Why Is There No E Sharp?

In an attempt to at least try and get to know my theremin a bit better, I caved and bought Carolina Eyck's The Art of Playing the Theremin. I mean, her instructional videos on YouTube are great, but they don't really give you a proper sense of how to move your fingers when playing a tune. Her book, on the other hand, does.

It's probably obvious to everyone else in the world, and I'm not sure what exactly I was expecting, but it turns out that you have to know how to read sheet music in order to fully benefit from the book. Crazy, right?

Unfortunately, to put it bluntly, I know pretty much nothing about reading sheet music - or music in general, really. Given that I really want to learn how to play my theremin, however, I decided to give it a go. What follows are some of my first impressions while learning the basics of this entirely new (to me) domain of knowledge, from the perspective of a 40 year old software developer starting almost entirely from zero.

Do Re Mi

Okay, so I'm not starting exactly from zero. Like most people, I was at least partially familiar with the Do-Re-Mi song from The Sound of Music. I understood, more or less, that the syllables were sounding out the notes in an octave and, furthermore, that octaves "repeated" - a pitch from one octave and the corresponding pitch from a higher octave were perceived, in some sense, to be the same note, in what has been referred to as "the basic miracle of music".

I even understood, in a limited way, that you could sound out the Do-Re-Mi musical pattern on a piano by hitting a certain contiguous sequence of white keys. And I knew that the sounds and the keys were associated with letters (the Do sound was a C, I knew, and the Re sound was a D).

But I didn't really give the topic much thought beyond that. The term "major scale" had not yet entered my brain. I was under the hazy impression that you could basically play any tune you wanted with only these 7 notes, repeated indefinitely as octaves are.

To be fair, I did have a vague notion that there existed these mysterious notes called "sharps" and "flats", and I had the sense that they were somehow related to the black keys on a piano, but I had no idea what role they played in a Do-Re-Mi world, so I basically just ignored them.

It's weird, I know. I mean, what did I think the black keys were used for? Jazz?

Major Scales and Colour Wheels

Read enough on the topic and you eventually discover that Do-Re-Mi is an example of something called a major scale - the C major scale to be precise. One line stands out from the Wikipedia article on major scales:

The simplest major scale to write is C major, the only major scale not requiring sharps or flats

This tells me a couple of things:

  • There are other major scales aside from C major, which means that there's more to music than Do-Re-Mi. Who knew?
  • The sharps and flats become important when you start constructing other major scales.

What's not immediately clear is why. Why are sharps and flats required for other major scales? How exactly does one go about making a major scale?

When faced with these kinds of inquiries, you very soon come across something called the chromatic scale. It's often depicted as a circle like this:

Chromatic scale

Chromatic means "colour" in Greek, and I'm not entirely sure why it's used in this context. Is it supposed to evoke the image of a colour palette? Are notes considered "colourful" to certain people? I don't know.

It's a bit of a simplification, but the chromatic scale basically contains all the notes that one ever hears in Western classical music. I find it amazing and disconcerting that the whole of Western music is built from a repertoire of only 12 notes, but there you have it.

All other scales are necessarily a subset of the chromatic scale. In particular, with a major scale, one selects 7 notes from the chromatic scale according to the following frequency pattern:

whole, whole, half, whole, whole, whole, half

A "half" in this context means one "hour" of the chromatic circle, so a "whole" means two "hours". A major scale is obtained by picking any note on the circle and counting out the interval pattern above until you get to the same spot again, thus obtaining an octave. Since you can start from any note, there are 12 major scales.

In particular, if you start from C, and you follow the pattern, you get C, D, E, F, G, A, B, and C again. You've just written out the C major scale, the simplest one because it skips all the sharp notes in between and thus can be played using only the white keys on a piano. As the above quote mentions, it's the only major scale with this feature; all the other major scales have at least one sharp in them. D major, for example, consists of the notes D, E, F#, G, A, B, C# and D again.

Why is There No E Sharp?

As someone mulling these things over for the first time in his life, I'm immediately struck by the weirdness in chromatic labeling. Why is there a note (C#) in between C and D, that feels like it was added as an afterthought? Conversely, why is there no note between E and F? Or to put it another way, why is C# not simply called a D? It's the next letter, after all. Or, if you insist on having sharps in between the notes, then why is F not called an E#?

All things considered, why not just label the notes 1 through 12, or A through L?

I mean, it's all very well and good to say that the C major scale skips all the sharp notes, but that's only true because someone decided, seemingly arbitrarily, that a major scale followed a certain interval pattern (W, W, H, W, W, W, H) and, furthermore, decided that there was no sharp in between E and F.

What's so special about a C major scale that we will seemingly bend over backwards in order to be able to label its notes with simple, unadorned letters - to the point where every other note in the chromatic scale is labeled as a kind of "correction" to these notes? I honestly don't know. I get the impression that asking these kinds of questions is akin to asking why a yard has 36 inches. There's an answer, of course, but it's not particularly germane to the task at hand, which is to be able to play a tune.

Idle Speculation

Of course, I can make what I hope are educated guesses.

If you look at the interval pattern for a major scale (W, W, H, W, W, W, H) you can see that it can be broken down into two patterns of intervals (W, W, H) separated by a whole interval.

If you consider just C major, for example, you get the first group of notes C, D, E, F and the second group of notes G, A, B, C, separated by a whole interval. For each group of four notes, the ratio of the heighest note to the lowest note is about 4:3.

I suppose that the ancient Greeks simply thought that these two notes sounded nice together in that ratio. If you consider that the quintessential lyre has 4 strings, you can imagine an ancient musician making sure the first and last strings on his instrument contained those two notes.

When deciding how to tune the two middle strings, I can imagine this hypothetical musician deciding to do something fairly simple - space them both one whole interval apart, starting with the first string. Doing so, of course, means that the distance between the third and fourth strings is only a half interval, but such is life. Label the strings and you have, roughly, half a major scale.

Is this accurate? I have no idea, but it seems plausible to me. One starts with some fixed constraints (for example, the constraint that one always needs two strings in a 4:3 ratio), and you fill in the rest around those constraints.

Of course this doesn't explain why the notes in C major scale, in particular, all get simple letters. Maybe middle C is just a really easy note to play?

Will This Help?

It says something about my personality that I find all this music theory somewhat more interesting than actually practising my theremin. It's a character flaw; I'm more bookish than practical.

So all this theory, while fascinating, does not help me play an instrument.

Not sure how to get around this, except to just put the research down and start playing, I guess. We'll see how it goes.