Please start with lesson one and read up until here if you haven't already.
Lesson 3: The Physics of Music
So in the last less we talked a lot about the fractal wave of music history moving from modal consonance to harmonic dissonance and back again. Interesting how our collective meme brain moves in this manner. It makes me wonder what the next version of tonal harmony will be as we come out of the current "bubble gum" era and start to ramp up the sophistication. I digress.
Let's talk about SOUND. In particular, "musical" sounds. I wish I had a better word for them. Perhaps "resonating tones" is less esoteric. I'm talking about sounds that have enough of a centered pitch that our ears can pinpoint the fundamental note of that sound. As I write there's a person outside with a weed-whacker that I can tell you is spinning around 100 times per second(I suppose if I were designing a weed-whacker I'd give 100/sec a try for a throttle speed on the motor). It's pitch is a low G#. That same G# on a piano will have the strings associated with that key vibrating at roughly 100 times a second too(103.83hz to be precise).
Here's where it gets interesting. Almost no sound in nature is going to resonate perfectly smoothly. A sine wave is a strange thing to our ears. If you listen to one for too long you'll probably start to feel like you're going nuts. If you get a nice low pitched sine wave going, you'll probably start hearing sympathetic vibrations of objects around the room or even get distortion from your speakers wrecking the smoothness of the wave. Those imperfections are called harmonics. Those harmonics are mathematically related to the fundamental pitch but are rarely perfectly in tune(this is called inharmonicity, a very fun thing). The amount of various harmonics and the imperfections in the harmonics tuning along with noise character(like the knocking sound of a piano hammer on the strings) give various musical sounds distinctive characters. The technical term for this is timbre.
You'll notice that once you get beyond the 6th harmonic, stuff starts to sound a little weird. This is because there was a point in history when composers wanted to start playing single pieces of music that contained various keys. By "keys" I mean music with a sound that has a strong gravitational pull towards a "home base" note(discussed at length in lesson two). Having a home base pitch gives you somewhere to depart from and then return to. You can't have a pull towards anything if you don't strongly define it. So in tonal music the composer will define a key center, depart from it, and then return back(like the hero's journey). The problem was, composers increasingly wanted to wander farther and farther away from home to increase the tension in the middle sections of their compositions. With singing voices this is not a problem because you can adjust the tuning of your voice freely, but baroque and medieval composers were experimenting with some new inventions and the renaissance cathedral builders needed some audible power to give their masterpieces some emotional weight. (notice the maze in the middle of the Chartres cathedral where you end up at the exact center of the cathedral. The renaissance European was really into those kinds of ideas).
Anyways, you'll remember from the videos about harmonics the slightly gross sounding 7th harmonic. At this point I have to let you in on an uncomfortable secret that the famous galaxy brain music theory lectures fail to mention explicitly: all intervals on keyboard, fretted and keyed wind instruments(save the octave) are deliberately tuned... out of tune. Do not ask me why God put this implicit inharmonicity into what could potentially be a perfectly beautiful, mathematically elegant system. Maybe music would suck if there wasn't this tiny bit of fudge factor giving a little bit of tension to the whole thing? I'm not a theologian but you can blame Bach for deliberately defying Pythagoras and Mother Nature outright.
We'll discuss more about this fudge factor in later lessons,(**pun alert**) it's actually a minor issue. For now let's ignore it so we can learn how scales are derived from the harmonic series.
Assuming a fundamental of C, here's what we get:
Fund.: C
2nd: C
3rd: G
4th: C
5th: E
6th: G
7th: Bb
Hilariously, what we have here is nothing like a scale. Rearranged into order we don't even get a proper pentatonic scale. We do get a C7 chord which doesn't ever feel like home. Soooo what the heck is going on here and why does Leonard Bernstein insist that the major scale is derived from nature??
It turns out that Western music as we know it is more of an artifact of Western philosophy and religion than thinkers like Bernstein have lead us to believe. But rather than boring you with a screed on why - jazz is awesome but claims that when we meet aliens they'll also play jazz - are ridiculous and completely false, you can just watch this dope video and we'll just get on with our lives.
So, starting with C you go up the interval of a fifth which corresponds with that 3rd harmonic, the note G. Then you take a another fifth from that G and you get a D. A fifth from the D is an A. And then a fifth from the A is an E. If you're Pythagoras and doing this mathematically perfectly because you believe in an elegant universe that E is so sharply out of tune with the E you get from the 5th harmonic(of the original C you started with) that it feels like you're being stabbed in the eye. This is the ancient Greek equivalent of the Double Slit Experiment. After centuries of messing around, Bach(who may have stolen the idea from the Chinese) decided that the best way to get it close enough to not be eye-stabbingly sharp is to tune the fifths 6% FLAT. Then you can go allll the way around the horn in the pattern(which you must now memorize forwards and backwards) and nail the starting C perfectly in tune:
C G D A E B F# C# G# D# A# F C
or
C G D A E B Gb Db Ab Eb Bb F C
This, as you may have astutely ascertained, is called the circle of fifths.
It's actually more important to memorize these in reverse because chords move in falling fifths - V to I - the reasons which we will continue to explore in later lessons. But for now here's how I like to memorize this pattern:
C F Bb Eb Ab Db Gb B E A D G C
F Bb Eb Ab Db Gb B E A D G C F
Bb Eb Ab Db Gb B E A D G C F Bb
Eb Ab Db Gb B E A D G C F Bb Eb
Ab Db Gb B E A D G C F Bb Eb Ab
Db Gb B E A D G C F Bb Eb Ab Db
Gb B E A D G C F Bb Eb Ab Db Gb
B E A D G C F Bb Eb Ab Db Gb B
E A D G C F Bb Eb Ab Db Gb B E
A D G C F Bb Eb Ab Db Gb B E A
D G C F Bb Eb Ab Db Gb B E A D
G F Bb Eb Ab Db Gb B E A D G
Write this pattern out on paper until you can do it quickly without making a mistake and music theory super powers will be yours!

 

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