More analogies between sound and the universe- The Heavens are ringing, what a carillon!

If you have read my previous blogs, you must realize by now that I am deeply fascinated by the parallels between acoustic vibrations and the universe. Recent discoveries keep fueling my curiosity about the interconnectedness of the realms of sound and the cosmos. My previous post explored how a neutron star might ultimately collapse into a black hole, focusing on the resonant tones it then produces. Now, here’s another intriguing discovery about the behavior of black holes themselves.

All these findings are directly linked to the rapidly advancing field of gravitational wave detection (see my post on these waves). Interestingly, even before we had the technology to detect gravitational waves, mathematics had already enabled us to explore these phenomena theoretically. The possibility of detecting them is directly tied to Einstein’s theory of relativity, developed in 1917. For much of the period leading up to their discovery, there was considerable doubt about whether gravitational waves would ever be observed. But that didn’t stop astrophysicists from delving into this field in theory. And, indeed in a recent article “ in 1997 a graduate student, Hisashi Onozawa from the Tokyo Institute of Technology (now Institute of Science Tokyo), discovered a curious irregularity in what these waves should look like. In other words, some of the vibrations were dissonant in relation to the expected partial series from the fundamental.” (source: https://www.eurekalert.org/news-releases/1081428)

Here is a short description of the resonance found in bells:

Common partials in a bell include:

• Hum: A low-pitched partial, one octave below the strike note (fundamental).

• Prime (or strike): The main note you hear, typically the fundamental.

• Tierce: A minor or major third above the prime (this depends on how the bell is tuned)

• Quint: A perfect fifth above the prime.

• Nominal (or octave): One octave above the prime.

Although bells differ in a number of subtle and debatable ways, there seems to be some common features. The sound of a bell is characterized by a large number of partials. Some of the upper partials harmonize (approximately) with the fundamental, but most do not. Assuming the lowest mode (hum tune) to be C0, the traditional bell is designed to have higher partials at C1, E1flat, G1, C2, E2, and C3 The minor third, C, - Eb, is desirable to give the bell its characteristic plaintive tone. In practice, the various partials do not match the harmonic series perfectly. The pitch (strike tone) will not necessarily coincide with the partial around C, but is apparently determined by some sort of an average fit to the nearly harmonic series. 3, 4 The clarity of the pitch seems to depend upon how closely the partials match the harmonic series. (source: Physics and Music, The Science of Musical Sound)

The sound of the bell is characterized by a large number of partials, and all these modes of vibration are interacting - which result in random partials that are unrelated to the fundamental. This is how these irregularities also form in black holes.

The article goes on “Now, after thirty years, Associate Professor Hayato Motohashi from Tokyo Metropolitan University, formerly affiliated with Kogakuin University, has resolved this problem using precision calculations and the nascent theoretical field of non-Hermitian* physics. Looking closely at the behavior of modes, he found that the dissonance was not isolated to one mode but was a result of two modes interacting with each other in a resonant fashion. In fact, by examining many modes, it turns out this kind of interaction between modes is not a rare incident, but one which turns up universally in a range of modes.  Through a series of theoretical analyses, this resonance between modes in black holes was shown to be one example of a whole host of physical phenomena in not only astrophysics, but optical physics as well, looking at electromagnetic waves instead of gravitational ones. The interdisciplinary application of a new theoretical approach heralds the birth of the new field of non-Hermitian gravitational physics, unlocking the true potential of global-scale experiments like the LIGO-Virgo-KAGRA Collaboration which are coming online." https://www.eurekalert.org/news-releases/1081428)

Here’s another analogy I find interesting: sound (acoustic waves) travels faster in denser materials. For example, sound travels faster in water than in air—because water is 800 times denser than air. Sound moves at about 1500 meters per second in water (roughly 4.3 times faster than in air, where it’s 343 meters per second). Another example is the trick (often used by train robbers in the Wild West—please don’t try this!) of putting your ear to the rail of a train track to hear an approaching train much earlier than by listening in the air. That’s because sound travels at 5120 meters per second in iron—almost 15 times faster than in air! (see formulas a the bottom of this post)

This makes me wonder: what about the speed of sound in a black hole, with its infinite density? Would it travel at the speed of light? Perhaps. But we’ll probably never know—since not even light can escape a black hole, we’ll never be able to hear it, except for gravity’s effects on the fabric of spacetime.

All these analogies between acoustics and astrophysics underline the universality of the laws that govern everything, from the everyday objects around us to the most remote objects in the cosmos—even the bells that ring from our church towers. Imagine all the stars in the universe as resonating bells. I can hardly imagine what a cosmic carillon it would create!

* In standard quantum mechanics, the mathematical tools we use to describe things like energy and momentum are called Hermitian operators. These make sure that the measured values (called eigenvalues) are real numbers. If we use non-Hermitian operators instead, the measured values can be complex numbers.

If you want to figure it out by yourself, here are the formulas:

Solids: 

• v = √(Y/ρ). 

• where:

• Y is Young's modulus (a measure of the stiffness of the material, in Pascals, Pa). 

• ρ is the density of the solid (in kg/m³). 

Liquids: 

• v = √(B/ρ). 

• where:

• B is the bulk modulus (a measure of the incompressibility of the liquid, in Pascals, Pa). 

• ρ is the density of the liquid (in kg/m³). 

• [? something to add here?]

Songs from Neutron Stars

Last week I attended a fascinating talk by astrophysicist Phiala Shanahan, a professor in the Center for Theoretical Physics at the Massachusetts Institute of Technology. It took place at the Simons Foundation in NYC (a unique forum that has, besides its scientific mission, an active interest in exploring the interaction between science and the arts). [The talk was on the subject of] neutron stars, very unique objects that have their unique voices broadcast throughout the cosmos. These voices, it turns out, are telling us more and more about the universe's mysteries.

I had read a recent article about what is called “the long ringdown” (a phenomena that occurs after these objects merge), and there was no other person better to ask about this phenomena; but I was not sure that my question would be relevant…. but I was there, so I had to ask. The answer was more than I expected, and the professor jumped right into answering me with enthusiasm and knowledge (to my great satisfaction). So I am emboldened to share my thoughts about these Neutron stars.

The signal emitted by two merging Neutron Stars resembles that of a tuning fork (Credit: L. Rezzolla/pixabay).

Stars do ring like bells and that can be measure by recording the motion of the Star surface, this can be done by sensing the movements in a form of a “doppler shift”. This in fact a special branch of astronomy called “astroseismology” (read a previous blog about this subject.) So it should obviously also occurs in neutron stars, since they are stars and also to their ultimate fate: black holes.

Neutron stars are one step away from being black holes. They are immensely dense: one teaspoon weighs as much as the whole Empire State Building. They are the result of the implosion of already massive stars (5 to 50 times the mass of our star, the Sun), a phenomena called a Super Nova. Matter is made of atoms, and as we have known for about 100 years, atoms are mostly empty space. So after the star explodes, the remnants are only neutrons (mostly) with no space in between. The remnants implodes, if massive enough, into a neutron star.

If you add any mass to this already very massive object, it collapses into a black hole. That new mass comes usually as a steady stream from another star, and in some instances, it comes from another neutron star that ends up merging in a violent event. As they orbit each other, closer and closer and faster and faster, as they reach the last few seconds, they radiate higher and higher pitched gravity waves as they merge into a black hole and become silent. But actually - not quite, because that violent moment acts like a strike on the newly formed object, not unlike the strike on a bell.

When a bell is struck, the first sound emitted is a complex irrational set of frequencies; but as the vibrating bell (in our case, vibrating black holes) settles, the sound becomes more and more pure and that pure pitch leaves us with a lot of information about the composition (wood, metal, stone, neutron, etc.) of the ringing object.

The evolution expected from the post-Newtonian inspiral is shown with a dashed black line. The inset offers a magnification of the long ringdown with the corresponding linear slopes indicated by thin lines of the same color. Lower panel: As in the top panel but in terms of the instantaneous GW frequency fGW. The data refers to equal-mass binaries but very similar behaviour is found also for unequal-mass binaries

That is exactly what we should expect from the newly formed black hole, which is the merger of two neutron stars. We do not really know what they are made of, but that residual pitch is a window into the nature of the object. These rings have not yet been [physically?] detected; they have only been theorized following the law of physics and more precisely, [the law of] acoustics. This is an example of the parallel between sound vibration and our understanding of the universe.

As the universe is big, there are millions of them out there. In fact, new telescopes are being built to be sensitive enough to detect these events: a new radio telescope in China called FAST (Five-hundred-meter Aperture Spherical radio Telescope) has, in its short life of about five years, detected over one thousand of them. Most stars are paired with one or two other stars, so the chances for mergers are high.

What does this all mean for us musicians? Well, I think that there is a symphony out there in the cosmos that we are just now discovering. There are implications to this sonic environment influencing our musical sensitivities, but this will be for another post.

Painted Rock: A Natural Alignment with Chumash Cosmology

In the heart of California’s Carrizo Plain National Monument, an ancient natural formation known as Painted Rock stands as a testament to the region’s rich cultural and ecological history. For centuries, the Chumash people painted many petroglyphs on it inside walls and regarded this site as a sacred place, using it for ceremonies, initiations, and astronomical observations. Recent observations reveal an extraordinary feature of Painted Rock: its alignment with key celestial events, echoing the cosmology of the Chumash in remarkable ways.

The Chumash were a highly advanced and vibrant society whose territory stretched from Malibu Beach in the south to the central regions of San Luis Obispo County in the north, bordered by the Carrizo Plain and Mount Piños to the east (the highest peak in the region at 8,831 feet), and the Channel Islands to the west. Archaeological evidence shows that the Chumash settled in the Carrizo Plain as early as 2000 BCE, with their population peaking around 1000 CE. However, the population diminished steeply after that, likely due to significant climate changes that affected the region’s resources, Some Peoples from the Yokuts settled and shared the area until the 19th century.

The Carrizo Plain is bordered on the east by the San Andreas Fault, a geographical feature that not only shaped the landscape but also influenced the water sources and ecosystems the Chumash depended upon. Painted Rock, located near the heart of the plain, became a spiritual and cultural focal point for the Chumash people.

Chumash cosmology divided the universe into three interconnected realms: the underworld, the middle world, and the sky world. Humans inhabited the middle world and were tasked with maintaining balance between the realms, which were permeated by a neutral energy. Unlike many cultures that revered the Sun, the Chumash held the North Star (Polaris) as the most significant celestial object, symbolizing stability and balance in the universe.

A map of the Carrizo Plain National Monument. You can see the location of Painted Rock on the center right.

“California's Chumash Indians thought of the sky gods this way. They saw a balance of nature and the world order in terms of a nightly gambling game played between two teams. Sun was the captain of one team, while the pole star, Polaris, led the other. Polaris was known as Sky Coyote, and its pivotal position among the stars made it a symbol of the night.

For a full year they played, and at the winter solstice the score was tallied. Moon, that expert at counting out the days, kept score. If, at the winter solstice, Sun was the winner, it would go bad for people on earth: rather than return upon his yearly journey back to the north, he might just continue on south and leave the earth in the dead of winter, with the cosmos out of balance. Sky Coyote was a benefactor, a benevolent influence. If his team won, the order of things would be restored.” E.C. Krupp Echoes of the Ancient Skies

A Petroglyph of the Sky Coyote on the inside of Painted Rock (unfortunately damaged like many of the other painting on the rock ) photo by Dan McCaslin / Noozhawk

My wife, Sarah Pillow, and I have been visiting the Carrizo Plain for many years, drawn by its unspoiled landscapes, pristine night skies, and rich history. Our connection to the area deepened through stargazing and learning about the indigenous Chumash culture, so vividly demonstrated at the Painted Rock monument. As an amateur astronomer with a passion for sky lore and archeo-astronomy, I was particularly intrigued by how the Chumash integrated celestial events into their cultural practices.

In August 2023, I conducted a detailed scan of the interior of Painted Rock using an iPhone and the Scaniverse app. The scan data was assembled in Blender, and I also created a 360˚ panoramic photo of the site, which I inserted into the Stellarium app for astronomical analysis. The results were striking: the rock formation, shaped like a large horseshoe, has its opening perfectly oriented towards Polaris, a celestial body of profound significance in Chumash cosmology. (see below a short video that show the North view of a whole year motion of the constelation around Polaris)

Another remarkable discovery emerged during my analysis: on the south side of Painted Rock, the Sun at noon during the winter solstice aligns precisely with the top of the formation. This natural alignment mirrors the Chumash’s understanding of celestial cycles, which informed their rituals and worldview. (see below a short video of the Sun, during a whole year at noon, looking south from inside the rock)

What makes this discovery particularly fascinating is that Painted Rock is a natural formation, not a human-made structure. Its alignment with these celestial events appears to be a fortuitous occurrence, yet it seamlessly supports the Chumash belief system. It highlights the deep connection the Chumash people saw between their sacred geography and the cosmos.

An aerial of Painted Rock South is at the top and North at the bottom, you can clearly view the opening facing Polaris and the notch or groove at the top where the Sun sits at the winter solstice. Photo: Marc Wagnon

Tragically, the Chumash population was devastated during colonization. The establishment of Spanish missions introduced disease, forced labor, and cultural disruption, and westward expansion by settlers led to further extermination of their population and heritage. Yet, the Chumash legacy endures through their artifacts, traditions, and the profound cosmological insights that continue to inspire and amaze.

Part of a large painting on the inner wall of Painted Rock, unfortunately vandalized modern inhabitant of the area (the location is now fenced in and you need to register to visit it)

The Carrizo Plain is more than just the home of Painted Rock. It is a vital ecological and cultural preserve, with vibrant wildflower blooms, rare wildlife, and one of California’s last native grasslands. Its dark, unpolluted skies make it an ideal destination for stargazers and those seeking to connect with the celestial traditions of the past.

I hope this discovery inspires further exploration of Painted Rock and its connections to the Chumash worldview. By uncovering and honoring the interplay between culture, nature, and astronomy, we can better appreciate the profound legacy of the Chumash and their relationship with the universe. If you are fortunate enough to visit the Carrizo Plain, approach Painted Rock with reverence, keeping in mind its cultural and spiritual significance. Together, we can ensure this sacred site remains a source of wonder and learning for generations to come.

Who is ignorant of motion is ignorant of nature

Posted on June 18, 2024

The major contributions to science that Galileo brought to the world are well known. But putting these discoveries in the musical context could turn out to be more relevant that one would think.

The origin of Western science is linked to the study of harmony. As it was understood, Harmonia comes to be in all respect out of contraries; for Harmonia is the unity of multiplicity, and the agreement of things that disagree (the fitting together of extremes). Full article here

Sounds from deep space

Posted on February 24, 2024

Since the detectors of the electromagnetic spectrum in which we bathe are receiving the full spectrum of its emissions, and since the visual part of this spectrum (the one we can see with our eyes) is only a small part of its range, we have to “transpose” its data so that we will be able to match our senses. This is usually understood as making it accessible to our eyes, as we are an intensely visual civilization. But the sound spectrum is increasingly being used, and there are several reasons for this development. Full article here

Can we hear all sound waves?

Posted on August 29, 2023

The obvious answer is no, because some waves are at frequencies our ears cannot detect (about 30 Hz on the low end and 18 kHz on the high end, although most of us have a hard time hearing beyond 12 kHz). But this is only a very anthropocentric view. Many other species can hear way beyond the human range, the most well known being elephants on the low end and bats on the high end, and we don’t really know the full extent of the animal kingdom’s ability to hear the full range of sound frequencies. Full article here

More Megalithic Musing

Posted on July 8, 2023

My last post about the navigational Heiau called Ko’a Holomoana in Hawaii made me notice another megalith that could be described as “navigational”. Although the scale of the map it appears to refer to is not as wide as the Pacific Ocean, it nonetheless describes a large area.

In this post, I will be making a case for “Les Menhirs de Lutry” as a geographical alignment. This megalith is made up of large and not so large stones on the shore of Lake Geneva (or Lac Léman, which is how it is called in the area, a name that dates from the Romans – ‘Lacus Lemannus’ – from a couple of thousand years ago). As I understand, no one has ever published this interpretation, but it seems to be an oversight, and should at least be contemplated as an explanation of its unique layout. Full article here

A Cosmic Misunderstanding

Posted on December 31, 2022

During my second trip on the Big Island of Hawai’i, a trip that turned out to be as spectacular as the first one, was made quite unique by the fact that the Mauna Loa volcano started erupting the day we arrived. This made me quite happy, especially since the weather predictions were not looking too good for the week. If I was not able to see and photograph the fire in the sky (i.e. stars), I would get to see it coming out of the ground. But this post will not be about this event, but about the ongoing controversy regarding Mauna Loa’s neighbor volcano Mauna Kea and the telescopes sitting atop it decoding the universe. Full article here

About the Monochord

Posted on May 15, 2020

Until recently, I had some difficulty explaining the origin of the link between music and science. Of course, I understood this deep connection, that frequencies are ultimately numbers, and they relate to each other in rational intervals. This understanding is due to the fascinating fact that the ear has both qualitative and quantitative abilities: it has the ability to understand the moods/colors and the ratios of sounds. This ability makes it a pretty unique sense; in fact, it is the only sense that can accurately measure and “feel” at the same time. Full article here

A world where Sound is a Mystery

Posted on January 16, 2019

The formulas of mathematics are the scores of that mind insight, they are symbolic representation system that describe what we cannot see, hear or touch: mathematics. The same thing applies to music: we could not see, hear or touch music in a world without sound.

See the latest post on the Science and Music Blog

earlier Blog posts

I started this Blog in 2009 to muse on this interesting topic. It is still hosted on our old server for a while so I want to make my earlier posts available.

Hope you enjoy reading these:

Posted on January 4, 2019 Moon in the News

Posted on September 19, 2018 Science and Music Quotes

Posted on June 14, 2016 Yes There Have Been Aliens

Posted on April 24, 2016 The Drake Equation

Posted on July 22, 2015 Waste or not to Waste (follow-up)

Posted on April 28, 2015 Waste or not to Waste

Posted on March 26, 2015 The Oldest Analog recording…by far

Posted on March 11, 2015 Facts and Fiction

Posted on March 15, 2011 Promoting Science Awareness

Posted on March 15, 2011 Music’s Origin

Posted on July 29, 2009 Music and Brain Recovery

Posted on April 6, 2009 Music and Synesthesia

Posted on April 6, 2009 Music and Memories

Posted on March 3, 2009 The Power of Sound

Posted on February 17, 2009 Feed-back loop, the groove, and other earth shattering phenomena.

Posted on February 3, 2009 The International Year of Astronomical

Posted on January 21, 2009 Science and music everywhere…

Posted on December 2, 2008 Welcome to this Discussion