A little puzzle

Hello again. I'm sure by now the endless talk about mathematical necklaces has left you gagging on the words Polya's Enumeration Theorem, but bear with me.

Consider a 12-bead necklace constructed of black and white beads, any number of each, so long as it adds to 12 exactly. No, this necklace cannot be taken off and put on the other way; you have to stick your head in the same way every time, otherwise

How many such necklaces are there? As is intuitively obvious even to the most casual observer, 352. But given a specific combination of black and white beads, how many can be constructed? Well, twelve white beads is easy: there's only one option, and it's the same with twelve black beads, and similarly there is only one way to arrange a single bead of one color along with eleven of another color. For counting (though not aesthetic) purposes, black and white are interchangeable: for instance, you'll get the same count if you're using ten black and two white as you will with ten white and two black. Take the latter option: how many necklaces can you form with two black beads and ten white? Well, the two black beads could be right next to each other, or one bead removed, two beads removed, and so on until they have five white beads between them on either side. This yields six necklaces of two black beads and ten white, and six more of the opposite arrangement.

The other arrangements are harder to count by inspection, but with the help of a visualization tool I found once, I cheated straight to the answer of how the 352 necklaces break out into the 13 possible combinations of white and black beads (see below). The first two ones represent using all beads of one color, and using eleven beads of one color and one of the other. The two ones at the end represent using just one bead of the one color, and using all beads of the other color (Make sense? Of course not. It's 10:30 PM and I was up at 4:20 this morning) In the case of using six and six, there are eighty possibilities:

1 + 1 + 6 + 19 + 43 + 66 + 80 + 66 + 43 + 19 + 6 + 1 + 1 = 352

What the heck does any of this have to do with music theory? Here's a hint: https://www.google.com/search?tbo=p&tbm=bks&q=isbn:1619114860

My apologies for being pedantic and cocky.

Why you should learn to read guitar in two clefs (part I)

I'm turning this blog into a forum for my musical interests. Right now I'd like to write a short post about why you should learn to read guitar in two clefs.

Grab your guitar and play the open fourth string in standard tuning. Now climb up the notes of the Dorian Mode (that's the C scale starting and ending on D): D, E F (moving to the 3rd string now) G, A, (and so on to the treble strings) B, C, D, E, F, G...

Stop!

You have just played *all* the notes in the key of C that either lie on or touch the guitar staff. Everything else must be notated with ledger lines. I should say here that guitar is notated with a treble staff, but sounded an octave lower than it would be on, say, a piano. I find reading these ledger lines to be endlessly frustrating as they lead to bothersome counting: "O wait, that's three lines down, so it's an F, not an A..." 

Now let's try that same exercise with the grand staff:

Your tour of the bass staff starts with the second lowest note on the instrument (in standard tuning): F on the first fret of the 6th string. Play the C scale starting there (i.e. the Lydian mode) and going all the way to the open B string. BOOM! The bass staff, like the guitar treble staff, overlaps entirely with the fretboard, and provides much more guidance for your bass playing than a bunch of ledger lines below the staff.

The treble clef is that same D Dorian mode from the first exercise, but played an octave up. I don't care how you play it, but it starts with the D on the fourth string 12th fret and ends on the first string 15th fret.

So with few exceptions (the open 6th string, middle C, and the very high 1st string) all the notes playable on the instrument are on one of the two clefs. That's why you need to learn to read guitar music in two clefs. Yay!

There are probably many reasonable complaints about what I've written here, but two main ones come to mind:

1) The best way to notate guitar is with tablature supported by standard notation. This provides the legibility of tablature and the ability to figure out the rhythms if you don't know them. Who, then, gives a shit about any of this?

2) It's not impossible to read standard guitar notation, and it's compact, with a legible (if cumbersome) notation that removes ambiguity if you just put in the time to learn it. For the few of you who can actually read guitar music, I'm sorry, you've wasted your time reading this.

No, actually, you haven't. While I personally believe that reading in two clefs easier and more fun than reading standard notation, the real reason to learn two clefs is to expand your repertoire of playable songs to anything written in a grand staff. That is quite an expansion--more on that later.

My Remembrance of Joshua Horky

This was read at Joshua's memorial last Thursday. I should have realized that the term "catechumen" would be lost on almost everyone, as it is apparently unknown even to my computer's spell check program. According to Wikipedia: "a catechumen is one receiving instructions from a catechist in the principles of the Christian religion with a view to baptism. The title and practice is most often used by Orthodox Christians and Roman Catholics."

"Joshua and I shared a propensity toward fear and doubt that stained everything in our lives. Joshua inspired me by clinging to scripture as the only thing that really could be trusted.  Before I met him, he found his Anchor in the Storm, and he clung to it until the end. When I met Joshua, I said something about dying for some cause and he said, from memory, an Authoritative List of Causes for Which a Christian must be willing to die: 1. The inerrancy of scripture, 2. The deity of Jesus, and 3. (I don’t remember number 3 and I thoughtlessly failed to write it down when Joshua repeated it to me in February). And like that, a question was answered for him. It was like he was some fourth century catechumen preparing for baptism. I couldn’t believe it: someone was actually taking the Christian life seriously.  

And so Joshua and I became friends. I had lingering doubts about Christianity, hell, and my own status in the eyes of God. Joshua, who shared many of these doubts, supplied Scripture and Reason. I became, as Joshua realized shortly before his death, spiritually dependent on him, buying his belief system wholesale since it seemed to have provided for him precisely the kind of clarity of purpose that I wanted for my life. So I was apprenticed to him in the ways of Conservative Evangelicalism. He drove me one night to the Half Price Books in Everett just to buy me an NASB, which I still have today.

A lot has happened since then. To Joshua’s chagrin I rejected the concept of inerrancy, losing some of the certainty I sought when I befriended him. He stuck with me despite my heresy, calling me every week for almost the entire time prior to Amber. We realized that our shared commitment to the truth kept us on the same page despite our disagreements. Since Joshua grounded his opinions in plain reason and his understanding of scripture, there were never raised voices, no accusations of backsliding or backwardness. He was always deeply respectful and fair. I couldn’t have asked for a better friend to see me through my first eight years of marriage.

What else is there to say? As I discovered in writing this remembrance: too much. What of his effortless sense of humor, razor sharp but never cutting?  He didn’t tell jokes (at least not very often); he perceived the world truthfully and simply stated his observations. Since the whole world is ridiculous he was never short of material. In short, his humor was a natural consequence of his personality. He never had to work at it; he just *was* funny.

What of his perfectionism and the outrageous standard he always held himself to, his immediate responsiveness to perceived needs, his turbo-geek preoccupations with ham radios and flash drives, the impossibly Spartan apartments that no other human being could live in, his hyper-rational scripture interpretation, Chess, the stench in the Illuminate II when he kept his wet shoes in the backseat, that *Helmet*??!?

It’s too much. You loved us well, and we love you dearly, good friend. Goodbye, Joshua."

Snomth

Welcome to my important blog post called snomth. The only rules are that you must pick strings of letters from the months of the year, and they must be pronounced the same way they are in the month. Try to make as many funny new words as possible. Perhaps there should be a snomth contest. Here are the months of the year, to get you going, followed by a few examples.

January, February, March, April, May, June, July, August, September, October, November, December

Februober
Julaugunary
Noptaych
Octoberl
Septune
Jarch
Temruary
Marpt
Eceryarch
Eceryune

Gezelligheid

Both of the houses I grew up in had wood stoves. These are not to be mistaken for fireplaces, which are largely ornamental and which let most of the heat go right out the chimney. Wood stoves, on the other hand, are little wood-burning furnaces that feature prominently in the living room of the house. Once the fire is built, you decide how long it burns by measuring the air that goes into it. So our primary source of heat over the winter was this wood stove. It was also our primary source of gezelligheid.

I don't pretend to have anything but an intuitive sense of what the Dutch adjective gezellig, or the related noun gezelligheid, actually mean. I don't speak Dutch, and don't really know any Dutch people, except one second cousin and my now deceased maternal grandparents. All I know is that the fire made our house cozy, and warmed fingers plagued by poor circulation. Add a family, hot cocoa, some roasting pumpkin seeds, a fresh cut Christmas tree, a box of ornaments dating from the 70's to two days ago, and a schlocky Amy Grant album, and there you have it: gezelligheid. (now for mentioning The Season out of it's given time, I realize that I am now due for a shotgun execution from Santa Claus himself. Bring it, Saint Nick. Bring it.)

I strongly associate gezelligheid with the cold months, and I have racked up a total of 4.5 cold months over the 6.5 years I've been married, having lived in California and Florida for most of that period. Now that's not to say that you can't have a gezellig experience when it's sunny out; it's just hard to cultivate a particular sense of belonging when, within reason, you can belong anywhere in the great sunny outdoors (not a term typically used of the Los Angeles metroplex, but I have a habit of using denotative meanings sometimes, in this case, the outdoors being whatever is not the inside of your dwelling.) In other words, I want a cold snap, a rainstorm, or a dreary night to drive me indoors. I want to feel safe and warm under my blanket, with Virgie, some S'mores Pop-Tarts®, and a Godzilla movie on VHS, while the world rages outside with a barrage of pointy icicles and an icy glassfull of cholera to blow in my direction.

Not tonight, world!

post 2*31

Today I performed in a puppet show. The police officer on my left hand was Balthazar, and the construction worker on my right was Melchior. Virgie played Caspar, an anonymous Bethlehemite, a rich woman, a sheep, and Mary the Mother of God/Eternal Queen of Heaven. What a woman.

I wonder if we could help fill the pews by doing one of these every week. Damn, they're a lot of work, though. I wouldn't do it unless they agreed to pay us a percentage of the increase over the average offering for that time of year. Hmmm... I guess there's no way to ensure that Virge and I are really the ones to credit.

While we're on the subject of things, here's a recipe for sauerkraut with bananas: http://www.theonion.com/articles/shitty-graffiti-artist-captures-19yearold-girls-he,26859/. No, dammit! That's an Onion article. Here's the recipe: http://www.worldcook.net/Cooking/MainCourse/MC-FrysianSauerkraut.htm Altogether now...Yuck. Thank God the Frieslanders (my ancestors) are known for their horses and practically nothing else.

Well, time to clean up after Twelfth Night and get ready for my week in San Diego. Goodbye.