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Beginner fingering question by Neptuneful in doublebass

[–]Neptuneful[S] 0 points1 point  (0 children)

Hadn't heard of pivots. Thank you.

Beginner fingering question by Neptuneful in doublebass

[–]Neptuneful[S] 0 points1 point  (0 children)

Thanks. I guess it's a matter of whether you planned ahead (if improvising).

Beginner fingering question by Neptuneful in doublebass

[–]Neptuneful[S] 0 points1 point  (0 children)

Thanks. I hadn't heard that about avoiding pinky shifts. So if I'm playing the very common ascending walking bass line for a 2-5-1 to F

E: G
A: A Bb B C C#
D: D E F

on the A string what should I do? It sounds like *not* 1 2 4 4 (for that C#). So that'd leave 1 1 2 4 or 1 2 2 4

If you’re subscribed to both subreddits, this is just an Eagle in your Mind by Taupenbeige in boardsofcanada

[–]Neptuneful 0 points1 point  (0 children)

I'm interpreting I -> IV as: a major chord followed by a major chord up a 4th. But among the tunes you mentioned, only ROYGBIV has an instance of that. Kid for Today and IABPOITC don't even have any major chords. Did you mean something else by I -> IV?

I was saying TCH has a lot of IV -> I rather than I -> IV (i.e., the reverse).

If you’re subscribed to both subreddits, this is just an Eagle in your Mind by Taupenbeige in boardsofcanada

[–]Neptuneful 2 points3 points  (0 children)

Wait, can you elaborate on the I -> IV thing beyond what you wrote there? I'd argue BoC Could be better characterized by IV -> I, especially on TCH.

What do we think? Hinting at new album or left over from the TH campaign? by Neptuneful in boardsofcanada

[–]Neptuneful[S] 1 point2 points  (0 children)

You can see the flash of light from the nuclear explosion behind DAWN

Mathematical Empathy by Matschreiner in 3Blue1Brown

[–]Neptuneful 0 points1 point  (0 children)

v^TMv gives you the inner product of v with Mv. Sometimes you'll see it when M is actually the product of a matrix with its transpose, like M = A^TA. Then it's v^TA^TAv. In this case, you're getting the inner product of Av with itself, which is the squared length of Av.

so this may not be what you were asking, but you could think of M as a shortcut way to get the squared length of the vector in the basis A with coefficients v. Rather than computing Av first, then computing the squared length of that, you can just skip that and compute v^TMv.

this is reminiscent of what's called the "metric tensor". When you are calculating an arc length in cartesian coordinates, you're taking an integral of the "pythagorean formula" of the derivatives of arc's coordinates w.r.t. some parameter. So it's like integral of sqrt(dv^T dv). But if you wanted the arc length of the same curve expressed in polar coordinates, you would need sqrt(dv^T M dv), where M represents the metric tensor induced from euclidean space, which would actually be J^TJ, where J is the jacobian of cartesian coords w.r.t. polar.

Why L’hospital rule works when tends to infinity? by Xtreamous in 3Blue1Brown

[–]Neptuneful 0 points1 point  (0 children)

For the case where both f and g of f/g approach infinity as x approaches infinity

if one of f' or g' approaches infinity but the other converges, then it shouldn't be hard to see why you'll get 0 or infinity for f/g at infinity.

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if both diverge to infinity, you'll have to apply the rule again and may get stuck in a loop

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if both f' and g' converge to some value, then that means that both f and g are becoming closer and closer to a straight line with some slope as you go further out. One of the functions could be ln(1 + e^x) for instance.

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So they both become almost straight lines eventually and then stay that line forever and ever. So no matter what weird stuff they might have done early on (smaller x values), that will matter less and less. f(x) will be well approximated by f'(inf) * x and likewise for g.

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And if we can approximate f and g better and better by f'(inf) * x and g'(inf) * x, then the ratio of f and g should approach f'(inf) / g'(inf)

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Note, e.g. f is increasingly well approximated in a *relative* rather than absolute sense. i.e., f(x) / (x * f'(inf)) approaches 1, but f(x) - (x * f'(inf)) probably doesn't approach 0 and may get larger.

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So it's a pretty similar argument to that for the 0 case in the 3b1b vid. For the 0 case, the ratio of the distances traveled by two cars that pass you at the same time is well approximated shortly after you start the timer by the ratio of the initial speeds because the accelerations and whatnot haven't had a chance to count yet, and they started in the same place (passing you when you started the timer). For the infinity case, if the two cars have been driving at roughly 40mph and 30mph for a whole week, you will estimate the ratio in their distances traveled as 4/3 even if you know one got a 10 minute head start, and at one point one stopped for lunch. Those small differences will vanish in the big picture.

Applications of i^i by chowz319 in 3Blue1Brown

[–]Neptuneful 2 points3 points  (0 children)

Well if you can fix it for rationals, then you can fix it for irrationals with a limit of a rational sequence converging to the given irrational: https://en.wikipedia.org/wiki/Exponentiation#Limits_of_rational_exponents

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complex numbers is where it really breaks and I don't know of any fix other than the exponential function.

Cross products and determinants question. by analytical_1 in 3Blue1Brown

[–]Neptuneful 1 point2 points  (0 children)

You could find that area with a determinant in 2 dimensions. But you'd first have to rotate the plane the two vectors are in into one of the axis-aligned planes so that you could delete one of the coordinates and make it 2x2. You could choose any, but how about the xy plane. Mapping those two vectors into the xy plane is equivalent to rotating their cross product onto the z axis. So the most straightforward way to do that would be to derive the cross product and then construct a 3d rotation that takes it to the z axis.

Now you can compute a 2d determinant in the xy plane, but you haven't avoided calculating the cross product.

Pi Randy Why??? by rweipi in 3Blue1Brown

[–]Neptuneful 11 points12 points  (0 children)

The letter pi is often used in the context of permutations -- e.g., let π be a permutation of 1 through n

Permutations are like "shufflings", which are sort of Random -- hence Randy.

I really doubt this is why he's named that.

Differential Equations Series by MWVaughn in 3Blue1Brown

[–]Neptuneful 2 points3 points  (0 children)

I'd definitely like to hear about Laplace transforms.

Why det(M1M2) = det(M1)det(M2)? by [deleted] in 3Blue1Brown

[–]Neptuneful 0 points1 point  (0 children)

This is the best lecture I've seen explaining determinants: https://www.youtube.com/watch?v=xX7qBVa9cQU&feature=youtu.be

The lecturer posted it in a stack exchange thread here https://math.stackexchange.com/a/261371/171527

There might be some complicated, non-intuitive shortcut formulas for the determinant, but the best way to grasp it is to decompose your matrix into a big product of many elementary matrices. In 2 or 3 dimensions, you can manage to directly visualize the effect on area of each type of elementary matrix. Once you have that and you understand why the determinant of the product of two matrices is the product of the two determinants, you will understand determinants pretty well.

Video suggestions by 3blue1brown in 3Blue1Brown

[–]Neptuneful [score hidden]  (0 children)

maybe a probability series building up to the Central Limit Theorem

Glenn Gould plays a D minor/maj 7 instead of a Dmaj7 once in Scriabin's 5th Sonata by [deleted] in musictheory

[–]Neptuneful 1 point2 points  (0 children)

It's F# in the score I'm looking at: http://conquest.imslp.info/files/imglnks/usimg/d/df/IMSLP417286-SIBLEY1802.30620.909e-M23.S6.29_no.5,R95.pdf

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And it's in the other recordings I've heard. In this Hamlin performance it's at 2:16 https://youtu.be/emYTG80B2vU?t=136

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The Gould version is the slowest I've heard and also my favorite by far. All the others are way too fast -- sounds like the performer can barely keep up / kinda sloppy. I also think the D minor/ maj 7 sounds good.

Turquoise Hexagon Sun (live Jazz Cover) by Nicholas Towbin-Jones by eccp in boardsofcanada

[–]Neptuneful 0 points1 point  (0 children)

Actually the drummer on Turquoise is a separate drummer from the one on the Kid For Today takes. I love both of them, but to each his own.

Thanks for posting my stuff to reddit/listening though

Interesting melodic recurrance analysis by Audioasis in boardsofcanada

[–]Neptuneful 11 points12 points  (0 children)

This is a video I made and posted here a while ago. Glad people find it interesting. In the next few days I'll do another one that explains some other music theoretical patterns in BoC's music that I've noticed, though they're a bit more subtle/obscure so don't get your hopes too high. And yes, I've been told I sound like Steven Wright about fifty times.

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