When I was a bored pre-teen, I used to sit at the family piano and hit keys on it, trying to figure out how they worked. I knew music somehow came out of it, but music itself eluded me. I was too caught-up in why music was music. WHY WERE THERE BLACK KEYS AND WHITE KEYS? WHY IS MIDDLE C NOT RIGHT IN THE MIDDLE? SHOULDN’T IT BE THE KEY EXACTLY IN THE MIDDLE? And so on. Not finding any joy in being forced to play the piano for the sake of playing someone else’s music, I never followed up on it. I did have two years of band in junior high school, when I played the flute very badly. And also from the 4th through 8th grade, I used to play the harmonica, working out how to play hymns because that seemed to be the only music that would play on a C Major harmonica. It drove me nuts when I discovered that there were other kinds of harmonicas, including ones with the ability to transpose with a little button. Eventually, I discovered computer graphics and was distracted by the wonders of code for the next 30-some years.

I’m 43 now, and it occurs to me that maybe now I’m capable of finding my own answers. I’ve done research here and there, as I’ve learned about digital audio and waveform synthesis. I’ve also gained an appreciation of music as a kind of arrangement of elements, and therefore composition is hugely interesting to me. It always struck me that there was some kind of emotional logic behind notes, scales, and their maddeningly illogical arrangement on the keyboard. I’ve talked to musicians and have been listening to jam sessions, courtesy of the awesome people at our local music temple Studio 99. I’ve sat through hours of piano practice with my pianist friend Angela, striving to listen for what she was listening for. The conclusion I’ve come to is that it may be worth starting again from age six, but this time paying attention to my questions so I can answer them in my own way.

With that, I’ve dragged out an old Kurzweil SP88 Electric Piano, 88 keys of weighted action, and have plugged it into the stereo to answer some of those old questions.

Middle C

I just noticed that the keyboard’s lowest key is an A. That makes sense. And then there are 8 of them. The very highest key is a C. There are 8 of those too.

Because we live in the magic land of the Internet, I can look up the piano key frequencies and see that the lowest A thrums at 27.5Hz. The highest frequency, of key 88 (C8) is 4186.01Hz. Interestingly, that roughly corresponds with the highest frequency that ISDN telephony could encode, at around 8000 9-bit samples a second, for a maximum frequency of 4000Hz or so for intelligible speech. Is the range of music regarded within intelligible speech range? I see that A440 is just a few keys above Middle C. This is the 440Hz tuning standard, I seem to recall.

I’m curious about Middle C. Why is it always mentioned? It’s probably just a reference point. It’s a good note that’s common across multiple instruments, perhaps. Who knows? A440 is sometimes known as “Concert A”, which is a tuning standard for an orchestra. Interestingly, there are multiple standards. The Concert A has wandered from 415 to 435 to 440. There’s some reference here to “transposing instruments” like a clarinet or trumpet. From what I can gather, the transposition applies to what note a given fingering will play; the example given is that a Bb clarinet plays that note with the C fingering is used. It has something to do with ease of transcription of music on the musical staff. Weird.

Anyway, back to pitch…it’s important to remember that there was no accurate way to measure pitch until the 1830s. Therefore, pitch wandered, and grew ever higher because higher pitches sounded “brighter”, leading to what Wikipedia calls “pitch inflation”, which strained voices. The French passed a LAW to set it at 435Hz. Then it eventually became 439Hz, then to become 440Hz (439, being a prime number, was difficult to reproduce in a lab so they bumped it up to 440).

It’s no wonder that I never learned how to play anything…the musical theory fascinates me so much that I am distracted from the actual practice.

Anyway, back to Middle C. I play it, and it’s surprisingly dour. That’s my impression right off. It feels slightly down. Then again, all the notes sound that way. Maybe it’s the timbre of this particular electric piano. It’s an unadorned, naked sound. Could it be the way I played it? I just whacked the key and held it down. Pressing it more swiftly and lightly produced a different emotional response. As I run through some of the other piano samples, I think my initial reaction to the note was that it was a little muffled sounding.

What goes with Middle C?

When I was a kid, I had noticed right away that certain notes sounds good with Middle C. I later learned that I had found something called a “Major Triad”, comprised of the 1, 3, and 5 keys. It drove me nuts trying to figure out why it was called the 3rd and the fifth, until someone explained to me that a “key” (as in the key of C Major, which uses all white keys and no black keys) is numbered 1 through 7. I think a “key” is the same as a “scale”.

Anyway, it baffled me that it was easy to find two-note combos. The 1-3 combo sounded (playing it again) good. The 1-3-5 (the major triad) sounded more resolved. The ultimate resolution, I discovered, was when you topped off the 1-3-5 with the same starting note one octave higher.

The next easiest good-sounding two-note combos, after the 1-3, was 1-4 (which sounded a little thinner to me) and the 1-5 (even thinner than 1-4). The 1-6 reminds me of the 1-4, maybe a little more shrill. The 1-7 sounded discordant. Then the 1-8 (unison…not sure if you can even call it an 8) sounds very thin indeed, but it is resolute and complete in itself. Those notes are an octave apart, which to our ears sounds like the restart of the notes, just pitched a “multiple” higher.

Recognizing that a unison shared common multiples of the same frequencies, I once plotted out a graph of frequencies relative to each other to try to see what consonance “looked like”. I just recreated this:

Where the colors combine to form black, that is where the greatest harmonic reinforcement is occurring. If there are many regular overlapping patterns, then they strongly stand out and I guess this somehow is pleasing to our ear. Or so is my theory. I was reading a bit more about just intonation to get an idea of where our musical scales came from as a vehicle for playing pleasing consonant tones together. I know that the piano is using a kluge called “equal temperament” to allow many scales to play on the piano, none of them quite perfect, but close enough.

And that’s my musical exploration for the day. On a side note, this post I found about the metaphysics of music has a lot of interesting relationships noted on one page; I found it when I tried to find out what “half an octave” would be.