Tau Day 2020

Happy Tau Day! What's this? Me remembering two interesting dates in a row? I'm as confused as you are! I guess it helps that both fell on weekends this year so I was less busy.

I've mentioned tau a few times before, but as a reminder, \(\tau=2\pi\). It's the ratio of a circle's circumference to its radius, and makes much more sense as the true circle constant rather than \(\pi\). I was reminded recently how much more sense when my mother asked for some help with some trigonometry problems (she's been teaching herself trig lately) and it was so confusing trying to think about the various unintuitive ½\(\pi\)'s and ¾\(\pi\)'s scattered about. With \(\tau\), a fractional value of \(\tau\) corresponds directly to a fraction of the way around a circle, which is so much simpler to remember. I think \(\tau\) makes more sense than \(\pi\) from a purely mathematical perspective, but the practical benefits to teaching and using trigonometry (and higher math that uses it) would be compelling all on their own—after all, we switched from Roman numerals to Arabic numerals primarily because the latter were easier to use and reason about; why shouldn't we do the same with other values? A hui hou!

Happy [Winter/Summer] Solstice!

Happy [winter/summer] solstice, [southern/northern] hemisphere readers! As an astronomer I always feel like I should comment on these astronomically significant dates, and then I always end up forgetting or being too busy to write anything. This year, at least, it falls on a weekend and since I've been working from home I've been even more aware than usual of the lengthening nights the past few months. It's actually rather relieving to finally reach the solstice, to know that this is as dark as it gets, and the days will begin to lengthen again after today (even if it won't really be noticeable for a few weeks, and the actual coldest part of winter is yet to come).

On an astronomically-related note, I wanted to share a website I found recently, called thetruesize.com. The idea behind it is to allow you to compare countries' sizes on a map that takes into account the distortions present in the projection, specifically the very common Mercator projection. You can input a country (or U.S. state) name to create a transparent copy of it on the map, and drag it around. As it gets closer to or farther from the equator, it'll shrink or grow according to the distortion present at that latitude (none at the equator, and increasing towards the poles). I found it absolutely fascinating, since I'm aware that there is distortion, but don't have a mental idea of its magnitude.

Probably my favorite country to visualize the distortion is Greenland, which looks to be bigger than South America in the Mercator Projection due to its great distance from the equator. But actually drag a copy of it down to South America and you'll see it's much smaller than Brazil, and comparable in size to Argentina. Comparing it to the U.S., the distance from north to south across Greenland is actually only just larger than the distance from the southern tip of Mexico to the Canadian border.

Anyway, it's lots of fun to drag countries around the map and see how they compare (you can have multiple countries active at once and also rotate them, allowing you to play games like fitting as many countries into another continent as possible). Hopefully you too can enjoy appreciating just how big (or small!) the world can actually be. A hui hou!

Satisfying Slug Shadows

Working from home as I have been the past few months, I've got a lot more time to appreciate the paintings I happened to have here with me when lock-down started. Or, to become more dissatisfied with my previous efforts, in some cases. Specifically, my blue glaucus painting, which has already gone through two different revisions. Turns out I still wasn't happy with the shadow I added (though I'm glad I added it), so I went back and reworked it a little more.

Primarily I found the shadow to be a bit too hard and sharp; it didn't seem like a shadow of something floating in shallow water, and being as sharp as it was it distracted the eye from the slug itself, muddying the focus of the composition. I've gained a fair bit of appreciation for the pigment transparent yellow oxide over the past few months (as it's one I have with me, and have been doing some experimenting with), so I decided to use a glaze of it to make the shadow look softer and less distinct. In the process I also ended up spreading some around on the sandy background too, to help the shadow blend in better. While I was checking reference images, I also noticed that on some the silvery coloration extended along the cerata, so I've gone over those with a thin silver glaze as well. Anyway, here's how all that turned out:

“Carefree Blue Dragon”, 18"×14", acrylic on canvas.

I think this shadow works a lot better now, being still visible but less distinct and not overpowering the main subject quite so much. At this point I think I'm finally satisfied with it, but then I've thought that three times before, haven't I? As the saying goes, “art is never finished, merely abandoned,” so we'll see if this truly is the final revision! A hui hou!

Orchestrating Handel's “The Harmonious Blacksmith”

Today I'm pleased to finally be able to share a new project I've been working on for a few months now. Back in February I mentioned I started learning LilyPond in order to engrave sheet music, and after finishing copying Ecossaise in E♭ Major by Beethoven as a warm-up exercise I was looking around for something new to practice with. I settled on Handel's piece known as The Harmonious Blacksmith, the name given to the fourth movement from his Suite No. 5 in E major for harpsichord. I discovered this fantastic piece last year, and in the process of writing the LilyPond code for it I listened to a whole bunch of different versions of it, including two versions of it orchestrated for a full orchestra. After copying a version for harpsichord(/piano), this inspired me to undertake something a bit more ambitious: making my own orchestrated version!

I settled on a sixteen-instrument ensemble, where two coincidences neatly dovetailed: MIDI handles channels in groups of 16, and the staves for those instruments also pretty nicely filled exactly one page vertically. It's scored, somewhat arbitrarily, for first and second violins, viola, cello, bass, harp, flute, oboe, English horn, bassoon, clarinet, trumpet, trombone, tuba, French horn, and xylophone. I started sometime in mid-March or so, and worked on it off and on for the next month and a half. In early May I gave a short talk at our astronomy department's weekly Monday lunch (which often features people talking about hobbies or interests) and gave the first public premiere of the (mostly) finished work by playing the synthesized MIDI audio. Since then I've tweaked a few little things (such as changing instrument parts to the correct keys for transposing instruments), and this weekend I finally worked out an easy way to render MIDI to audio. (Turns out there's a convenient Python package, midi2audio, which makes it a snap.)

Anyway, here's a video I made so I could display the sheet music along with the audio:

This was, obviously, my first such attempt at orchestration and I have to say, I really enjoyed it. I'm sure if I actually knew music theory I'd be able to weave even more beautiful passages, but even so I stumbled upon quite a few bits that still give me goosebumps, or which just sound lovely: the gentle introduction of the harp in the first variation, the punctuating xylophone taps on pages 8–10 (but especially on page 9) like little blacksmith's hammers, the interplay between trumpet and oboe (page 11), the pastoral, sublime repetition of the second variation (page 14) right after the bombastic introduction a page before, the staccato viola (page 17) interspersing with the flute*, the introduction of the third variation with its gentle, lilting interplay between the woodwinds and harp, the xylophone intermittently shadowing the oboe (page 23), the growing crescendo involving nearly all the instruments which ends that variation (page 24), those  two insistent growling low notes from the bassoon in the fourth variation (page 27), the trumpet making a surprise appearance in the fifth variation (page 34), the four-part instrument unison between the violins, viola, and trumpet on page 38 (never fails to bring out the goosebumps), and the entirety of the last two pages as everything slows, and builds, and crescendos before the final cascading descent to the finish. I've listened to this piece I don't know how many dozens of times at this point (both my version and others), and I have yet to tire of it.

Anyway, enough of my rambling. I hope you enjoy the music, and feel free to point out any musical mistakes I might have made—I did have an experienced violinist friend look it over so I'm fairly confident the strings don't have any unplayable notes (he found those already), but I might still have made mistakes with the other instruments. A hui hou!

*The staccato markings were one of the few liberties I took with the original notes along with adding a few trills in places, though there are a number of trills in the second variation in the original. The dynamics markings and tempi are also mine.