Updated Picture

I updated my profile picture. Something about a jester behind the arbalest just hit my funny bone.

I was at the store doing my weekly grocery shopping earlier this week. As usual I stopped by the Lego section to see what was on sale. I shop at one of those big we-sell-everything stores because I only have to go to one store and they're the only place around here that sells groceries without one of those %&@@&*! loyalty cards. I dislike the idea of someone tracking what I buy, and I'm not going to pay twice as much because I don't want someone tracking what I buy. (And yes, I know I'm paranoid; but am I paranoid enough?)

Anyway I had to buy set 7079 "Drawbridge Defense" because of the jester mini-fig. I attempt to juggle and made a jester costume for Halloween several years ago. Though my good one is red, white and black rather than the red and blue in the Lego set.

In 1994 friends of mine and I won the costume contest at the Hilly Hundred bicycle ride in Bloomington Indiana. He and I were jesters and his wife was a mime. You might say we had one mime between the two of us. We won mostly because he and I wore our costumes all day and juggled at every rest stop. We never have figured out how to pass objects between each other, but we do a pretty good side-by-side juggle where he's the right arm and I'm the left. That jester costume is yellow orange and green.

I also bought set 8942 "Bionicle Jetrax T6" while I was at the store because it was about 1/2 price and I didn't have any Bionicle sets.

Oh, did I mention I have about 30,000 Legos?

I have about 30,000 Legos. That's not really very many as you can see by the picture to the right. They are more impressive dumped into one big pile, but they take about 40-50 hours to sort back out by size/shape.

To really do anything interesting you need between 250,000 and 500,000 blocks.

Tons of Work && Musical Stuff

Well I've been doing tons of work in the garden...quite literally. This is a shot looking north of the new garden path that runs magnetic north and south. The main path runs magnetic east and west from the gate to a chair I made that sits at the west end of the garden. I put the "magnetic" in there because the compass rose visible in the next photo points (nearly) true north.

This part of the path has one ton (2000 pounds) of gravel plus several hundred pounds of brick edging. I need another ton or so to finish the part of the path south of the compass rose and to finish filling up between the bricks. I neglected to go get a shot of the completed path and it's dark out now (and it's just a path...not terribly exciting, but a lot of work none-the-less.)

I tried, and failed, to complete this before I hosted a cook-out a couple of weeks ago. I dumped the first wheelbarrow full of gravel (yes that black one in the second picture) into the path and then stepped down on it and proceeded to sink past my ankles in mud THROUGH the gravel. I decided to wait a couple of days for it to dry out. A friend of mine was making fun of the amount of gravel I put down. His paths have about an inch-and-a-half of gravel. Mine has about 8 inches. But mine also act as drainage ditches. I put about 6 inches of gravel down, cover it with landscaping cloth to keep the dirt from sifting down through (or slowing it down a bit anyway) and then top with another two inches of gravel. Seems to work pretty well. I've about 80 feet of paths in the garden done this way.

The cookout went pretty well, but did lead to another project. Their are a bunch of children in our church group; somewhere around 24. About 12 or so showed up for the cookout. (My house is very popular with the under-12 crowd as I have about 30,000 Lego blocks that I put in one room. The Legos are supposed to stay in that room and do for the most part.)

Anyway one of the girls who is about 6, found a "flute" (for lack of a better description) that I made many years ago out of a piece of 1/2 inch copper pipe and an end cap (second from right in the picture). She said that she always wanted a flute and wanted to take it home. I told her that, no she couldn't have that one, but I would make her one. So I went and bought 20' of 1/2 PVC schedule 40 pipe and a 5/8 inch dowel and made three "G" flutes plus some experiments with whistles. I had to make three because she has a little sister and of course I need one too.

I've still a lot of PVC to play with (especially since I bought 10 feet of 1 inch a few days later). I've another project on the to-do list that involves lots of PVC and noise. The red thing on the right is a PVC and fiberglass slide trumpet I made for an engineering competition in 1995. It's also popular with the kids, but not with the neighbors. (Yes, that bell was made with a program I wrote to figure out how to stack cones into bell shapes.)

I found "recipies" for flutes on Pete Kosel's web site. I mostly followed them except I couldn't find my 7/16ths drill bit so I used a 11/32 instead.

The other "musical" projects that I have been working on (after it gets too dark to work outside, as mentioned in the previous post) all involve playing with the prime and Fibonacci sequence.

It started by thinking about sine waves with frequency and amplitude related to the sequence (prime or fib) as harmonic overtones. I started just by graphing them in a spreadsheet. Turns out the Fibonacci sequence(left) has a slightly modulated sine wave while the prime sequence (right) has a more triangular/saw tooth wave. The various lines are as you add more and more component sine waves in. I'd have to go look to see exactly what I used as frequency and amplitude in these graphs, but it's along the lines of frequency = sequence and amplitude = 1/sequence. (So for the first prime 2, frequency = 2 and amplitude = 1/2)

I want to (but haven't got around to yet) write a MIDI instrument file using FM synthesis and the sequences as a basis.

What I have gotten around to is making MIDI sequences out of the prime and Fibonacci sequences.

I initially started with hand-entered drum sequences using GarageBand. That was a pain. But it did sound sorta promising. I then wrote a Java program that can produce MIDI sequences of any length using arbitrary sections of the prime, Fibonacci or any other sequence you want to program.

I also found that GarageBand doesn't handle 30,000 note sequences very gracefully. I found that out by producing sequences to where they repeat, without paying much attention to the fact that sequences of prime numbers don't repeat for a very, very long time even if you're only using the first 6 primes. In fact it doesn't repeat for 30,030 notes. I've since trimmed them down to 600 notes (about 2.5 minutes).

What I did to turn a sequence into a "song":

Say you have a trigger sequence: 2, 3, 5, 7, 11, 13 (the first 6 prime numbers).
And you have a note sequence: C, E, G, C (C major cord).

If you think of a song as a numbered collection of 8th notes, when you get to an 8th note number that divides evenly into one of your trigger sequence, you play the corresponding note from your note sequence.

So at note zero (yes, I started counting at zero, I'm a computer geek after all) all the notes play.
At note 1 no notes play.
At note 2 the low C plays.
At note 3 the E plays.
At note 4 the low C plays again (4/2 = 2 with no remainder (modulus 0))
At note 5 the G plays
At note 6 the low C plays and the E plays
At note 7 the upper C plays.
At note 8 the low C plays.
At note 9 the E plays
At 10 the low C and the G plays
At 11 the upper C plays
At 12 the low C plays and the E plays
At 13 the upper C plays
...
At 17 -- Wait! We're out of notes! Well not really. At that point the notes wrap around again (modulus note number) and everything divisible by 17 will have a low C play. Everything divisible by 19 will have the E play and everything divisible by 23 will have the G play etc.

Having the notes wrap that way keeps the "song" in the same key and adds some interesting rhythms, but not enough on it's own. I also set a maximum note length (usually one whole note or 8 in our example) and modulus the number in the sequence by the max note length +1 to get the actual note length.

The upshot of this is that the low C is 1/8th long, the E is 1/4, the G is 3/8 (or a dotted 1/4) etc. But when you're using the first 120 primes (as I've been doing) you get some interesting rhythms like 1/8th followed immediately by 1/4 note, Some half note cords and arpeggios etc.

I actually used a much larger note sequence too, several C major cords in different octaves, some tone clusters (F, G, A), some extra C's in multiple octaves and also added a drum beat using the start of the prime sequence.

I dumped all that into GarageBand, slid the drums around until I got the drum sounds I wanted, added track reverb and some echo, switched the "melody" to acoustic guitar tossed in a LOT of reverb (60% or so) and some echo (12%), and viola: instant yuppie wall-paper music. (That's "New Age" or anything produced by Wyndam Hill for the uninitiated.)

The reverb and echo make a big difference. The start and end are lame, but in the middle it sounds pretty decent. Not bad for a bunch of prime numbers. Fibonacci doesn't sound as "good." But that may be that I've been on a prime number kick for the last couple of rounds.

I'd let you hear all this (I made a MP3 file) but I don't have anyplace to host it yet. (It's kinda stupid that I can upload a video but not an MP3...go figure.) And since it's now officially tomorrow, I should probably head toward bed.