Talk:Music theory

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Revised Music Theory - Based on geometric logic, namely, the tetrahedron
I have grown tired of the confusion, so I thought I'd start a new article. But I want to talk about my theory first and see what kind of responses I'll get. I'm still developing it.

However I think my theory is pretty solid and I would like to share it.

Introduction
In geometry, the tetrahedron, which is comprised of 4 equilateral triangles stuck together, is the most basic, simplest 3-dimensional solid that can be created. No other solid has less faces or total sides than the tetrahedron. Because of this, I thought to use this shape as a basis for my revised musical theory.

Firstly, I posit that music DOES have objective universal laws that it must follow. Music is a structure, and like all structures, there are rules you must follow and there are things that simply should never be done when building a structure. Many people will say that "music is subjective, there is nothing objective about it", but I disagree. I'm not going to delve too deep into philosophy, but subjectivity is not the opposite of objectivity, rather, subjectivity is when something requires uniqueness for a specific function, whereas the objectivity are the universal rules that must be followed regardless of any special circumstance. Paradoxes can't truly exist by default, so there is no reason to separate subjectivity from objectivity.

Now with that out of the way...

My theory is that, like colors that can be mismatched, so can notes. Therefore, there must be notes you can play, and notes you cannot play, at least at certain times. While this is already a part of traditional music theory, it has historically failed to clearly demonstrate why this is. But let's dive deeper into the comparison of notes and colors.

So we have a TRIANGLE of primary colors in nature. Blue, Red and Green. Together, they can create any color you can imagine. You could say the same for *additive* CMY, cyan magenta and yellow, but those colors can be broken down into RGB, whereas you cannot do the reverse. Also, being that blue is the darkest of all non-gradient colors, and green is the brightest of them all, (not on modern computer screens they do not have the power/watts to show green properly) it makes sense to use RGB as the primary colors.

So, like RGB, I believe musical notation follows a very similar pattern. Now I can prove this with a modified, corrected color wheel, but we'll deal with that some other time. I believe that 3 notes are necessary to create all musical structures. Just as with a equilateral triangle having 3 sides, which is the minimal amount of sides you can have in any shape, (circles don't count because curves have "infinite" or many sides), we need 3 primary notes to complete a section of a song. This tells the listener not only what key you're playing in, but what to feel about it, and which direction the song is going.

With the understanding that out-of-key notes don't sound right unless fixed, as mismatched colors do, we can be sure that we need a music scale so we can avoid that from happening.

Tetrahedronic Scale
We make an abstract tetrahedron here. The idea is to create 4 triangles of notes, with each triangle built on top of the last, and each one getting more spaced out and larger. A growth pattern if you will. So the idea is to land on THREES. And count by threes.

First Triangle
The first triangle is the base in our scale. We have 1,2,3. While in our scale we will skip the 2, it's necessary to build the first triangle. Now, we have 2 notes in our scale so far. The first note is used because you have to start somewhere, and we also use the third note. (land on threes).

Second Triangle
The second triangle is 1,3,5. It does the same thing, except when we get to 3, that becomes "1" triangle. So we overlap a "1" on top of it and do the same thing we did with the first triangle. So now we start at 3, skip over 4 (2) and land on a 5. So now we have 1,3,5 out of the notes we can play. That's three notes and that creates a triplet that allows for the next triangle to do something a little different.

Third Triangle
The third triangle is 3 triplets. We had one triplet last triangle, which was based on skipping over the "twos". So now we are going to do 3 of those.

The pattern now becomes: 1,3,5 (first triplet) and now we overlap 5 to a "1", and we get 5,6,8 (second triplet) and then finally 8,10,12 (third triplet).

These three triplets complete our THIRD TRIANGLE. But to clear something up, the reason we have a 6 instead of a 7, is despite what we did with the first two triangles, we already have a base set of THREE notes we can PLAY in our scale, therefore we don't need to build another "3" above that, as it is it's own triangle. Therefore, we can just do a half step up and get 6. Now that we start from 6, we skip over 7 and get to 8. (the idea is to build threes like we did with the first two triangles). Now that we are at 8, and is both a "3" therefore an overlapped "1", we now start ALL OVER again, and do the same thing to get 8,10,12. This creates the entire major scale, although we overlapped the notes.

Fourth Triangle
The fourth triangle is very straightforward. Just like in the other three triangles, we skipped some notes to create three. Aha, but we want this one to be bigger to continue in our little growth pattern. So that means, instead of skipping over notes we DON'T play in our scale, we skip over notes we CAN play in our scale. So instead of 1,3,5, we'll skip over 3 and get 5. Start from 5, skip over 6 and go to 8.

Now we have: 1,5,8. The reason we don't go to twelve, is because we only need 3. 1,5,8,12 would be FOUR. And as 12 is the end-of-octave note, and to go higher is to just start over from scratch on the next octave, we leave it at 1,5,8.

This completes our tetrahedron. It is these 3 notes, which you may call Blue (1), Red, (5) and Green (8), if you desire, that are necessary components of all songs. I believe this means that per each key in the song, you must play, in any order or in-between other notes, 1,5 and 8. Or your 1st, 3rd, and your 5th of the major scale.

To recap: Tetrahedronic Music Scale: 1,2,3 1,3,5, (playable triplet) 1,3,5 5,6,8  8,10,12 (three playable triplets) 1,5,8

This is our completed musical tetrahedron.

Colored Notes
If you play all three 1,5,8 notes (1st, 3rd, 5th) at the same time, you get what is called a regular "major chord". It's just those 3 notes. Notice how neutral and flat they seem to sound. Very "middle ground" and pleasant to hear. This is because, like when you mix RGB together you get a comfortable and neutral, flat, WHITE color, when you mix these three notes together, you get a WHITE chord. It's a "white canvas" of sound.

Musical Note Count Comparison:
To compare our notes to a physical tetrahedron we can use the following picture:

This is a pentagonal bipyramid, only problem is it was built using equilateral tetrahedrons. So it leaves a small gap in between the FIRST and the FIFTH triangle. If you count the amount of exposed triangular faces, it's a total of TWELVE faces. If you count just the top faces and the 2 faces in the small gap, you have SEVEN faces. There are 12 notes in the chromatic scale, and 7 notes in the major scale. We can do more with these equilateral tetrahedrons, however.

We can put 5 more on top of them and 5 more on the bottom, for a total of 15 tetrahedrons. So now you have 3 layers of 5 tetrahedrons. At this point, you are unable to stack anymore tetrahedrons onto our strange creation. The first correlation I noticed between this and our music scale, is that if you count the triangles we had earlier, and only the triangles that have 3 notes we can PLAY, you end up counting 15 notes.

1,2,3 is skipped because you only get 2 notes you can play. The idea is to count 3 PER TRIANGLE. 1,3,5 = 3 notes 1,3,5 5,6,8 8,10,12 = 9 notes total 1,5,8 = 15 notes total.

15 notes, 15 tetrahedrons.

Physical Comparison
Yes, and another correlation is the 1 tetrahedron, and then the 5 tetrahedrons stacked together. That's obviously correlated to our notes, but where's the 8? Well the idea is to attempt to do something similar to what we did with our music scale. So we start at 1, and then we count to 5 for the next shape. Now we start at FIVE, and count a total of 3 x 5 tetrahedrons. So, 5, and then immediately 6 for the second layer, which we then start over at 6, the middle layer becomes "7" which then gets covered up by the last layer, our magic "8". I know that sounds strange, but it's perfectly logical. With our music scale, we grew the notes based on all of the prior triangle, correct? So we can do the same thing with our tetrahedrons. Only problem is people aren't used to thinking that way. But it works.

Song Structure
There are so many things people get wrong about song structure. They think you can pretty much slap whatever sections you want in a song together, but this rarely has a pleasing effect to the ear. In fact in can be downright cringeworthy, and teeth grinding.

All songs have a main melody. This melody is what the song is *supposed* to revolve around, but like I said many musicians tend to randomly slap different sections together that have nothing to do with each other. Now, the way I see it, is we should continue growing our song with a tetrahedron.

Fundamentally, an AAAA song structure works perfectly well. It is simply 4 main melodies, as it's the only melody in the song. 4 main melodies, much like 4 triangles. Now we have another tetrahedron!

What if we wanted to add other sections though? That's where it gets a bit tricky. Like I said most song structure have very obvious flaws. But first of all, you always need 4 main melody instances in every song. For the purpose of this explanation, we will automatically designate ALL MAIN MELODIES as "A".

Examples:
Ex 1: AAbAA This works. You have your 4 main melody sections (tetrahedron), but we have a b in the middle. This is allowed because it's symmetrical and does not interefere with our main melody therefore.

Ex 2: AABBAA This is correct for the same reason as above, just with an extra b.

Ex 3: AAABBA This works because the pattern becomes a decrement of 1 for each section switch. We start with 3 As, then decrement by 1 and get 2 bs, and then back to A and get 1 a.

You could even draw it like this to see the pattern more easily: A B B A A A

Ex 4: ABABABAB

This one is the simplest. You just alternate until you get 4 of each. There's many variations of this, but all simple.

Ex 5: ABAABA

Another example that is self-explanatory.

So you see, even song structures look better when stringing them together in a pattern. I think if everyone did this instead, we'd have much better sounding songs. But that is not all.

Notational Patterns
Within your main melody, you can be as creative and wacky as you want, as long as you have 1,5,8 being played somewhere somehow for each key, doesn't matter the octave or instrument arrangements, as long as they are played the same way in the next instance of the A (main melody). The hard part is getting your other sections (b,c,d .... etc.) to revolve around your A.

This means we need to "patternize" our sections to reflect the main melody in a certain way. This requires more and more work the crazier and wackier the main melody is. But it can be done.

Examples:
STANDARD C MAJOR EXAMPLES: Ex 1: A (main melody ) = 1st, 3rd, 5th, 5th B = 3rd, 5th, 7th, 7th.

So what is the pattern here? Yes we went from start at 1 to starting at 3. Makes sense doesn't it? We then just have the same pattern of skipped notes. So we get 3rd, 5th, 7th, and 7th.

This works because we can EASILY attribute it to what the A (main melody) did.

Ex 2: A = 1st, 3rd, 5th, 5th B = 1st,3rd,5th,5th,1st,3rd,5th,5th

Now the only way this works is to play B twice as fast as A. Otherwise you're just getting 2 more of A. The reason this works is because it is a factoring of A. You're doing A sped up 2x in tempo. Why not 3 times? Because in order to reflect our A, it must be a factor of A in some way, because you can easily derive a pattern simply by copying what A does in some way. So if A is played at 60 bpm, then you can play b at 120bpm. You're just copying A's tempo twice. Now again, the factoring is done in the first example, but it can also be done with tempo, even with octaval changes. There are many ways to do this. But you must either multiply a property of A, or divide it in half. It is always a "n2" (number x 2) algebraic equation if you will. Or n/2. (division).

That's all for now I'll update this later. Thanks for reading.

— Preceding unsigned comment added by 65.114.164.32 (talk) 20:14, 16 April 2021 (UTC)
 * We don't publish original research. intforce (talk) 19:15, 16 April 2021 (UTC)

revised tetraheadtronic
This is most helful nice and understandable Basavraj satyappa marennawar (talk) 06:31, 11 September 2021 (UTC)

ÑÑÑ This article misrepresents the goal of Schenkerian music theory. The supposed underlying structures which the article describes as being subject to interpretation by Schenkerians are, themselves, mere interpretation, and are not even essentially analytic. Unless readers are to understand that the goal is to interpret a prior interpretation of something - something already interpreted as being underlying structure - readers stand to become misled about the wrong thing. Further, this interpretation-of-interpretation is not the goal; the goal is to mystify musical structure in such a way that members of an elite group of scholars can represent itself as having supernatural musical insight that non-members can only achieve by means of subscription to the group's dogma. - Joshua Clement Broyles ÑÑÑ — Preceding unsigned comment added by 190.24.21.66 (talk) 21:13, 16 December 2021 (UTC)

Wiki Education assignment: Introduction to Public Musicology
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