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Monday, January 30th, 2006
ABC Notation is described over here, it's an ASCII system of musical notation. Shareware products are available for translating ABC to standard musical notation and to audio files; of these I have tried abc2ps, abc2win, and ABCEdit. I couldn't get the first two to work properly but ABCEdit is awesome. Very basic user interface but powerful enough to do everything I want it to; I can cut-and-paste from ABC notation on the web and see and hear the music right away.
posted morning of January 30th, 2006: Respond
➳ More posts about Fiddling
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Saturday, January 28th, 2006
Pressing ahead with the music-reading -- today I played a couple of the jigs I had been playing yesterday, and learned two new reels -- "Judy's Reel" and "Paddy Handley's Goose". The latter is the first song I have been able to play from memory after reading from sheet music.
posted morning of January 28th, 2006: Respond
➳ More posts about Music
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Friday, January 27th, 2006
Tonight we watched Duck Soup again, this time on DVD which I recommend strongly -- I have never seen such a good print of a Marx Brothers film before. Sylvia was way into it and wrote her grandparents a long e-mail about the mirror scene.
posted evening of January 27th, 2006: Respond
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More music reading tonight -- I learned the A part of "A Wink of Her Eye" and all of "The Cork Road". Both songs are very slightly more complex than "Bundle and Go" (Which I played for Ellen and Sylvia to dance to before dinner). Learning jigs is bringing back a bunch of musical memories -- "A Wink of Her Eye" brought to mind a similar tune (which I don't know the name of), which I was able to play straight off note for note. Also I found the Fiddler's Companion, which has many traditional tunes written out in ABC notation, which I can download shareware to convert to musical notation and to audio files.
posted evening of January 27th, 2006: Respond
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Last night I read music! I bought a book of tunes from Amazon, and when I sat down and looked at it, I surprised myself greatly by being able to translate the notes on the page into sounds. The tune was a simple jig called "Bundle and Go" -- it helped greatly that almost every note in the song had the same time value, and that most of the intervals were thirds.
posted afternoon of January 27th, 2006: Respond
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Wednesday, January 18th, 2006
I have been playing my fiddle increasingly often over the past year, hardly playing guitar at all any more. Today I am going to take my first ever lesson in traditional fiddle playing from Kenny Kosek. Looking forward to it.
posted afternoon of January 18th, 2006: Respond
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Monday, January 16th, 2006
Going to the zoo in January has two downsides: it is very cold, and many of the animals, the ones which are used to warm climates, are not out where you can see them. Upsides: there are few people there, so you've got the place pretty much to yourself; the animals which are used to cold climates include some that are fun to watch; and there are indoor displays like the reptile house, where you can warm up between walking around outside. We took Sylvia and her friend Sasha to the Bronx Zoo this afternoon and had a great time. For me, primates are the name of the game at zoos, the animals I can spend the longest interested time just watching. And the Bronx Zoo has some great primates. We had been walking around for about half an hour and seen some nice stuff -- bison, tigers, snow leopards, red pandas, the many nocturnal species in the House of Darkness... when we got to the Congo Rainforest exhibit. No animals were out in the outdoor part of the exhibit of course; but the indoor part is one of the best zoo displays I have ever seen. First we saw the guenons, small orange monkeys -- one of them spent about half a minute sticking his tongue out at me and Sasha -- then moved on to the living room of the gorillas. The largest female gorilla was sleeping right next to the glass partition, holding her newborn son in her arms. (I think I got a good photo of the two of them.) Behind her, another female was sleeping; after a minute or two a male came over and tapped her on the shoulder. She started up and glared at him but he made nice and cuddled behind her, laid his head on her shoulder, closed his eyes and grinned. She lay there for a minute or two, eyes open, with an irritated expression, then jumped up, picked up the pillow of straw she had been resting on, carried it over a little ways and went back to sleep. The rejected male followed after a minute or two and sat right next to her, carefully not touching her. Sylvia and Sasha sat next to the glass for easily fifteen minutes, narrating everything the apes were doing. More simian fun at the Monkey House, where the largest enclosure is home to about 15 capuchins. Sylvia and Sasha spent another ten minutes or so watching these extremely high-energy monkeys jumping around and playing with each other. Their favorite playthings seem to be empty containers.
posted evening of January 16th, 2006: Respond
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Sunday, January 15th, 2006
I refined that program from Friday night a bit, to make it a little more readable and to make it calculate numbers that can be expressed as the sum of two squares in more than three different ways. The code is: #include <stdio.h>
#include <stdlib.h>
#include <string.h>
bool exclude(int n, int *x)
{
while (*x)
{
if (n == *x)
return true;
++x;
}
return false;
}
bool IsSumOfSq(int s, int &a, int &b, int *x)
{
for (int i = a + 1; i < s; ++i)
{
int sq = i * i;
if (s < sq)
return false;
int diff = s - sq;
for (int j = 1; j < diff; ++j)
if (exclude(j, x))
continue;
else if (j * j == diff)
{
a = i;
b = j;
return true;
}
}
return false;
}
int main(int argc, char **argv)
{
int reps = atoi(argv[1]);
int i;
for (i = 1; i < 4000000; ++i)
{
int x[10];
memset((char *) x, 0, sizeof (x));
int pairs[10][2];
pairs[0][0] = 0;
if (!IsSumOfSq(i, pairs[0][0], pairs[0][1], x))
continue;
bool match = true;
for (int j = 1; j < reps; ++j)
{
pairs[j][0] = pairs[j - 1][0];
x[j - 1] = pairs[j - 1][0];
if (!IsSumOfSq(i, pairs[j][0], pairs[j][1], x))
{
match = false;
break;
}
}
if (match)
{
printf("%d", i);
for (int j = 0; j < reps; ++j)
printf(" = %d^2 + %d^2\n", pairs[j][0], pairs[j][1]);
}
}
return 0;
}
Results: the smallest number that can be expressed as a sum of squares in three different ways is still 325. Four different ways, 1,105. Five different ways, 5,525. Six different ways (this result I find really cool), 5,525. Seven different ways, 27,625. Then I got bored and stopped checking. Note that this program could easily be optimized, it's pretty slow as presented. Update: Wowie zowie! 27,625 is also the smallest number which can be expressed as a sum of two squares in eight different ways! This seems awesome to me though I'm not sure what to make of it. Update: Frederick points out that 1,105 = 5 * 13 * 17; 5,525 = 5 * 1,105; 27,625 = 5 * 5,525. No idea what's going on here but it sure looks like something. I have confirmed that 138,125 (5 * 27,625) can be expressed as the sum of two squares in ten different ways; 690,625 (5 * 138,125) can be expressed as the sum of two squares in twelve different ways; and 3,453,125 (5 * 690,625) can be expressed as the sum of two squares in fourteen different ways! I do not however know if those numbers are the smallest number that can be expressed as such. (Further update: The Online Encyclopædia of Integer Sequences has some interesting stuff on this.)
posted afternoon of January 15th, 2006: Respond
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It snowed last night -- there is not a lot on the ground but Ellen thought Sylvia and I should take the opportunity to head down to the park and go sledding. I was a little skeptical, whether there would be enough snow to bear the sled; but we set off. A good thing right off the bat -- I had forgotten that we got Sylvia a new sled last year, a very lightweight orange thing to replace the ponderous red sled we had two years ago. The red one would not have stood a chance; this one floated along under Sylvia. Good thing two -- when we got to the park there was a lot of ice in the grass under the snow. As it turned out the lightweight sled could move quite a distance on that thin layer of snow and ice. Sylvia was hesitant but once she took the leap, she was loving it. And no-one else had come out to go sledding -- I guess it did not seem worth-while with so little snow; so we had the big hill all to ourselves. This afternoon we will go ice-skating.
posted morning of January 15th, 2006: Respond
➳ More posts about Sylvia
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Friday, January 13th, 2006
Over at Unfogged, Frederick suggests that 325 is the smallest number which can be expressed as a sum of two perfect squares three different ways. I just wrote a program to check this which confirms Frederick's suspicion; here it is if you want to check my logic. #include
int perfect[] = {
1, 4, 9, 16, 25, 36, 49, 64, 81, 100,
11 * 11, 12 * 12, 13 * 13,
14 * 14, 15 * 15, 16 * 16, 17 * 17,
18 * 18, 19 * 19, 20 * 20
};
bool IsSumOfSq(int s, int &a, int &b, int x1, int x2)
{
for (int i = a + 1; i < 20; ++i)
{
if (s < perfect[i])
return false;
int diff = s - perfect[i];
for (int j = 0; j < 20; ++j)
if (j == x1 || j == x2)
continue;
else if (perfect[j] == diff)
{
a = i;
b = j;
return true;
}
}
}
int main()
{
int i;
for (i = 0; i < 400; ++i)
{
int a = -1, b;
if (IsSumOfSq(i, a, b, -1, -1))
{
int c = a, d;
if (IsSumOfSq(i, c, d, a, -1))
{
int e = c, f;
if (IsSumOfSq(i, e, f, a, c))
{
printf("%d = %d^2 + %d^2\n"
" = %d^2 + %d^2\n"
" = %d^2 + %d^2",
i, a + 1, b + 1, c + 1,
d + 1, e + 1, f + 1);
break;
}
}
}
}
return 0;
}
Output:
325 = 1^2 + 18^2
= 6^2 + 17^2
= 10^2 + 15^2
posted evening of January 13th, 2006: Respond
➳ More posts about Programming
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