195.9K
SC1:2…99:100 spectral polyrhythm #sheetmusic #polyrhythm
@scorefollower
#Spherical Harmonics
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THVolume of a Sphere: Spherical Coordination.
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#physics #science #fyp #amazing #explore
@thephysicist_boy
7.2K
UMThis animation visualizes the angular probability distribution of an electron in a hydrogen atom, described by a spherical harmonic $ Y_{l}^{m}(\theta, \phi) $(with l=m=4) . The surface represents the probability density $ |Y(\theta,\phi)|^2 $, which determines how likely it is to find the electron in different directions around the nucleus. The shape is not a classical orbit, but a quantum “cloud” with distinct lobes and nodes that arise from the angular momentum quantum numbers $l$ and $m$.
Color and transparency enhance regions of higher probability, while scattered points mimic the probabilistic nature of quantum measurements. The rotation helps reveal the full 3D symmetry of the orbital, showing how its structure depends on angular coordinates rather than distance from the nucleus.
Overall, the animation illustrates a key idea of quantum mechanics: electrons are not localized particles in fixed paths, but are described by wavefunctions that encode probabilities in space.
@umtiquinhodefisica
4.1M
MA🎵🔢 Sonificación de Funciones Matemáticas - Segunda Parte: Timbre, Armónicos y Texturas Sonoras
📊 Exploración avanzada de cómo distintas funciones generan firmas espectrales únicas al ser traducidas a frecuencias audibles.
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▶️ Nuevas funciones y perfil sonoro:
· Función Gaussiana (e^{-x²}):
Transición suave, tono que asciende y desciende simétricamente. Carece de armónicos agudos.
· Función Sinc (sen x / x):
Resonancia principal con lóbulos laterales audibles como ecos suaves. Común en procesamiento de señales.
· Onda triangular:
Armónicos impares decrecientes rápidamente, sonido más suave que la onda cuadrada.
· Modulación en frecuencia (FM) simple:
Dos senoides interactuando generan espectro rico y variable.
· Ruido rosa (1/f):
Densidad espectral decreciente, sonido "cálido", presente en fenómenos naturales.
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⚙️ Vínculo matemático-sonoro:
· La transformada de Fourier actúa como puente entre dominio temporal/funcional y espectral/auditivo.
· La curvatura, continuidad y tasa de cambio de una función determinan contenido armónico y envolvente.
· El decaimiento espectral clasifica funciones por su "color" sonoro (blanco, rosa, marrón).
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📌 Aplicaciones adicionales:
➡️ Medicina: Sonificación de señales EEG y ECG para detección de patrones anómalos.
➡️ Astrofísica: Traducción a audio de curvas de luz de estrellas variables.
➡️ Educación inclusiva: Representación auditiva de conceptos de cálculo y análisis funcional.
➡️ Instalaciones interactivas: Obras que traducen datos ambientales en paisajes sonoros.
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🎯 Dirigido a:
Matemáticos aplicados, ingenieros de sonido, artistas digitales, científicos de datos y educadores interesados en representaciones alternativas del conocimiento.
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💬 Si pudieras "escuchar" una ecuación famosa (Ej. Euler, Schrödinger, Black-Scholes), ¿cuál elegirías y qué crees que expresaría su sonido?
Comparte tu propuesta en los comentarios.
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#mathematics #physics #sounds #fypシ❤️💞❤️ #mathidea
@math.idea.ec
732.8K
LOThe first 9 overtones of the harmonic series visualized on a Tektronix 760a Vectorscope. By modulating the gain of the fundamental and its harmonics I was able to achieve this animation. Each circle is created by first offsetting a sine wave to the left and right audio channels, then shifting the phase of one of the channels. #harmonics #cymatics #audioengineer #audiovisualart #vectorscope #vectorsynthesis #overtones #musician #looma #loomamusic #oscilloscopemusic #oscilloscopeart
@loomamusic
![#Spherical Harmonics Reel by @digital.harmonic - dreamy clouds of pitch set into motion through the outwards unfolding of wide and concentric lines
theory stuff:
- i've discussed mothra [6] before o](https://image.pictame.com/img/500228104_1069320131923505_1793938589245479002_n.jpg?hash=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)
11.9K
DIdreamy clouds of pitch set into motion through the outwards unfolding of wide and concentric lines
theory stuff:
- i’ve discussed mothra [6] before on the channel. it’s the supermajor hexatonic scale and has it’s own set of modes. it’s a unique tonal space all together. the “chromatic” equivalent is an 11 pitch space. representing it as a spectral chordscale with the “brightest mode” (10|0) creates the supermothra object. basically, Au7‡2‡6 or ultramajor7 with ‡2 and ‡6 in a more tertian expression. Extending this up gives Moth♮9‡10‡14 or more simply Imoth/IImoth lol.
- taking this Imoth/IImoth and superimposing it b8 from a central root creates a beautiful upperstructure against a maj7. this is expressed as b8supermoth/Imaj7. Enharmonically equivalent to ‡VIIsupermoth/Imaj7 but the b8 will make the superstructure clearer to the actual player since it creates triplings of the third, seventh, and ninth.
- i call this superstructure a hypermajor object because its core base is a maj7 chord while populating the interval spectrum with:
3, ‡10, #10
7, ‡14, #14
2, ⇂9, b9
6, ⇂6
it does not specify a fourth though!! which totally keeps it open as like a dense but still be defined hypermajor base quality open to being pushed lydian, roselike, lydia, ionian, etc.
#musictheory #harmony #microtonal #chords #scales #musiceducation
@digital.harmonic
1.8M
JAWhat does the harmonic series sound like?
“The universe exists solely of waves of motion.There exists nothing other than vibration.” ~ Walter Russell
🎥: @AlexanderChen
#sacredgeometry #cymatics #frequency #hz #sound #healing #vibration #energy #fractal #music #cyclical #musical #soundwave #resonance #healingmusic #octave #octaves #healingsounds
@jain108academy
309.2K
ROThe Circle....Squared...with an Oscilloscope.
Can't wait to design something like this for the inherent inner geometries (Platonic, Archimedean, Catalan, Johnson, and Granthedra) that dance to the music that underlies the structure. Could be cool no?
What do you think? Comment 👇
🎥: @Pleasedropout (TT)
@robertedwardgrant
522.8K
FA🌈 Harmonic Hues 🌈 (3D sound🎧)
Correction : The second half of the equation shall have 0.95 as coefficient , which is responsible for the hole in the center.
#mathematics
#satisfying
#oddlysatisfying
#rainbow
#loop
#math
#geometry
#pattern
#sacredgeometry
#fibonacci
#goldenratio
#spirograph
#spiral
#educational
#programming
#calculus
#coding
#3d
#8d
@fascinating.fractals
95.5K
MUIn WHAT MUSIC IS, we address why scales exist in the universe at all. There are profound truths at play here, to be grasped one concept at a time.
In this video, Bill Barclay @barclayarts and Shawn Feeney @shawnfeeney - the show’s creators - show a snippet that gets at the heart of why there is order in music rather than chaos.
Physics dictates that only integer multiples of vibrations survive as harmonics in any medium, be it a violin string, trumpet, or vocal folds. Harmonics provide the hard wiring that give us scales heard around the world.
Join us February 22 and 23 with @sanjuansymphony conducted by @heusertg in Colorado and New Mexico for the Workd Premiere of #whatmusicis
#billbarclay #shawnfeeney #thomasheuser #concerttheatre #concerttheater #concerttheatreworks #musicandscience #physics #harmonics #overtones #harmonicseries #multiverseastronomer
@multiverse_astronomer
575.3K
PI1. Non-relativistic Schrödinger Equation (without potential)
The Schrödinger equation is like the “manual” that governs the behavior of particles in the quantum world. It tells us how the “wave” that represents a particle (called the wave function) changes over time. In a situation where nothing influences the particle (no forces or potential energy), the equation describes how the particle moves freely through space.
In simple terms, the Schrödinger equation describes how the probabilities of a particle’s possible location change over time.
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2. What is a wave function?
A wave function is a way to describe the possible location of a particle. However, in quantum mechanics, we cannot know exactly where a particle is at a given moment. Instead, the wave function provides us with a "cloud" of probabilities. This cloud shows where the particle is more or less likely to be found.
The shape of this wave tells us how the particle behaves: it can oscillate, spread out, or move over time. Imagine it as a soft, blurry glow around where the particle might be, with brighter areas indicating a higher likelihood of finding it there.
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3. What is a Gaussian wave packet?
A Gaussian wave packet is a special type of wave function. It describes a particle that is relatively localized—in other words, we have a good idea of where it is. But since we’re dealing with quantum mechanics, there’s always some uncertainty.
You can imagine it like this: the particle is represented by a small “bump” that moves over time. This bump is concentrated mostly in one spot, but it’s not perfectly precise. Over time, the bump spreads out due to the uncertainty in the particle’s position.
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4. How are they related?
The Gaussian wave packet is one way of describing a particle in quantum mechanics.
Via erik_alan_normon
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#quantummechanics #wavefunction #physics #schrödinger #quantumphysics #particlephysics #science #mathematics
@pi.mathematica
89.0K
GEResonance experiment: Cymatics, the study of visible sound.
According to the physician and natural scientist Hans Jenny, these structures, reminiscent of the mandala and other forms recurring in nature, would be a manifestation of an invisible force field of the vibrational energy that generated it.
Jenny explored this science in his work, documenting the effects of sound vibrations on fluids, powders and liquid paste. He concluded, "This is not an unregulated chaos; it is a dynamic but ordered pattern."
What is responsible for the shapes is the resonance between the frequencies of vibrations and the medium that is being vibrated.
The phenomenon of resonance is responsible for giving form to matter, for this reason, the morphology of both organic and inorganic shapes in nature, being symmetric or asymmetric, are all results of the resonance generated by relationship of waveforms — thus, the patterns generated by Cymatics are often found in nature, like the geometry of flowers, the spot patterns of a leopard, the symmetry of diatoms and so on.
The science of geometry has its roots in the resonance of wave phenomena.
Vibration and geometry are two inseparable things.
@geometry.in.nature
✨ #Spherical Harmonics Discovery Guide
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