The Monochord

Posted on May 15, 2020 by Marc

The Monochord.

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.

But this did not explain that since antiquity, music was made an equal to geometry, mathematics and astronomy (The Quadrivium); it is only recently in the modern era that we are able to understand frequencies and compute them, and this is only made possible by the use of scientific instruments. Although ratios between the partials were understood to be rational in their fundamental nature: 1:2, 2:3 and 3:4 for the octave, 5th, 4th, and so on, that knowledge dates from antiquity. But how did this realization come about? I was aware of the monochord but I took it as a demonstration tool, illustrating the phenomena of musical ratios. I had it wrong: the monochord is not the message, it is the medium. It is the “instrument” that led to this discovery, and in fact, the monochord is the first scientific instrument which allowed accurate measuring of a physical phenomena, to display geometrically these acoustic relationships and to translate them mathematically. The origin of the monochord is unknown: “the Greeks attributed its invention to Pythagorus; however, like most musical technologies it was probably imported from Babylonia or Egypt…No more accurate tool for investigating musical tuning was invented after the research of Helmholtz in the later half of the nineteenth century.” [An Introduction to the Monochord, Seimen Terpstra]

Modern monochord with four strings

Initially what the monochord was able to investigate is the rational division of the whole. This term is taken as “wholly” a quasi-“god”- like concept, in a cosmological sense. In other words, the rational division visually demonstrated by the placement of the “bridges” dividing the strings at various divisions of the “whole”, illustrated the inner working of the cosmos, revealing the inner harmonies of the world that were at the core of philosophical inquiry up to the nineteenth century.

Back in antiquity, truth for the Pythagoreans manifests itself through the world of physical phenomena. (Fideler in Guthrie, 1987) “The Number was the essence of a sacred order, and nowhere was this better expressed for the Pythagoreans than in cosmic music, paradoxically unperceivable because [it was] permanent.” (“Star Music”, Eduard C. Heyning, 2017)

“As the eyes are designed to look up at the stars, so are the ears to hear harmonious motions; and these are sister sciences – as the Pythagoreans say.” (Plato Republic VII 530d; 1937, I. 790)

Boethius

“The ears of mortals are filled with this sound, but they are unable to hear it….The sound coming from the heavenly spheres revolving at very swift speeds is of course so great that human ears cannot catch it; you might as well try to stare directly at the sun, whose rays are much too strong for your eyes.” (Cicero, The Dream of Scipio),

So this music of the spheres is music that we cannot hear because we’ve been hearing it since birth. Only the semi-divine Pythagorus could, and he was able to make us hear and see on a string, this music to which the planets of the solar system who can be made to intone a dominant chord, (see “Waves Passing in the Night”, Walter Murch). What can it reveal to us?

Kepler 3rd (Harmonic) law

Closer to us in history, Johannes Kepler is the one who began to bridge the two world views of wholistic antiquity and the birth of modern science. Kepler is a “rational mystic”: in one way looking back over the centuries to the platonic theories, and in the other, laying down the laws of planetary motion which generated the foundation for the future work of Newton on the laws of gravity. This is culminated in Kepler’s third law, which rules that the ratios between the semi-axis (half the diameter) of the orbit of a planet and the period (a planet’s path around the Sun in a year) is harmonically related (r³= P²). This third law of Kepler’s is called “the harmonic law”, which has one foot in antiquity and the other in the modern world.

As it turns out, many examples of harmonic relationships exist in astronomy. The most evident example that illustrates this relation and that we can all witness in the sky, is the 1:1 relationship locking the Moon to the Earth (one revolution = one rotation) so that we can only see one face of our satellite (incidentally, many exoplanets are gravitationally locked to their stars); another more distant example are the three inner moons of Jupiter which are in a 1:1, 2:1 and 4:1 harmonic lock, with their rotation also, like our Moon, on a 1:1 relationship with their revolution around Jupiter.“Jupiterians” would see only one side of each of these moons.

These relationships arise from the reciprocal gravitational influences of these celestial bodies; although they are harmonic in essence, they arise from different processes than musical harmonics. On the other hand, both share a surprising consistency with whole numbers.

Pythagorus

Further numerical musings about whole numbers and speculations have been made, and are probably the root of numerology. Pythagorus was obsessed with whole numbers; he realized that the sum of 1, 2, 3 and 4 make 10 and went on from there to many speculations about the number ten. Of course there is the theorem that bears his name: 3² + 4² = 5² which probably set the standard for “beauty” in mathematical formulas. Going back to the monochord, my point is that simple rational relationships of integers are at the base of both music and science – astronomy in this case, and that, interestingly enough, in the process of codification of these disciplines, music did precede or at least showed the way.

These whole numbers are in use in the ratios visually displayed on the monochord from the root, fifth, fourth, third and so on to build scales…as 1, 2, 3, 4… although to say the astronomical and musical harmonics are one and the same seems enticing, until we understand more about both phenomenas, the jury is still out. Also, it is important to note that there are many incommensurablities. The “pythagorus comma” is a good example (the sum of twelve fifths = B#; this does not add up to the sum of 7 octaves = C8).

To summarize, these “explorations” were initiated with this perfect hybrid: the monochord, which is an “instrument,” a word used both to describe the tools to conduct science and music, and are etymologically linked for a good reason.

A world where sound is a mystery

Posted on January 16, 2019 by Marc

I came across a powerful analogy, I was listening to a discussion a series of talk called “Conversation on the Nature of Reality” from the New York Academy of Sciences. The whole point of this talk is understanding the meaning of mathematics in society, is mathematic constructed or is it discovered. This is an age old puzzle, where do insight in the nature of things come from explained by the workings of mathematic coming from intuition, visualization in the mind the mathematician, and then laid out in formulas, which make sense to only a few.

We are blind to these insight, it is we cannot see them. We go through the world with the perceptions that we need to go on our daily musings, sure our life has been improved by our deepening understanding of the mysteries of nature. But how to understand this process, how make us un-initiated imagine what is going on.

An attempt at an explanation was proposed by theoretical physicist S. James Gates Jr. during that aforementioned discussion, and it is one that us musicians can have a particular advantage in understanding. Imagine a world without sound, not that it cannot exist, but that it has not been experienced yet. Some of the inhabitants of this far away world, who are like us thinking beings who share our ability to imagine, start to hear in their minds ear sound, not unlike when composing music earthlings hear it first in their mind before putting it down to paper, and by reflecting on their insight find a way to write musical scores to describe what their intuition has lead them to discover. To anyone else these “scores” mean nothing, they question the “musicians” what do they mean, and how did they came up with these notions, they ask does music exists as a separate physical fact and they are discovering it, or do the musicians are constructing it?

These same questions arise when we think about mathematics: is it there to be discovered or is it a construct of the rational mind as an attempt at understanding the physical world? Has music always been there and we are just discovering it, or are we creating it. The link between music and physics started when Pythagoreas to his own amazement, discovered that the ratios of partials of a tone are whole numbers; 1,2,3,4,5,… In a linear progression.

I find this particular story to be a particularly interesting parallel; 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.

This also leads us to a fascinating conclusion as the other participant in the discussion science writer Margaret Wertheim, pointed out: by inverting the argument we can say: scoring music is only one way we can learn and appreciate music, there are countless musicians throughout history that do not read music, so if the parallel holds between mathematic and music understanding the equations should not be a prerequisite to understanding mathematics, and that brings us to the conclusion that as music mathematics can be understood intuitively.

Of course this is a “thought experiment”, it would be hard to find a world without this very important physical element. But it might be that this world is just space, like the one that separates us with the rest of the universe, and in interstellar space there is no medium, so no sound.

Here is a YouTube link to: The Mystery of Our Mathematical Universe

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.

Music and brain recovery

Posted on July 29, 2009 by Marc

It is now more and more fashionable to talk about the effect of music on the brain. As I had mentioned it on an earlier blog, books are coming out about the subject, and now the PBS show Nova has an episode on the subject, centered on Oliver Sack’s book Musicophilia. But it is another PBS show that struck me, and although I usually don’t watch it, P.O.V. showed a 80 minute film about the story of the struggle of guitarist Jason Crigler overcoming the debilitating effect of a stroke, which occurred while playing a gig in a club.
Jason basically lost all normal higher brain functions, and had to re-learn how to function as a human being. The movie describes the hardship Jason family went through to help him recover his brain function. Against many odds and the prognostics of doctors, Jason made a full recovery. But what did fascinate me is that obviously music, and of course all the love and patience of his family, was very much instrumental (no pun intended) in his recovery.
Jason’s insurance eventually ran out, leaving him in a state where he was totally dependent on outside help. The ‘normal’ route was to go into hospice care, but his family decided against it and decided to take him home where he could be in a more stimulating environment. There he would be able to reconnect with familiar things, like all of his music making tools, and in particular his guitar.
As Jason’s dad recounts it, after a while in the house, Jason got drawn back in his music room, and the moment Jason picked up a guitar and began to play again was the milestone that seemed to validate the family’s faith. Jason started with small ostinato phrases of four or five notes that he would repeat as he was practicing. A few months later he sat in at a friend’s gig, then a whole set, and then his own gig in downtown NYC. After the gig where all his friends came and were quite impressed by his control of the instrument, Jason recalled: “I had trouble connecting,” but at Jason’s first concert in New York, something clicked and he suddenly connected with the music. “It’s the first gig I played that I felt really good,” he later said. That was the moment, a year and a half after his brain hemorrhage, when things turned around.
Jason is now fully recovered, although he does have a somewhat deeper relationship with music.
Well this is quite an amazing story, and I have to say that I kept thinking, at the point he picked up his guitar, that since music involves so many areas of the brain, it must be the way to recovery. And off course there is no way this would have happened without the incredible support from his family. But, some regions where damaged, on the other end there also must have been some other regions that still functioned well, and it was a matter of remapping them all back together. Some of the good parts of Jason’s brain must have been involved with music, and they could act as some kind of crutches to his healing brain, that led to recovering the damaged part.
It seems that the ability for repair exists in anyone with a brain injury, but the challenge is to find the crutches, and in this, music seems to be unique, since music stimulates so many areas in the brain, rendering those areas potential crutches in the event of a brain injury. I would be interested if other examples of recovery are linked to other kind of activities of the brain. It might not be that music has a monopoly on this but, to me, it seems self evident.
Here’s a few links to the movie and the P.O.V. site:
http://www.pbs.org/pov/lifesupportmusic/film_description.php

Music and memories

Posted on April 6, 2009 by Marc

Here is a change from all of the nebulus topics I’ve been consumed with recently. Music has a very deep relationship with the brain, especially when considering how many regions of the brain are put to the task when music is experienced. Therefore as the tools to look at the brain become more sophisticated, to the point seeing its functioning in real time, so the effect of music on the brain comes to the fore front. There is seldom a week that passes without some bit of news about it. A recently published book by Oliver Sacks (Musicophilia) is making everyone aware of the influence that music has on our “control module”.

Recently I listened to a radio show with the topic of how one could help Alzheimer patients use music that they learned during their youth to help them recover some of their lost memories. People working with them (most of them from another generation) are actually learning about the music of their patients’ youth in order to expose them to tunes that could help them. I think that as the baby boomers come to age, the Beatles will come as an unexpected rescue to the unfortunate ones who suffer from these kinds of diseases of the brain.

I use my own experience as an example: in my youth, I listened to a particular recording while reading a particular book. I had not listened to this recording in at least twenty years, but when I rediscovered the music, and heard the first notes played on my stereo after all of that time, it was as if I was in the middle of that book, the memory was so clear.

Now one can suggest that we create some of these memories. But since the brain, as we recently discovered, is the only part that does not lose growth potential in our body, the chances are pretty good. It would be more of a conscious effort than the free-association we make in our teens, but it might be worth it; as when memories are recalled this way, it always gives us a warm feeling of connection.

I am wondering if any of you reading this might have made some of these connections and what kind of interesting, except the summer of …. ( fill the blanks) association you’ve made with a particular recording or song. Let me know, we can compare experiences.

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).

Feed-back loop, the groove, and other earth shattering phenomena.

Posted on February 17, 2009 by Marc

Feed back is a term that musicians who use amplification, like myself, are very familiar with. For those who might not be used to the phenomena, an audio feed back can be quite annoying, in particular for singers who walk around concert stages with a microphone. When a mic gets too close to a speaker, it picks up the resonant frequency of the room and sends it to the speaker after being amplified by the P.A. system. This is then picked up by the mic again which sends it a second time (feeding it back) through the system around the same loop. Soon enough it amplifies itself out of control and produces a loud whistling sound. By moving the mics away from the speaker you break the loop.

On the other hand musicians, in particular electric guitarists, have learned to use this to their advantage, and have created a unique blend of guitar tones and controlled feed back into the rich sustained sound that is so unique to the instrument. One example would be the tone of Carlos Santana’s guitar.

So there is two sides to the feed back loop- the Dr. Jekyll and the Mr. Hyde.

There are many examples of feed-back loops, and one of them has to do with bridges, which I’ll get to in a minute, but in thinking about this it came to me that this could also explain another musical phenomena. I am thinking of the one we call “groove”. As a percussionist I am always concerned about it; is it good, or is it not good? What makes it good, or what makes it lame? What is a groove, anyway? I’ve never seen a definition of it; the only thing I know about it is if it is there or not. I then read this story about the London Millennium walking bridge and as an analogy it made perfect sense…..

The closest thing to a string in the everyday world in which we live is the bridge; it is long, stretched, and subjected to all kinds of vibrations.

When the London Millennium bridge was open to the public, people enthusiastically started to walk on it in great numbers, but it wobbled a little bit, which then fed back to the people, which made them want to synchronize their footsteps to the bridge’s motion, which made the bridge’s motion worse. In other words, the situation created a feed back loop between the bridge and the foot steps of the people. It is not a new phenomena, it has been well known for a long time; military parades have to break their lock step while walking on a bridge, because they could create such a feed back loop that they could collapse it.

So, to me, a groove does behave in a similar way. There is no physical bridge or amplification system as previously, but only the sympathetic relationship between the different elements that constitute it. They re-enforce each other by feeding back in a looped pattern. The common denominator is the down beat, which can be present or only suggested by the interlocking parts. A groove is made of at least two parts (bridge-steps or mic-speaker), or, in this case, down beat and syncopation. But it can include many different parts.

When a groove is locked in, and it is important to stress that this word is a paraphrase helping us describe the “groove” phenomena the best we can (there is no lock on a groove), in this case the analogy is the lock step of the aforementioned parade. When a groove is locked, it means that the feed-back loop is enabled and is re-enforcing each part in relation to the other. To make another ‘bridge’ to the scientific lingo, you can say that the synergy is at its highest, the whole become larger than the sums of its parts.

Just listen to African, Latin American, Jazz and Funk music, and when the feed – back loop is enabled, feel your step locking with the groove, and as with the Millennium Bridge– shake your whole body.

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

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