Who is ignorant of motion is ignorant of nature

Posted on June 18, 2024 by Marc

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).

The Pythagorean school of philosophy sought to integrate scientific inquiry into the nature of Number and a mythical awareness of the musicality of universal law. In particular, the harmonic series consisted of whole numbers: 2/1, 3/2, 4/3, 5/4…and so on.

The instrument that was used to investigate numbers was the monochord (see my previous blog post on the subject), which is used to measure the relationship or ratios between harmonics of a root note (the fundamental).

In fact, some historians of science contend that the division of the monochord strings is possibly one of the earliest scientific-empirical experiments ever to be carried out with mathematical rigor.

Throughout the whole of history, right up to the eighteenth century, the monochord was associated with cosmic concerns…the stretched string stood for the universe, with the various harmonics representing the planets in the solar system. Music, mathematics, and astronomy were inexorably linked in the monochord. The universe was thought to obey musical laws; therefore, the study of the monochord yielded information considered relevant to the other sciences, the humanities, and religion. Keeping with this harmonic-based cosmology, Kepler discovered a numerical relationship, his third law of planetary motion where the major semi-axis of the orbits of planets and their periods are proportionately related. He called it the “Harmonic Law”, and like all the philosophers of the time, he studied the ancient world of Pythagorus and Plato (Kepler also attempted to fit all the orbits of the 6 planets in nested Platonic solids).

Ancient cultures, before the invention of the printing press and the proliferation of books, were far more sonically oriented than visually focussed. That made them more receptive of the subtleties of the nature of pure tones.

Galileo was born into a musical family, and his father Vincenzio, beside being an excellent lutenist, was also a music theorist, and was investigating tuning. There was at the time a controversy about which form of tuning was best: on one side was the ‘natural’ tuning based on the harmonics of the monochord, and on the other side a more “tempered” tuning, which sounded more pleasing to the ears, in particular the major third- which sounded a bit harsh in the ’natural’ tuning. Also, the pure tuning limited the number of keys the instruments could play in. Galileo, who also played the lute, helped his father in his research. This research involved weighted strings which were set up similar to monochords.

There are several examples of how Galileo would have used music in his research:

In order to keep time while conducting his studies of the motion of bodies and their rate of fall, he used a ball rolling on an incline, by spacing frets at increasing distances from one another in order to hear a steady beat. If the frets were spaced evenly the ball would hit them at an increasing rate. At the time there was no clock precise enough to measure this. The obvious solution was music. Sing a song and the beat will be steady. This was first suggested in 1973 by Stillman Drake, a leading Galileo expert.

After Galileo discovered the moons of Jupiter, he spent a long time figuring out their periods, in an unsuccessful attempt to use their orbits as a clock to help navigators establish their position at sea, since the first three moons- Io, Europa and Ganymede, were locked in a harmonic ratio of 4:2:1 at one octave from each other.

I think it makes sense to mention that during the experiment at the Tower of Pisa (if it ever happened), the sound of the two objects hitting the hard surface of the ground would have been much more accurately measured by the sound made than by looking at them. The rate at which our ears can distinguish singular events from one another is four times more precise as the one our eyes can.

So thinking about Galileo and the work he did assisting his father with tuning, I am sure his inquisitive mind must have stretched the boundaries of these investigations, and I dare to come up with the following insight:

Coming back to the experiment at the Tower of Pisa, I started to wonder if there was not some connection with the “weighted string experiment” which is how some monochords are set up: by hanging weights at the end of strings. And trying to understand what would be the common phenomena of the falling object and the production of the tones on the strings put into tension by the weights. It dawned on me that there could be a direct connection:

the weight (let us say they are stones), initially are at rest, and have potential energy, each linked to their mass
this energy is unlocked when put in motion, either when released from the top of the tower or from being hung from the strings they are attached to. None of the phenomenon in these configurations – the falling of the stones or the tones emitted by the strings in tension from the weights – are possible without gravity.
as the weight of the stones’ sizes differ, the tension on the string varies.
in order to reveal their tension, we have to pluck them, which gives them energy (the same goes for the stones- we have to nudge them over the tower’s edge to use gravity to put them in motion)
as it is apparent in the stones’ varying sizes, each string produces a tone that is proportional to the size (in that case inversely proportional, the smaller stone giving the lowest tone) of the stone
the energy given to the string manifested in its tension is equivalent to the energy produced by the gravity acting on the stone, both directly related to their potential.
you could assume that if you pluck two strings together, they should not reach our ears at the same time, as the lower frequency (being of a lower energy tied to the lighter stone) would take longer to travel in the air than the one with the higher frequency (tied to the heavier stone) as you would assume that the lighter weight would fall at a slower rate. But they don’t, they reach our ears at the exact same time (we never question this because it is so obvious).
but both phenomena, the plucking and the falling, are merely a translation (or to use a musical term, a transposition) of the same initial fact: the size of the stones, and both are a form of motion. The only difference is that one (the sound waves) do not have friction (actually traveling through the medium of the air). So if we remove the friction on the stones, you should end up with the same result and they would hit the ground at the same time, as demonstrated by cosmonaut David Scott of Apollo XV on the Moon – as the different notes reach our ears at the same time.

So it could have been that this correlation was revealed to Galileo during the experimentations he performed with his father, and the root of these physics could very well be music. it seems to me that we have the same initial state give rise to a similar effect, demonstrated by two phenomena, connected through the bridge of the Monochord acting as a phase transition acting on the energy of the stone.

The various stones fall at the same rate and the various sound waves travel at the same rate.

Of course these are conjectures; it might not be the way his train of thought worked out. But I think there is a chance, and it is an interesting proposition, and it shows that the Law of moving bodies can be deduced with this old instrument, the monochord.

To close, it is interesting to know that in the past ten years the relationship between science and music has been revived and has revealed to us elements in our data set that would not be so easy to discern if the information was offered to us visually only. There are many examples – from exoplanet systems, asteroseismology, gravity waves, and so on. (View my previous posts)

When you listen to the music of Galileo’s time, it is important to try to imagine what was the acoustic environment in which it was conceived and performed. It clearly illustrates the unique position he held in the history of human knowledge with one foot in the ancient world and the other in the modern world. He was, to use a trendy word, an inflection point not possible without the past but enabling the future.

More Megalithic Musing

Posted on July 8, 2023 by Marc

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.

Megaliths come in many shapes and forms, and their interpretations are a part of guesswork and careful investigation of their geographic situations. There are two main categories that often overlap: they can be ceremonial, such as for a burial or place of ritual; and/or cosmological in their intent, meaning they are astronomical alignments which are in use as a calendar where the heliacal rising and setting of stars is marked, and allows for the study of the motion of planets, stars, the Sun and our Moon.

The finding of the navigational Heiau in Hawaii, and now the possible representation of this alignment of stones in the town of Lutry might elude to a third category, which could be named “geographical” or geodetic.

Full disclaimer: obviously, I am not trained as an archeologist. I am just curious about astronomical alignments that megaliths often demonstrate. This kind of cosmological stone construction is most often found in two typical layouts: rings or circles (like Stonehenge in England), or straight lines which are often parallel (like Karnak in Normandy). The stones in Lutry are loosely aligned with the summer and winter solstice, but their alignment falls in between the two typical layouts – the Lutry megalith stones are placed in a row; but at some point they bend to the south, as you can see in the image below:

Layout of the stones at the “Menhir de Lutry”

Secondly, there is a vertical progression, as the eastern part is composed of larger and taller stones that progressively get smaller as it moves to the west and starts bending to the south, as shown in the next image:

The alignment is on the shore of Lac Léman, and across this body of water, a large massif of Prealps mountains dominate the horizon. Unfortunately, due to the fact that the monument sits in the middle of a small town, this imposing view is obscured by houses and therefore separates the geographical features that these stones are representing. In order to recreate the original setting, I scanned the alignment and placed it in plain view of the landscape as it would have been originally. I removed the houses and placed the monument as it would have looked when it was built:

Each stone matches a large mountain block, and as the mountains recede, the stones get smaller. There are two stones that must have been lost through time. When we take a different view from above, there is more that matches the geography. As we see in the plan above, the stones bend to the south as they get smaller. This replicates quite accurately the natural bend along the south shore of the lake as it it moves to the west. To highlight this, I have highly magnified the stones to show how accurately they match the curve of the lake.

Les Menhirs de Lutry” from above (the south shore of the lake is on the top of the image)

Here is another view from the south

“Les Menhirs de Lutry” view from the south and at an angle (the north shore of the lake is on the top of the image)h

These two montages highlight the close match between the alignment of the stones with the shoreline of the lake. The combination of the silhouette view of the mountains as shown in the first montage with the stones matching the curvature of the shoreline shown from above in the second and third, reinforces the theory of intentional map making.

The question then arises: why would the builders of this megalith need to build such a representation of the mountains and lake shore on their side of the lake? Obviously, we don’t know; so I ask myself, why do we use maps at all? Especially such a large map that obviously we cannot fold and transport in our backpack? These kinds of maps are used in situations (i.e. situation room) where we need to plan some kind of collective action: hunt, prepare for war, celebrations, exploration – where you want to coordinate and plan the movement of a number of people.

It could also be that these mountains and this lake have mythical meaning to the megalith builders, and to recreate it in a more manageable scale, it allows them to have some control over the elements. The alignment seems to not have any particular astronomical alignment – it does not face east or west, where most celestial movements occur and are more obvious.

So, is geographical mapping a category for these megalithic structures? I first experienced one, as I mentioned above, when visiting the navigational Heiau on the Island of Hawaii, a megalith that maps the major islands of the Pacific Ocean. It seems to me that Les Menhirs de Lutry appear to follow that pattern. If this theory holds, it shows that the builders of these ‘geographical megaliths’ had some impressive geodetic knowledge and abilities.

Facts and Fiction

Posted on March 11, 2015 by Marc

I just heard this statement on NPR:

“There are more and more studies that show that giving people information does not change their mind.”

And although that is somehow not new in itself, and has been particularly obvious in the news business and the political world, it did put it quite starkly into focus. Fact-based reality is indeed a very fragile thing. The times in world history when facts did have bearing on human affairs are far and few apart, but what was achieved during these periods had a lasting influence.

Western civilization still resonates from the Greek philosophers’ insight into the physical world. Most of the stars in the sky have Arabic names, reflecting the intense interest in the calendar and orientation of the early Muslim scholars a thousand years later than the Greeks. On the other hand, these ideas reached a very small number of people.

The philosophers and mathematicians of the Renaissance looked back 1500 years to seek logic and reason from those who came before to guide their thinking process, which led to an evolving view of our world. These facts-based success stories were not widely understood by many until the 20th century, coinciding with a rise of the middle class in the western world. This was probably due in part to a more equitable education and success of the technology issued by the fact-based science behind it all. Unfortunately, the mismanagement and corruption of knowledge acquired was partly funneled into armament (the atomic bomb is a good example), and environmental abuse, which opened a wedge for doubt to fester.

Of course this is simplistic, but these drawbacks were enough for other forces to gain momentum, and utilize this breach of trust to declare full war on the factual philosophy that we still need so urgently. We cannot solve these problems by burying our heads in the sand. It is worthy to note that this development coincides with a widening of the gap between rich and poor.

There is a lot more to be said, but the main concern I have is: what can we do about it? Can we make facts sexy? Any other suggestions?

Music’s origin

Posted on October 19, 2009 by Marc

Imagine a long early summer sunset, and the only sounds heard are from some late crickets, and the crackling of the fire a few yards away. Venus is shining just under a young moon crescent. Other bright stars are slowly appearing, and the first to be seen is the brightest in the sky, which leads to the coldest parts. As the sky grows darker, a bright milky band shines from where the sun rises to where the moon sets.

A light breeze is blowing; you are thinking of today’s hunt, and tomorrow’s festivities celebrating the sun rising again at that point on the horizon when its path moves back to where it first came six moons ago. A big bird flies off of a nearby tree, and the coming darkness leads you into a dream.

The beauty of the still twilight inspires you to reach into the leather pouch you always keep close to your body. You take out your magic flute and start to blow into it; softly at first, recalling one of the melodies you heard at a gathering long ago near the big ice wall over in the direction of that brightest star in the sky. Then you feel the melody could sound a different way, and you go more deeply into the sounds you are producing.

Others gather: someone has brought a hollow piece of trunk, on which he has stretched a piece of abix skin held tightly by some wood pegs. Its pulse lays a foundation for your improvisation. Some of the people who have gathered around you start to move in unusual ways. Not walking, not running, not expressing a particular feeling– but just moving to the pulse generated by the sounds you and your acolytes are producing.

It is something new, these movements, that previously were static and meant either anger, love, hunger, or danger. But with these sounds you are producing, all of these movements become blended, in a complex meaning that is not so clear but much more nuanced. there were even some that were completely new. They must have meant something, but it was yet not clear to anyone; could it be that these movements could be combined into groups? Everyone was feeling calm, and someone even started making sounds with her mouth in a sequence, repeating the same sound over and over, synchronized with the movements and mysteriously related to your melodies….could that have meaning?

There is so much to discover and understand; somehow that evening it became just a little bit more clear. Definitely a night to remember.

This fictitious but, I think, possible scenario happened a Platonic year* and a half ago in what is now called Ulm in Germany, where Professor Nicholas Conard of Tubingen University found in one location three flutes made of bird bones.

“We report the discovery of bone and ivory flutes from the early Aurignacian period of southwestern Germany. These finds demonstrate the presence of a well-established musical tradition at the time when modern humans colonized Europe, more than 35,000 calendar years ago”.

Experimenting with the replica, he found that the ancient flute produced a range of notes comparable in many ways to modern flutes. “The tones are quite harmonic,” he said (they were pentatonic in nature: a five tone scale which skips the fourth and the seventh degrees of the diatonic scale). He adds:

“It’s becoming increasingly clear that music was a part of day-to-day life,”…. “Music was used in many kinds of social contexts: possibly religious, possibly recreational – much like how we use music today in many kinds of settings.”….”Music could have contributed to the maintenance of larger social networks, and thereby perhaps have helped facilitate the demographic and territorial expansion of modern humans…” his team wrote.

In fact, it is hard to imagine the development of musical abilities without the parallel development of spoken language. There are strong indications that language has its root in singing (I will develop on this concept in a future post).

It so happens that the Hohle Fels flute, as it is called, was uncovered in sediment a few feet away from the carved figurine of a busty, nude woman, which was also estimated to be around 35,000 years old. Now, I’ll let you make your own deductions about this synchronicity.

* A Platonic Year is 24,000 solar years. It corresponds to the period it takes for the earth axis to wobble, like a spinning top in one complete turn. This phenomenon has resulted in a shift of constellations. To an observer on Earth, Vega was the north star, and the Milky Way was flowing in a different direction.

The Power of Sound

Posted on March 3, 2009 by Marc

Most of us understand that sound needs a medium to transmit itself, but not, at least in my case, that this includes any form of matter that constitutes our Baryonic universe. It turns out that this has monumental implications in how fundamental sound waves are in the universe we live in.

When I am talking about a ‘medium’, this applies to all matter in its many forms:

– gases, the most common of which make up our atmosphere in which sound travel at 1,235 meters per second;

– liquids, water from which we are made mostly, in which, due to its higher density, carries sound waves at 1497 m/s;

– solids of course of still higher density, for steel the most dense of solid, the speed is 5930 m/s. Another less well known form of matter is:

– plasma found in extreme invironment like stars or the early universe, but nevertheless does conduct sound waves, like other states of matter, as of the sound speed in a plasma, it must vary as in the other medium as the pressure or temperature changes I could not find a actual number, but I can assume that the speed in it is higher still to many magnitude. if you have the knowledge to figure out the formula here it is:

Baryonic matter, is anything that constitutes our visible universe, which is about 4% of its composition. The bulk of the universe is made with 23% Dark Matter, and since we do not know what it is made of, we do not know how sound waves behave in it; but since sound is so instrumental in the shape of the universe, there is no reason to think that it is not affected as well. The rest, 73%, is made up of Dark Energy, an even more puzzling phenomena but on which sound could help shed light.

All this brings me to the point I want to make: sound waves have an influence on matter of all kinds. They have an elastic or kinetic effect due to the slow rate of their frequencies, compared to the electromagnetic spectrum (light, etc.) which, due to the shortness of their frequencies only have influences at the atomic level.

What is the loudest sound ever created in this universe? Well, it has been very adequately named, as we are all calling it the “Big Bang”– just think about what it means!

The Big Boom, right? But we all have seen those science fiction movies with silent explosions, as being in space, there is no medium, so no sound. That is right, except for the fact that in the case of the Big Bang, it is sound that created the empty space. The Big Bang was infinite pressure, so sound must have traveled infinitely fast, its wave spreading to every corner of the young universe, pushing matter with its peaks and valleys in clumps and creating voids, engineering stars, galaxies and galaxy clusters, and somewhat its own demise– empty space or vacuum.

Now, sound is left vibrating, isolated in the islands of matter that dot the universe, where the original Boom still resonates from all directions. It can be measured and it has a name. It is called the “Baryon Acoustic Oscillation” or BAO. The following is a quote from an article by Richard Panek in the February 2009 issue of Sky & Telescope:

‘Early in the Universe, sound waves (“acoustic oscillations”) coursed through the primordial gas, creating peaks at intervals of 436,000 light-years. As the universe has expanded, so has the spacing between these peaks; today they are 476 million light years apart. And because galaxies tended to form on the peaks of these large waves, astronomers can measure galaxy distributions at different eras, allowing them to see how the peak spacing changed over time, and thus how fast the universe has expanded.’

This will help us measure the effect Dark Energy has on accelerating the expansion of the universe, and help predict its ultimate fate… And fittingly this all was discovered about forty five years ago with the use of a giant ear! (see picture below)

This is only the genesis of the much under-reported fundamental influence that sound plays in our existence that we shall explore in future postings, so tune in (you have no choice).

Welcome to this discussion

Posted on December 2, 2008 by Marc

To every musician and scientist, this discussion is dedicated to you!

The links between science and music (and art to a wider extent) is by far not a new concept, you can actually hold an argument that they were united in most of their history, as science and art were both considered as philosophy. The root of the western scientific method can be traced to Aristotle who as he explored the physical world created the scientific method, which led him to study scales, modes and harmonic relationships, with the use of weights. from this it is not far to see the relationship: weight = mass = creative energy = emc2.

Yes, it is quite a short cut from one to the other; even absurd. But this kind of thinking is needed now, since the recent (about the past 100 years) trend is to compartmentalize the creative thinking process. But the history is on the other side. Besides Aristotle, Galileo’s father was a famous musician, Einstein played the violin and Richard Feyman played the bongos (quite well, I can attest, as a percussionist).

Another fascinating recent development, is the rise of techniques to study the brain. Neurology is opening a window in the process how music is understood by conscious and unconscious.

I think this is a fascinating subject, where there is still a lot of unknown that deserves to be explored. I also think that the answers can be explored by the people who are at the forefront of each discipline.

So please be open to offer your opinion and observations.

Marc Wagnon

Buckyball Music

Musing on the relationship between science and music

Tag Archives: science