Talk:Musical acoustics/Archive 1

message: Re: "Scales which do not adhere to just intonation, and instead have their intervals adjusted to meet other needs are known as temperaments, of which equal temperament is the most used." The Pythagorean scale does not "adhere to just intonation", but it can hardly said to be a temperament. In fact, the Pythagorean scale is the paradigm of the Western European diatonic scale, and the just scale was first proposed (in any historically meaningful way by, Ramos in the Renaissance) as a modification of the just scale. Thus the just scale can be reasonably said itself to be a temperament of the diatonic Pythagorean scale. The twelve-tone equally tempered scale flattens the fifths of a chromatic Pythagorean by slightly less than two cents, effectively removing the Pythagorean comma of approximately 23.5 cents. The equally-tempered scale is not a temperament of the just scale; it is a temperament of the chromatic Pythagorean scale. TheScotch 12:06, 10 December 2006 (UTC)
replies: text: Umm, first off, the Pythagorean is just. How does it not adhere to just intonation? (Maybe "adhere" is a funny word to use?) Secondly the article doesn't call it a temperament. I think the problem here is a question of what temperament is. No form of just intonation is a temperament. To call 5-limit intonation (the diatonic scale described in the article) a temperament of 3-limit just intonation (pythagorean) is, well, a very strange idea to me. Of course the 
Pythagorean chain of fifths was fundamental to the development of temperament, but... well, do you want to have a history of temperament on this page? I think there are other articles where this kind of information belongs (and is already there, generally). - Rainwarrior 20:34, 10 December 2006 (UTC)

text: I am not sure why you think there is only one "just scale", and I do not know why you think that the suggestion that there are many forms of just intonation is somehow invalidated by music history. There lots of just intonation systems, so many that there are ways to classify them. I do, however, think the just scale mentioned in the article is one of the easiest rationalizations of the diatonic scale. - Rainwarrior 10:08, 11 December 2006 (UTC)

text: None of the information you have offered so far has been unknown to me. Please don't make assumptions about my educational background. Ask, if you want to know, but don't assume. The source of my disagreement is not lack of information, but rather that you think that there is only one system of just intonation. We have different definitions of what constitutes "temperament" as well as "just intonation", yours being rooted in the history of western tuning theory, and mine being categorical. You've already stated that you don't really want to see history in the article, and you've already dismissed everything except two ways of making scales as "fringe", so I don't know what kind of argument you're looking for here or what you'd like to see happen to this article. (Though there is possibly a more glaring issue below regarding Bob Fink's theories that probably deserves more attention at the moment.) - Rainwarrior 03:16, 12 December 2006 (UTC)
thread_title: just scale

message: Just a start, very simple and maybe teh perspective is wrong, so I expect people to edit and expand the article!  I have used the term Musical Acoustics, instead of Music Acoustics, because there already was a link to that (previously empty) article from acoustics. --Blondel 22:19, 9 Jan 2005 (UTC)
thread_title:  Comments on "musical acoustics" 

message: The section Musical acoustics#The natural scale has some problems. First, and least important, it should be called the diatonic scale because natural scale is slightly ambiguous (at first I thought it meant the harmonic series, but that may have been because I expect to see things about the harmonic series in an article on acoustics). Second, how come this article attributes it to Aristoxenus while Diatonic scale doesn't mention him? Third, why should an article on musical acoustics even mention the diatonic scale at all? "Musical acoustics" should apply equally to all kinds of music, for example Balinese gamelan, which doesn't use the diatonic scale. Including the diatonic scale but not the pelog scale indicates a Western bias, and it's also pointless, because that's what the Diatonic scale article is for. Please keep things in their proper places. —Keenan Pepper 23:06, 19 November 2006 (UTC)
replies: text: Aristoxenus describes a few scales in his writing on harmony (including the diatonic), but without any reference to harmonic ratios or mathematics of any kind really. I've never seen anyone attribute it to him before, though. - Rainwarrior 00:46, 20 November 2006 (UTC)

text: Though I also think that "natural" is an assuming term (I think it's being used as a lead-in to the whole "evolution" section) and should be replaced by diatonic. We should mention at least one source for the properly-described 5-limit tuning itself; Kepler is the oldest reference to it I can remember offhand (see here), though I seem to recall Partch attributing it to Ptolemy? (I don't know how reliable that attribution is.) - Rainwarrior 01:34, 20 November 2006 (UTC)
thread_title:  "Natural scale" 

message: This is my comment: I think I've figured out Rainwarrior's "game," if one exists:
I cannot read minds, but Rainwarrior seems hell-bent on diminishing my credentials, and without evidence he also portrays my views, which are about the acoustic basis for scale evolution,  as views which are unknown, unadopted, unproven and unprovable.
On the latter, he refuses to give any specific reasons for those assertions. The assertioins themselves are presented as being "reasons." On my credentials, likewise, he doesn't give any evidence for his claim I have no credentials apparently worth his recognition of them, other than his own experience at not having heard of me. They are just his opinions and assertions. 
When contrary evidence is presented to him about it, he never rebuts the evidence. As Norton said, he changes the subject and tries another method for what I believe is his desire to eventually remove these views about the "natural" basis for scales entirely from Wikipedia -- probably because he opposes those views and wants to save us all from them. Who knows why, for sure.
He was told I was invited by the Lorenz Institute in Vienna to come and speak on my views about the origin of music (all expenses paid). The person inviting me seems he's heard of my work. He said:  "Fink is one of those rare people who could give a comprehensive overview of this complex field [of the origin of music]."   - Adolph Heschl, director:  KLI., 2001. 
I was asked by the editor of Nature  journal, among the leading science journals  (Mr. H. Gee,  at the time) to serve as a juror on an article about prehistoric Chinese flute scales. Someone at Nature seemed to hear about me and recognize my expertise. 
What does Rainwarrior do with this information? He acts as though he hasn't even read it -- and following upon our presenting it, keeps writing the same false claims, such as:  "If you want to argue the validity of your own work, cite an author other than yourself." And: "If you cannot cite someone other than yourself holding your theory, you should not be allowed to put them into this wikipedia article, " And: "This entire section appears to be outlining a little-known theory; I can find no reference to it in any electronic journal I have access to, and no mention of it on any website except the author's own." and so on. However there are many websites which like it, review it, and link to my website on my theories and other writings. 
Why does Rainwarrior keep insisting on establishing this fabrication about me? It would appear that it might later serve some agenda of his own -- Could that agenda be to rid the wiki-world of the natural basis of scales viewpoint? Why not ask him, folks?
For example, something we did not put in the wiki article was the term "The Natural Scale." It's inaccurate. There is a natural basis for scales, but not just one scale. The change should have been to " A Natural Scale," rather than  "The" natural scale. But the overkill change Rainwarrior made certainly is consistent with someone anxious to get rid of the word "natural," rather than the word "The." He went on to remove every reference to the word "natural" or "natural scale" by others writing in this Wiki article (who appear to agree with my views). Ask him: Does he believe there is A Natural Scale? That is, one which natural acoustics has helped bring into existence?
Additional reviews (from the list below) were provided to Rainwarrior in the discussion , all of which prove the claims of Rainwarrior are patently untruthful:  
"I think this remarkable book [Origin of Music 1970] could become a classic if given the exposure it deserves." - Ron Brown, Assistant editor of Jazz Journal, March 1971, U.K. Sounds like he sort of agrees with it, yes?
The editor of Performing Arts in Canada wrote that views in my Origin of Music book "...and (its) apparent approach remarkably coincide with concerns and attitudes of my own" - Michael Schulman, 1975.
 
"To say that we are intrigued (about the Origin of Music) is an understatement."  - T.C. Fry, President, Musical Heritage Society Sept., 1970, N.Y.C. (Fry had offered to reprint my book as a gift premium to give away with sales of his hi-quality classical recordings.)
Commenting on the Origin of Music: "...a searching study...very sensible." - Henry Pleasants, Long-time music critic: Int'l Herald Tribune. Aug., 1971. U.K. Author of: Serious Music & All That Jazz, & The Agony of Modern Music - clearly another noted author who accepted my views as agreeable.  
"I certainly do like and am profiting from The Origin of Music. " - Prof. Anne D.Kilmer, U of Calif., Berkeley - Deciphered cunieform of oldest known song (4,ooo years old). My views were also cited by Prof. Sandra Trehub in her paper at the Origin of Music world conference held in 1998-9.
This is only a part of it. Further, there are many letters sent me from readers, students, teachers and newspeople who have endorsed and praised my work -- many published on my webpages. I could fill a book with the many hundreds of linking URLs and favourable letters and reviews I have. 
All of that was available to Rainwarrior in this discussion but he continued to act as though "if you cannot cite someone other than yourself holding your theory, you should not be allowed...in Wikipedia," yatta yatta. So in order to remove my views, there seems to be a need to deny the truth that anyone knows of me, approves of my views and that my views are a growing part of  established literature which demonstrate a general trend of thinking regarding the biological or physiological (i.e., "natural) basis for the rise of acoustic scales. That could then be one excuse to work for deletion, if that's the agenda. 
But Rainwarrior's secret weapon in a possible agenda seems to be the short-name "trio theory" which doesn't even appear in my book, but was coined haphazardly much later. Yes, he may very reluctantly admit in a "phase 2" of his agenda that "Fink has adherents and good reviews and recognition, but not under the name 'trio theory.' " 
Well by god, that's true. Therefore what? That the "trio theory" should be removed to its own distant corner of the wikiuniverse until Rainwarrior and the International Acoustic Society adopts my book or theory? But Rainwarrior should realize not even the science of evolution gets that kind of blanket acceptance, but it is taught in most schools. My view isn't - although I have been invited to high school and university classes to speak more often than ever. At first, for many centuries, Copernicus was similarly locked out of the mainstream by his opponents. I have such opponents in mainstream arenas, and Rainwarrior claiming that they have not yet adopted my views should never be a reason to disallow those views on acoustics, or anything else, from Wikipedia.
As in any article or view, knowing the subject matter carefully -- not just private views or the wikipedia rules -- should be the only method by which an editor judges an article. No encyclopedian would or should be taken seriously if he admitted he could condemn a viewpoint and an article and then say, as Rainwarrior did: "No, I have not read about "trio theory" with care or at all. All of my comments on this talk page were in response to what is written in this wikipedia article...." In that case,  we can only wonder why no attempt was made to suggest improvements, clarifications, et al. There was total condemnation, and it was based on invented and false assumptions, without reading up on the subject. 
Then when his untrue assumptions were challenged, he switched gears. He does that a lot. He even claimed the trio theory was by Schoenberg, and by Helmholtz and Kepler and more. Then he fights mere days later that "Bob Fink" should be the only acknowledged author in the title of a separate article on the trrio theory, as my name as author appearing in the article text was not good enough for him. Why not? His flip-flops never cease. We never intended the short-name "trio theory" to be a book title, or anything but a convenience in typing a reference to it within a letter or article. Someone unknown to us made it a subhead in this article. But I think Rainwarrior needs to keep this nickname prominent for some purpose of his own, as if it was the official title of my life's work, or to justify some other goal he has.
I have spent a lifetime debating academics and composers whose stake in modern atonal (polytonal, post-tonal, you name it)  theories run deep and who often have all the zealotry of theologians rather than use of the scientific method. They have for decades until recently (but even still recently according to on-going testimonials) avoided tonality, decried it, opposed it, punished students for using it, avoided teaching the history of popular music, jazz, Broadway. - Why? Because it competes with their own indoctrination view that there is no natural basis for the most widespread scales, it's all "relative," and any other view is out-of-date and/or even "harmful," as at least one composer put it in a newspaper attack on me. I can recognize an "agenda" in the manner in which these people argue -- and in Rainwarrior's arguments, there seems to me to be the same kind of outrageous denial of evidence.
As I said, I cannot read minds, but I believe a hidden agenda is there and that Rainwarrior has shown enough duplicity  and slippery avoidance of specifics and consistency to now warrant my complete distrust. I do not believe he has Wikipedia quality and scholarship at heart on this matter (even when a view may be disputed by some, and almost any subject is disputed and disputable). I'm just telling the truth about my feelings. Like Norton I will no longer deal with him. If this matter is ever mediated, I will represent the theory and its inclusion although I am not an editor of this article.
Bob Fink 65.255.225.42 03:17, 23 November 2006 (UTC)
replies: text: I think you have severely misunderstood me, but you have the right to say what you wish here. If you want to know what motivates me, what my goals are, you don't have to try to read my mind, you can ask me (though this talk page isn't the place for personal correspondence). - Rainwarrior 04:23, 23 November 2006 (UTC)
thread_title:  Rainwarrior's "game" 

message: That title should not be changed while awaiting comments &/or mediation. Edits should be minor: grammar, syntax, spelling, phrasing -- but not so as to change the intended meaning, like substituting other words to replace "evolution." If someone -- perhaps with a creationist bent? -- wants to challenge that meaning? If so, then write a passage of challenge -- with verifications. Use sources about theories of musical acoustics which deny "evolutionary" changes in music are taking place. Or whatever your reason for removing that word from the title. But for now, suggest your title changes and reasons in the discussion area, please. Norton, 65.255.225.44 19:17, 25 November 2006 (UTC)
thread_title:  Still awaiting comments/consensus on "Evolution of the diatonic Scale" section 

message: I'm willing to read two or three screenfulls of text, but not thirty. The more you write, the less chance I or anyone else will read any particular part. Please be brief! —Keenan Pepper 20:49, 29 November 2006 (UTC)
replies: text: I don't understand why you think it was "replaced" by me, or even when you think it was replaced. Check the edit history. I think you're a bit confused as to who has done what, perhaps because you've inserted the same material from your book into two different pages. (Check Prehistoric music.) - Rainwarrior 06:47, 1 December 2006 (UTC)

text: You linked to your own edit, mine was the one before: this one, which didnt' actually add anything (just accidentally moved some spacing around). You should read the edit history before you make assertions about it. - Rainwarrior 18:47, 1 December 2006 (UTC)
thread_title:  Brevity 

message: The false source "trio theory" has been replaced by Rainwarrior. This terminology, "trio theory," contains a link to a commercial vender which can be removed anytime. That title, unknown by any except relatively recent Wikipedia editors, is innaccurate. It offers no information whatever about where the theory below it comes from. It was a convenient "short-title" used by an earlier editor but cannot serve as a true verification or source. 
It therefore will be removed. Also the term "trio theory" exists in no book known at the time the theory it refers to below it was written and published (1970 and again in 1981). The theory's concept itself is found in the book "The Origin of Music," and is known, but the actual nickname or term "trio theory" does not exist inside that book. At Talk:Trio_theory this information was personally verified by the author and transmitted to Rainwarrior, who read it. Rainwarrior also wrote then: "I had assumed that 'trio theory' was a major part of his work, which is why I gave this article such a name. Now according to you, it is not." 
The term will be replaced with the exact and proper verifying source (the title of the book, but without any vender or sales link). Why Rainwarrior would still insist on a nickname as a false source title after he knew it was never in the real source cited, seems unfathomable. --Bob Fink 65.255.225.37 09:50, 30 November 2006 (UTC)
replies: text: I don't understand why you think it was "replaced" by me, or even when you think it was replaced. Check the edit history. I think you're a bit confused as to who has done what, perhaps because you've inserted the same material from your book into two different pages. (Check Prehistoric music.) - Rainwarrior 06:47, 1 December 2006 (UTC)

text: You linked to your own edit, mine was the one before: this one, which didnt' actually add anything (just accidentally moved some spacing around). You should read the edit history before you make assertions about it. - Rainwarrior 18:47, 1 December 2006 (UTC)
thread_title:  Title again 

message: ANSWERS TO QUESTIONS. The theory of the evolution of scales was originally already in Musical_acoustics. for about a year, with little change. Rainwarrior created a new page and moved the section to it, titling it "Trio Theory," even though objections were raised and ongoing.  The article was reverted back into Musical_acoustics. Comment concerning the term "trio theory":
#  It was initially written in the article: "The 'trio theory' (in the Origin of Music ISBN link), claims...."
#  What was meant: "The theory here called "trio theory," outlined in this article, is found sourced in the book the Origin of Music (but not under the term "trio theory")." But that subtle detail obviously wasn't clear.
#  Rainwarrior seems to be saying that what was originally meant by the above was: "The 'trio theory,' under that name, is in the Origin of Music...." But now, if claimed it's not there, then Rainwarrior appears to conclude that the theory is unpublished and is original research. I think it'd be best to just drop the nickname causing such confusion. Further, Rainwarrior, off the bat, condemned the theory with many claims that weren't true, including that Shoenberg invented the theory, as well as Helmholtz, and maybe even Kepler. Then perplexingly, fights to name me as the author, at Talk:Trio theory.
About my publication lists: Dozens of them are found all through this discussion above ("Notability of Fink's works...") and elsewhere. There are journals, reviews, e-mails -- all demonstrating that I meet Wiki policy on citations, references, links, verifications that "material may be acceptable when produced by a well-known, professional researcher in a relevant field or a well-known professional journalist. These may be acceptable so long as their work has been previously published by reliable third-party publications." 
Previous to this section's article, as the lists and e-mails above show in excess, my acoustic ideas on scale origins was published in many peer-reviewed or "reputable" or reliable journals, magazines and news articles. It is outlined in the Neanderthal Flute essay as well. The ideas (and me) were known, adopted or recognized, and are verified by other notable authors, journalists, and researchers in and around the field, including a new e-mail yesterday from a teacher wanting lesson plans from me on my tonal scale/harmony views for his students.  If more detail (dates, content etc) is wanted please ask me.
Archaeologia Musicalis (A.A.) -- peer reviewed -- is a journal of the working study-group "Music Archaeology" in the International Council on Traditional Music, which holds biannual world music Archaeology conferences, followed by publication of the books of conference proceedings such as Studies in Music Archaeology III, 2003. I was asked to write a rebuttal article for that book by its editors (publisher: Verlag, Germany). Earlier, they published a different article by me in the (Feb., 1988) A.A journal. Most of my articles contain references to the acoustic theory of scale evolution. You can   find this journal  under its name at worldcat.
The theory outlines ideas about prehistoric music origins, tonality, melody, harmony and acoustics. It belongs (as it explains things about each) in several locations just as info about Mozart's work would belong in composition, music history, opera, classical music, sonanta, symphony and on and on. Just one final correction: Above, Rainwarrior wrote: "The relationship between the harmonics 1 3 and 5 and the diatonic scale has been covered many times by many authors, and I can come up with citations to accomodate.... However, the theory I developed is not based on the 1, 3, 5 harmonics, but on the scale-notes 1, 4, and 5, and their overtones. -- Bob Fink 65.255.225.40 11:45, 2 December 2006 (UTC)
replies: text: Hello Rainwarrior and Bob Fink. Thank you both for your answers. I'm debating on wether I should refactor the comments to summarize. I will need to read over this again. The important thing is that we comme to an agreement, so Bob Fink, though you may still be frustrated, I would ask you to not comment so much on what rainwarriors past actions where and how they may have offended you. (I would even go as far as that the current one may have even been offencive). If you're looking to concentrate on possible past issues we could bring that up in a special RFC on the user. (I think we can all get allong! Right?) The important thing is to concentrate on the article. I think you have both demonstrated your ability and knowlege of the subject matter. There are a couple solutions we can do. One is to request a comment (RFC) on the article. (I doubt we will get any good response unless we ask a very specific question... yes or no... and even then). The same thing but we can do  it in the form of a vote (usualy no comments are given in the feedback). There are other steps but I don't think they are appropriate at the moment. Again I think the best thing would be to solve the problem between each other. To do that, we must all first recognize what the problem. I'm going to have to think of a couple things... again often many things are written in the things that where not written. --CyclePat 07:08, 4 December 2006 (UTC)
thread_title:  Answering questions 

message: Well, Rainwarrior: You've clearly caught me out, and I might as well confess. Confession is good for the soul, I'm told. At the watchlist page, you wrote that:
:"(Fink's) IPs usually are of the form 65.255.255.*  -- where * ranges from 33 to 52, though 40,41,42,50, and 51 were also used briefly by someone claiming to be Kate McMillan during a debate at that page some time ago. I'm assuming these are IPs from a Saskatchewan dialup ISP. There are also some older edits by 204.83.156.17, 28, 36, and 38, and a look at the edit histories of any of these IPs will reveal editing entirely related to the work of Bob Fink (adding links to his website, particularly, and often adding...to the reference lists of article). I made a list at User:Rainwarrior/Bob Fink, because all of this anonymous editing makes it difficult to evaluate the depth of the problem here otherwise." 
Actually that "204.83.156.17" IP is unkown to me totally. The edits made from it indeed referred to a website about Prof. Anne Kilmer's work, and linked a webpage of mine which contained Kilmer's work on the oldest known song. But not made by me nor from the computer I use. I don't use any others. At 71, and only on a pension, I can't afford internet accounts like they were water, and being disabled, cannot get out often (except through my special -- uh -- well,  this confession may help explain that 2nd IP mystery.)
I checked with my Internet Server (who like my publisher, is a close personal friend) and discovered that Kate McMillan indeed has the same IP address as mine.  I never realized that. Here I was hoping that by using the Internet I could broadcast my special magic spell which I call Svengaliac (actually, an electronic invention of mine, which like radio waves, can travel even to other villages like Delisle, where McMillan lives ). With this spell, I can control others into becoming editors in Wikipedia from their own computers for my own promotional benefit. 
I get a lot of press here because of my activism (the local Poster Man) and so I have thousands  of close personal friends and supporters whom I can reach with my Svengaliac waves. Even the City fathers have changed the face of downtown with hundreds and hundreds of Poster-Drums (which I designed for them and which, under Svengaliac influence, of course (with a little help from the Canadian Supreme Court and my poster rights case of 1986 See Bob_Fink), the City Council agreed to manufacture. The drums are all welded to most of the city poles which allow for thousands of posters to now be placed -- just like Wiki edits -- all over the place. I am the greatest litterbug known on the planet. Local musicians dedicate songs about me, like Poster Squad by Don Freed. Come see our city to realize this. " Today Saskatoon, BUT tomorrow the whole world will be 'Under A Tack' -- or a pin, or masking tape, or glue, or scotch tape,"  as I always shout from the rooftops. 
I mistakenly thought all the slave-edits I engineered could carry a different anonymous IP and slip under the Wiki-radar and be accepted without appearing as WikiSpam. Little did I know that many of my IP slaves had accounts on the same ISP server as me, and their IP, being the same, like Kate McMillan's (who I only heard about today from you), would call enough attention to give me away. 
But technically, all the edits of these slaves are wiki-legal, and many have been made even without my knowing about it, the same IP notwithstanding, from likely many others of my hypnotized fans and supporters from their computer accounts. And many have been made even from other people using their own accounts from other servers -- like the "204" account Rainwarrior listed above, no doubt -- but I probably reached whoever they are too, with my Svengaliac waves. Thus Rainwarrior's removal of their edits may indeed be vandalism. But no matter! ALL the edits ever made in the world of musicology are  really  mine, mine, mine, ALL MINE!!! Ack!! Cough, Sputter Hack!! (Now if only I could enhance the reach of my waves to reach Burlington -- or even California!)
However, my conscience pangs have now got the better of my evil ways -- Ah yes -- I cannot sleep at night knowing how many dupes out there are promoting my theories and POVs. It's like the King's porridge, which keeps filling the bowl however fast you eat it -- I can't stop the cloning of more spam-o-Svengaliacs!
I've been caught; take me to Wiki-court and have my madness musicology musings banned from luft-wafting out to the whole wide world. Save me (and all of Wikipedia) from myself!! Give me the Repentence Sentence.... Bob Fink, Greenwyk 05:16, 7 January 2007 (UTC)
replies: text: Is this entirely satire, or is there some argument here you wish me to understand? Is any of this related to this article? Why not post it at the noticeboard if it is a reply to something I said there? - Rainwarrior 14:22, 7 January 2007 (UTC)
thread_title:  C O N F E S S I O N 

message: Perhaps I should jump in on the fun! "Just" refers strictly to a measurement of intervals, based on simple numerical ratios. It is NOT a kind of scale...in fact to attempt to build a scale upon just intervals would be an exercise in futility! Prof.rick 06:04, 12 February 2007 (UTC)
thread_title:  Just scales? 

message: The trio theory is interesting, but does nothing to justify a diatonic major scale as being "natural". First, in order to form a one-octave scale, harmonics of the Tonic must be transposed several octaves.  (Human intervention number 1.)  Second, even if we can "hear" Harmonic 3 (Soh), which is not difficult for a trained ear, we must then regard it as a fundamental tone.  It must be sounded to generate it's harmonics...which in turn must be transposed through several octaves. (Human intervention number 2.) Third, the fourth note of a major scale  does not exist as a harmonic of the fundamental.  Instead, we must regard the Tonic as Harmonic 3 of "some other note", and apply inverse reasoning to arrive at "fah", then, of course, transpose it and its harmonics into the desired octave.  (Human intervention number 3.)
There are ancient Inuit melodies, still being sung, which use only tetratonic scales (e.g. G, A, C, D on a piano). Considering the origins of the Inuit, this may be a fore-runner of the pentatonic scale.  It is difficult to reconcile these notes as stemming from an application of harmonics.  (There is no major 3rd present, and even as an incomplete circle of 5ths, the E is missing.)
This article also has a strong Western bias. To attempt to define "satisfying" sounds as those of our harmonics-based thinking is absurd.  Consider the SLENDRO of Bali and Java...almost a perfect 5-edo scale. This music is very pleasing to the ear, but TRY to explain it in terms of harmonics!  
Also, consider the songbirds, particularly those of Africa. Amongst them, probably any interval (and even triads...even inverted triads) can be heard.  Consider (a kind of goose, I believe) in China...a few dozen will gather at the river's bank, and each bird sings one note of a pentatonic scale...but in all, only five distinct notes are heard, regardless of the number of birds.
Human beings are great imitators, and no doubt we are all, to some degree, bird-brains.  Prof.rick 06:50, 12 February 2007 (UTC)
thread_title:  A natural scale?