Learning Music theory logically

What's the best logical progression of learning music theory?

I learn things best from a logical standpoint - if I know the bare basics, then I can expand on that easily on my own.

For example, learning something like geometry, you start with the properties of a line and from that derive the properties of a triangle.

I already know scales (though I need practice on implementation ;), but where would be a good place to start? The circle of 5ths? Somewhere before that?

Thanks ;)

Learning how chords are built on each note of the scale and how the different chord types are constructed seems like a good place to start................

Is there anything about why they are constructed the way they are? I do have to work on the how of these things too (that's what implementation is), but I feel it'd help me understand it more if there was a reason a major scale is built 1-1-1/2-1-1-1-1/2. (And why, the 1st, 3rd, and 5th notes in the scale make up a basic major chord)

Actually, that's all a matter of convention. It comes from the greeks, that have calculated the way scales and mode ought to be. We stick to 12 notes per octave, but some countries have 18/20 etc... notes per octave. Their music sounds weird to us, but it's the same thing the other way around.

And the notes were set with the harmonics (see the 12th 5th and 7th fret) of a resonating body, brought back to an octave. There were lots of problem, since some of those notes aren't quite 'equal', so to build some instruments, like the guitar, you have to have some 'off' notes.

"The Overtone Series" plays a big part in developing western music theory. There is a special way of doing it on the piano (I forget) where if you play a note you can hear the harmonic of a perfect 5th ringing above it, then an octave above that, then a 3rd etc, etc..Peter Bernstien did a 3 part lecture series on it that was quite fascinating (its on video)some libraries have it.

if you like math you'll enjoy these links about the overtone series:
http://graham.main.nc.us/~bhammel/MUSIC/ovrtns.html
http://www.phy.mtu.edu/~suits/overtone.html
http://www.2.smu.edu/totw/overtone.htm

[Edited by chris mood on 10-23-2002 at 10:37 AM]

well - there are severyl kinds of approaches for why nowadays music sounds the way it sounds.

There are a few kinds of tunings:

Clean Tuning (Natural tuning/diatonic tuning)

is the mathematically correct way to tune an instrument.
It is based on a partial tone series which is divided by 12 tones per octave. A fifth for example whould have factor 1.5 and a third factor 1.25 from the root tone.

The problem with this tuning:
Since frequencies of the partialtones depend on the root tone the tone "f" for example would sound slightly different on an instrument that is tuned in G than on an instrument that for example is tuned in C. In other words: on an instrument that is tuned in C with this kind of tuning you would only be able to play C Major. Playing in another scale would sound like crap for the intervalls would not be correct anymore.

In order to avoid this problem the "well tempered tuning" has been set up at the beginning of the 18th century (which was replaced by equal tempered tuning in the 19th century)

Well Tempered Tuning:

From aprox 1700 the well tempered tunings where winning through (yes - there where more than just one well tempered tuning). Those where specific tunings with the same goal - a tuning that allows you to play all scales on one instrument. The most common one of those was probably the "Werckmeister-Tuning" introduced by Andreas Werckmeister in 1691 in Europe.

In the first half of the 18th century Johann Sebastian Bach was inspired by Werckmeisters work and wrote his pieces of "the well tempered Clavier" which finally helped the well tempered tuning to make its breaktrough. From this point on it began to replace the still conventional diatonic tuning more and more.

All those well tempered tunings have one thing in common: a very distinct tone-characteristic. since the frequency-ratios are not identical to those of the equal tempered tuning, every key has its own characteristic sound.

Equal tempered tuning (chromatic tuning):

In 1559 price Chu Tsai Yü (china) was doing calculations on frequency ratios that allow to play an instrument cromatically (actually he worked out the 12th root of 2:1 precisely to 9 places). The resulting equal tempered tuning is therefore also called "Cromatic tuning".

Basically this tuning is a controlled detuning of the partialtones. The definition of a halftone is a frequency that is multiplied by (aprox) 1,0594631 (1,0594631 = 12th root of 2). A wholetonestep therefore would be a multiplication of a frequency with factor 1,0594631².
An equal tempered fifth would be 1,0594631^7 respectively the root multiplied by 1,4983. IN diatonic tuning the fifth would be 1.5 (see the difference?)

Because of the equal tempered tuning there comes a special intarvall into play: the tritonus. It is an intervall of exaclty 3 fulltones and divides the octave in exactly two halves. The tritonus cannot realy be compared with an interval of the diatonic tuning and therfore it sounds extremely out of tune to peeps who are used to diatonic tuning. Thats why it was called tonus diabolicus or diabolos in musica (devil in music).

[Edited by Azrael on 10-28-2002 at 10:32 AM]

now that sounds fun... I'll have to work out some of the math - especially on the "Equal Tempered Tuning" - thank goodness we have calculators now... the twelfth root of two must have been a bear to figure out to nine decimal places!

Uh ya . . . all this BS is nice, but it's not gunna help you learn theory at all. You're not gunna stand there during your guitar solo wondering which note is 1.25 factor from the root tone. If you want to learn how to play your instrument effectively, learn how to play all the scales, chords, and intervals in every position across the fretboard. Then you'll be on your way to "logically" doing something.

thats typical - not knowing anything about how something works but bitchin around.

"i dont give a damn at quantumphysics - i dont need that ****" .. saying that he went away and turned on his CD player...

you are one of those who believes that electricity comes from the outlet, eh?

Without all those dudes who sat there and did some serious research on this "BS" as you call it, you would not even HAVE theory and scales that you could learn!

[Edited by Azrael on 10-28-2002 at 12:21 PM]

So what . . . ???

You don't have to be an electrical engineer to plug in and use a toaster, and you don't have to understand the physics and mathematics of sound waves to play an instrument.

as well as you dont have to call everything you dont understand bullsh*t.

Thats not the way someone who leads a Music THEORY forum should act like IMHO



[Edited by Azrael on 10-28-2002 at 01:31 PM]

I have to agree with Azrael. I may not have a Masters in Music, but this is music theory, not just the ravings of modes and chords.

To use your slightly unfounded metaphore... you certainly don't need an electrical engineering degree to plug in and use a toaster, nor do you need a music degree to listen to a stereo.

You don't need an electrical engineering degree to put together a toaster, but you need the knowledge of a technician in order to do it; neither do you need a music degree to play or sing a song, but you need at least the basic training of how to do it. The more pieces you know how to put together, the better you'll do (at either job).

You do need a basic understanding of electronics to design a toaster. If you have really deep understanding of electronics, perhaps you can design a radio or computer. Similarly, if you have basic understanding of how music works, you can certainly design a song or play a riff around a chord - if you have much understanding of music theory you can create your own songs.

With both professions, the more you know - the better you'll be able to do what you do. If you know why music exists, perhaps you'd be able to bring music to an entirely new level. The guitar wasn't a god given instrument (nor was the calculator) - someone had to come up with it, and there has to be a reason they did.

Everyone has their own strengths - if one person's is math, but another's is performance, who are you to say how they should go about learning music. (After all, music is just an application of the science of sound - and all science is based on mathematics).

Ya whatever . . .

Originally posted by Azrael
Thats not the way someone who leads a Music THEORY forum should act like IMHO

LOL . . . I stand corrected. I guess I fail to see how understanding all the mathematics is going to help anyone construct a better solo or write a better song. An electrical engineer gets the same toast as everyone else. Peace out, biz-atch! :)

Heh, just kidding about that biz-atch thing. :D

as far as i´m concerned i expect a theory forum to talk about music theory/history and not how to write a better solo or song - we have other forums here that handle these topics (guitar basics, songwriting, Technique & Style)

The answer to your question.
Steven pinker wrote about overtones, the fundamental note.
U see in nature when a monkey makes his mating call, u only preseeve the one note, The fundamental. But in way he sang out 8 notes at once, each one double the frequency of the last(why? becauce it proved to be easy for evolutionaryly construct voice box to reproduce) these notes are mind compreend on a sub concience level. These overtones can be heard on they´re own. Theses notes have been re-arranged and now comprise our scales. You probably got more then what u baggined for but this point zero on why we have the inventory of notes that we do.
This is a very incomplete explantion, i´m sorry. And my english is pretty bad, i´ve been attending a brazilian school for the last 3 years.

of course alot of overtones are included in almost EVERY tone you hear - that is what makes a piano sound like a piano and a horn sound like a horn - you can tell what instrument it is even when they play the same note - its the color of the tone and it depends on the overtones (not only , but to a very very big part)

O.K. guys, I dont' follow the scary science and for the moment I'm not even going to try to much as I'd love to understand but perhaps some of you would be interested to see Edward Lucy's site on tuning. He recons that 12 tone even-tempered tuning should be supplanted with a tuning system based more completely on overtones which he explains at some length on his website; along with all of theory there are also some transcriptions of popular melodies like Fur elise etc into Lucy Tuning. He even provides ratios of fret distances so people can make Lucy tuned guitars. Personally the challenge looks to scary to comprehend; 18 or 21 semitones per octave and hundreds more scales doesn't seems unatainable for me but it gives me a queesy feeling that we're using out moded (pun intended now i've spotted it) methods. Check it out, it's brilliant!

http://www.harmonics.com/lucy/ltindex.html