Sunday, March 20, 2022

Slicing Pi

It's highly likely I'm the only one who's been bothered by this, but my 3/14 post stretching a familiar 3/4 minuet into 3.14/4 time has stayed on my mind since the notation system I devised was a bit sneaky. I knew each 3/4 bar needed 0.14 extra beats, and I found a way within Lilypond to multiply note values in a way that achieved that (at least for playback purposes). But I cheated with the time signature. I just made my own time signature sign that showed a 3.14 over a 4 and then used Lilypond's "cadenza" function, which allows the user to place barlines wherever one wants. Essentially, this means the internal calculations act as if there is no time signature, so as long as the various parts line up rhythmically, the musical output will sound right, even though the barlines aren't generated by time signature calculations.

During idle moments this week, I tried to imagine a way to create a time signature which is precisely three beats plus 0.14 beats long. At some point, the old use of 22/7 as a fraction which approximates Pi came to mind, and that helped me to think about this a different way. After flirting a little with the idea of an irrational time signature like....well, 22/7, I realized that what I really need to do was add a single septuplet note to the three quarter notes in each 3/4 bar. 

It's a curious and sometimes forgotten (by me, at least) fact that our names for note values are really just ways of dividing a whole note. So a quarter note means nothing more specific than that it is 1/4 the duration value of a whole note. I finally realized that dividing four quarter notes into septuplets means that it would take 28 septuplet notes to equal one whole note, so a septuplet value could also be called a 28th note.* One doesn't see a lot of 28th notes out in the wild, though curiously the name sounds a lot like a 128th note, which is a thing. (There are 32 128th notes in a quarter note.) But that's basically just a coincidence. 

For my initial "Minuet in Pi" video, I used a special notehead with a pi symbol inside to indicate values which need to be stretched. It's now clearer to me this symbol could be defined as meaning the basic note value is stretched by 1/7. (This is similar to how a dotted note value extends the duration by 1/2.) This makes the notation pretty simple, but that's because I invented a sign to smooth things out.

Anyway, I finally realized that using Lilypond's wonderfully logical design, I could create a composite time signature of 3/4 + 1/28. Since each quarter note beat contains seven 28th notes, the signature could also be written as 22/28, but that doesn't show the additive process as clearly. Of course, one could notate more or less the same thing using 22/16 time, but that wouldn't allow the use of quarter notes to show simple beat values. Using 28 as denominator allows the use of quarter notes more or less as they'd be used in 3/4 time except on the third beat which requires stretching. (I don't think there's a truly elegant way to handle the ties required for that stretched beat.)

Is this all a little more than you want to think about? That would be fair, but I have found this a good challenge to help me think more clearly about how time signatures work. The two videos below are thus more precise than what I posted last week, though also a little less elegant. The first one is probably a little more proper, though the second one is maybe a little easier to read as it preserves more of a 3/4 look. [UPDATE (3/21): See also important footnote version in 22/7 below!]

Minuet in 3/4 + 1/28 Time, version 1

Minuet in 3/4 + 1/28 Time, version 2

* If you're like me and have flirted occasionally with irrational time signatures (which basically have denominators that aren't multiples of 2), you might be tempted to think a time signature with 7 on the bottom is the way to use septuplets as a primary division; but remember that a 7 would just mean a whole note is divided into 7, so that would provide a pulse which would be notated as quarter note septuplet. This would not fix my problem of needing a nice way to show standard quarter note beats which look like the way this minuet is usually notated. I needed a septuplet division of the quarter note itself, which is how we end up with 4 x 7 = 28. 

In other words, although a 22/7 time signature would look cool, it would only work if the primary beats in each bar were indicated as whole notes like below. And, whaddya know? Having added this as a "day after" footnote, I now think this is my favorite way of notating this meter!

Minuet in 22/7 Time

Monday, March 14, 2022

Minuet in π

Somehow, I only realized mid-day that today is Pi Day (3/14). Soon after, I had the idea of a dance in 3.14/4 time, but not so much time to work on it. However, I didn't want to wait a year! So I did get something roughed out in time to post it here, unvarnished as it is.

If you're a clumsy dancer like me, you might find that 3.14 beats per measure is just what you need. That extra 0.14 beats give you time to think about what comes next. I invented a quick notational symbol in which the pi-noteheads indicate notes that are stretched out to extend the third beat of each bar by 0.14 beats. And that's all I have time to say today!

[Quick research confirms as I expected that others have had this kind of idea, although I like how easy it is to hear here.]

UPDATE (on boring ol' 3/15): If you'd like to hear this with the downbeat stretched, this was my first effort. However, I found that this sounds too much like simple downbeat emphasis since 0.14 of a beat is not very much. I ended up preferring the idea of 3/4 time with the 0.14 essentially added at the end, although a case could be made that I should only have lengthened the final 8th note of such bars rather than the final two 8th notes.

Sunday, February 27, 2022

Epiphany Fugue 8/8: The Lasst one

This post will be brief after a busy weekend, but I did meet my goal of writing eight new fugues for each Sunday of Epiphany. This is the last Sunday Alleluias are sung until Easter, so I had the tune Lasst uns erfreuen on my radar for a while as it is associated with multiple hymn texts ending in Alleluias. A few weeks back, I’d considered the Old 113th (known to Lutherans as O mensch, bewein) as a fugue subject, and it happens to begin with the same opening phrase as Lasst uns erfreuen. Thus, one could theoretically write a fugue which serves equally well for each tune, though I decided to allude to the latter’s Alleluias in the countersubject here.

(I also realized while working on a diminution of the subject that the opening phrase is the same as that of Simple Gifts minus its pickup notes.)

I wanted to end the series with a grand postlude style suitable for organ, so this achieves that, although it’s pretty short. I ran into that curious composer problem where I’d written a good bit of a fugue early in the week and tacked on a temporary ending. The temporary ending grew on me, I was short on time, so it became more or less the ending. (It's amazing how powerful repetition is as a means of making something sound 'right.')

Perhaps later I’ll come back and write more about this fugue set. One of the ongoing challenges was to deal with the tension of not wanting to write the same fugue every week while also wanting to develop some consistency of style. Among others things, I realized after a few weeks that I wanted to avoid always using the same opening formulas. This week, the fugue answer comes in at the Dominant (very normal), but in minor (not normal). The most common procedure would then be to have the next voice back in Tonic, but I have it enter in the Submediant (which is naturally in minor, meaning the two middle entries of this major key fugue are minor) so that the entry of the bass voice in tonic has a strong sense of arrival. Thus, the entries are in: D Major, A Minor, B Minor, D Major.

(25 total / 8 new in '22)

Thursday, February 24, 2022


What a boring blog post title! Today is indeed the fifteenth anniversary of MMmusing, but I haven't come up with a clever angle on this. I've realized that 15, though roundish, is actually a pretty uninteresting number. I thought of posting a list of Top 15 Posts or Top 15 Videos or whatever, but 15 seems like too many for a well-curated list. 

So, here's just a quick "State of the Blog" spiel. Let's see...2007 was a pretty long time ago, so I guess I've been doing this a while. The past year was relatively slow after a strong January/February start to 2021, but I've had another busy start to 2022 with seven (soon to be eight) new fugues, some syncopated loops, and some general rambling. The future is bright.

Though it still may not be totally clear why I keep doing this in fits and starts for a fairly small audience, I am grateful to have so many half-baked thoughts and unique proof-of-concept videos and webpages archived. It's been long enough and I'm now old enough that I can find posts I'd completely forgotten about. I think that's the main reason I do this. I walk (drive, sit) around a lot thinking about these sorts of things - might as well preserve those ephemeral thoughts in....whatever this is.

I was thinking this week about a competition that took place around 2011 or 2012 for "best classical music blog." Blogs were still a good bit more hip and relevant then, but I remember being struck by two things (for what admittedly was a pretty gimmicky contest). Because the judging was to be based on a series of writing challenges, 1) the competition was stuck with the idea that a blog is just like an informal version of writing for print (newspaper, magazines) and thus fundamentally about words, and 2) the competition was really only about a limited series of exercises, not the building of a unique, long-term brand. 

Meanwhile, I as I've said and emphasized way too many times but will say again, the attraction of a digital platform for me is not just the free, unedited publishing (though I enjoy not being edited as evidenced by parenthetical diversions like this), but rather the idea that writing about music can be seamlessly integrated with audio and other multimedia illustrations. I love to read and can even enjoy the imagination required to look at printed musical examples or read a description of some musical process. But here's an example of a video I'd forgotten about which makes several complex points quickly and efficiently; I'd rarely want to be stuck merely with words, even though I love words. I absolutely did not set out to create a multimedia-themed blog, but that's the shape things have taken, and I've done so many cool things I'd never have imagined without taking that first step.

I suppose one of the many reasons blogs have lost a lot of influence is that talking-head videos are now the preferred, more likely viral medium for this kind of work. Adam Neely gets millions of views for his very well-conceived and multimedia-rich videos. He's a very sharp thinker who zeroes in on topics really well, so I'm not suggesting I could match his abilities if I tried. I have thought of trying my hand at the talking head thing (though I hate hearing my own voice), but generally I still prefer the asynchronous experience which reading allows, with links and multimedia provided to let the reader explore as needed. Though this is clearly not the best way to get views, I'm content to continue documenting whatever I'm thinking about at the pace it naturally happens with good ol' old-fashioned Blogger as my home base.

As always, you're encouraged to try the Magical Multimedia Musing Machine to see where the winds take you. Hope to be back here next year when I can title the post: "I am sixteen, going on seventeen."

And, ok, after all of that, here is a quick list of fifteen - not necessarily the Top 15, but a post from every year featuring a fairly wide variety of things. Compositions, Arrangements, Mashups, Performances, Programming, Animations, Words, etc. I intentionally tried to avoid some of the things I've already promoted over and over. (Some of these, like the first five listed, involved a lot of work, so as lighthearted as the tone here generally is, I'm proud of the investment of time and problem-solving that goes into projects like these.)
  1. The Birth of Coulenc (2021)
  2. Chaconne at a glance (2020)
  3. Haydn a Surprise (2019)
  4. Barber: Guitar Concerto (2018)
  5. Alternative Facts (2017)
  6. Sundays at the Improv (2016)
  7. What it the great composers wrote the music for the closing credits of 80's TV shows, Part I (2015)
  8. The Luigi Rag (2014)
  9. Moonlight Mashup (2013)
  10. Ballade Blogging (2012)
  11. Atonality on Ice (2011)
  12. Reflections on a Two-Part Invention (2010)
  13. Name that bassoon (2009)
  14. Ambigramania (2008)
  15. Hyperspace (2007)

Wednesday, February 23, 2022

Parody Parade

This Sunday, my daughter's youth orchestra will be playing a big program which begins with Ravel's La valse. I've been thinking about my unusual affection for that piece, an orchestral showstopper which I love best as played by....pianist Glenn Gould. This preference is unusual both because this work is known for Ravel's brilliant, colorful orchestration and because Gould is decidedly not known for playing French or Impressionistic music in general. It strikes me that my attraction to his particular recording reveals several layers of distance from the origins of this music - and I like investigating such layers. 

Let's back up a little and note that pretty much ALL music gets part of its communicative and imaginative power by building on music that already exists. This is obvious enough, but ignored a lot as well. No waltz is an island, one might say.

So it is that one can trace many subterranean layers beneath Gould's version of Ravel's piano transcription of Ravel's own work originally conceived as ballet (the rejection of which almost led to a duel between Ravel and Diaghilev!*). I suppose one could go back to the earliest example of humans dancing, follow that trail to the evolution of formal dances like the waltz, then observe the way in which composers like Chopin and Strauss turned waltzes into concert pieces which inspired Ravel to write a nostalgic evocation of nineteenth-century ballroom waltzing. Ravel's work is thus a parody* of an older style, but the way in which Ravel and Gould re-imagine the colorful orchestral timbres in black-and-white piano context has elements of parody as well, even if not intended to be humorous. (Worth noting that, going back to the Renaissance, a parody just meant basing a work, like a mass, on a pre-existing work; doesn't have to be funny.)

I have always loved piano transcriptions, but will admit there's something a bit silly about having one piano re-create La valse. (There was a time when Ravel's two-piano version was the acknowledged best option, but the solo version seems to be becoming more popular as a vehicle for transcendent technique.) What I love about Gould's approach is that he seems to relish that absurdity. Rather than try to sound like a smoothly blended orchestra, Gould is happy for certain details to receive a new and unexpected spotlighting. This is most obvious at the very beginning where - speaking of subterranean! - Ravel has all sorts of primordial goings on submerged in the bass. (By the way, I only just noticed that the two pitches Ravel alternates, E and F, are the same two featured at the beginning of some famous below-the-surface music by John Williams.)

Whereas Ravel's opening is all muted, pianissimo rumblings, Gould sets his own tone right away.

It's comically different from Ravel's original, and the funny thing is that the piano can do this kind of blurry/submerged thing really well as demonstrated by plenty of other pianists. Gould, ever the iconoclast, seems to be clearing the air right from the outset with a mezzo-forte-plus Bartók sound. THIS IS A PIANO, NOT AN ORCHESTRA! So, although Gould's version does not fit the literal definition of a parody, it has that feeling, and yet I find it thrilling and colorful in its own way. Because it's all played by two hands (assuming Gould didn't do too much cheating in studio), it's more exhilarating listening for me than the almost-too-much orchestral original (though I'm very much looking forward to hearing the orchestra play it live in the great Symphony Hall).

The other thing that interests me here is that I'm not a big fan of the types of waltzes (Strauss, etc.) that Ravel is parodying, but I DO like his parody of them. I've found that dynamic at work in many contexts. For example, I love Fritz Kreisler's Praeludium and Allegro, which is an early 20th century parody of early 18th century style, and I find the Kreisler more compelling than a lot of music from the early 18th century. Kreisler here trades on a lot of the expressive devices of Baroque style while adding in a Romantic virtuoso mindset. The Vitali Chaconne is a similar sort of piece - probably not by Vitali! - though I find it a bit more tiresome than Kreisler's work. I could also happily go the rest of my days without ever again hearing Grieg's From Holberg's Time (in piano or orchestra dress), so I'm not always an easy mark for cross-century parody.

Another more modernist parody I enjoy is Stravinsky's Pulcinella, supposedly based on music by Pergolesi. Worth noting that just as Stravinsky adds dimension to these old tunes, their inspiration brings out something new in his own voice. I'm especially fond of the violin/piano Suite italienne drawn from this ballet, so again it's a transcription of a parody that hits the sweet spot. Maybe I am predictable?

My attitude about this is probably not the most mainstream, but my fascination with mashups and other distortions suggests how much I'm intrigued by off-center re-imaginings, whether of specific works (La valse) or general styles (Baroque). In this way, parodies (and mashups) are a kind of conversation. They are not just music - they are about music. (Which, again, is true of all music to some degree, but it's true in a special way with a parody.) I also have special affection for some of the Romanticized piano parts in the notorious 24 Italian Songs and Arias book, used by countless voice students, and I've always been disappointed by efforts to provide these 17th and 18th century songs with more authentic accompaniments. The piano-vocal versions that have come down to us are parodies of a sort (many by Parisotti), but none the weaker for that as they take advantage of sonorities natural to the piano. As with the works I've mentioned by Kreisler and Stravinsky, music from the past is viewed through the prism of intervening centuries, and that kind of mixing can be really rich and satisfying because there are so many layers.

Recently, I watched a video called "How Allegri's Miserere should really sound." You can watch the whole thing for yourself, but the basics are as follows: 1) Allegri's original work from the early 1600's is already meant as an homage to an older style, so it began life as a parody. 2) Various performance traditions evolved over centuries as the work acquired legendary status connected to its use in the Sistine Chapel and Mozart's supposed copying down of the work from memory. 3) Somewhere along the way, a part was mis-copied a fourth too high in a way that leads to a very memorable high C which, in my experience, is THE most famous thing about this music, but it's the creation of a much later nineteenth century point-of-view. When I hear mention of this piece, I immediately hear the part you may hear here (at 12:10). This is an unintentional parody, but though the video seems to want to say, "let's go back to Allegri's original vision," my temptation is to say that the distorted tradition is more interesting. (Of course, this kind of distortion happens in all sorts of contexts, and I'm not saying it's always a good thing.)

Popping over to another genre, I've never really felt any attachment to 60's folk music, but I simply adore just about all the music written for A Mighty Wind, which is just one affectionate parody after another. In that case it is partly the humorous aspect, but the creators and performers of those songs achieved something magical that transcends parody, and I'm forced to give some credit to a musical tradition which otherwise doesn't interest me. So the power of parody means there might be hope for...who knows what? In the meantime, my apologies for the parody in the footnote below.

* Perhaps worth mentioning as well that I love Ravel's dance even though I'm not such a big fan of dancing. Serge Diaghilev also seemed to agree that this dance music is better for listening than dancing, which I guess led to his almost dueling with Ravel. Unfortunately, I then found it impossible not to imagine this Diaghologue:

You should be able to click on it to enlarge, if you dare. For comparison, the original is here.