Golden ratio in guitar solos?

_{Denyse O'Leary

December 2, 2014

Intelligent Design, Mathematics, News}

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Golden rectangle/Ahrecht (Original), Pbroks13, Joo

Further to Does the golden ratio, 1.618, unify science?

A reader kindly writes to say that his high school guitar teacher told him that one can find the golden ratio in guitar solos that sneak into songs:

Golden section and golden rectangles, the harmonic series and the model of its ideal behavior simplified, equal temperament and just intonation and a description of the beat frequency conflict produced by the deviations between simultaneous sounding of harmonic partials and prime frequencies and how it affects the tone and timbre of the guitar. Read to the end for some cool videos demonstrating the properties detailed here.

Design? Chance? Chance only if there are a zillion universes that don’t have anything like this. So the evidence for their existence is… ? Uh, right.

Chances are, today’s art establishment won’t take the golden ratio seriously unless it helps chimps fling poop at each other. That’s art too, didn’t you know? Well, it will be if some project gets funded.

See also: The multiverse: Where everything turns out to be true, except philosophy and religion

and

Human origins: The war of trivial explanations

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Comments

So... Not sure if any musicians here already pointed this out, but... As a musician, I know that an easy way to pull a guitar solo out of nowhere (or to play something that sounds good even if you are lost) is to play along a pentatonic scale. Whereas a normal major scale would have 7 unique tones, the pentatonic only includes 5 of those tones, which are broken into two sets: One set of two, and one set of three. I'm not a mathematician, but according to the simple calculations for the Golden Ratio... it would seem that this extremely common technique for guitar solos is within range of the golden ratio. The set of 3 divided by the set of 2 is 1.5, while the sum (5) divided by the larger set (3) is 1.66666... pretty spot on, right? Guess this explains why pentatonic scales are so useful for soloists and general improv.bloodymurderlive_{December 30, 2014
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fifthmonarchyman: a collection of organisms necessarily has more information than the sum of the organisms taken individuality. 1. The sum would depend on what is included within the fuzzy edges of the group. 2. Algorithms can determine the sum of group. fifthmonarchyman: What accounts for the sensation? Remember It can’t be an algorithm like Darwinian evolution. Why not? fifthmonarchyman: Godel proved conclusively that all formal systems including TOG are necessarily incomplete. That is incorrect. Formal first order geometry is complete.Zachriel_{December 16, 2014
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'Fibonacci quasiparticle' could form basis of future quantum computers - Dec. 15, 2014 Excerpt: "The Fibonacci anyon is a non-Abelian anyon whose quantum dimension is the golden ratio (1.617...), and is the simplest anyon capable of performing universal quantum computation," Vaezi explained. "Using the fusion rule of Fibonacci anyons, it can be shown that the degeneracy of the ground state in the presence of n well-separated Fibonacci anyons on a sphere is the nth number in the Fibonacci sequence." http://phys.org/news/2014-12-fibonacci-quasiparticle-basis-future-quantum.html notes: In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than fermions and bosons;,,, ,,,the Nth Number is some arbitrary positive integer in a sequence that can be whatever anyone chooses it to be.bornagain77_{December 16, 2014
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ZAc said, “Species” generally refers to the collection of organisms themselves. I say, a collection of organisms necessarily has more information than the sum of the organisms taken individuality. The extra something is the form. check it out http://en.wikipedia.org/wiki/Cantor%27s_theorem ZAc says, Forms are an abstraction, a type of sensation of the mind. I say, What accounts for the sensation? Remember It can't be an algorithm like Darwinian evolution. Zac says That sort of navel-gazing applies to the Theory of Gravity, or any scientific theory, which are all abstractions. I say, Well of course. Now maybe you are getting it. Have you even heard of Godel and incompleteness? Godel proved conclusively that all formal systems including TOG are necessarily incomplete. They must rely on something beyond themselves. Something that must be assumed but can't ever be proved. Let that sink in while you stew. peacefifthmonarchyman_{December 12, 2014
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fifthmonarchyman: Thus confirming the claim that evolution being an algorithm can’t account for the origin of forms (like species). "Species" generally refers to the collection of organisms themselves. http://www.merriam-webster.com/dictionary/species The platonic form is called the type. http://en.wikipedia.org/wiki/Type_(biology) In any case, you are incorrect. Computers can make the same generalizations as humans with regards to grouping organisms into species, characteristics of which tend to be statistically lumpy. fifthmonarchyman: 2)The forms are an illusion in our brains. Forms are an abstraction, a type of sensation of the mind. fifthmonarchyman: Either way there is a something in biology (I would argue the most important thing) is not the result of Darwinian evolution. That sort of navel-gazing applies to the Theory of Gravity, or any scientific theory, which are all abstractions.Zachriel_{December 12, 2014
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ZAc says, When we consider the objects we call “mice” and group them into a species, we might create a platonic form called “mouse”. However, the objects have no obligation to conform to your platonic form, and in the case of biological organisms, they often don’t. I say, Exactly, Thus confirming the claim that evolution being an algorithm can't account for the origin of forms (like species). Finally You are now left with an obvious dilemma. either. 1) The forms actually exist independent of us yet we can access them with our minds. or 2)The forms are an illusion in our brains. Either way there is a something in biology (I would argue the most important thing) is not the result of Darwinian evolution. Unless you have a point that in some way gets you out of this spot I will leave you there to stew and let you have the last word on this one. peacefifthmonarchyman_{December 12, 2014
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fifthmonarchyman: You don’t observe the ocean you observe water and infer that is part of an ocean. Never been to the ocean, eh? http://upload.wikimedia.org/wikipedia/commons/0/05/20100726_Kalamitsi_Beach_Ionian_Sea_Lefkada_island_Greece.jpg Anyway, you don't observe "water", but reflection of light on something we infer has certain properties we call "water". If we use instruments, we only see the light from the instruments, and have to infer that it provides information about the properties of the thing we infer as "water". Generally, in English, we very well might say we observe the ocean, or more specifically, we observe properties of the ocean, though at some level, we are merely inferring the existence of a distinct entity called "ocean". When we consider a species, we obviously don't see a species, but individual organisms. When we consider an organism, it's actually not a single whole, but a collection of cells. Even its molecules are replaced over time. But we observe something that seems to have consistency in space and time. We often say we observe something, even though we are actually inferring it as a separate object with distinct properties. Nevertheless, we say we have an "ocean observing system" and people know that we mean a system to observe properties of the entity known as the "ocean". http://www.ioos.noaa.gov/ When we consider the objects we call "mice" and group them into a species, we might create a platonic form called "mouse". However, the objects have no obligation to conform to your platonic form, and in the case of biological organisms, they often don't. Leaving semantic quibbles aside, species tend to be sets with fuzzy edges, just like an ocean is a body of water with fuzzy edges.Zachriel_{December 12, 2014
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zac says, That’s like saying the sea or atmosphere isn’t an observable because the edges are fuzzy. I say, You don't observe the ocean you observe water and infer that is part of an ocean. You don't observe the atmosphere you observe gasses and infer they constitute part of an atmosphere. Use your head man. This is what the forms are all about. Forms combine the discrete particular many into the unified one. The form "circle" combines discrete particular individual Geometric Shapes into a unified exclusive set. The form "mouse" combines discrete particular individual organisms into a unified exclusive species. The form "Shakespearean Sonnet" combines discrete particular individual strings of text into a unified grouping of literature. This is pretty elementary stuff check it out http://faculty.washington.edu/smcohen/320/1ovrmany.htm peacefifthmonarchyman_{December 11, 2014
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fifthmonarchyman: Forms http://en.wikipedia.org/wiki/Theory_of_Forms Yes, we understand what is meant by a platonic form. However, you haven't shown why algorithmic processes can't produce forms. A simple example is "two". fifthmonarchyman: Irreducible complexity http://en.wikipedia.org/wiki/I.....ion_theory Yes, we also understand what is meant by Integrated Information, though you used the term Irreducible Complexity which is nowhere found in the article you cited. fifthmonarchyman: A concept is an abstraction or generalization from experience or the result of a transformation of existing concepts. Computers are capable of abstraction and generalization from experience. They can also transform existing concepts. fifthmonarchyman: But you have repeatedly demonstrated that “actually observed” (meaning phyiscal) species don’t really exist. Where did you get that idea? Species are observed. fifthmonarchyman: You said this is a core claim of Darwinism. No. That the sets have fuzzy edges (grades of reproductive isolation) is a core claim, however, that doesn't mean we don't observe species. Just because something doesn't fit into your box doesn't mean it isn't observed. That's like saying the sea or atmosphere isn't an observable because the edges are fuzzy. No wonder you are so confused about platonic forms.Zachriel_{December 11, 2014
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ZAc said, “IC concepts” and “Forms” require operational definitions. I say Once more around the merry-go-round. I think this is the fifth time. Forms http://en.wikipedia.org/wiki/Theory_of_Forms quote: The Forms are expounded upon in Plato's dialogues and general speech, in that every object or quality in reality has a form: dogs, human beings, mountains, colors, courage, love, and goodness.....Form answers the question, "What is that?" end quote: Irreducible complexity http://en.wikipedia.org/wiki/Integrated_information_theory quote: In a system composed of connected "mechanisms" (nodes containing information and causally influencing other nodes), the information among them is said to be integrated if and to the extent that ..............there is a greater amount of information in the repertoire of a whole system regarding its previous state than there is in the sum of the all the mechanisms' considered individually............ end quote: concept http://en.wikipedia.org/wiki/Concept quote: A concept is an abstraction or generalization from experience or the result of a transformation of existing concepts. The concept reifies all of its actual or potential instances whether these are things in the real world or other ideas. end quote: you say, Perhaps not, who knows; but it can account for actually observed species. I say, But you have repeatedly demonstrated that "actually observed" (meaning phyiscal) species don't really exist. You said this is a core claim of Darwinism. You drove this point home by adamantly claiming that the sets that define "species" have no real boundaries. peacefifthmonarchyman_{December 11, 2014
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fifthmonarchyman: Premise 1) algorithmic processes (like evolution) can’t produce the forms Premise 2) IC concepts (Like species)are forms "Forms", "IC concepts" and "Forms" require operational definitions. fifthmonarchyman: Evolution being algorithmic can’t account for IC concepts like species. Perhaps not, who knows; but it can account for actually observed species. fifthmonarchyman: The only way disprove the conclusion is to disprove one of the premises. One doesn't disprove incoherent claims.Zachriel_{December 11, 2014
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ZAc said, Algorithms are certainly limited, but you haven’t shown any relevance. I say, It's possible even likely that I've done a poor job of explaining. But the math is sound and the relevance is obvious it follows necessarily from this syllogism Premise 1) algorithmic processes (like evolution) can't produce the forms Premise 2) IC concepts (Like species)are forms conclusion........ Evolution being algorithmic can't account for IC concepts like species. The only way disprove the conclusion is to disprove one of the premises. You've certainly tried but I can't see how you have done this. Not even close. Now you can cling to the hope that a phyiscal algorithm will be discovered that can somehow produce an immaterial concept or you can assume with out evidence that immaterial concepts are merely illusions created by a process that is unable to approximate them. Either way it looks like you are screwed. Both approaches have blatant contradictions at their very core. peace conclusionfifthmonarchyman_{December 11, 2014
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fifthmonarchyman: I would argue that that is because that the Mathematical limitations of algorithms has yet to filter down to your average biologist. Most biologists work with mathematics all the time. Algorithms are certainly limited, but you haven't shown any relevance. fifthmonarchyman: I do, I know the form. Then tell us, is pi normal? fifthmonarchyman: Is there a point there? Sure, it means that instead of pi being an infinite algorithmic expansion, it's simply the ratio of the circumference of a circle to its diameter. fifthmonarchyman: This discussion is not about computers can do it’s about what they can’t. There's lots of things computers can't do, but you haven't mentioned any. fifthmonarchyman: Computers can’t 1) approximate the forms sufficiently enough to fool the observer 2) “know” anything at all 1) Your attempt to operationalize this concept has failed, and you have ended up reverting to 2) some unoperationalized concept of "to know".Zachriel_{December 11, 2014
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zac says, The question is the form of the mouse. The vast majority of biologists say the form is the result of evolutionary processes. I say, I would argue that that is because that the Mathematical limitations of algorithms has yet to filter down to your average biologist. I don't think that Godel and Penrose are required reading in most biology departments. This is where something like my game can come in handy. You say, Your claim was that you “knew” the actual infinite sequence. I say, I do, I know the form. The form will yield the sequence as precisely as I want it too given the necessary time and resources. You say, Furthermore, computers can do geometry without the arithmetic too. I say, Is there a point there? computers can do a lot of things many much better than me. This discussion is not about computers can do it's about what they can't. Computers can't 1) approximate the forms sufficiently enough to fool the observer 2) "know" anything at all peacefifthmonarchyman_{December 11, 2014
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fifthmonarchyman: I don’t need to know level 30 on the y-axes to know level 4. Your claim was that you "knew" the actual infinite sequence. Furthermore, computers can do geometry without the arithmetic too.Zachriel_{December 11, 2014
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fifthmonarchyman: The study of the evolutionary history of mice is not the same as the study of mice. The question is the form of the mouse. The vast majority of biologists say the form is the result of evolutionary processes. fifthmonarchyman: Many systematists continue to use phenetic methods, particularly in addressing species-level questions. There are a few dozen species of mouse which form a phylogeny. http://www.lsa.umich.edu/ummz/mammals/research/tucker/images/fig1-tree.gif fifthmonarchyman: Biologists doing actual Field work are the kind of experts I’d consult when learning about what it takes to be a mouse Let's hope you don't mean the Orkin man. You never did say what a "mouse" was. Lundigran, Jansa, & Tucker, Phylogenetic Relationships in the Genus Mus, Based on Paternally, Maternally, and Biparentally Inherited Characters, Systems Biology 2002. Chevret et al., Molecular phylogeny of the genus Mus (Rodentia: Murinae) based on mitochondrial and nuclear data, Biological Journal of the Linnean Society 2005.Zachriel_{December 11, 2014
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You say, You said to consult experts on mice, not philosophy. I say, The study of the evolutionary history of mice is not the same as the study of mice. Not even close You say, Jones doesn’t represent anywhere near the consensus position of biologist even with regard to cichlids. I say, Lets see do I take the word of a anonymous commenter on an obscure internet blog or a Ph.D. in biology? Check this out. for here http://en.wikipedia.org/wiki/Phenetics quote: Many systematists continue to use phenetic methods, particularly in addressing species-level questions. While a major goal of taxonomy remains describing the 'tree of life' - the evolutionary path connecting all species - in fieldwork one needs to be able to separate one taxon from another. Classifying diverse groups of closely related organisms that differ by very subtle differences is difficult using a cladistic approach. Phenetics provides numerical tools for examining overall patterns of variation, allowing researchers to identify discrete groups that can be classified as species. end quote: Biologists doing actual Field work are the kind of experts I'd consult when learning about what it takes to be a mouse peacefifthmonarchyman_{December 10, 2014
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fifthmonarchyman: How many of these experts are Platonists do they assume that the forms don’t exist fron the get go? You said to consult experts on mice, not philosophy. fifthmonarchyman: I found the cichlids to be an unmistakably natural group, a created kind. The question concerned "mouse". In any case, Jones doesn't represent anywhere near the consensus position of biologist even with regard to cichlids. As for Jones and cichlids, he claims "evolutionary lines of descent were nowhere to be found", yet there are many papers on cichlid phylogeny.Zachriel_{December 10, 2014
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Zac says, Because the experts you said to consult nearly universally say the form of the mouse isn’t a platonic form. I say, How many of these experts are Platonists do they assume that the forms don't exist fron the get go? quoting BA77's article: quote: “For all the diversity of species, I found the cichlids to be an unmistakably natural group, a created kind. The more I worked with these fish the clearer my recognition of “cichlidness” became and the more distinct they seemed from all the “similar” fishes I studied. Conversations at conferences and literature searches confirmed that this was the common experience of experts in every area of systematic biolog..." end quote: looks like the experts might be on my side on this one, Although they might not word it the way I do or share my skepticism on the power of algorithms to approximate the forms Peacefifthmonarchyman_{December 10, 2014
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fifthmonarchyman: What in the world does that have to do with the form of Mouse Because the experts you said to consult nearly universally say the form of the mouse isn't a platonic form, but the result of a long process of divergence and adaptation. A mouse is a derived rodent which is a derived mammal which is a derived amniote, and so on.Zachriel_{December 10, 2014
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Zac says, When we consult the experts, the vast majority agree that the mouse shares a common ancestor with other rodents. I say, I assume that the that the mouse shares a common ancestor with other rodents. What in the world does that have to do with the form of Mouse or the price of tea in China? Do you somehow think that Plato was YEC? you said, You don’t know how pi as a geometric ratio translates into digital notation, which is a very subtle relationship which is still not completely understood. It’s not even known if pi is a normal number. I say, I don't need to know level 30 on the y-axes to know level 4. Peacefifthmonarchyman_{December 10, 2014
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fifthmonarchyman: In fact I don’t even much care about “any arbitrary digit of pi” I “know” the actual infinite sequence. Um, no, you don't. You don't know how pi as a geometric ratio translates into digital notation, which is a very subtle relationship which is still not completely understood. It's not even known if pi is a normal number. fifthmonarchyman: I just simply type in (4/1)-(4/3)+(4/5)-(4/7)+(4/9)……. Which is an algorithm you read about somewhere. fifthmonarchyman: But in general I don’t need to because I know the form. Computers can do geometry without the arithmetic too. fifthmonarchyman: Algorithms can’t ever know those sorts of things because being finite and preceding from the bottom up they can’t grasp the infinite top down reality that is pi. Pi isn't infinite. Pi is a finite number between three and four. Pi's digital expansion in integer bases is infinite. fifthmonarchyman: Mouse it the top down lossles data compression (form)of everything it takes to be a mouse. Which is? ... fifthmonarchyman: As to the specifics of the form of Mouse I’m no expert but there are plenty out there. When we consult the experts, the vast majority agree that the mouse shares a common ancestor with other rodents. http://www.ucmp.berkeley.edu/mammal/rodentia/rodentia.htmlZachriel_{December 10, 2014
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Zac asks The algorithm can provide you any arbitrary digit of pi that you want. What can you do that is different? I say, That is a good question for once I Know the form/key I know that Pi is much more than 3.1415....... Its actually the ratio of ratio of a circle's circumference to its diameter. This knowledge allows me to easily best any approximation of Pi that an algorithm can ever produce. In fact I don't even much care about "any arbitrary digit of pi" I "know" the actual infinite sequence. All of it with out any approximation. That is what lossless data compression is all about. I might not be able at present to spout out the 1097th digit of Pi but I don't need to do that. I can get any old calculator to do that any time I want to. I just simply type in (4/1)-(4/3)+(4/5)-(4/7)+(4/9)....... And I'm off the the races But in general I don't need to because I know the form. I know what it means and I can discover when it will come in handy. Or when a particular approximation deviates from the Ideal Algorithms can't ever know those sorts of things because being finite and preceding from the bottom up they can't grasp the infinite top down reality that is pi. That why my using the dictionary definition of computable is appropriate in this discussion. you say Please delineate “mouse” as a platonic form. I say, Just like Pi is the top down lossless data compression (form)of 3.1415....... Mouse it the top down lossles data compression (form)of everything it takes to be a mouse. Just as a calculator could begin plugging away at Pi one digit at a time a reductionist might begin to plug away at Mouse one gene or one protein or one anatomical feature at a time. Just as the calculator will never make it to the last digit of Pi the reductionist will never make it the complete essence of "mouse" On the other hand I don't need to know every last particle or gene or feature. If I know the form I can easily pick out the gene or feature or particle that does not fit. Knowing form is what enables a doctor to know that a mass is cancer and not part of the patient even if he has never seen this particular mass before. It's what enables paleontologists and ecologists to say this organism belongs to the set and that one does not even if he has never seen the organism before. As to the specifics of the form of Mouse I'm no expert but there are plenty out there. Folks that study the mouse and become familiar with the various "patterns" that describe it. hope that helps peacefifthmonarchyman_{December 10, 2014
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fifthmonarchyman: A form is just the non-materiel essence of something. Gee whiz. We're asking about the platonic form called "mouse". fifthmonarchyman: So the form of a mouse is simply what a mouse is. pretty simple concept. That's what we're asking. Please delineate "mouse" as a platonic form. fifthmonarchyman: Ive addressed that objection about 15 times already. Yes, by redefining computable to match your preconceived conclusion. fifthmonarchyman: No I am observing to see if an algorithm can do something. The algorithm can provide you any arbitrary digit of pi that you want. What can you do that is different? fifthmonarchyman: So no observation at all then just some wild speculation. Yes, that seems to be your position, but you had indicated you knew the answer, and more importantly, you could demonstrate it. You haven't even grasped the very basics of the problem.Zachriel_{December 10, 2014
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Me_thinks says, Everything that Trustev for Publishers checks for can be spoofed or changed. I say, In a nutshell, My hypothesis is that no matter how a troll attempts to change his behavior he will never be able to convince an observer he is an approved commenter. With the following caveats. 1)The troll is an algorithm 2)The observer has as many resources and as much time as he wants to study the data set 3)The the troll does not possess the key that the observer is using to make it's determination. This seems to me to be a perfectly testable scientific hypothesis. Surely you agree peacefifthmonarchyman_{December 10, 2014
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fifthmonarchyman @ 242
http://www.newsweek.com/one-tr.....ing-290623 Apparently I’m not only on the cutting edge but this approach of looking for the “Key/Form” of a data set is poised to offer huge practical benefits to places like UD
Everything that Trustev for Publishers checks for can be spoofed or changed.Me_Think_{December 10, 2014
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All, Here is example of the principles I'm exploring with with game in action to permanently prevent internet trolls. http://www.newsweek.com/one-trolls-permanent-solution-trolling-290623 Apparently I'm not only on the cutting edge but this approach of looking for the "Key/Form" of a data set is poised to offer huge practical benefits to places like UD. ;-) peacefifthmonarchyman_{December 10, 2014
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zac says, You claimed it was a platonic form. You tell us what you think it means. I say Are you unfamiliar with the forms? Think of a "lossless data compression" or a "specification". A form is just the non-materiel essence of something. from here http://en.wikipedia.org/wiki/Theory_of_Forms quote: The Forms are expounded upon in Plato's dialogues and general speech, in that every object or quality in reality has a form: dogs, human beings, mountains, colors, courage, love, and goodness. Form answers the question, "What is that? end quote: So the form of a mouse is simply what a mouse is. pretty simple concept. you say, Yes, pi is irrational, but it is computable. I say, Don't you ever get tired of this merry go round? Ive addressed that objection about 15 times already. You say, Your answer was by looking at an algorithm for the answer. I say, No I am observing to see if an algorithm can do something. I'm judging the power of an algorithm not using an algorithm to judge something else. The algorithm is object not subject you say, Not sure it has an easy answer. Consciousness may be .....then it could be I say So no observation at all then just some wild speculation. duly noted peacefifthmonarchyman_{December 9, 2014
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fifthmonarchyman: Just because I’m not an expert right now do you think that means I couldn’t learn what it takes to be a mouse. You claimed it was a platonic form. You tell us what you think it means. fifthmonarchyman: check it out Yes, pi is irrational, but it is computable. From your link:
The computable numbers include many of the specific real numbers which appear in practice, including all real algebraic numbers, as well as e, pi, and many other transcendental numbers.
fifthmonarchyman: I’m not using an algorithm I’m using an observer. You said "It means the observer will always be able to tell the difference between what an algorithm produces and the form/spesfication 'Pi'". Your answer was by looking at an algorithm for the answer. fifthmonarchyman: Are you assuming that observers are algorithmic??? No, but that's what you're trying to show. fifthmonarchyman: What possible observation would ever lead you to believe something like that?? Not sure it has an easy answer. Consciousness may be non-algorithmic. Of course, if there are analog components, then it could be non-algorithmic and still be very much a natural mechanism.Zachriel_{December 9, 2014
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Zac said, We wanted to explore what that meant, what characteristics constitute “mouse” by looking at examples. I say, OK If you want to shoot me some examples knock your self out. Like said I'm no expert in mice so I'm not sure what it will prove. It's highly possible even likely that I will get it wrong more than not. Just because I'm not an expert right now do you think that means I couldn't learn what it takes to be a mouse. With feedback of course? You say, It doesn’t require magic. You could show such an algorithm is impossible, such as through a mathematical proof. I say, check it out http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational You say, If you’re using an algorithm to test the algorithm, then you haven’t demonstrated anything non-algorithmic. I say, I'm not using an algorithm I'm using an observer. Are you assuming that observers are algorithmic??? Talk about materialistic presuppositions. What possible observation would ever lead you to believe something like that?? Peacefifthmonarchyman_{December 9, 2014
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