Found this link and just had to share it, so I figured, why not open today’s blogification with it?
Some fellow on the internet decided to do a very simple experiment : assign numbers to the musical scale we all learned about in school, and then use that to turn the digits of pi into music.
The layering was a smart idea, because as just a melody, pi kinda sucks. That is, in fact, the key to the lure of pi as music to me : the whole deal with pi is that there is no pattern that we know of to the digits. Patternless forms make for lousy music. All music requires some order… even the chaotic kind.
But, and here is the catch : human beings are very good at detecting order, especially if we engage our aesthetic senses, and music is one of those senses.
Therefore, there is a possibility, admittedly very remote, that if enough of us listened to pi turned into music for long enough, one of us might suddenly hear a pattern in it and be able to predict what the next note is time and time again.
That would require all of pi, and not just the 31 notes that the composer of the above piece uses in order to give the thing some kind of regularity.
But who knows? Maybe the human ear for music can do what thousands of mathematicians and trillions of flops of computer time have been unable to do : find a pattern in pi.
I am sure that must have some practical applications as well as just being an ages old math barrier. Would make some things easier to compute, or something.
Of course, in order to compose his tune, the composer of the above piece had to cheat slightly and use more than just one scale. There are ten digits and only eight notes to a scale, after all. So I assume that he just used the C D and E one octave higher than the previous ones.
I mean, you could go digital and use a ten tone scale where all the notes are exactly the same frequency range apart from one another, but I am pretty sure that would end up sounding horrible, at least to ears raised on Western eight tone scale music.
Those raised in a pentatonic tradition might find it quite nice, actually.
Moving on to extremely local news, right now the cells of my body are taking in oxygen and glucose in a process known as metabolism.
OK, maybe that is a little too local. Right now, rice, a chicken patty, and a banana are digesting in my stomach and probably just about to enter my small intenstine.
Still too local. I feel OK right now. Still not super happy with my life, but I am working on that. Cannot beat myself up for not being able to do what I simply cannot do yet.
And directing all my anger and frustration at myself gets me nowhere.
Speaking of anger, I was pretty angry at Joe yesterday. We are three weeks overdue on our monthly trip to Costco, where we 80 percent of our groceries, and yesterday he decided he just didn’t feel like it.
And that just made me so mad.
The first week we were overdue, it was because we were at Vcon. No problem there. These things happen. We were all having too much fun to worry about groceries.
And the second week, Joe was sick with a throat infection. Also understandable. I caught a buit of it myself, although luckily, I fought it off. Must be all that rest I get.
But last weekend, he had no excuse. And he is the driver, so it is not like we can do it without him. Costco is not built with people on foot in mind.
Last night would have been his last chance to come through this weekend. But he decided he just did not have the energy to do it. This despite having had all day to lie around in bed and listen to CBC on the radio. He was in bed when I went by at 1:30 AM, and he was still in bed at what would have been his last chance to get to Costco before it closed at 4:30 PM.
I think we would all agree that fifteen hours is a pretty good lie-in, don’t you? So to me, what he was really saying was “Nah, just don’t feel like it, and you can’t make me. ”
And this pissed me off pretty good. So for a while, I seethed about it. Then, seething wasn’t enough any more, and I started glowering.
The thing is, I can’t just confront him over it, because he already does a lot for me, including driving me to therapy and doctor’s appointments, and so I do not exactly feel like I have enough standing to just demand things of him.
And maybe that is a problem in me. I have trouble asserting myself and asking for what I want because I always feel so indebted to people and like that means I don’t deserve to ever ask for anything. That is certainly how I was raised… be grateful for whatever you get and never, ever ask for anything.
Plus, I just dislike conflict. I am a harmony seeking creature. Conflict hurts my tender nerves.
But still, I feel pretty let down by Joe and I think I did manage to convey my anger to him without quite coming right out and saying it. I asked him rather pointedly whether I needed to get more microwave popcorn or not, that being something that normally we pay for with the groceries.
And I think he got the underlying message that I am not at all pleased with the lack of Costco.
It is not exactly one hundred percent by the book, if the book is an assertiveness manual, but I think it is a good first step towards greater assertion.
And who knows, learning how to assert myself against others might lead to learning to assert myself against myself… or the universe.
OK, 2 things:
1) about pi: nothing says that it has to be expressed in decimal.
“Of course, in order to compose his tune, the composer of the above piece had to cheat slightly and use more than just one scale. So I assume that he just used the C D and E one octave higher than the previous ones.”
(You mean “octave” rather than “scale” here, I think. Felicity would know.)
And yes, that’s what he does. Watch closely as he is playing the notes on the piano the first time around; for the ‘9’, he plays a note in the next higher octave.
And there are only 7 notes: A, B, C, D, E, F, G, so one would “cheat” (encroach into the next higher octave) even if using a full octave, which re-uses the fundamental note one octave higher.
“There are ten digits and only eight notes to a scale, after all.”
You can choose your number base, and thus can have as many digits as you would like. Using octal, the mapping would use 8 notes. Duodecimal would use 12 notes: you could get the black keys involved too. 37 or 61 or 88 keys on your keyboard? Just use base 37, 61, or 88.
“I mean, you could go digital and use a ten tone scale where all the notes are exactly the same frequency range apart from one another, but I am pretty sure that would end up sounding horrible, at least to ears raised on Western eight tone scale music.”
It’s worth a try! Western music in fact has done a similar thing, using “equal temperment” tuning for the notes. Including the black notes (sharps and flats, or “accidentals”), you get 12 tones (the “12-tone scale”), spaced 1/12 of an octave apart from each other. The advantage is that you can switch (or “modulate”) from one key to another, without having to re-tune your instrument. The disadvantage is that the notes aren’t precisely in harmony with each other, as is the case with the “just temperment” tuning. (J.S. Bach’s “The Well-Tempered Klavier” illustrates the usefulness of equal temperment.)
The frequencies of notes in the Western scale are related by fractions with denominators of 2, 3, 4, and 5; Harry Parch (in “Genesis of a New Music”) adds 7 to the mix. And with modern computer-controlled keyboards, it should be possible to switch to different tunings on the fly, although I have yet to see this actually done. (This has been suggested by Bruce Irons, an engineering professor at the U of Calgary, and also a CBC listener and classical music buff.)
2) about Joe and you: How about accepting some personal responsibilty for getting food for yourself, rather than getting angry at Joe for not meeting your expectations? (I know it’s a goal you’re working towards… how about using this as an opportunity to take a step in that direction?) Make a Safeway run when you need to. Joe is not normally like this, so there’s likely a reason for him being this way lately, be it the shorter days or the colder weather or something. Cut him some slack — everyone has their own moods and problems from time to time. You’re entitled to be angry, but I think that it’s inappropriate and maladaptive in this case. I love you dearly. I want to see you become more independent… and getting mad at Joe tells me that you feel more dependent on him than perhaps is healthy.
Or, in the words of my former roommate/landlady when she needs to tell her teen-age kids to grow up a little: “Suck it up, Princess!” (Not meaning to sound harsh, I just find the phrase amusing.)