by liberal japonicus
A bit early, but I have meetings all day tomorrow. My youngest daughter has started piano. The older daughter started at a Yamaha school and is now taking private lessons and the younger one had to have the same as her older sister is doing now, so she has started private lessons with the same teacher. With Yamaha, there were lesson books and homework, so there wasn't much of a chance for me to do anything, but the private teacher is starting with a 30 minute lesson a week and the youngest comes home and wants to do more. So I started having her write the solfege for the tunes in her piano book.
If you don't know about solfege, it's the system that is related to the syllables that Rodgers and Hammerstein used for the 'Do Re Mi' tune in The Sound of Music. Unfortunately, what I wanted her to learn was the movable do system, where do is the tonic, so that if the song was in the key of C, do would be C, but if it were in the key of F, do would be F. People who learn it this way learn the system as a set of relationships, so learning upon what do is, they can sing the melody and easily identify the intervals. I say unfortunately because the piano teacher said that she (and apparently most Japanese) learn the fixed do system, where the syllables are just names of different notes, so do is nothing more that C. Wikipedia on this point is a bit confusing, saying that Japan uses fixed do in one place, but movable do in another, but I think they correctly note that solfege with a movable do is a Germanic tradition.
I never learned solfege, but the idea of learning a system where I could immediately place the intervals seems too cool for words. There is a lot of argument about which system is better and one of the arguments against a movable do is that music that does not have a clear tonality. On the other hand, the bulk of western music is tonal, with a clear and discerible tonal center. It's a bit strange, in terms of classical music, Japan had and continues to have a great affinity for Germanic music and Prussian education was the model on which Japan based its education system, but doesn't use the movable do. Since I've not done any musical education in Japan, I don't know if there are places that teach movable do solfege but it is not something that is in elementary school music. Anyway, helping my daughter now seems a bit more mundane. A related subject below the fold
It reminds me of another thing that I'm going to introduce to the class I teach to exchange students here, and that is the use of the abacus or soroban as it is known in Japan. People who reach a very high level of ability with an abacus no longer need the actual abacus to do the calculations. This video shows how, after you learn the system, you no longer need the tool, you can just picture the abacus in your mind's eye and calculate.
Of course, there is the story of Feynman vs. the abacus salesman, where Feynman trounced an abacus salesman when he was able to calculate a cube root faster than the abacus wielder. Feynman, being Feynman, uses the incident to illustrate the superiority of understanding the principles, or as he says:
I realized something: he doesn't know numbers. With the abacus, you don't have to memorize a lot of arithmetic combinations; all you have to do is to learn to push the little beads up and down. You don't have to memorize 9+7=16; you just know that when you add 9, you push a ten's bead up and pull a one's bead down. So we're slower at basic arithmetic, but we know numbers.
Perhaps, but when he explains how he was able to do that, he notes the following:
The number was 1729.03. I happened to know that a cubic foot contains 1728 cubic inches, so the answer is a tiny bit more than 12. The excess, 1.03 is only one part in nearly 2000, and I had learned in calculus that for small fractions, the cube root's excess is one-third of the number's excess. So all I had to do is find the fraction 1/1728, and multiply by 4 (divide by 3 and multiply by 12). So I was able to pull out a whole lot of digits that way.
So Feynman's advantage was basically getting a lucky number, one that he had remembered a fact about and was able to exploit. Feynman obliquely acknowledges that by the name of the chapter, which is 'Lucky Numbers'.
In doublechecking the anecdote, another anecdote about 1729 came up.
The famous anecdote is that during one visit to Ramanujan in the hospital at Putney, Hardy mentioned that the number of the taxi cab that had brought him was 1729, which, as numbers go, Hardy thought was "rather a dull one". At this, Ramanujan perked up, and said "No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways." This was the sort of thing that prompted Littlewood to say "every positive integer was one of [Ramanujan’s] personal friends".
Interesting to have two anecdotes about the same number. Anyway, something for you music buffs and you math fiends. Have at it.