when I just read it, I couldn't resist commenting:

It took me a second reading to realize that "7/8-baked" referred not to an irregular meter but something only 87.5% realized. Before that realization, I enjoyed imagining Chopin's 6/8 finale limping along in 7/8 time, especially as the performance was also described as "slightly hesitant" with "small fits and starts." Perhaps a mashup of this finale and the finale to Prokofiev's 7th sonata?

And then, I couldn't resist tinkering around with the limited notation tools I have on my vacation laptop to see what this might sound like. Here is Chopin's "version":



And here's a taste of what might have been if Chopin hadn't been so conventional (forgive the horribly tinny "piano" sound):

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See also:

• Chopin's 'Minute' Waltz in a Minute
• Chopin's Funeral March (with ghosts!)
• Sleigh Ride in 7/8 Time

Happy Augmented Sixth Day! (2016 ed.)

It's been awhile on the blog, but I couldn't let Augmented Sixth Day pass without a post. (OK, I did let it pass the last three years without a post, but here's the inaugural celebratory Aug 6th Day post from Aug 6th, 2012.) However, I don't have much time as we're also leaving soon this morning for the last weekend of concerts at the magical Greenwood Music Camp, where our oldest daughter has spent her last five summers walking around barefoot and playing chamber music. Tonight she'll play movements from quartets by Beethoven, Dvořák, and Debussy, but in typical Greenwood fashion, each of the two marathon chamber music concerts will end with Mendelssohn, the greatest youthful composer ever. The last piece on the second program, which will happen around 11pm, will be the first movement of Mendelssohn's Octet (written when the composer was 16!), which may be my very favorite thing ever, even if Daughter of MMmusing won't be playing that. (She gets to go next-to-last, though, leading this bit of transcendent middle-period Beethoven.)

Anyway, as I was trying to think of a favorite augmented sixth chord to feature, I suddenly remembered some magical Mendelssohn this same daughter's young string orchestra performed six years ago. I wrote about that music in this blog post, trying to explain all the reasons why a low-quality recording of kids too young to know better is THE definitive recording of the slow movement of this particular string symphony Mendelssohn wrote when he was 12(!).



I mentioned briefly in that post that THE most magical moment in this movement occurs in the transition to the recap. The music has meandered from C Major into the relatively distant key of A-flat Major and in a classic "treading water" motion, the second violins and viola are slowly arpeggiating in A-flat as if lost and wondering where to go. In the third measure below, the harmony changes to C Minor* over the same A-flat in the bass (creating an achingly lovely major seventh sonority) and then the G changes in bar 4 to an F-sharp, so that we have the classic augmented sixth interval between the bass (A-flat) and F-sharp, and in classic augmented sixth fashion, this German Sixth chord resolves outwardly by half-steps, with the A-flat heading down to G and the F-sharp leading up to G. G is the dominant in C Major, and suddenly we're back in C Major with the opening theme back in the right key, although beautifully poised above the expectant dominant G in bass rather than tonic C. It is all SO much more sublime than I've just made it sound.

[The audio excerpt begins about 5 seconds before the score excerpt above.]

And there you have it. I'd love to say more, but I've gotta pack the car!

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* This is really better understood not as a C Minor harmony, but as the A-flat in the second violins descending down chromatically to a G in bar 3 above and then to the magical F-sharp.