Furno Partimento #1 – Gigue

Giovanni Furno wrote 10 partimenti for beginners. They can be found at Dr. Robert Gjerdingen’s website.

Here is one of my realizations of the first partimento. The right hand melody is in the style of a gigue in 6/8 rhythm. I’ve taken the liberty to shorten the cadence at the end to fit it into an even number of bars.

Furno partimento #1 bass line only
Furno partimento #1 realised in the style of a gigue.

Finding the Nuts and Bolts of Western Music

I’ve had a patchy journey in music with more than one long gap of several years in between where I hardly touched the keyboard. But I can confidently say that western classical music is an integral part of me, since it keeps coming back to me in different forms, but always with the same intensity.

The most recent pursuit to learn historic improvisation has been the most exciting yet, truly a revelation. And whether I end up being able to improvise in real time or not, the inner workings of eighteenth century music is no longer a mystery to me.

The one thing that has been truly eye-opening is to learn that the music is built bottom-up, the bass being the most important voice. This was totally counter-intuitive to me, always having thought of music as melody-first and all other stuff going on below as “accompaniment” whose only role was to add harmonic colour to the melody.

Also, probably adding to the difficulty in understanding the primacy of the bass is the physiological fact that the higher frequency notes tend to be more prominent in our perception. But to some extent I have started hearing the bass notes and when I sight-read new music I have begun to pay more attention to what the bass is doing.

Of course, I knew of cadences and chord progressions but they seemed more like an analytical superimposition to make sense of polyphonic music rather than actual tools to create music. Getting to know about partimento and playing some of the simplest ones, has therefore been mindblowing.

A partimento, a single voice line in the left hand that holds within it the clues to the voices which need to be sounded above it, is probably the most ingenious pedagogical tool that has ever been developed to explain to the music student what lies under the hood. The best part is that it doesn’t explain it in words but through puzzles which the student has to solve.

And getting to know the nuts and bolts in this way actually means being able to make your own music.

Bass Motions in a Handel Gigue

This is probably a highly technical post to start off with. However, it’s something I worked on yesterday and I thought I’d get started with posting such stuff. I do plan to write more generally about my interest in historical improvisation, but that will have to wait until later.

The following is a copy of the gigue from Handel’s Suite in F minor (HWV433), with the bass motions marked. I was surprised to see how obvious the patterns are. Hope to work on this scheme and create some variations.

The abbreviations used (following the conventions of Dr. John Mortensen) are:

  • TDO – Tonic Dominant Oscillation
  • C5 – Circle of Fifths
  • RO – Rule of the Octave
  • Pedal pt V – Dominant Pedal Point
  • DA3 – Descending Alternating Thirds

Restarting the Quest

It has been almost eight years since I last posted anything on a blog. The quest for the right questions has continued during this period, albeit offline. And now when I thought of restart blogging, I decided to keep the same title as I felt that it still applied.

In this age, especially belonging to the stratum of society that I do, it’s perhaps odd for someone in his early thirties, not suffering from a terminal illness, to be thinking of impending death. Statistically, it is highly probable that I’ll continue to live for a few decades still. However, the pandemic reminds you that life is precarious – the pathogen itself, of course, but in a far bigger way by making visible the deep vulnerabilities of the intricate web of economic activity and how little it takes (literally, just an RNA molecule!) for it to be disrupted.

That makes me want to try to find out where I am in this drift called life. Recall the beautiful things I have seen. The futile attempts at rowing against the drift. Remind myself of the things that I want to do when I don’t need to attend to the boat. Knowing fully well that there is no destination. And that’s what I want to do through this blog.

Charge on a battery’s terminals

Recently when I was studying electrochemical cells, I was thinking about the fact that for a cell to drive current through an external circuit, the two electrodes must be at different potentials, and surely this means that there is a static charge on one or both of them. Otherwise how would they be at different potentials to begin with? I wanted to try and detect this charge.

I had come across this simple FET electroscope circuit some time back. It’s an amazing circuit where an LED is glowing by default, and turns off when a charged plastic scale is brought near the hanging gate of the FET. The electric field of the negative charge on the scale induces charges on the gate which turn the FET off. When you remove the charged scale from its vicinity, the LED comes back on.

The charge on the plastic scale is probably at a potential of thousands of volts, and the field is strong enough to make the FET turn off at a distance. But the charge on a battery’s terminal is obviously at a much smaller potential. So when I brought the negative terminal of a 9V battery near the gate of the FET nothing happened. But when I actually touched the negative terminal of the battery on the FET gate, the LED turned off and remained that way.

I think the LED stayed off because when I touched the gate of the FET with the negative terminal of the battery, some negative charge must have been transferred onto the gate, as opposed to the induced charges when the plastic scale was brought close. I could get the same result by rubbing the scale on the gate (not every time, because charge transfer from an insulator is not easy). If I now touch the gate with my finger the charge flows to me and the LED comes back on!

Unfortunately this doesn’t happen with single 1.5 V cells. I don’t understand why, but I read somewhere that the FET needs the field corresponding to around 7V or so of potential, to turn off. But the article linked to above says that it can detect potentials as small as one volt. But then I used a different FET to the one mentioned in the article. I need to understand FET’s better to make better sense of this.

According to what I’ve recently read in electrochemistry, it seems that even a single zinc plate dipped in acid, without a second electrode, develops an electrostatic charge, due to the different rate of oxidation of zinc atoms and reduction of hydrogen ions. It would have been amazing to be able to detect this charge.

Holding on to radical questions

What is a radical question? Why do I get drawn to them? Why do they frustrate me?

I have a radical question when I believe that the way we generally do something is not smart, that there is a better way to do it. But we stick to the old way of doing things just because we have been doing it that way for a long time, and it’s convenient to just continue. And just keeping it going that way takes so much of our energy that we don’t look at things afresh.

This state of affairs pains me, since it pulls my energies in other directions rather than focusing them on work I believe in, work that I believe is best for myself and the people I’m working with. It’s not just the idea of this waste of time and energy, there’s a real pain and frustration coming from the organism within. I feel that pursuing the radical question has the potential to make my work more of play, at the same time making it more useful for the people I’m working with. There’s a romantic notion of a more wholesome, happier life associated with the radical question.

Wherever you are, there will be some constraints which you have to accept as existential. Obviously you are not going to change the whole world! When you put on paper what are the constraints you are willing to work under to pursue your radical question, and what is the test to decide if it’s useful to hold the radical question within the constraints you have accepted, I think the radical question has the potential to become real and woven into your work. If it’s unrealistic you can drop the radical question and live with the status quo or look for another situation with a different set of constraints to pursue your radical question.

And either way you would have probably learnt a lot in the process.

Simple programs for teaching integers and overflow

Click here to download

While teaching unsigned and signed binary integers, I wrote these programs so that the students can run them and see overflow in action. There are four programs- addu, adds, subu and subs- for adding and subtracting 8-bit unsigned and signed integers. The numbers to be added are given as arguments when running the program. The result is printed on the screen and also saved in a file, which can be opened with a hex editor to see the result in binary format.

While the students where running the programs they obviously had questions about the the dot-slash. That was a good opportunity to tell them that all the commands they run, ls or cd or chmod or anything for that matter, are all executable files residing somewhere in the file system. I made them type which ls and find that ls is actually /bin/ls.

I pointed out the interesting fact that ls, which was somewhere else in the filesystem, could be run by just typing ls and not necessarily /bin/ls, while the addu program which was right here in this folder you needed to specify that it is in the current folder (they knew that dot stands for the current folder). Then I showed them how by adding the current directory to the PATH variable, you could run it by just typing addu, like any other command in the system.

Current without a ‘closed circuit’?

It’s common knowledge that you need a ‘closed circuit’- an unbroken, continuous, conducting path- for an electric current to flow. If you are using a battery, this usually means an unbroken path from the positive terminal of the battery, through an LED (or whatever device you are running), all the way to the negative terminal of the battery.

But the closed loop between the terminals of the battery is strictly not necessary. What is important is that an electric current needs to flow through the LED, and for this all that is required is that the LED is connected between two points at different electrostatic potentials. The terminals of a battery contain static charges, and one could theoretically draw a small current for a small duration if we connected an LED between one terminal of the battery and a neutral object. The neutral object will act as a source or sink of electrons, depending on whether we are connecting it to the positive or negative terminal respectively. But for the chemical reactions in the battery to continue happening to provide a continuous current, the other terminal also needs to be operating (this is something that needs discussion, but I’ll do it in another post).

To test this out, I connected the positive lead of the LED to the positive terminal of a 9V battery, and held the negative lead with my fingers (myself being the neutral body). Obviously the LED didn’t light up. But then I connected the negative terminal of the battery to the earthing in an AC mains socket, so that it can act as a sink for electrons from the negative terminal of the battery. And the LED lit up! Not brightly, but that’s understandable, since my body has a large resistance.

Here’s a photograph of the LED glowing when I touch its negative terminal. The second picture shows the LED when it’s off, so that you can see the difference.

Teaching Computer Science Bottom-Up

When I started teaching the new batch of Computer Applications students this year (class 9), I had it in my mind to do it bottom up, to try and give them a good sense of how computers actually work, how the 0’s and 1’s get so many things done. I wanted them to not only be able to write java programs in the prescribed IDE, but also have a good command over the machine, visualize what happens when they run a java program and easily learn other programming languages, work with microcontrollers and so on.

I started with teaching them how to use the GNU/Linux command line interface, to carry out the various tasks they normally do by clicking, dragging and dropping. Typing commands and making things happen turned out to be an exciting thing for them to learn. I had soon taught them to navigate the file system, copy and move files and folders, find out and change file permissions, open files using appropriate applications etc. It helped that I have just 4 students, all of whom are quite excited learning about computers and working on them.

Making them open files of different types with different applications gave me a context to introduce binary numbers and the different ways in which binary digit sequences can be interpreted. Usually it’s just stated that computers can work with only 0’s and 1’s, and that the 0’s and 1’s refer to different voltage levels etc. Then the focus turns to learning the binary number system, and the procedures to convert decimal numbers to binary and back, and some binary arithmetic.

But I saw the whole world of binary numbers in a new way, for the first time. What struck me was that computers interpret binary digit sequences in a variety of ways, not just as numbers. We want the computer to interpret binary numbers in several ways, as different kinds of data- text, numbers, images, audio- and instructions. I felt it would be exciting to try and pass on this understanding to the students.

I gave them a simple introduction to the binary number system, and then went on to making them edit text files and bitmap images using a hex editor. This gave them an idea of how the same set of bytes can be interpreted differently. As a project they even drew a 10×10 pixel image and typed in the hex code referring to the bitmap file format and saw the picture in an image viewer!

I then spent a few classes discussing the different kinds of numerical interpretations of binary numbers- unsigned integers, signed integers, fixed point numbers and floating point numbers. They also learnt about the problem of overflow because of the limited range of numbers. To illustrate overflow I wrote a few programs in C and made them run the executable from the terminal. That also gave me a context to talk to them about source code, compilation and the executable. (I was able to even explain to them the difference between proprietary and free software.) This was very useful, because the next interpretation of binary numbers I wanted to show them was that of instructions. I could easily tell them that the executable file contained bytes which the processor interprets as instructions.

And to actually show them this, I used the Hack CPU emulator developed by the authors of the book/course “The Elements of Computing Systems”. It uses a-simple-to-understand-yet-fully-functional hypothetical processor. I explained the architecture and instruction set to them, and even made them write an assembly program to add two numbers, to compare two numbers and to multiply two numbers by repeated addition. This made them learn important concepts like sequential execution of instructions, memory access, usage of registers, rudimentary arithmetic and logical operations, conditional and unconditional jumps- together they cover most of the concepts in elementary programming. And for each assembly program, I kept showing them the equivalent C program, and they were exclaiming how easy and intuitive the C programs are!

I’ll write in more detail about each of these later. But it’s been exciting for me to discover how children of 14 can learn computers at a level of detail that one would normally think is too advanced. And I strongly believe that this what’s-under-the-hood understanding will stand them in good stead whatever they learn in computers.

Rewriting ‘About me’

I was rearranging my blog, and thought it was time to rewrite the ‘about me’ page- it turned out to be an interesting exercise. I thought I’d put it up as a post.

I or Me?

I wandered into teaching not with any clarity or passion for teaching, but confused and seeking a quiet place, and work where I could mess around with several interesting things. After two years and a little more of teaching science and computers, I find that I like teaching.

But larger questions in education remain. Having read radical thinkers in education like John Holt, I realize that the problems with schools and with education is a problem with the way our society has organised itself (right from the way families are organised, how parents have full time jobs that make it impossible for them to take care of their children, how the institution of childhood makes children inferior citizens with regards to things like how they spend their time and decisions that affect them- there is a cluster of issues) and it’s not something that can be solved in schools.

John Holt writes in Instead of Education, “During most of my teaching years, this is what I spent most of my time thinking about- immediate, concrete, practical matters. Not, how can I make schools better, or even help children learn better, but how can I help this child learn to spell this word or do this problem?” I try to keep myself grounded and live in my concrete reality, and not get lost and frustrated in the land of ideas and ideals. But I find that it’s difficult.

The radical questions can never go away, but I see that to pursue them would require stepping out of the designed environment of a school, and connecting with the world, which could happen one day if energies and momentum gather organically.

***

I’ve been writing this blog for over five years now. When I go through some of my old entries (some not so old), it strikes me how much I’ve changed over these years. I laugh at some of the things I’ve written. 🙂 Sometimes you think you’re writing something profound and later when you read the same thing it looks like nonsense.

Of course I’ll continue writing nonsense, but I also plan to start writing about more concrete things, like my explorations in science, or some ideas that I tried out in class, or some computer program that I wrote, stuff like that which gives you a reassurance that you’re living in a concrete, physical world, and everything’s alright!

P.S. The title “I or Me?” is based the terms used in The User Illusion by Tor Norretranders to refer to the small part of ourselves that we become conscious of (I) and the whole organism that is Me.