Absolute basic theory question(s)

Not so rambling... those questions form the foundation of theory.

1. Why do some notes sound good with others? It's mostly interaction between frequencies. A (440 vibrations per second) sounds good with E, because E is vibrating at about 660 times per second - so several times per second, the vibrations reinforce each other... when E has vibrated twice, A has vibrated three times.

2. We use the same letter name if notes are exact multiples of each other. One A will be at 440 times per second, the next at 880. Since these are exact multiples, they're the best sounding (most 'consonant') combinations you can get.

3. Sharps and flats came late to music. We started out in one key - the white notes of the piano today. After a while, people discovered that certain notes sounded better if they were sung flat, rather than exactly matching the pitch. Eventually, we noted these changes as sharps or flats.

But the underlying white keys aren't symmetrical. Scales came about long before we understood (or could measure) the frequencies involved. So the original notes were just ones that sounded good together. As a result, sometimes when you flat a white key you get another white key - and sometimes you don't. In theory, any note can be flatted or sharped - but 'F flat' ends up being the same note as 'E'.

Not so rambling... those questions form the foundation of theory.

1. Why do some notes sound good with others? It's mostly interaction between frequencies. A (440 vibrations per second) sounds good with E, because E is vibrating at about 660 times per second - so several times per second, the vibrations reinforce each other... when E has vibrated twice, A has vibrated three times.

Oh, wave interference and vector addition. Ok, I can get my mind around that.

2. We use the same letter name if notes are exact multiples of each other. One A will be at 440 times per second, the next at 880.
That's what I thought. At least I had something right.
3. Sharps and flats came late to music. We started out in one key - the white notes of the piano today. After a while, people discovered that certain notes sounded better if they were sung flat, rather than exactly matching the pitch. Eventually, we noted these changes as sharps or flats.

But the underlying white keys aren't symmetrical. Scales came about long before we understood (or could measure) the frequencies involved. So the original notes were just ones that sounded good together. As a result, sometimes when you flat a white key you get another white key - and sometimes you don't. In theory, any note can be flatted or sharped - but 'F flat' ends up being the same note as 'E'.

Ok, that helps. Thanks.
The fog isn't gone, but there may be a slight glimmer of clarity on the horizon. I just hope I can hold onto that when I get home and try to hear what it sounds like.
I have the feeling that I am getting too hung up on "getting it all" right away. I was hoping to have an "AH HA!!!" moment, but itis looking like this is the sort of understanding that is best snuck up on.

Kent! You need to read "Fundamentals of Musical Acoustics" by Arthur Benade.

Ill just simpily say after playing for enough time all those sounds will fall into place and it becomes second nature.

Kent,

I'm guessing if you follow Ricochet's suggestion and pursue reading in acoustics, it'll raise as many questions as it answers. I'm all for learning as much as you can - but going into any study of music theory, acoustics, etc. you need to be aware of a couple of things:

1. Music is an art. Although we sometimes discover things that 'explain' the art with science, like the octave relationship between intervals... there are other times science won't quite do it.

2. Music production, i.e. instrument building and modern analog/digital engineering, is a craft. Improvements are made as new materials and building technqiues are discovered, and as our understanding of the underlying science of sound changes. As a result, music itself changes over time! Many of the instruments of Mozart's day aren't capable of producing the sounds we get from the same instruments today... but some of today's instruments aren't capable of getting what Mozart heard, either; when you hear 'old' music played, it won't sound like it did then, unless it's done on period instruments.

As a result, applying a hard science like acoustics, or an organizational system like music theory, is very dependent on the time period involved, and the compromises dictated by our abilities and understanding. I didn't get into the evolutionary details in my earlier post, but if you're going to look into things deeper, I probably should :)

I said the interaction between E and A was 3:2 (660:440). That used to be true, about 400-500 years ago. Today it's not quite true... because if you step through fifths from A until you get to the next A, you find it's not an exact multiple of the first one - it's a little too high. This anomaly is called the 'Pythagorean comma'. It wasn't a big deal back then, because as long as you stay in one key, the distance you have to go to really get things out of tune is about the full range of human hearing. But as we started to modulate between keys, it made for jarring changes between, say, C major and C minor - so our tuning adapted as we kept adding sharps and flats.

I also said F flat was the same note as E. That's true today, but wasn't about 600 years ago - back when they tuned according to Pythagorean intervals, they ended up being different notes*. Builders of keyboard instruments forced the change into the system we use today, a process that actually took about 400 years to arrive at the tones we use today.

Because music is an art at its core, rather than a natural phenomenon, the music we produce is a reflection of the science of our times. In other fields, like physics, developments in science simply refine the way we view an unchangeable natural truth - in music, it's the 'truth' that adapts as we go along.

*- again, I'm simplifying. Fb and E weren't played differently.... but D# and Eb were! Our understanding of the Pythagoran comma took time, and it's when things got totally out of hand - when keyboard instruments needed about 17 keys to the octave - that we changed; we never actually got around to dealing with Fb/E.

NoteBoat, you ought to read that book, too. It's a book on musical acoustics for musicians, written by a physicist who was a musician and an instrument builder/modifier. Will it raise more questions, and make you think about things that you never would've thought of otherwise? Certainly!
8)