Heterobasic Temporally-Convergent Fugue on Pi

So evidently the idea of a “pi song” (python?)  has spread quite a bit. What people seem to not realize though, is that most of the pi songs out there (at least, all that I’ve seen and heard) aren’t really pi songs. Why? Those pi songs use pi in decimal base, but that’s certainly not pi in music, as it is in no way natural to use base ten for music—music is either base twelve, base seven, base five, or perhaps base eight, depending on how you scalarly (?) think of it. In other words, in writing a pi song, one shouldn’t be using the decimal representation of pi, but rather some base that has a nice mapping to the tones of the conventional scale.

Additionally, pi is transcendental and irrational. There’s no last digit. So at one glance it just might not be the right representation to put pi in the sense of a piece, where there is a definite end. Of course, it initially seems ridiculous to attempt the otherwise, but in actuality, one can find ways to store infinite information in finite space. As you all probably know, some geometric (as well as other) series converge, like that with first term 1 and common ratio less than 1 (or that with first term 0 and common ratio anything). Thus, in such a piece, if we make the general tempo accelerate by a common ratio in certain parts of the piece that are divided evenly, we can achieve fitting the representation of an infinite amount of digits in.

I wrote a piece that tries to address these. As you can see, I wrote in a megacluster for the infinitely increasing speed to be represented at the end, which I guess might be considered cheap like the very-quick solution to constructing a regular sixty-five thousand five hundred thirty-seven-gon (tyrtwyihsriramka yirtgrozavyftween-gon), but at least it considers that issue.

By the way, if you do attempt to play this:

1) Prepare for extreme dissonance.

2) You might want to try a slow tempo.

Oh, and also, I’m still sitting on the fence between pi and tau. I guess generating a tau song from this shouldn’t be all that hard.

Piano Performance

The first thing, unfortunately, is formality. Formality has always been something I highly disapproved of, especially in music, because the way a person dresses has literally nothing to do with the music they produce on their instrument. But in this world where you have to get famous first and deviate afterwards, I unfortunately can’t do anything about any part of it, including my parents’ rants a few minutes onto the road noting I left my concert shoes at home. Thankfully, we were close enough to go back to get it.

The performance was set in a “magnificent estate” in Atherton. I would have thought that meant a mansion, but it wasn’t as big of a mansion as I expected (but still something I would call a mansion). It had a beautiful backyard, and the pillars and pavement had a really neat pattern of minute holes in them, in what is in reductionist viewpoint fairly random spacing but holistically clearly arranged in stripes—very natural and nice. I guess the main part of the “mansion” air is the format of the neighborhood (for example, the very interesting street signs). We arrived early so I could try the piano plentifully. At the front, we got name tags. I’ve always thought name tags were dumb, especially because at that point I really needed to go to the bathroom and thus my mom was writing my name tag for me, which meant that (1) it was in her rigidly neat handwriting and (2) the name that went on was going to be my legal name. At least the name tags were pretty neat—they had a magnetic mechanism that makes it so we don’t have to use those mark-leaving and potentially dangerous pins.

Back to piano. I was surprised that given the fact that the piano was in a mansion it was only a Baldwin baby grand. Oh well, at least it was one of the better Baldwins (one I would call a piano, as opposed to most Yamahas)—there was some juice in the music it outputted.

Then I saw the program. Apparently I was playing first (which I actually don’t mind that much) and the program dictated that I was playing Liszt before Beethoven. That was pretty unfortunate, because I was planning to play Beethoven before Liszt so I wouldn’t be sweaty while I played Beethoven. Fortunately, the piano was loud, so I didn’t have to be as loud on the Liszt as I normally was. Maybe it was actually great that it was a Baldwin.

Apparently, this is one of those rare occasions where reception came before performance, so we went to get a bite (or in most cases, multiple bites, but not in mine, as I will explain later) to eat. Unfortunately, all the food they had was either stuff I was allergic to or stuff I was “allergic” to. I just took two cups of lemonade. Meanwhile, the other performer practiced on the piano, much more diligently than I did—oh well. I’m quite sure there must have been some food there that he was neither allergic nor “allergic” to, so that made me slightly guilty. The social atmosphere in reception was terrifying. First, a lady greeted me, having apparently met me before, but whom I absolutely do not remember from where. Apparently I forgot to say hi to my piano teacher for her from her request last time we met—I’ll try to remember this time. Then, a person of the Beethoven foundation came and had a chat with me about music and asked for what else I like to do—when I mentioned mathematics, he asked if I did abacus and mentioned a half-Filipino half-Japanese girl who was internationally ranked in both abacus and golf as the reason he asked. He said that he couldn’t play instruments or even hum the way other do. I was glad he mentioned that, because that allowed me to say something other than “thanks”—something I have been trying to get rid of—and tell him that it’s perfectly fine to not do anything the way others do. (I didn’t get to saying that being different is better, since that is something for some reason people consider weird.) And then came the moment I regretted my name tag—an Asian lady came over and pointed out from my name tag that I have an Asian last name (evidently, her ability to conclude from faces about anything is even worse than mine), and said right there that all the winners of music competitions tend to be Asian (for your information, the other guy I was talking to at the moment was White). I decided to criticize about half as much as I wanted to about this ridiculous Asian pride mentality. Anyway, reception finally was over, and thus we could settle down and perform.

The Liszt piece I played, Transcendental Etude No. 6, was always a piece I enjoyed. It’s a piece full of zyxyvy that follows the extraordinary evolution of a slow, dark theme in the low registers of the piano through variations to a barrage of resonance leaping in arpeggios everywhere, calming down slightly to marvel at the wonderful musicscape produced over the course of the piece before drumrolling to a final magnificent climax. I actually played it without any noticeable mistakes, to my definite delight. Then came the Beethoven Sonata (Op. 90). I’m sure I played it musically, albeit with a couple slips. It’s the Beethoven Sonata that miraculously manages to end on an open octave, of all endings. Apparently I was supposed to bow twice after. Whoops. Formality. Grra.

The other performer played really wonderfully, played an excerpt from Albinez’s Iberia and Beethoven’s Op. 78 Sonata. I liked his style in ending pieces, swooping his hand over the ending phrase in both pieces.

The most notable thing that happened during that was a lady in the audience fainting near the start of his playing the Sonata and a temporary pause being called to call 911 and send the lady to the hospital. I liked how he continued playing a bit even after someone called for a stop, looking for a nice place to leave off like a true musician. During the break, I had a pretty enjoyable conversation (surprise!) with the founder of the Beethoven competition on her favorite subject, philosophy. It was pretty funny because due to her soft voice I had to listen very carefully and when another lady came to join our conversation the first thing she asked was if I understood English.

Afterwards, a group of singers and two pianists from the Beethoven center played a really nice Schumann song. I’m not sure whether the contrast between the two sections of the song is more stunningly beautiful or more drastically abrupt. I’m leaning towards the former, possibly due to the supporting oxymoronic lyrics that comprise of eighty percent of the song.

After the performance was over and we left we went to eat at a Sichuan restaurant. It was one of those Sichuan restaurants that could have saved ink by using a “Not Hot & Spicy” symbol instead of a “Hot & Spicy” symbol. There was a surprising lack of Chinglish on the menu, but there was still some, so at least there was hope that it was a good Chinese restaurant—actually, I really like the food.

Anyway, we went home afterwards.

An Overview of Twenary

By ctzmsc3’s request, I shall explain Twenary.

In 14-Ohe (Gregorian: September 2010), I was at the peak of defiance of the decimal system, regarding it as a bad system—unlike numbers around 10 which had very interesting properties, the only thing that seemed special about 10 was that it was somehow the number of fingers we have. Since then, I have gradually reconciled with base ten, mostly using the excuse that since ten is the product of the numbers involved in the expression of the golden ratio, that was a reason beautiful enough to give it a respected status, although whatever connection there actually is is clearly very contrived, if existent. Thus, I developed Twenary to be used as an alternative system in base 12. I thought that the reason other bases lived in shadow was because digits there didn’t have their own set of names, so I assigned them new names. Now, I’m probably fine with either system, but Twenary names are still very fun to say, and thus I still use them to entertain myself (and sometimes others).

Here’s the digits:

0=oh, 1=ih, 2=swa, 3=tyr, 4=qua, 5=vyf, 6=zyk, 7=zyv, 8=ku, 9=nyn, 10=quet, 11=yirt,

Here’s the powers:

12=twen, 144=groza, 1728=sriramka, 12^6=zykexpa, 12^9=nynexpa, 12^12=twenga


Four thousand five hundred sixty-seven→swasriramka zyvgrozakutwyzyv

The Less-Nonsense Calendar

The Gregorian Calendar is a horrible logical failure. There’s many reasons why the Gregorian Calendar is more suboptimal than suboptimal:

-The distribution of days in months is ridiculous, and clearly arbitrary. At least the calendar could have been symmetrical, but there just has to be February, a month that clearly developed with insufficient growth hormone. Children have to memorize the awkward sets of days in months in brain cells that could have been used for something else.

-There are seven days in a week. There possibly can’t be a worse choice for the number of days in a week. Having seven days makes it very difficult to plan things for half-weeks, for example.

-The number of days in a week doesn’t divide the number of days in a year (or even the number of days in most months). That means there’s always that annoying frameshift for the next year which means we actually have to print a different calendar each year and have to realize different possible days of the week for a given date.

Fortunately, no one ever told anyone to follow society’s standards, although people for some reason like to be masochistic in terms of the populace. Thus, I’ve developed the Less-Nonsense Calendar, the Dvorak keyboard of intrayear division. The idea for such a calendar started about 18 months ago, and I have gradually developed it further—I have finally felt it is good enough to “publish.”

In the Less-Nonsense Calendar, every year has 366 days, with day 1 corresponding to August 23* on the Gregorian calendar, but usually day 191 (February 29) is left out. This is done as opposed to having 365 days and an occasional extra day because 366 has nicer factors to work with, which means we could put 6 as the number of days in a week, as 6 divides 366. Now, not only is it easy to talk about half-weeks, but one can also talk about third-weeks. Now, there could be 61 weeks in a year, but 61 is a prime number. Thus, we take 6 days out and designate them holidays (“Quidivians”) , so that a year has 60 weeks with 6 holidays that don’t belong in a week. That way, there’s the added bonus that after a holiday one doesn’t have to deal with the weirdness of starting a week on a Tuesday, for example. Each of these 6 Quidivians are separated by a 10-week set, which is the Less-Nonsense equivalent of a month (“Quidivion,” pronounced ending with short o followed by n to distinguish from ‘Quidivian’). Thus, there are 6 Quidivions in a year, just like there are 6 days in a week, which produces a nice self-similarity. Here’s an example of a month.

The months are called Ohe (Gregorian August 24 to October 22), Ihe (G. October 24 to December 22), Swadve (G. December 24 to February 21), Tyrdve (G. February 23 to April 22), Quadve (G. April 24 to June 22), and Vyfdve (G. June 24 to August 22), from Less-Nonsense Twenary. Also, from Less-Nonsense Twenary, there is a nice coincidental isomorphism between the first six Less-Nonsense names for nonnegative integers and the English vowels. Thus, the days of the week are O, I, A, E, U, and Y, and because the number of days in a week divides the number of days in a month, we never have to worry about frameshift. The weeks of a month can therefore naturally go by consonants. Since there’s 10 weeks in a month, we might as well use the base ten names and extract consonants: Z, N, W, H, R, F, X, V, G, and K. (The last one is K because the ‘n’ in “nine” is taken by “one” and K fits well with the other letters).

Each day of the year can now be represented by three characters: a number for the month, a consonant for the week, and a vowel for the day, except for the Quidivians

August 23: 0QD or 0NY (Less-Nonsense New Year)

October 23: 1QD (First Quidivian or Ihdivian)

December 23: 2QD (Second Quidivian or Swadivian)

February 22: 3QD (Third Quidivian or Tyrdivian)

April 23: 4QD (Fourth Quidivian or Quadivian)

June 23: 5QD (Fifth Quidivian or Vyfdivian)

Here’s some examples. March 10 on the Gregorian calendar is in the fourth day, second week of Tyrdve. It is therefore designated 3WU, 3 for Tyrdve, W for second week, and U for fourth day of the week (note this system starts from “zeroth”). April 20 on the Gregorian calendar is 3KE. September 11 is 0HO. February 12 is 2GA.

(Now, if only people could actually understand me when I use this system. That’s a long way to go. =P)

Of course, my main point is to point out that conventions are very frequently silly. I would definitely encourage others to develop their own calendars if they find some way to arrange the days of the year cleverly. There’s way too many things that other people hand to us that we just believe on impulse; in fact, almost all of the standards there are in society are stupid—QWERTY keyboard, the international language being English, the way books are printed, etc. They’re there to be fixed, and thus, we might as well fix them.

*[EDITED] The usage of August 23 as New Year has been deprecated.

An Introduction

Hello, and welcome to my blog, the Titularly-Verbose Sesqui-Reqursive Cyber-Alcove of the Dotted six-and-eight-fourth-th Note, also known as “zyxyvy.”*

*zyxyvy: (noun) grandeur associated with smooth motion within a fluid medium (flying, swimming, etc.

EDIT: Cleaned up this page.

EDIT2: “the Titularly-Verbose Sesqui-Reqursive Cyber-Alcove of the Dotted six-and-eight-fourth-th Note” is no longer the title of this blog; it is now “for tomorrow and tonight”.