#complex ratio and proportion

[ratblazer]

oh i do have to ask— do you have any suggestions on how to.. cartoonify your art? your “main” style ig is still pretty cartoon, but like muppet john especially! i like how simple but still nice and clean and kind of detailed ur art is so i figured i’d ask!

I actually started out drawing cartoons- and cartoon animals at that. So had to kind of work backwards to figure out making my art more complex and realistic- though even my more "realistic" art has that more cartoony look to it. It's just how it be. That being said, I think I can offer a few tips for simplifying your characters! Let's take our two Johns here, one standard and one chibi/muppet styled

The differences are already clear, there's much less detail on the cartoony one, his proportions are more exaggerated. I like to pick out key details to highlight in a cartoon character, so for John it's his eyes, nose, and tummy. This becomes even more clear when we break him down into his basic shapes:

The more simple fella is made up of more simple shapes, mostly circles with a triangle nose and simple tube limbs (the clothes and hair are also mostly triangles and squares but I'm focusing on the basic anatomy right now!) Maybe the character your want to simplify is more angular and strong-looking, or maybe they're lanky and skinny. The key is to find the shapes that make up who they are and exaggerate them into cartoony proportions. And on the topic of proportions: A good measure of how realistic vs how cartoony something is, is the head to body ratio. A real human is roughly 7.5-8 heads tall, my typical John is about 5.5 heads tall, and muppet John is 3.5 heads tall

It really is all about playing with shapes and exaggerating key details until you find something you like! I hope this helps!

[yandere-wishes]

⋆ Anomaly ⋆

❤Summary: Reader is an anomaly. A noblewoman of foreign descent. She doesn't belong here. But oh how she wishes to burn the world down just like William.

❤Author's note: A little something for Ana (@yandere-romanticaa) I hope you enjoy it!!

❤Warnings: Reader is traumatized, Yandere behavior, killing and blood, cryptic. I swear I know how math works…I've just been slaking this summer.

There are equations written over your skin. Complex formulas he's yet to solve. Exponents and variables freckle your body, scattered shards that try to tell him something, whispering the world's secrets every time he kisses your hand. You are an anomaly he thinks. Face full of cracks where the stars seep through. You're a mistake in the universe. A perfect doll misplaced. You are something, William is almost sure of it.

At heart, William is and always will be a mathematician. It just so happens that crime and math follow the same principles. Both require diligence and practice. Carefully throughout plans of how one must approach such a conundrum. One may call it a formula or a modus operandi or anything else as jejune. But in the end, a rose by any other name would still smell as sweet.

And yet to Moriarty, you are an equation that refuses to be solved. An enigma he's desperately sought to unravel since your first meeting.

William notices something odd as you stroll down an exquisite exemplar of the golden ratio. Something the lord of crime can't fully place. You're akin to a puzzle missing far too many pieces to properly depict its picture. Maybe it's the setting he ponders as he watches you take careful steps in heeled shoes. Maybe it's the music from the ballroom or the meaningless prattle of the aristocrats that robs your form of all logic. Something is amiss with you and he's frantic to find out what it is.

William introduces himself when you reach the bottom of the staircase. He's never been one to show primary interest in the ladies. Rather he waits in the faint glow of the moonlight until someone approces him. Maybe it's the need to distinguish himself from the other aristocrats, maybe it's the repulsion for their customs and manners that refrains him from ever commencing idle chatter. Yet with you, a girl he's never met before, he finds it fitting to say hello first. To talk, about nothing and everything in the same breath. He mentions his admiration for the staircase in passing. Never expecting you to latch on to the words and morph them into the divine proportion. "My father was a mathematical enthusiast, he's passed that on to me as well." Your words slip into his veins like a narcotic, like the melody of an ancient tune lost to time.

William smiles, easy and bright like the melting rays of the desert sun. "Quite the coincidence, I'm a mathematics professor at Durham University". There's a giggle that bleeds from your rose-tainted lips. Reverberating in the chambers of his heart. "A toast then" you propose "to the lethal magnificence of calculation"

You click your champagne glass against his, as something feral festers within the young nobleman.

It's only days later when he's replaying that night in his head as he sips his afternoon tea. That he realizes your champagne glass was empty that whole time. How strange he pondered, wondering if he'd even seen you touch a single intoxicant all evening.

Four days and three sleepless nights later William finds himself tracing the letters of your name with tender adoration. As if he's engraving prayers upon his bones. He needs to see you again as desperately as he needs to breathe. The letter he writes is aloof, meticulous. Prying on your curiosity, hoping you'll take the bait. One miserable day later Louis delivers a letter bathed in your fragrance. Informing the lord Moriarty of your acceptance of his invitation for tea. William folds the letter with the leniency of a biologist regulating their slides. Tucking it away within his breast pocket.

You wear red when you oblige his invitation. An odd red, one that breaks his perception of the color. It's too vibrant yet too opaque. He's beginning to wonder if everything about you is an irregularity. When he ushers the conversation to your garment you merely laugh and brush it off as having belonged to your mother. There's something wrong with that reply as if the universe weeps at your every word. William watches astonished as if he's been told a secret lost to time.

It becomes a habit, an obsession, an addiction really. Tea thrice a week with the woman who plagues his dreams. He lets his cover slip between sips of tea. Permitting you glances into his dark affairs. There's a moment that breaks the norm. A bizarre instance when you ask him to spare no detail in recounting how a poor tormented man murdered the marquess that raped his wife. William stops the proclean cup mere millimeters from his lips. His voice dies in his throat as his mind races to find an appropriate way to tell a lady such a bloody tale. For a second reality slips away.

Reality has a tendency to slip away unnoticed when he's with you.

You weave William tales of foreign lands that sound like they belong in children's fairytales. You tell him about heroes who've done the impossible and kings whose hearts are as pure as the summer skies.

Something about you reverberates in his subconscious. Oh, how he wishes to engulf you, to pick apart your flesh revealing all those dainty secrets you keep in your pretty little chest.

He asks how you know of such utopic lands. You smile. "Because I once lived there"

One day, as Louis serves black tea with rose petals, you bring up a rather peculiar request. "Permit me to assist you in your quest for equality lord Moriarty." William's beginning to believe he's going mad when he hears you. Albit it may as well be expected. Any sane noble lady would have run away many times over. Yet you remain. Forever poised in your adorned seat. Now more than ever William wishes he knew what you truly are. "I want to help you", you plead. "Allow me to aid you in burning this world down and starting anew". He shouldn't have accepted, he shouldn't have nobbed. He shouldn't have left his seat to trace the side of your face with more love than he knew he possessed.

Sometimes, William wonders if something is haunting you, an apparition nesting within the depths of your heart. He ponders what could drive a brilliant mind such as yours to crave the blood of the rich. You once told him about a heritage disrespected. A legacy buried under sand and water lilies. He's yet to find the true meaning behind those words. Does that make you a threat or an ally? Can either be exalted to a lover?

Moriarty promises you the world. Promise you revenge. He's not sure if he too will burn away in your vendetta. Yet he's willing to take the risk if he can hold you close after every murder case.

"I've tried to kick the habit of strolling around the cemeteries at night. Yet I must admit I rather enjoy this." William smiles at your twisted words as he leads the way. If everything has goes as planned -which is most often the case- then the two of you should be prepared for quite the spectacle. A certain Count - who had shown more interest in you than Moriarty could permit- would be getting knifed by his butler whose life he had ruined. A whole new meaning to the term 'the butler did it'. Quite comedic from William's perspective.

You lean on a withering oak tree, hidden by London's thick fog. William stands by your side, the personification of a grim reaper. You watch the play begin, the cobblestone stage illuminated by the blood-red moon. The confrontation, the knife being thrust into the rich vermin's heart. Again and Again and Again. The butler screams into the bloodstained night. His words quelled by his sobs and screams of agony from his dying tormentor. You only catch half of his reasoning, half of his allegations. And yet that is more than enough to comprehend his motive. You sympathize with the poor man, one whose scars mirror your own.

William's scarlet gaze befalls you, as the performance nears its end.

You pick at your nails in a manner that William finds a little too adorable.

You are an anomaly masquerading as a human. Depression lays heavy over your bones as stardust gathers in the corners of your eyes.

You pray to the creator of the moon, pray for a place long since destroyed.

"I've yet to find someone who truly understands me," you say as the two of you begin the journey back to the Moriarty estate.

"Then we share the same burden, my lady," William says, stopping in his tracks.

He lays a firm hand on your shoulder pulling you backwards into his embrace. Somewhere in the distance, three crows consecrate you with their blessings. Willian's hands rest heavy on your sides. He holds you like a little boy holds his father's arithmatic books. Full of care, full of wonder. "What are you" he whispers into your ear. Leaving a playfully hard bite to the shell. His lips trace yours like one traces a treasure map. Trying to unearth all the riches of the world. "My anomaly" he mutters before he finally commits.

When Moriarty kisses you the whole world melts away.

There's an intriguing lightheadedness that follows. As if the stars themselves have exploded within you. You wonder if basking in his presence will mend your tattered heart.

"My precious little anomaly"

Tag list: @elvyshiarieko @himerurun @latolover @aru-nightmare @guidingstarsstuff @myfancollections

[talonabraxas]

The true origin and purpose of the pyramids

Basic theory of pyramidology is, that inside of a pyramid is accumulating and transforming universal energy called "orgon". Pyramids in their principal shape polarizing physical vacuum on both contradictory energies that is why they can act both as a transmitter or receiver, is a vibrational device which is able to receive, transform, concentrate, direct and emit energy. In an ancient Egypt they were energizing and uplifting vibrations in whole society.

Pyramid contains of a two words "pyro" or fire and "amid" or center. Pyramid is a device with fire in the center. Where center is well known king's chamber. Precisely in this center most of an energy is concentrated from where it spiraling to the top.

Builders of Egyptian pyramids used technique of harmonic resonance. They strictly observe measurements and proportions, which allows connection to the Earth's harmonics vibrations. Using words sacral geometry in a connection with pyramids we mean, that a builders were using same proportions and ratios, which we can find in nature and whole universe namely golden section (phi Φ=1.618033...)

They were also using a principles of resonance and sound to neutralize earth's gravity to be able to move a massive blocks. This effect occurs by tuning sound source to an exact frequency of a material. Pyramids where also connected to cooperative complex.

Egyptian pyramids were build mostly of limestone and crystal. Atoms of crystal vibrate at the same frequency as a planet earth, by this resonance an electric piezoelectric effect is occurring in inner mass of pyramid . Where one form of limestone is used as a isolating material the other form with magnesium is used as a negatively charged coat of an pyramid. It's acting like a massive wire. Granite is slightly radioactive which helps to ionizing air in all passages and caverns. Great Pyramid of Giza has also spiritual connection mostly to Orion and Sirius.

One of the functions of a pyramid is star gate and multiverse vortex. Pyramid as a portal allows people to reconnect with a source unity consciousness field. Energy of a pyramid reacts to operator's thoughts and intentions. It's acting like a huge amplifier for manifestation reality whatever it is healing, communication or interdimensional or astral travelling.

Energy of pyramid

Pyramidal energy of high vibrations calls cosmic is relating to torsion fields. It is favorable for human body and mind and other living beings. This energy is optically breaks, reflect and polarizing similarity to visible light. Pyramids walls attracting energy inside in all directions. This concentrated energy is affecting molecules or crystal structures of matter within a range of pyramid.

Scientists proved that no matter of a proportions, pyramids are amplifying mentioned energies of torsion fields (cosmic energies) and also energies of electromagnetic spectrum. American scientist Dr. Flanagan says, that Cheops pyramid concentrating energies in a very high frequencies and that is based on fact it has five angles. These corner angles of a pyramid concentrates and directing into energy beam where all four meets in the kings chamber.

Pyramidal energy is healthy for human organism as well as environment around and has multifunctional purpose. It strengthens the organism, heals humans and animals diseases, eases a pain of any kind, quickens healing of ambustion. Pyramid is also good for keeping a food fresh and healthy. Great for balancing a water for drinking or watering your vegetable and fruit. Softens taste of coffee, tea and quickens a germination of seeds. Growing never been faster than when you using a pyramidal energy. Strengthens a vitality, defends reproduce bacteria and microorganism which causes a break up of an organic matter. Living cells would not be affected by dehydratation as it still holds an electric charge and that is why plants or bodies would not be affected. Paradoxically if you like to slow down growth of your plants you don't give them any water they will still keeping very well under the pyramid and wouldn't need watering for a long time.

Many people have been personally convinced, that a pyramid is able to recharge our bodies when we are feeling exhausted, heals and tune our biological processes, but also gives us a tool to work with our psyche, consciousness and better connection to a higher frequencies and dimensions of reality. It's only up to us to what extend we are capable of operating these emitters. Many researchers were made in a wide range of branches as for example biochemistry, medical, agriculture, electronics or practical use for every day of life.

Pyramid Meditation and Manifestation Practices

Because of their physical properties and symbolic meanings, pyramids can be used in spiritual, meditation, and manifestation practices. Here are some ways you can use them to expand consciousness and receptivity to spiritual guidance:

1. Focus and Alignment

Just as pyramids form a point, or apex, at their top, they can represent focusing your attention in meditation. Some people find focusing on a mandala or lotus flower can help to reorient wandering thoughts in meditation. The pyramid can serve in the same fashion, whether it’s a figurine, a piece of art, or even in your imaginations.

In addition, you can focus your thoughts on moving up from the base of the pyramid, which can represent your experience in the material world to its pinnacle, which can represent a higher state of consciousness.

2. Energy Channeling

Pyramids are thought to channel cosmic energy, making them helpful tools for energy and even healing sessions. Placing a small pyramid on or near the head or body during energy and healing sessions is said to help balance and harmonize the body’s energy fields.

3. Manifestation Amplifier

The stable base and ascending sides of a pyramid can also symbolize staying grounded in the earthly plane while reaching for higher goals.

Writing down your intentions and placing them under a pyramid can be a helpful ritual in your manifestation practice. It can also serve as a request for blessings from higher powers when it comes to your endeavors.

4. Generating Creative Ideas

Given their association with enhancing focus and channeling energy, pyramids can be in creativity and problem solving when you want to channel higher energies and spiritual guidance.

In addition, the presence of a pyramid shape can serve as a visual and energetic reminder of your goals, aspirations, and unlimited capacity to create.

5. Gateways

Reflecting ancient practices, pyramids can be used as symbolic gateways during spiritual initiations or significant transitions, representing the journey from one state of consciousness to another.

This can involve meditating within or near pyramid structures to tap into transformative energies.

6. Enhancing a Sacred Space

Incorporating pyramids into the design of a creative, meditation, or other sacred space can elevate the area’s vibrational qualities. The pyramid’s base provides stability and grounding, while its ascending sides support creativity, the quest for higher wisdom, and spiritual ascension.

Energy Pyramid Real Fun, Wow!

[inkalight]

You are like seriously a god, goddess, your a Devine entity and holy hades, ok um, I'm trying to get onto drawing but I'm not very good at getting the bodies to be perportionate and was wondering if you know of anything that could help me.

I did not see this soon enough I’m so sorry!!

How I started was I drew really really tiny stick figures like 1 inch tall in poses then I’d redraw it larger in a light colored pencil then I’d draw over top of that. I’d say once ur comfortable building a simple stick figure you can grow into more complex drawings. You don’t need to know everything right away! (You don’t need to know how to draw abs on the first drawing lol)

Furthering your learning on proportions is fun and a bit challenging I recommend turning into a dragon and hoarding 2 things: tutorials and your favorite arts. (In other words you are what you eat, so seek out what you want to be)

Doing a quick search on your preferred search engine on human porportions will help you a lot , collect your favorites that explain things the best to you and show the proportions you want to master.

But break down the body to pieces, find the simpler shapes and flat planes in the complex objects from a reference. I shared some easy starting tips in the drawing below. That show some of the basic shapes.

The great things about proportions is that you can change them! No two humans are the same so once you feel comfortable (or even when you don’t) exploring how to change things up will open you up to new ways to draw! Most often I see if the eyes are bigger then the whole ratio of the body gets smaller in comparison to the head which is a popular approach but that’s not a rule.

If you have more questions feel free to ask (I need to make better tutorials tho)

[deniisu-sims]

Clothing and shoes converters

I'm willing to trade.

Basically, if you're open to simple requests or something similar, I can convert accessories or Buy Mode items in a 2:1 or 3:1 ratio depending on the complexity of the accs/items - all unmorphed accs or static items, 3:1, more complex stuff, 2:1.

(yes, it means that for every piece of CC you convert, I'll pay you back 2~3 items, you can choose them)

The reverse is true and you guys can ask me for some items and "pay" me with clothes/shoes. For sets, the "payment" will be proportional - 2~3 items for one piece, 5~6 items for two pieces, etc.

(although if you guys want me to convert kitchen counters/islands or stuff like huge sets we'll negotiate in private, those things take a lot of time)

Won't expand the offer for Build items because I'm not proficient on all of them, I can't convert double doors and I would hate to deliver an incomplete build set like that :P

[knightoftherosecross]

The universe is not made of matter — but music...

When walking past a blacksmith, Pythagoras noticed a strange harmony in the sounds of banging hammers.

He realized that two hammers make a harmonious sound if one is exactly twice as heavy as the other.

He worked out this 2:1 weight ratio produces an octave (notes separated by an octave sound alike).

Likewise, a 3:2 ratio creates a perfect fifth, and 4:3 a perfect fourth. This discovery evolved into our musical scale of today...

It wasn't just weight — a note's pitch is inversely proportional to the length of the string that produces it.

Pythagoras had discovered that sounds can be harmonious together because of a mathematical relationship between them...

This got him thinking. If music is essentially math, perhaps the universe *itself* is also governed by mathematical patterns?

Eventually he came to the idea that the universe and everything in it is vibrating. As math and music are interconnected, the universe too is musical. In that sense, "physical matter is music solidified."

He developed a theory called the "music of spheres," that celestial bodies "hum" a kind of music as they move, unheard by human ears:

"There is geometry in the humming of the strings, there is music in the spacing of the spheres."

He mapped the sun and planets, assigning each a unique tone based on distance and orbit.

We cannot hear this music with our ears — but it's heard by the soul...

Pythagorean thinking carried into the Middle Ages, with Boethius explaining the 3 kinds of music:

Musica mundana: unheard music of the cosmos

Musica humana: harmony between body and soul

Musica instrumentalis: music of instruments

These weren't just radical, isolated theories. This worldview permeated society for centuries.

People believed the universe was bound by a mathematical, musical harmony.

The idea was that music, math, and the cosmos were inextricably linked.

The universe was deeply mathematical and God must himself be a divine geometer.

So, if the universe is one great musical composition, how do you live your life to be in tune with it?

Well, by making music that connects you to that divine order — but you can do it in visual art too...

Art from antiquity to the Renaissance and beyond tapped into that mathematical order.

The Golden Ratio fascinated artists from Da Vinci to William Blake, who knew mathematical harmony touches us with a sense of otherworldly beauty.

In architecture, cathedral builders wove Gothic facades with immensely complex geometry.

As Pythagoras had found harmony in the mathematical order of music, geometry could produce visual harmony.

Music and visual beauty were bound by the same divine forces — notice the similarity of vibrations of musical notes in water and rose windows.

"Music is liquid architecture; architecture is frozen music."

Medieval people's obsession with math might seem strange or unnecessary to the modern-day architect.

But the results speak for themselves.

[antisocialxconstruct]

okay I've been thinking about this poll all day and. I have some thoughts lmao

Obviously we all know a tumblr poll is not exactly a reliable way to do a demographic survey and of course you're disproportionately going to get responses from active rebloggers because... the people who don't reblog aren't going to reblog your poll, are they? BUT I do think there's something to be said for the evidence that people currently active on tumblr are disproportionately people who have been on tumblr a long time, and trying to lay the issue of declining engagement at the feet of "new users" not understanding site etiquette is... well, flattening a more complex issue (gasps of shock and horror). So I've been thinking about other things that could explain the supposed issue people are identifying:

new users who don't know site etiquette: okay yes, I'll admit that it IS A Thing. I have seen the very very small sampling of people who recently joined and didn't think reblogging was "for" them for whatever reason--they think it's rude to reblog from someone you don't know, or they feel obligated to add something insightful to every reblog, or whatever else. But I also don't think people realistically operate under these misunderstandings for very long. All you have to do is use the site for a while and follow a few different people to realize no one else is abiding by those kinds of rules, and people who want to be active and engage with other blogs will start doing it pretty fast.

a lot of early users left: there have been a few waves of people leaving tumblr for various reasons, especially the porn ban and various other Bad Decisions made since then, and also some people just migrated to other social media sites that suited their needs better or aged out of their interest in fandom/blogging/etc. Some of the people who used to most actively use tumblr the way you think is "correct" may just not be around anymore.

shifting demographics: I know tumblr used to be almost exclusively associated with fandom, but you have to accept that there are a lot of people doing a lot of different things here now. Some people are treating it like a diary, or a dev log, or just a place to be really obsessed with something singular and niche. They may enjoy your work, but if it's not what their blog is for, they're not going to put it on their blog.

larger numbers don't translate 1:1 into more interaction: I can tell you this one from extensive personal experience. After a certain threshold, your follower count, the size of a fandom, the overall userbase of the site, none of it actually means a proportional number of new people engaging with your work. You will have a stable base of established fans/followers who have stuck around long enough to be invested, and an occasional new person who discovers your work and is enthusiastic, but for every one of those there will be five, ten, twenty tourists and casual enjoyers who might like to see what you make but don't resonate with it enough to directly respond to it. (Double that ratio again if you're asking for money.) Expecting all or most of them to make the switch to active fans will drive you nuts.

you're confusing interaction you want with interaction you "should" be getting: look. Nobody wants to hear this one. But is your engagement actually bad or are you just not reaching your desired audience? This could mean any number of things, if you're trying to build a presence or start a career, are you posting at peak hours? Are you posting in a way that's accessible to people? Are you using relevant tags, doing enough self promotion? It's grueling. People want to be so proud of how tumblr has no algorithm and no influencers so you have to accept that you're playing on hard mode. Alternatively, if what you want is a cozy, close-knit fan community, are you cultivating that? Are you engaging with other people's work with the energy you expect from them? Are you starting conversations and respecting boundaries? These communities don't just spring into being organically, they have to be fostered and maintained.

[lakesbian]

“We’ll come with you, hear you out, have a serious discussion with no time limit, but…” Mary dropped her voice, “Percy dies.” My breath caught in my throat.  I almost sputtered. I wasn’t the only Lamb reacting with shock.  All eyes were on Mary. “And,” Mary continued, meeting Lillian’s eyes, “You promise to excise all portions of your work that deal with the biology of children.  The ratios, the specific formulas, growth charts, scales, proportions…”

there's certainly some zest to the girl best friendship where one of em is a human experiment who's like psychologically incapable of much conscience but unasked for tries to mercilessly handle what her doctor-in-training bestie finds upsetting. however i struggle to give a fuck for the following reasons:

twig basically doesn't care at all about mary & lillians relationship so i can't really get into one isolated moment. they're like a parian and foil

i know evil and bad things happen later. you know what i mean

this entire scene is profoundly politically stupid for previously mentioned reasons

wildbow doesn't understand that lillians cognitive dissonance over being fine w the lambs but upset by how the rebels treat kids is cognitive dissonance. because he's also not aware that the academy is evil. this removes much of the complexity and with it much of the zest

[bossymarmalade]

Okay, here's the thing about the Netflix live action Avatar: the Last Airbender series --

Is it as complex and near-perfect in pace and characterization and message and narrative as the cartoon? No. Nothing could be. Sometimes a piece of media hits right the first time, and all you can do is make a different version of it.

Does it deserve to be watched anyhow? Absolutely yes. And you know why? I've watched white-focused media that was on the same level in terms of satisfactory adaptation (Sandman, seeing as I was reading the comics thirty years ago and am fond of it) and also media that's been way worse, and still enjoyed it for what it was.

You have to enjoy it for what it is, not that it's not the A:TLA cartoon. The story's condensed but it's not as wretched as all these reviews make it out to be. The problem with Katara's feminism/Sokka's misogyny not being satisfactorily represented is blown out of proportion imo. It's not a 1:1 ratio to the cartoon. The live action has to handle it in a slightly different way.

Honestly I'm enjoying it and I'll tell you why: it looks EXACTLY like the cartoon. Because it's people of colour in those costumes, in that world, using those items. Every episode produces some Asian actor I've known and loved in some new role and it's enough to get me teary-eyed because even if it's not a perfect and flawlessly-rendered version of ATLA, we're there and we're represented as real people. The voice actors for the cartoon were wonderful and mostly white. This is us in the LIVING FLESH.

Maybe it's a sign of my age that I'm more willing to go easy on this show and not hold it to the super-stringent standards that anything made by poc gets held to, I dunno. That's entirely possible. But I truly don't think it deserves the bad press it's been getting.

[justforbooks]

Per Nørgård

Danish composer driven by the concept of musical metamorphosis and a renowned symphonist

“I don’t know where the lyrical element comes from,” the Danish composer Per Nørgård, who has died aged 92, once remarked. “I can’t construct the lyrical element. It is like when you stick your head out of the window on a spring morning and can simply sense the scent of flowers in the air. It can’t be controlled. In a way, the lyrical element is the sensual side of existence, which always comes as a gift.”

One of the most lyrical expressions of that gift among Nørgård’s 400 works was in the finale of his small-orchestral diptych Voyage Into the Golden Screen, composed in 1968. Ironically, its free-flowing melody derived not from chance “scenting of [music] in the air”, but rather the technical dictates of Nørgård’s then newly formulated “infinity series”, where the notes follow mathematically from the proportions of the “golden ratio” and the Fibonacci series: a telling musical counterpart to the prevailing Scandinavian concern, across all the arts at the time, of design-driven expression.

As a young man, taught by the great Danish symphonist Vagn Holmboe at the Royal Danish Conservatory of Music, Nørgård had become fascinated with the music of Sibelius and the underlying concept of musical metamorphosis, where themes and motifs gradually evolve into new entities.

However, the infinity series became a primary building block of Nørgård’s music, whether laid out straightforwardly, as in the Second Symphony (1970), or as an unlimited thematic reservoir in his operas (including Siddhartha, 1974-79, and The Divine Circus, 1983), symphonies, 13 concertos – including two for percussion, the first, For a Change (1982-83), based on the Chinese “wisdom book” I Ching, the second, Bach to the Future (1997), reworking three Bach preludes – and a large body of vocal and chamber music, including 10 string quartets.

The end results sometimes baffled early audiences; Kalendermusik (1970), written to accompany the test card on Danish television, was broadcast until audience protests prompted its removal after a few months; others proved contentious through their complex, seemingly chaotic inspirations and textures, as with the choral triptych Wie ein Kind (1979-80) and the Fourth Symphony (1981), two of a group of works derived from the ideas of the Swiss artist and psychiatric patient Adolf Wölfli. At other times, the results could be disarmingly spare in texture, for example in his music for the Oscar-winning film Babette’s Feast (1987).

Nørgård was born in Gentofte, on the northern edge of Copenhagen, to the tailor Erhardt Nørgård and his wife, Emmely (nee Christensen), who ran a business specialising in wedding attire. Per loved to draw and with his elder brother, Bent, made up cartoon stories. It was a musical family (Erhardt played the accordion) and both brothers studied the piano, Per from the age of seven.

His innate musical ability showed early and he was admitted as a boy chorister into the Copenhagen Municipal Choral School in 1942 before going to Frederiksberg grammar school. By 17 he had set his mind on becoming a composer, producing his first work, Sonata capricciosa, in 1949.

Holmboe took him on as a private pupil in 1950-51, before becoming one of his teachers at the conservatory in Copenhagen, where Nørgård studied between 1952 and 1955. Following graduation, the conservatory staged a well-received all-Nørgård concert in January 1956.

By the end of that month Nørgård had married, been awarded a Lili Boulanger award, and moved with his young wife, the singer, dancer and ethnomusicologist Anelise Brix Thomsen, to Paris to study with Nadia Boulanger, whose former pupils included Aaron Copland, Roy Harris and Astor Piazzolla.

Returning to Denmark in 1957, he began teaching at the Funen Academy of Music in Odense (until 1961), writing for the Danish daily newspaper Politiken (1958-62) and, from 1960 to 1965, teaching at the conservatory in Copenhagen, where one of his pupils was Carl Davis. Finding the atmosphere too conservative, he moved – taking his students with him – to the Royal Academy of Music in Aarhus. There, he taught some of the most important Nordic composers of the ensuing generations, including Hans Abrahamsen, Hans Gefors and Bent Sørensen.

His own music extended his influence much further, to composers across Europe from Thomas Adès to Wolfgang Rihm to the Finnish composer-conductor Esa-Pekka Salonen. Salonen conducted the premiere of Nørgård’s Fifth Symphony in 1990 at a concert featuring the Fifth Symphonies of Sibelius and Nielsen, to celebrate their 125th anniversaries.

Nørgård was the recipient of many awards and honours, including the Nordic Council music prize (1974, for his opera Gilgamesh), the Léonie Sonning music prize (1996) and the Wihuri Sibelius prize (2006). In 2005 his glorious, expansive choral-and-orchestral Third Symphony (1972-75) – which was given its UK premiere only at the 2018 BBC Proms – was incorporated into Denmark’s official Culture Canon.

He received the Marie-Josée Kravis prize for new music in 2014; the following year the Vienna Philharmonic’s recording of Symphonies Nos 1 and 8, conducted by Sakari Oramo, won the Gramophone award for contemporary music; and in 2016 he was awarded the Ernst von Siemens Music prize for lifelong service to music.

Nørgård’s marriage to Anelise ended in divorce in 1965; he is survived by their children, Jeppe and Ditte. In 1966 he married Helle Rahbæk Hansen; she died in 2022.

🔔 Per Nørgård, composer and teacher, born 13 July 1933; died 28 May 2025

Daily inspiration. Discover more photos at Just for Books…?

[jswatson]

you know about musical tuning right? harmonics? equal temperament? pythagoras shit? of course you do (big big nerd post coming)

(i really dont know if people follow me for anything in particular but im pretty sure its mostly not this)

most of modern western music is built around the 12-EDO (12 equal divisions of the octave, the 12 tone equal temperament), where we divide the octave in 12 exactly equal steps (this means that there are 12 piano keys per octave). we perceive frequency geometrically and not arithmetically, as in that "steps" correspond to multiplying the frequency by a constant amount and not by adding to the frequency

an octave is a doubling of the frequency, so a step in 12-EDO is a factor of a 12th root of 2. idk the exact reason why we use 12-EDO, but two good reasons why 12 is a good number of steps are that

12 is a nice number of notes: not too small, not too big (its also generally a very nice number in mathematics)

the division in 12 steps makes for fairly good approximations of the harmonics

reason 2 is a bit more complex than reason 1. harmonics are a naturally occurring phenomena where a sound makes sound at the multiples of its base frequency. how loud each harmonic (each multiple) is is pretty much half of what defines the timbre of the sound

we also say the first harmonics sound "good" or "consonant" in comparison to that base frequency or first harmonic. this is kinda what pythagoras discovered when he realized "simple" ratios between frequencies make nice sounds

the history of tuning systems has revolved around these harmonics and trying to find a nice system that is as close to them while also avoiding a bunch of other problems that make it "impossible" to have a "perfect tuning". for the last centuries, we have landed on 12 tone equal temperament, which is now the norm in western music

any EDO system will perfectly include the first and second harmonics, but thats not impressive at all. any harmonic that is not a power of 2 is mathematically impossible to match by EDO systems. this means that NONE of the intervals in our music are "perfect" or "true" (except for the octave). theyre only approximations. and 12 steps make for fairly close approximations of the 3rd harmonic (5ths and 4ths), the 5th harmonic (3rds and 6ths) and some more.

for example, the 5th is at a distance of 7 semitones, so its 12-EDO ratio is 2^(7/12) ~= 1.4983, while a perfect 5th would be at 3/2=1.5 (a third harmonic reduced by one octave to get it in the first octave range), so a 12-EDO fifth sounds pretty "good" to us

using only 12-EDO is limiting ourselves. using only EDO is limiting ourselves. go out of your way, challenge yourself and go listen to play and write some music outside of this norm

but lets look at other EDO systems, or n-EDO systems. how can we measure how nicely they approximate the harmonics? the answer is probably that there is no one right way to do it

one way we could do it is by looking at the first k harmonics and measuring how far they are to the closest note in n-EDO. one way to measure this distance for the rth harmonic is this:

adding up this distance for the first k harmonics we get this sequence of measures:

(this desmos graph plots this formula as a function of n for k=20, which seems like a fair amount of harmonics to check)

the smallest this measure, the "best" the n-EDO approximates these k harmonics. we can already see that 12 seems to be a "good" candidate for n since it has that small dip in the graph, while n=8 would be a pretty"bad" one. we can also see that n=7 is a "good" one too. 7-EDO is a relatively commonly used system

now, we might want to penalize bigger values of n, since a keyboard with 1000 notes per octave would be pretty awful to play, so we can multiply this measure by n. playing around with the value k we see that this measure grows in direct proportion to k, so we could divide by k too to keep things "normalized":

plotting again, we get this

we can see some other "good" candidates are 24, 31, 41 and 53, which are all also relatively commonly used systems (i say relatively because they arent nearly as used as 12-EDO by far)

increasing k we notice something pretty interesting

(these are the same plots as before but with k=500 and k=4000)

the graph seems to flatten, and around 0.25 or 1/4. this is kinda to be expected, since this method is, in a very weird way, measuring how far a particular sequence of k values is from the extremes of an interval and taking the average of those distances. turns out that the expected distance that a random value is from the extremes of an interval it is in is 1/4 of the interval's length, so this is not that surprising. still cool tho

this way, we can define a more-or-less normalized measure of the goodness of EDO tuning systems:

(plot of this formula for k=20)

this score s_k(n) will hover around 1 and will give lower scores to the "best" n-EDO systems. we could also use instead 1-s_k(n), which will hover around zero and the best systems will have higher scores

my conclusion: i dont fucking now. this was complete crankery. i was surprised the candidates for n this method finds actually match the reality of EDO systems that are actually used

idk go read a bit about john cage and realize that music is just as subjective as any art should be. go out there and fuck around. "music being a thing to mathematically study to its limits" and "music being a meaningless blob of noise and shit" and everything in between and beyond are perfectly compatible stances. dont be afraid to make bad music cause bad music rules

most importantly, make YOUR music

[darkmaga-returns]

by Nicolas Hulscher, MPH

The study by Dr. James Thorp et al, titled, Are COVID-19 Vaccines in Pregnancy as Safe and Effective as the Medical Industrial Complex Claim? Part I, was just published after successful peer review in the journal Science, Public Health Policy and the Law:

Introduction: In Part I of this three-part series, we report a retrospective, population-based cohort study assessing rates of adverse events (AEs) in pregnancy after COVID-19 vaccines compared to the same AEs after influenza vaccines and after all other vaccines. Methods: Data were collected from the U.S. Centers for Disease Control and Prevention (CDC) and the U.S. Food and Drug Administration (FDA). The CDC/FDA Vaccine Adverse Event Reporting System (VAERS) database was queried from January 1, 1990 to April 26, 2024, for adverse events (AEs) involving pregnancy complications following COVID-19 vaccination. The time-period included 412 months for all vaccines except COVID-19 vaccines, having been used for only 40 of the 412 months (December 1, 2020 to April 26, 2024). Proportional reporting ratios (PRR) by time compared AEs after COVID-19 vaccination to those after influenza vaccination, and after all other vaccine products administered to pregnant women. In cases in which the PRR was not applicable, Chi-square analysis and Fisher’s exact tests were used according to CDC/FDA guidance. CDC/FDA stipulate a safety concern if a PRR is ≥ 2 or if a Chi-square is ≥ 4. Results: The CDC/FDA’s safety signals were breached for all 37 AEs following COVID-19 vaccination in pregnancy including miscarriage, chromosomal abnormalities, fetal malformations, cervical insufficiency, fetal arrhythmia, hemorrhage in pregnancy, premature labor/delivery, preeclampsia, preterm rupture of membranes, placental abnormalities, fetal growth restriction, stillbirth, newborn asphyxia and newborn death. All p values were ≤ 0.001 with the majority being <0.000001. Conclusions: We found unacceptably high breaches in safety signals for 37 AEs after COVID-19 vaccination in pregnant women. An immediate global moratorium on COVID-19 vaccination during pregnancy is warranted. The United States government, medical organizations, hospitals, and pharmaceutical companies have misled and/or deceived the public regarding the safety of COVID-19 vaccination in pregnancy. The promotion of the COVID-19 vaccines in pregnancy by The American College of Obstetricians and Gynecologists (ACOG), The American Board of Obstetrics & Gynecology (ABOG), and The Society for Maternal Fetal Medicine (SMFM) must cease immediately.

[hwei-theories]

╰┈➤Jhin and Hwei's Secret Quest - Analysis

The secret quest in League of Legends involving Hwei and Jhin killing each other, called "Golden Ratio," adds an interesting dynamic to their interactions.

The Golden Ratio has been recognized and utilized in various fields, including art, architecture, and design, due to its perceived visual appeal and balance. It is believed to create a sense of harmony and proportion that is pleasing to the observer.

Perfection and ideal proportions are frequently attributed to the Golden Ratio. By naming the quest "Golden Ratio," it could suggest that the completion of this quest represents the pinnacle of achievement or the attainment of perfection for both Hwei and Jhin. It implies that their clash and subsequent mutual defeat result in a state of artistic excellence or transcendence.

Balance and harmony are widely recognized as defining characteristics of the Golden Ratio. It represents a proportion that is aesthetically pleasing and visually balanced. The quest name could imply that through their confrontation and simultaneous demise, Hwei and Jhin achieve a moment of perfect balance and artistic harmony.

The Golden Ratio has long been associated with artistic composition and design principles. It has been applied in various art forms, such as painting, architecture, and sculpture, to create visually appealing and well-balanced compositions. By naming the quest after The Golden Ratio, it could suggest that Hwei and Jhin, as artists within the game, are striving for artistic mastery and using their confrontation as a means to achieve a higher level of artistic expression. Their death is their greatest artistic achievement.

The color gold is often associated with both Jhin and Hwei for different reasons (click here for more information, regarding this topic). Gold symbolizes Jhin's elevated status and the grandiosity of his artistic vision.

When Hwei wins the quest, he gains 3.33% Magic Penetration. The statement "Hwei made Jhin witness the depths of his visionary mind" implies that Hwei showed Jhin his new skills and artistic capabilities.

The quote "Understand, Jhin. Understand pain, and peace, and art - like I do, now" suggests that Hwei has gained a profound understanding of the complex emotions and concepts associated with Jhin's artistry, including suffering, tranquility, and the aesthetic beauty of his killings.

If Jhin kills Hwei in the quest, he gains 4,444 Lethality. The statement "Jhin made Hwei into his virtuosic magnum opus" implies that Jhin has turned Hwei into his greatest masterpiece.

The quote "Our fourth and final act draws to a close. The painter falls, and I arise the maestro of death" signifies Jhin's triumph over Hwei, suggesting that he has achieved a pinnacle of artistic expression by eliminating his "rival."

[artpassion3]

The Ephebe in Classical Greek Statuary.

The ephebe is a young boy who has just emerged from female authority and, to enter adulthood, undergoes a military period: the ephebia.

Bronze Ephebe, circa 450 BC Copy of an original, placed in a 2nd-century AD villa complex near the contemporary town of Antequera.

The sculpture is identified as a boy of about 13 years old, standing with a composed expression, his head tilted slightly to the right. His arms are outstretched, probably holding a tapeworm, and his head is crowned with ivy.

Although the broad face and thick hair correspond to stylistic preferences of the 2nd century AD, these elements were probably treated differently in the original work from the 5th century BC. A comparable bronze ephebe was discovered during excavations at the Casa dell'Efebo in Pompeii, now housed in the National Museum of Naples. This Pompeian copy, dating from the Augustan period, shares only its posture with the Antequera ephebe.

The Pompeian Ephebe is a figure of the "lampadophores," or torchbearers, type.

Preserved at the Archaeological Museum of Rabat The Ivy-Crowned Ephebe, a bronze from the early 1st century AD, found in Volubilis (Morocco) in the "classical" style of the ephebes of Volubilis, with languid poses full of youthful grace. Found near the triumphal arch of Volubilis,

This figure is characteristic of the classical style. Well-proportioned nudity with fine muscles represents the ideal of youthful beauty.

This "lampadophore," whose torch has disappeared, is an example of Polycletian influence, following a canon invented by Polycletus (5th century BC) based on a set of numerical ratios between the different parts of the body, with the torso and legs having the same height, three times the height of the head. The pelvis and thighs measure two-thirds of the torso and legs, respectively.

In the following century, a different type of figure emerged, corresponding to the second classicism.

The Pouring Ephebe

This figure would have held a rhyton (vase) in its right hand and a cup in its left. Although it revisits the theme of youthful beauty, the pouring ephebe is influenced by Praxiteles.

Praxiteles (4th century BC) is an influence reflected primarily in male nudes by pronounced swaying of the hips, less pronounced musculature, and a more feminine grace with more accentuated curves in older figures emerging from the ephebian state.

The Marathonian ephebe is also an older figure, around 20 years old, in a complex pose consistent with the rules of Polykleitos' contrapposto. Leaning on the left leg, the foot of the free leg is set back and rests on its toes.

The swaying of the hips is more accentuated than in Polykleitos. The outline of the muscles, the protrusion of the pectorals, and the lower abdomen are less pronounced. The head, tilted to the left, is encircled by a band to which is attached a leaf- or horn-shaped ornament.

[alphaketoglutaricacid]

hater moment alert

Cannot stand the girl autism is more acceptable than boy autism bc masking take….i can abide by shitty takes on fictional shit but i cannot let shallow analysis of real issues slide. What the hell is boy autism and girl autism!!! The neat splitting of the complex process of socialization, the ways healthcare works as a system of control that often disregards symptoms of women, the complex way ppl punish the ways ppl diverge from gender roles esp for women, and how diverse of a disease autism is. I know this is a complicated discussion in healthcare bc how we view behaviors differently w gender but dare I say a big reason women (just like poc in america) are underdiagnosed is medical neglect LMAO.

This is like an actual pet peeve of mine. Theres so many stupid long held medical myths in the field like the symptoms of heart attacks are different for women vs men w no statistical bearing or were borne out of statistical malpractice (nuanced topic im not gonna fully get into abt how health data is analyzed). We (i hope) are moving away from this stupid biological determinism ohhh diseases present differently in different genders/races/whatevers bc of (biological differences/genetics/epigenetics and ooo this doesnt have anything to do w the long standing beliefs eugenics still has on how we view health ooooo bc eugenics was #cancelled and theres no troubling inheritances from it ) and acknowledging the reason why mortality differences exist are overwhelmingly bc of health inequities. I know behavioral issues are different. But they are often medicalized similarly and demographics are often homogenized when within groups ppls experiences are incredibly diverse. Anyways.

edit: this is not a dont trust the medical system go to a naturopath instead thing. Naturopaths are scammers. I generally think its a good thing medicine has moved to having evidence behind it, but our ways of collecting and executing it can be deeply flawed.

edit: its in bad form to make medical claims without sources and i dont aim to spread medical disinformation. Here are mine and you can draw your own conclusions:

the most commonly cited study on difference on presentation based on gender for heart attacks is the framingham heart study. A more recent cohort is the GRACE (the global reg of acute coronary events). U may look at these stats and go hey some of these proportions in initial disease presentation do look different between the sexes and even is statistically significant. Which is true. But it must be noted that atypical symptoms are common in both men and women (1/4 roughly vs 1/3) which means when assessing for a heart attack, you should be checking for atypical symptoms in both men and women because it occurs often. I dont believe these ratios are clinically actionable, tho some ppl disagree. Now the fact women get advanced heart treatments, get put on standard medications less often than men etc, I think thats much more actionable.

There is also something to be said abt what statistics measure. Which in population studies is: are the prevalence or outcomes of the disease different between these two populations? Which if you theoretically rounded up every man and every women in the US that has had a heart attack (which the populations in these studies are a proxy for) the answer would be: yes. But also if you rounded up everyone in the state of Minnesota vs everyone in the state of Montana, you would also have differences between manifestation of disease in these two states. The question is how large and why—the why is a question stats have a harder time elucidating.

Another question is what is the utility of dividing the groups to compare each other when there are infinite ways you could split groups up. You probably would not argue that there are inherent biological differences between people who live in Minnesota and people who live in Montana, but if you found enough difference, perhaps you could make an argument that there may be a difference in health infrastructure or policy thats driving that gap. But then youd have to further investigate. There is no approach in statistics where you can avoid the responsibility of interpretation. Now how does that get into how sex and or gender is traditionally interpreted in health studies. Well stay tuned to if i still feel like talking abt this. Bc this is complicated.

[sokowachi]

STON.fi’s Next Evolution: Unlocking a New Era in Liquidity Provision

The way we provide liquidity in DeFi is about to change. STON.fi is rolling out two groundbreaking features that will give liquidity providers more control, flexibility, and efficiency than ever before.

These are not minor updates. They address some of the biggest limitations in traditional liquidity pools—the rigid 50:50 ratio requirement and the inefficiencies in stablecoin trading.

If you’ve been providing liquidity in DeFi, you know how restrictive the current system can be. But that’s about to end.

Here’s what’s coming.

Wstableswap Pools: Smarter Liquidity, Less Friction

Liquidity pools have always operated under fixed rules: if you want to add liquidity, you must provide an equal value of both assets. But real markets aren’t that rigid, and liquidity providers need more flexibility.

Wstableswap pools introduce a new level of control.

Instead of forcing a 50:50 split, these pools allow liquidity providers to set custom asset ratios, giving them greater control over capital allocation.

Key Benefits

🔹 Optimized stablecoin trading – Stableswap technology minimizes price impact when trading assets with similar values.

🔹 Adjustable liquidity ratios – Set your own token balance instead of following a fixed ratio.

🔹 More efficient liquidity management – Maintain high liquidity levels even in unpredictable market conditions.

For those trading and providing liquidity in stablecoin pairs, wstableswap pools mean better efficiency, fewer losses, and higher returns.

Arbitrary Provision: A Simpler, More Flexible Approach

Until now, providing liquidity meant holding both tokens of a pair in equal value. This created friction, especially when one token was more available than the other.

Arbitrary provision removes that restriction.

Liquidity providers will now be able to supply liquidity with just one asset or with both in any proportion they choose.

This upgrade isn’t just about convenience—it’s about removing barriers that have made liquidity provision unnecessarily complex.

How This Changes the Game

✔️ No more strict token requirements – Add liquidity using whatever assets you have, without worrying about ratios.

✔️ Smoother user experience – Providing liquidity is now straightforward, with no need to balance token values manually.

✔️ Efficient capital utilization – Deploy funds immediately instead of holding them idle while waiting to match a ratio.

With this feature, STON.fi is making liquidity provision more accessible to everyone, from beginners to experienced DeFi users.

A More Intelligent DeFi Future

STON.fi is not just improving liquidity provision—it’s redefining how it works.

By removing unnecessary restrictions and giving liquidity providers more options, these upgrades will make STON.fi one of the most efficient platforms in DeFi.

🔹 Wstableswap pools eliminate rigid liquidity rules, making stablecoin trading smoother and more profitable.

🔹 Arbitrary provision removes the entry barriers to liquidity provision, allowing users to participate more easily.

These are not small improvements—they’re fundamental shifts that will shape the next phase of liquidity management.

As these updates go live, the benefits will be clear: more control, better efficiency, and higher earning potential for everyone involved.