|
About This Author
Come closer.
|
Complex Numbers
Complex Numbers
A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.
The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.
Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.
Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.
April 25, 2021 at 12:04am April 25, 2021 at 12:04am
| |
I mentioned before that I had at least one more thing about Leonard Cohen's song Hallelujah and that I'd get to it one day.
Today is that day. And oddly enough, the source is Cracked.
Incidentally, free idea for Cracked (hey, one of them might read this, just like Halle Berry might come by my house in the catsuit carrying two growlers of craft beer): Start a dating app for comedians. Call it Crackd.
You're welcome. And while I did say "free" if you wanted to funnel me, say, 5% of the profits, I wouldn't complain. Much.
Okay, anyway, after that massive side of aside, back to the actual article.
According to Leonard Cohen and also, like, the Bible or whatever, there's a certain chord that God particularly likes, but everyone rudely refuses to tell us what it is.
Add that to the list. Hell, no one even knows God's actual name. Some actually refer to God as HaShem, which translates to "The Name."
In the unlikely event that you're still here reading this and you're not familiar with the lyrics from which this springs, here's the first verse of the song:
Now I've heard there was a secret chord
That David played, and it pleased the Lord
But you don't really care for music, do you?
It goes like this, the fourth, the fifth
The minor falls, the major lifts
The baffled king composing Hallelujah
It's entirely likely that the chord was meant to remain, you know, a secret, but plenty of people think Cohen left us clues as to what at least he thought the secret chord was.
I'd lay all kinds of money that it's not the mysterious chord that opens The Beatles' A Hard Day's Night. Maybe the one at the end of A Day in the Life? ...Nah.
Or maybe it's a B chord. Ever try to play a B chord on guitar without retuning or faking it? ...Okay, so I never got too far with guitar lessons.
In fact, Cohen's secret chord may not be a chord at all. It might be a metaphor for divine inspiration, and the subsequently described chord progression could be a code leading the listener to certain Bible verses, which are indeed eerily appropriate.
A metaphor? In a Leonard Cohen song?! Impossible!!!
That's sarcasm, by the way. You can tell by the plurality of punctuation marks.
But the biblical David was, in fact, a musician, and Cohen's song is more about bangin' than religion, so let's assume he's speaking literally because that's also a lot more fun and involves something called the Devil's Interval.
Unless he was a liar. Liar... lyre? Get it? Crap. Back to the professionals.
We may not be totally clear on how God jams, but it turns out "the devil's music" isn't just a term applied by grandmas to bands with haircuts they don't like. "The devil's interval" is a chord a half-step below a perfect fifth that sounds so dissonant to our ears that it was banned in churches in the Middle Ages because it was thought to induce sinful thoughts.
Bet the organists back then (or whatever, if this was before organs) snuck into the church at night just to play that banned chord.
According to one theory, if the devil loves this chord so much, God's fave must be the opposite: a perfectly harmonious major chord. Probably C major, which also happens to be the key of "Hallelujah."
C major is, coincidentally or not, also the easiest key on piano, because you don't have to mess with those annoying black keys.
But maybe we're thinking too hard: When Cohen recites the chord progression, he also plays it, so maybe the secret chord is just the chord he plays when he says "secret chord," which would be A minor.
And A minor uses the same keys as C major. Look, don't ask me; I've forgotten more music theory than I ever learned, but that little tidbit stuck with me. What's the difference, then? Go ask an actual musician.
Or maybe it's something totally different. Go onto any music theory subreddit and ask people what they think the secret chord is and you'll get 100 different, equally compelling and confusing answers.
Also coincidentally, that's what happens when you ask anything on reddit.
In any case, mostly I wanted to post about this because I don't have many opportunities to make a lyre pun, and I'll take one whenever I can get one. And also because, like I said, I'll never get tired of that song.
Mini-Contest Results!
Thanks for all the opening sentences / paragraphs from yesterday. Really, I liked all of them, from the flowery to the laconic. It was hard to choose just one favorite, but I suppose the poetic imagery in the one Kåre Enga in Montana  posted just barely edged out the others. So a MB to Kåre Enga in Montana will be on the way soon, and we'll do this again sometime. |
© Copyright 2024 Waltz en France (UN: cathartes02 at Writing.Com). All rights reserved.
Waltz en France has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.
|
![Merit Badge in Quill Award
[Click For More Info]
Congratulations on winning Best Blog in the 2021 edition of [Link To Item #quills] !](https://images.Writing.Com/imgs/writing.com/writers/badges/group-Quill_Award-1375927_6.gif)
![Merit Badge in Quill Award 2
[Click For More Info]
2022 Quill Award - Best Blog - [Link To Item #1196512] . Congratulations!!!](https://images.Writing.Com/imgs/writing.com/writers/badges/group-Quill_Award_2-1375927_6.gif)
![Merit Badge in 30DBC Winner
[Click For More Info]
Congratulations on winning the Jan. 2019 [Link To Item #30dbc] !!](https://images.Writing.Com/imgs/writing.com/writers/badges/group-30DBC_Winner-2064535_14.gif)
![Merit Badge in Blogging
[Click For More Info]
Congratulations on winning an honorable mention for Best Blog at the 2018 Quill Awards for [Link To Item #1196512] . *^*Smile*^* This award was sponsored by the blogging consortium including [Link To Item #30dbc] , [Link To Item #blogcity] , [Link To Item #bcof] and [Link To Item #1953629] . For more details, see [Link To Item #quills] .](https://images.Writing.Com/imgs/writing.com/writers/badges/type-Blogging-2180.gif)
![Merit Badge in Highly Recommended
[Click For More Info]
I highly recommend your blog.](https://images.Writing.Com/imgs/writing.com/writers/badges/Kudos-Highly_Recommended.gif)
![Merit Badge in Opinion
[Click For More Info]
For diving into the prompts for Journalistic Intentions- thanks for joining the fun!](https://images.Writing.Com/imgs/writing.com/writers/badges/genre-Opinion-1150.gif)
![Merit Badge in High Five
[Click For More Info]
For your inventive entries in [Link To Item #2213121] ! Thanks for the great read!](https://images.Writing.Com/imgs/writing.com/writers/badges/Kudos-High_Five.gif)
![Merit Badge in Enlightening
[Click For More Info]
For winning 3rd Place in [Link To Item #2213121] . Congratulations!](https://images.Writing.Com/imgs/writing.com/writers/badges/general-Enlightening.gif)
![Merit Badge in Quarks Bar
[Click For More Info]
For your awesome Klingon Bloodwine recipe from [Link to Book Entry #1016079] that deserves to be on the topmost shelf at Quark's.](https://images.Writing.Com/imgs/writing.com/writers/badges/group-Quarks_Bar-2046190_12.gif)
