I really need to use more diagrams

Previously, re absolute pitch:
The only real way out for me is to read it as a different clef -- which I didn't consciously figure out until I got to college, but it is effectively what I was doing the whole time with horn parts from 5th grade on.

To wit: Treble clef means the top line of the staff and the first space from the bottom both denote F. And what I needed to do was find a way to read both of those as being (concert) B♭s. Which means reading the next whole step up, whether this be the space immediately above the staff or the second line from the bottom, as (concert) Cs.

at which point what you needed to see was an example, like this:

So F-transposed treble clef horn music, can also be read as concert pitch music written in mezzo-soprano clef with an implicit extra flat (i.e., what you need to make the bottom space or the top line of the staff be a B♭ rather than a B).

meaning what I'm actually seeing when I'm reading the above as an F horn part is this:

the thing to understand about the C clef being that it's this fancy cursor that tells you which line is C.

Likewise, B♭-transposed (trumpet/etc) music is actually concert pitch music in tenor clef with two implicit flats.

So reading it as a trumpet part gets you this instead:

And E♭ (alto-sax/etc) music is likewise bass clef with three implicit flats.

and whump:

Just in case you were unclear on what any of that meant the first time around (and maybe I'll get around to editing this into the original post) and perhaps now you'll have a slightly better idea of what I mean when I say there's no actual transposing happening here.

(go back to the original post…)

(Translation: Yay, I now have this vague template for doing music in unicode and SVG. Although I think I need to find a better font for the clefs, because these helvetica clefs look stupid.)

(Also: Boy am I looking forward to the day when dreamwidth will allow hosting of SVG images [why don't they??!!!]...)

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What it means to have Absolute Pitch

a healthy respect for the challenges of playing on a transposing instrument.

So I was originally going to answer this in the comments but this is really a huge topic worth its own post. It's always been a bit weird what people think should be difficult vs. what actually is difficult.

See, playing a transposing instrument isn't supposed to be a challenge. In fact, I'm sure the whole reason transposing instruments exist was to make it easier, and for folks who only have relative pitch sense, which is most of the population, I'm pretty sure that's the case.

That is, you see a C on the page, C has a particular fingering ('O'/open, if we're talking about a typical valved brass instrument) and you're done. You blow, and you'll know whether you have the right note if it's the correct interval away from whatever pitch you're using as a reference, whether it's a previous note that you played, or that somebody else played, or there's this huge chain of inference leading back to the start of the session when whoever it was blew on the pitch pipe. If, say, your reference happens to be denoted as B in your part, and you're now being called upon to play a C, then you need to be up a half step, and you'll be able to hear that. And that's really all you need.

The question of what the actual concert pitch might be is quite irrelevant. That you might be playing on a B♭ trumpet so that a denoted C comes out as a (concert) B♭, or a D trumpet where the same written note comes out as a (concert) D, or that the person who's playing your reference tone thinks of it as some note that's completely different from what you're thinking it is, you don't have to care.

This way the individual instrumentalists just get to focus on playing the notes that are on the page in front of them. Making sure that the corresponding sounds will match up with what everybody else is doing is the composer's problem, not yours.

Now, I'm sure that, for the conductor, this is a huge fucking mess, but dealing with that is part of why they get paid the big bucks (hahahaha).

At this point, I'll just note the weirdness of having to reverse-engineer how relative-pitch-only people think of things. Which is the best I can do because I have no personal experience of this.

I can only tell you how it works for me. I can't even be sure how much my experience generalizes to how other absolute pitch people experience things, because this only shows up in 1 out of 30,000 people on average, and I still have yet to encounter anyone else who has it.

(except possibly for my son Philip, who I have reason to believe has it, or, rather, there are certain things that he's done that would otherwise be very difficult to explain if he didn't have it, but because he's autistic and thus doesn't have the language to talk about it, I'll probably never know for sure).

But first we need to straighten out some misconceptions:

What is Absolute Pitch?

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Stupid French Horn Tricks a.k.a Why I Hate Transposing Instruments

Weird thing I saw today (well okay, actually this was several days ago, because these take me a while to write): A horn player using the 3rd valve all by itself, a fingering I was taught never to use. And then I started noticing other WTFery.

Granted, all of my horn playing was in middle school and high school, and I never actually got to the Advanced Private Lessons stage, this being merely the instrument I played so that I could be in the band (as opposed to piano which is what I cared about, but is kind of useless in a band), so maybe they would have covered these sorts of fingering nuances if I'd gotten that far. But I didn't.

And wikipedia is no help. They seem to think the '3' and '12' fingerings are equivalent, which they aren't, but that's wikipedia for you. It's also quite possible these are questions that simply don't have answers beyond, "It sounds better that way." (File under: Why Music Theory Isn't a Science). But I think there's room to beat on some things, so …

You can see what I'm talking about here (in which Radek Baborák does Richard Strauss's 2nd horn concerto, which is apparently the most popular version on YouTube at the moment. You should, of course, listen to the whole thing, but for this you can go 8m26s in, if the t= parameter isn't working for you).

The sequence of pitches up to the point where everything resolves is as follows (note that even just to say what the pitches are I have to digress on pretty much everything that is screwed up about the French Horn … and me):

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Getting Trilorne to Hover

Well okay, I guess there is a way to get Trilorne to hover.

If we're willing to toss the usual definition of "North" (rotation axis points that way), we can put the sun over the equator, and then we can have it be tide-locked. Meaning this planet is basically Mercury but farther away so that only the stuff directly underneath the sun is getting fried to shit.

And maybe having an actual atmosphere will help, too, in various ways, though I can't imagine there not being freaky weather patterns, e.g., some kind of permanent cyclone storm around the solar-maximum point wherever it happens to be at the moment, but that won't damage the story too much because nobody ever goes to the Fire Lands anyway.

The Wall then runs around Collapse ) This entry was originally posted at https://wrog.dreamwidth.org/63934.html. Please comment there using OpenID.

Arthur C. Clarke and the Projective Plane

So there's this Arthur C. Clarke short story, "The Wall of Darkness" (1949). I read it as a kid and found it really haunting. Clarke does Haunting really well.

If you haven't read it already and want to go read it before I completely and totally ruin it, feel free.

(I found the whole thing by searching for "Trilorne" in google, which then gave me a google books hit; we'll see how much longer The Algorithm lets people do that).

But you've already had 70 years, so… onward…

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Asshat Opera Company Presents: Carmen


Georges Bizet
(premiered in Paris, 1875)

[Trigger warnings:  domestic violence, rape, animal cruelty]

Dramatis Personae

  DON JOSÉ     "nice guy" who is also the protagonist, for some reason
  CARMEN       young woman from "Bohemia", 
               because heaven forbid anyone should try to
               actually learn anything about the Roma 
               (hint: they're not actually from Bohemia)

  ESCAMILLO    bullfighter guy
  MERCEDES     friend of Carmen
  FIAT         friend of Carmen

  (plus a half dozen other people I'm just going to leave out.  cope.)
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Spherical Geometry 4 — Mommy, Where Does Trigonometry Come From?

Continued from Part 3, what happens when there is no "parallel", the rules for circles aren't what you thought they were, and so on.

Napier's Rules

So how does trigonometry work in this world?

See, I belatedly realized that spewing walls of equations like this is not actually going to be much use when you're stuck in a rowboat in the middle of the North Atlantic having to navigate by the stars with no cell phone and no GPS. Because, chances are, you also have No Internet, and then my blog entries with their handy tables go to waste.

It would be far better if I can teach you how to derive these relationships instead, i.e., in a way that you might actually be able to vaguely remember while sitting in a boat in the middle of the North Atlantic.

But first I'm going to introduce a bit of gratuitous extra notation. Write


— pronounce it "co-theta" if you want — to mean (90° − θ). I do this because:

  1. I can,
  2. it's less typing,
  3. it's way less degree vs. radian waffling, which I already do too much of,
    but also,
  4. you get all of the following useful and amusing equivalences (no, really; read them aloud):
sin ᶜᵒθ = cos θ
cos ᶜᵒθ = sin θ
tan ᶜᵒθ = cot θ(= 1/tan θ, in case you've forgotten)
cot ᶜᵒθ = tan θ
csc ᶜᵒθ = sec θ(= 1/cos θ, and no, I don't know why reciprocals get these special names)
sec ᶜᵒθ = csc θ(= 1/sin θ, because, seriously, WTFF?)

You'd almost think they planned it this way.

Hopefully, it goes without saying that ᶜᵒ(ᶜᵒθ) = θ, except I had to go and say it, didn't I? (Damn.)

And now let's start with a right triangle, with vertices/angles and sides/lengths labeled a,b,c,A,B, the way you usually see it in trigonometry class, Collapse ) This entry was originally posted at https://wrog.dreamwidth.org/63204.html. Please comment there using OpenID.


Spherical Geometry 3 -- A bit of Circular Reasoning

Continued from Part 2, exploring the benighted universe where "parallel" is Not a Thing.

How circles work

So, to review the weird things we've seen so far:

  • When we have a circle radius of 90°, otherwise known as a straight line, and we're traversing the circumference, i.e., measuring the total length along it as we sweep out 360° from the pole in the middle, we get 360° worth of path (phrasing it this way so that if this turns out we're on a projective plane rather than a sphere and what we're really doing is traversing the same 180° path twice, I won't have been lying to you), which, being 4 times the radius, is slightly less than one might have expected (2π being roughly 6.28).
  • If we attempt a circle of radius of 180°, we stay firmly nailed to the antipode of the center, our circumference traversal goes nowhere and thus we get a circumference of zero.

Meaning if we have to explain to the residents what "π" is, we're going to lose horribly. Best we can do is, "So: Circumference to radius? That's a ratio. It's literally all over the map. But as radius approaches zero, once you're under 90°, you'll notice the ratio is always getting bigger. If you work at it, you can prove that it's bounded and it converges to this weird transcendental number like e. And, no, don't ask us how we came up with this…"

We need to understand better how curved paths work. Collapse ) This entry was originally posted at https://wrog.dreamwidth.org/62752.html. Please comment there using OpenID.


Spherical Geometry 2 -- Deficits Matter

Continued from Part 1, in which we discover at least one consequence to doing away with the concept of "parallel lines".

Let's talk about Area

Having noticed that isoceles right triangles give us a natural way to define/measure distances, we see that we can do area this way as well. That is, the area of ΔAPX is clearly the angle at P times some constant, which we may as well just take to be 1 if we haven't defined a unit of area yet. Collapse ) This entry was originally posted at https://wrog.dreamwidth.org/62716.html. Please comment there using OpenID.


The Essence of Spherical Geometry, Part 1

So, as part of my possibly-continuing "Geometry on Drugs" series, here is a prequel to my post on spherical geometry, which was more of a "hey, this is useful" post in which much there's a whole lot you're expected to take on faith. It was really more intended for the hardcore engineering type who needs to see that use case up front.

This version is going back to first principles, where we do the axiom wanking and you (hopefully) get a sense of why things turn out the way they do.

Also, this is the practice run before I launch into the Essence of Hyperbolic Geometry, so, … Onward …

The Geometry Axiom Everybody Hates

Start with this diagram and the inevitable question that comes up:

Start with a line ℓ and a point A not on it. How do you put a line through A that doesn't intersect ℓ?

(In other news, I am now convinced that the Unicode committee contained at least one disgruntled geometry teacher. How else to explain why there's this isolated script ℓ code point?)

We can drop a perpendicular from A meeting ℓ at some point X, and then it's obvious that the line you want (dotted) is the one perpendicular to XA. If you tilt it even slightly away from 90°, then it simply must intersect ℓ somewhere.

Proof by diagram. We're allowed to do that, right? Collapse ) This entry was originally posted at https://wrog.dreamwidth.org/62392.html. Please comment there using OpenID.