= 27d567bc2d48d9f40e9ccc20ea370b15)
thescoundrel comments on Harry Potter and the Methods of Rationality discussion thread, part 15, chapter 84 - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
Comments (1221)
I'm experimenting with reproducing the sound of the really horrible humming in Mathematica. I haven't changed the duration of notes yet, but I've experimented with trying to make things sound as horribly off-key as possible. I've started out with just changing the pitches of the notes by adding normally-distributed noise. So far the main discovery I've made is that for greater effect, the magnitude of the change should be proportional to the length of the note. Any ideas for things to try?
I'm using MIDI sounds, which are the simplest to set up, but also have the drawback that every pitch must correspond to an integral semitone, which limits how horrible things can sound. Also, what is a good standard MIDI instrument for simulating humming?
I would think the real key to horrible humming would not be to have it be uniformly horrible, but so close to brilliant that the horrible notes punctuate and pierce the melody so completely that it starts driving you mad- a song filled with unresolved suspensions, minor 2nds where they just should not belong, that then somehow modulate into something which sounds normal just long enough for you to think you are safe, when it collapses again, and the new key is offensive both to the original and to the modulation. This is not just random sounds, this is purposeful song writing, with the intent to unsettle- in my mind, something like sondheim at his most twisted, but without any resolution ever.
Well, first we're dealing with variations on a specific tune. The reason I suspect that random variations might work well is that if the probability of a change is sufficiently low, it would have exactly the effect you suggest: mostly the original "Lullaby and Goodnight", but with occasional horrible. Of course, if I were actually a cruel genius, I could do better, but it would be foolish of me to admit to being one.
Another reason random changes might work well is that they are by definition unexpected. If I did something purposeful, it would have a pattern; the real Quirrell might break that pattern by observing his victim's reactions, but not having a pattern at all might also be an interesting thing to try.
My music theory is rusty and anyway underdeveloped. But I don't think individual notes can be disturbingly off key. It is the relationship between notes that takes them out of key. A single note of any frequency will produce harmonics with anything in the environment that is capable of responding, and thus create its own meager, on key accompaniment.
I think MIDI keeps you from even approaching the kind of terrible close but not quite right tones you want to reproduce.
Changing one individual note in a monophonic tune absolutely can be horribly off key. Melody is harmony, and harmony is counterpoint; even with a single voice humming, if the tune is "classical" enough your brain understands intuitively where the chord changes are and what the bass line should be.
You don't need microtonal pitches to violently defy people's expectations.
(EDIT: Though you almost certainly do need microtonal pitches to precisely mimic the effects described in the text. But I think you certainly could do something horrible without them.)
I don't think you need to even venture into the world of quarter pitches in order to create horrible humming. To give an idea of a song that twists your expectations of keys and time signatures and melodic progression, and breaks it in specific ways to ramp tension, check the epiphany from sweeney todd.
I didn't really notice anything wrong with that. it jumped around a lot, and it wasn't especially good, but it didn't much bother me.
I forget that when I listen to it, I have the background of the story and buildup already, so I start with different expectations- perhaps not the best example.
Also, I've listened to a fair bit of weird proggy music.
There's a continuous spectrum of pitch. The character is kind of showing off, like he always kind of is.
He's probably hitting notes that are multiples of irrational numbers when described in Hertz.
Retracted because it seemed the best way to acknowledge the correction: the vast majority of common musical notes are multiples of irrational numbers when described in Hertz.
FYI, in the tuning system commonly used for western music, all notes except A are irrational frequencies in hertz. Example: A below middle C is 220 hertz, and middle C is
(220 * (2 ^ (1/12)) ^ 3) hertz ~= 261.6255653006 hertz.
(To go up a half step, you multiply the frequency by the 12th root of 2.)
At risk of derail, how the hell did they ever get a twelfth root into music?
We think of intervals between tones as being "the same" when there is a constant ratio between them. For instance, if two notes are an octave apart, the frequency of one is twice the other.
Thus, if we want to divide the octave into twelve semitones (which we do have twelve of: C, C#, D, D#, E, F, F#, G, G#, A, A#, B) and we want all of these twelve semitones to be the same intervals, then we want each interval to multiply the frequency by 2^(1/12).
Every part of that makes sense except for the lack of E# and B#, and why x2 is called an octave. Thanks for the info, and for reminding me why musical theory is one of three fields I have ever given up on learning.
Look up "equal temperament." There are 12 half-steps in an Octave, after each octave the frequency should double, and the simplest way to arrange it is to make each step a multiplication by h=2^(1/12) so that h^12=2.
Many people report that "natural" intervals like the 3:2 and 4:3 ratio, sound better than the equal temperament approximations, though I don't hear much of a difference myself.
It's really obvious if you expect any decent math to invoke exponents of 2.
The vast majority of humans don't have perfect pitch, so the specific pitch of the note is far less important than the relationships to the notes surrounding them. I agree that he is rather showing off, but unless you spend a very large amount of time ear training, you likely cannot tell when a note is a quarter tone sharp or flat. However, just like there are cycles of notes that always sound amazing together when you run them through variation (see the circle of 5ths), there are notes that sound horrible and jarring. Furthermore, the amount of time it takes to reliable sing quarter tones is ridiculously high- it is something that life long trained musicians cannot do. (Of course there is another discussion about how our formulation of music causes this, but lets set that aside for now.) I think it is far more likely that he has studied a circle of 7th's and 2nd's, or something to that effect- he has created a musical algorithm where the pattern itself is so convoluted, it is not intuitively detected, and the notes/key changes produced so horrible, it wears on the mind.
Even without a lot of ear training, you can quite likely hear if a note is a quarter-tone out relative to its predecessors and successors.
Here is a quarter tone scale. While the changes are detectable right next to each other, much like sight delivers images based on pre-established patterns, so does hearing. When laid out in this fashion, you can hear the quarter tone differences- although to my ears (and I play music professionally, have spent much time in ear training, and love music theory) there are times it sounds like two of the same note is played successively. Move out of this context, into an interval jump, and while those with good relative pitch may think it sounds "pitchy", your mind fills it in to a close note- this is why singers with actual pitch problems still manage to gain a following. Most people cannot hear slightly wrong notes. However, none of this approaches the complexity of actually trying to sing a quarter tone. The amount of vocal training required to sing quarter tones at will is the work of a master musician- much like the the person who can successfully execute slight of hand at the highest level is someone who spends decades in honing their craft.
I just tried some experiments and I find that if I take Brahms's lullaby (which I think is the one Eliezer means by "Lullaby and Goodnight") and flatten a couple of random notes by a quarter-tone, the effect is in most cases extremely obvious. And if I displace each individual pitch by a random amount from a quarter-tone flat to a quarter-tone sharp, then of course some notes are individually detectable as out of tune and some not but the overall effect is agonizing in a way that simply getting some notes wrong couldn't be.
I'm a pretty decent (though strictly amateur) musician and I'm sure many people wouldn't find such errors so obvious (and many would find it more painful than I do).
Anyway, I'm not sure what our argument actually is. The chapter says, in so many words, that Q. is humming notes "not just out of key for the previous phrases but sung at a pitch which does not correspond to any key" which seems to me perfectly explicit: part of what makes the humming so dreadful is that Q. is out of tune as well as humming wrong notes. And yes, the ability to sing accurate quarter-tones is rare and requires work to develop. So are lots of the abilities Q. has.
(Of course that doesn't require that the wrong notes be exactly quarter-tones.)
Python code snippet for anyone who wants to do a similar experiment (warning 1: works only on Windows; warning 2: quality of sound is Quirrell-like):
See, I'm the sort of person that reads that and wants to buy that record. Probably from the small ads in the back of The Wire.
(Breaking musical rules sufficiently horribly is a well-established way to win at music, even if you're unlikely to get rich from it. Metal Machine Music actually got reissued and people actually bought it.)