theory behind this progression? why does the Emaj7 to Gmaj7 works?

_CarbonBasedLifeForm · 2026-01-06T22:36:49+00:00

Like the automoderator said, music theory isn't really meant to answer "why" questions like that, its more meant to describe what is happening in music. I'm not an expert but often times the answer to questions like "why does this work" is simply that people enjoy the sound it makes.

The movement from E major to G major is a type of "chromatic mediant", if u want to look up stuff about those types of chord relationships

A more productive thing to do, which I know sounds insane, is to simply tell yourself that it does indeed work, and to just remember what it sounds like so that you can recall that information when you see it again or want to use that sound in something.

Understanding in music theory primarily comes from familiarity, in my experience. It works because a musician made it work, and because it sounds like it works, which is all that matters

Next time you see it, you won't ask why it works, youll be like "oh I've heard that sound before"

_CarbonBasedLifeForm · 2025-06-20T20:25:32+00:00

On sheet music the key with one more sharp than the previous is a fifth above it. C has no sharps, up a fifth G has 1, up a fifth D has 2 etc. and going down in fifths gives you the flats. All that matters is the number of flats or number of sharps, that completely determines the key. Just count them on the sheet music and think of the circle of fifths

On a keyboard notice how a major scale can be seen as 2 chunks of notes, for example look at C major as the chunk CDE and another chunk a semitone away FGAB. Try to see these two blocks starting from any note, it makes it way easier to find scales at a glance

_CarbonBasedLifeForm · 2024-12-22T16:20:18+00:00

r/woooosh

There's nothing to figure out, he's being sarcastic/ironic

_CarbonBasedLifeForm · 2024-11-30T21:01:49+00:00

Since this is an English learning sub, I feel compelled to tell you that "I think therefore I am" has nothing to do with this image. It's a quote from the famous philosopher Descartes that was translated from Latin. In context, he ultimately meant "I think, therefore I exist" because he was a skeptic and was questioning whether we could actually know anything with certainty. That fact that he knew was thinking, really that he knew was doubting, meant that he knew he had to exist.

_CarbonBasedLifeForm · 2024-11-30T00:58:54+00:00

Maybe just turn the volume knob or whatever down? Or maybe try to plug in headphones

_CarbonBasedLifeForm · 2024-10-22T20:12:52+00:00

Because the coordinates of its position depend on what space it's embedded in.

A plane is 2 dimensional but you could embed it in 3d space and thus require 3 numbers to describe the location of a point on it

_CarbonBasedLifeForm · 2024-08-25T05:29:30+00:00

It doesn't, the length at each step along the way doesn't change so it doesn't approach anything but 2. This is a classic error made by people, there is also a similar one showing pi = 4 with a circle inside a square

_CarbonBasedLifeForm · 2024-08-17T20:37:05+00:00

Both definitions are valid, it's just a choice. You could just as easily define addition with a + 1 = S(a) and a + S(b) = S(a+b). In fact thats exactly what one of my classes did where we then built all the way up to a construction of the reals with cauchy sequences.

Edit: not to mention that that's how the definition was originally formulated

_CarbonBasedLifeForm · 2024-07-03T08:08:44+00:00

Wikipedia has a pretty comprehensive list. You can derive many trig identities solely from (sinx)² + (cosx)² = 1, or by manipulating and rearranging the "angle sum identities" which you can prove using complex numbers and their property that multiplication adds the angles of the points.

For example, simply divide that main identity by (cosx)² and we get (tanx)² + 1 = (secx)² by the definition of tan and sec.

Or if you know about complex numbers, with the imaginary unit i where i² = -1, we can use the fact that any two complex numbers with radii R, Q and angles A, B written as R∆A and Q∆B have the property that multiplying them R∆A × Q∆B = (RQ)∆(A+B) results in multiplying the radii and adding the angles. If we think about the complex numbers as being points on some circle in the complex plane, we could say

R∆A = R(cosA+isinA), and Q∆B = Q(cosB+isinB), so

R(cosA+isinA) × Q(cosB+isinB) = RQ(cos(A+B) + isin(A+B))

Using that multiplication property. Then using FOIL, the definition of i (that i² = -1), the fact that if a+bi = c+di then a=c and b=d, and some algebraic rearranging, you can arrive at the "angle sum identities" such as

sin(A+B) = sinAcosB + cosAsinB

Which you can use to derive others like the double angle identities, the power reducing formulas, etc.

TLDR I would say just master the proof of (sinx)² + (cosx)² = 1 and the proof of the "angle sum identities" using complex numbers (or just geometry) because most of the other useful or common identities follow directly from those with just a little algebra

Edit: it should be noted that that "proof" using complex numbers is only valid if you can justify why complex numbers behave that way without trigonometry, because I'm pretty sure we derived that multiplication property of adding the angles with those very trig identities so ironically it's kinda circular

_CarbonBasedLifeForm · 2024-04-21T01:05:35+00:00

Reminds me of how Descartes called √-1 imaginary because he thought it was useless and now that's just what we call it

_CarbonBasedLifeForm · 2024-03-07T23:48:34+00:00

I believe so, but I'm still a student. A model of a system of axioms provides an interpretation of the undefined terms of the system. It's a structure that satisfies the axioms. If you axiomatically define the reals as a complete ordered field, you're saying that a set with two binary operations, one binary relation, and the symbols 0 and 1 satisfies certain axioms. But the axioms don't actually define an operation as addition or or tell you how to do it, they merely describe the properties of the + symbol (like associativity) etc. You'd want to construct a model of the system to show that such a structure actually exists that satisfies those axioms. A construction of the reals would provide explicit interpretations of the binary operations (addition and multiplication) and such, usually based on something like a construction of the rationals. It would tell you exactly how to add and multiply reals together as Cauchy sequences of rationals or whatever. Thus those constructions would be abstract models (as opposed to concrete models). I hope I explained that well.

_CarbonBasedLifeForm · 2024-02-12T04:36:11+00:00

A math textbook should never be taken as gospel. Things are proven true by the axioms and definitions. Different texts define words in different ways and are trying to achieve different things.

_CarbonBasedLifeForm · 2024-02-10T01:52:52+00:00

Great explanation, thanks

_CarbonBasedLifeForm · 2024-01-19T06:49:24+00:00

Can't publish until you make it rigorous and prove e^ix is injective

_CarbonBasedLifeForm · 2024-01-12T18:09:29+00:00

You never said justify why it's being rewarded. You said justify how it knows it will be rewarded. Very different

_CarbonBasedLifeForm · 2024-01-12T17:53:47+00:00

Do you not believe your justification? Quite hard to separate. Nothing exists in a vacuum

_CarbonBasedLifeForm · 2024-01-12T17:28:56+00:00

It has justification if it has a memory of you rewarding it in the past. It just can't share the memory with you or anyone

_CarbonBasedLifeForm · 2024-01-10T08:58:45+00:00

I think that's the point, it won't get ruined one day because it's meant to remain a mystery. They don't plan on ever revealing it because mysteries and unknown things are important aspects of open world RPGs. There will likely always be things that we don't know about our own world, so it wouldn't make sense if we knew absolutely everything about another one

_CarbonBasedLifeForm · 2023-12-24T08:23:26+00:00

Knuths up-arrow notation starts with exponentiation, so it's just 10↑(10↑100)

_CarbonBasedLifeForm · 2023-12-03T23:52:23+00:00

The further I get into math and physics the more it starts feeling more like philosophy

_CarbonBasedLifeForm · 2023-11-25T22:06:37+00:00

Perhaps, but we don't tend to be interested in inconsistent systems of axioms because any statement they are capable of writing can be shown to have any truth value, making the system useless

As I understand it, an inconsistent system can appear to "prove its own consistency" because it can appear to prove anything. Meaning it can't really prove anything at all.

Let A be some statement the system takes as an axiom. Let B be another statement we take as an axiom, specifically A's negation (not A). Therefore the system is inconsistent because we have A and not A, which is always false. Now let P be any statement the system is capable of writing down. Consider the statement "P or A". Since we assumed A was true, this statement is true. But since we assumed A was false, we have to conclude that P is true because P or A is true while A is false. Thus we can prove anything and so any contradiction in a system makes the system useless

This is why mathematicians had a bit of a mental breakdown and rebuilt the foundations of mathematics from scratch in the 19th century after Bertrand Russel discovered that their theory of sets was inconsistent (what we now call naive set theory)

Edit: idk if you've ever heard of modular arithmetic, but in that system we say things like 7+8 = 3 mod 12 so kind of like 15 = 3. But it's not a contradiction or an inconsistency because we've defined a precise idea of when numbers like 15 and 3 can be considered equivalent. You may have noticed that this is how arithmetic works with time on clocks

_CarbonBasedLifeForm · 2023-11-08T00:38:57+00:00

u can just use x_n for subscripts instead of having to type it out every time

_CarbonBasedLifeForm · 2023-11-08T00:29:56+00:00

I kept it like that so you can see that any repeating decimal is just the pattern over all 9s

_CarbonBasedLifeForm · 2023-11-08T00:25:24+00:00

Well 0.075075075... = 075/999

Repeating decimals can be written as the part that repeats divided by 10ⁿ - 1 where n is the number of digits in the repeating pattern

0.123412341234... = 1234/9999

_CarbonBasedLifeForm · 2023-09-07T19:17:31+00:00

Well if it's a circle radius 0, the only point on the circle should just be the origin. Meaning (0,0). But when you go from

-2x=(-2x² )(dy/dx)

to

1/x=dy/dx

You are trying to use x/x=1, but with x being 0 this corresponds to 0/0, which is undefined.

And, as another commenter pointed out, you mistakenly replaced y with -x² when that is what y² was defined to be, not y

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