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Talk:Pentatonic scale

Request for audio examples
Please, can we have some examples? Like ones we can hear. Or is Wikipedia a text-only medium?
 * I have tried to add some MIDI examples. BTW, i have midified the gamelan scale although it is irreducible to chromatic scale ;) Raoul NK (talk) 18:29, 24 June 2008 (UTC)

Hear it, please?
Right, all this wordy stuff is meaningless unless we can hear it. Can we have examples we can hear, please? If Wikipedia has visual media (see it) why can't it have audio media (hear it)? This applies to pretty well any music-related article. (Grendlegrutch (talk) 19:09, 10 August 2010 (UTC))

Jazz
moved much of the jazz-specific discussion to jazz; as someone familiar with non-Western music, the assignment of minor pentatonic scale to the jazz idiom--{A, C, D, E, G}--rather than to that of the tuning of the koto--{A, B, C, E, F} belongs in idiom-specific pages rather than on the main page. I kept the introduction of the major pentatonic scale here, since in Western European classical music, the major pentatonic scale is commonly referred to as simply the "pentatonic scale." -jp2

this paragraph, under major pentatonic scale
''Another construction, derived from Western European classical music, begins with a major scale and omits the fourth and the seventh scale degrees: a C major scale is {C, D, E, F, G, A, B}. By omitting the F and B, the remaining notes are G flat, A flat, B flat, D flat, and E flat, the notes in the G flat major pentatonic scale. These notes are also the black keys on the piano keyboard. This scale is used for many popular pentatonic songs such as "Amazing Grace", "Auld Lang Syne", and "My Girl".''

I don't understand something here. Perhaps I just don't get it, in which case, never mind. But... if you omit the 4th and 7th of the C major (F and B, respectively), wouldn't you be left with (C, D, E, G, A) instead of (G flat, A flat, B flat, D flat, and E flat)? It seems that the demonstration switches from C major to G flat major halfway through.--Lf1033 20:03, 21 January 2007 (UTC)

It's a simple matter to fix the problem you're complaining about (which is not the only problem with this passage): just say, "By omitting the F and B, the remaining notes are transpositionally equivalent to G flat, A flat, B flat, D flat, and E flat, the black keys on the piano keyboard". Oh, I'll do it for you. TheScotch 11:04, 27 January 2007 (UTC)

pentatonic modes
Re: "They [anhemitonic pentatonic modes] can also be named by their corresponding diatonic cousins: Ionian pentatonic, Mixolydian pentatonic, Dorian pentatonic, Aeolian pentatonic and Phrygian pentatonic."

Pentatonic Scales for the Jazz-Rock Keyboardist by Jeff Burns, published in 1997 by Hal Leonard of Milwaukee, Wisconsin, uses these terms to refer to the various hemitonic pentatonic subsets of the diatonic scale. It calls, for example, C, E, F, G, B, C the Ionian pentatonic and F, A, B, C, E, F the Lydian pentatonic. The idea is that these are derived as analogues of the anhemitonic pentatonic scale within the diatonic scale--which is itself an extension of the acoustically derived anhemitonic pentatonic scale (in other words, it is also a set of Pythagorean fifths). TheScotch 12:54, 12 November 2006 (UTC)

Unless someone can give me the source of the application of the Greek place names to different dispositions of the anhemitonic pentatonic scale, I will delete this part of the article. Should I (at another point) refer to the application of the Greek place names to different hemitonic pentatonic scales? TheScotch 07:21, 20 January 2007 (UTC)

No one gave me the source of the application of the Greek place names to different dispositions of the anhemitonic pentatonic scale, so I deleted this part of the article. TheScotch 07:46, 10 February 2007 (UTC)

jazz
I feel that jp2's earlier exile of minor pentatonic to jazz was completely sensible, but only under the assumption that this scale is unique to jazz. Since (as it turns out), the scale is common to both jazz and Appalachian folk song, I think it ought to be discussed on the pentatonic page after all.

My source for the existence of minor Appalachian pentatonic songs is Cecil J. Sharp, Folk Songs from the Southern Appalachian Mountains, Oxford University Press, 1932.

I left jazz completely alone, so there's now a bit of redundancy here, which I consider to be beneficial.

Perhaps a koto expert could add a bit on the pentatonic scale for this instrument, thus helping to distinguish the different types of minor?

--Opus33 23:56, 30 Nov 2003 (UTC)

Tuning
From the page: "Deriving the pitches from the major scale leads to a just scale of either {1/1, 9/8, 5/4, 3/2, 5/3} (a 5-limit pentatonic) or {1/1, 9/8, 21/16, 3/2, 7/4} with blue notes of the flatted fourth and flatted seventh."

A flatted fourth is a major third, isn't it? If so, is this meant to be a minor scale with a flatted fourth, or is it a flatted fifth? -- Jim Regan 00:28, 7 May 2004 (UTC)

See: blue note. Hyacinth 02:07, 7 May 2004 (UTC)

 * OK, so it's a flatted fourth in the context of a minor pentatonic then. -- Jim Regan 19:44, 8 May 2004 (UTC)

Um...I don't see that the blue note article mentions a flatted fourth, and if it did it would be a very eccentric blue note article indeed. Blues notes are flatted sevenths, flatted thirds, and flatted fifths. It's not altogether out of the question that someday someone might invent a new one, but so far those three are the only ones with significant cultural currency....I see that since Jim's last remark someone has corrected "flatted fourth", changing it to "flatted fifth", but unfortunately the corresponding frequency proportion has not been changed: A frequency proportion of 21:16 above the note C is thirty cents flatter than a tempered F: it is, in fact, a flatted fourth. This isn't the only problem with the section in question, however. More anon. TheScotch 06:12, 21 January 2007 (UTC)

Re: "Deriving the pitches in a pentatonic scale from stacked fifths leads to a Pythagorean scale of {1/1, 9/8, 81/64, 3/2, 27/16}. Deriving the pitches from the major scale leads to a just scale of either {1/1, 9/8, 5/4, 3/2, 5/3} (a 5-limit pentatonic) or {1/1, 9/8, 21/16, 3/2, 7/4} with blue notes of the flatted fifth and flatted seventh.":

First: A Pythagorean diatonic scale is (a tuning of) a major scale. In fact, it’s the only major scale tuning advocated consistently by music theorists for two thousand years, in very round numbers, from 500 B.C. until 1500 A.D., when it began to be supplanted by the just scale.

Second: The term “5-limit’’ is a microtonal-fringe neologism. We can properly speak of just intervals, which diverge from Pythagorean intervals by a syntonic comma, approximately 21.5 cents, or a diatonic just scale, which is derived by stacking 4:5:6 major triads thus: F A C, C E G, G B D, and that’s it.

Re: "The blues scale can be tuned {1/1, 7/6, 4/3, 7/5, 3/2, 7/4}.":

Blues notes are alternate inflections, which means they do not generally correspond to specific frequency proportions, but are subject to all sorts of expressive “deviations”. There is some justification for the “7/4” flatted seventh because trumpet players tend to play this blues note with the seventh harmonic, but as a whole this tuning is merely theoretical speculation.

I recommend that the Tuning section of this article be deleted altogether. TheScotch 06:59, 21 January 2007 (UTC)

I changed my mind and merely reworded the passage, throwing out references to the blues scale, which are irrelevant anyway because this is an article about the pentatonic scale.

I've left for now the last bit (in slightly altered form): "The pentatonic scale used by the Gogo people of Tanzania is said to be tuned thus: 1:9/8:5/4:3/2:7/4. This anhemitonic scale can be thought of as a section of the harmonic series, from the 5th or 6th overtone up to the 10th, transposed to other octaves."

There are problems still, however. For one thing, a remark like this badly needs a citation considering the enormous temptation for ethnomusicologists, especially amateur ethnomusicologists, to impose aesthetically pleasing but unjustifiable tunings onto ethnic musical practices. The slendro anhemitonic scales of Java and Bali are said to approach (very roughly) an equally-tempered five note scale, but, in fact, their tunings vary dramatically from gamelan to gamelan. Another problem with the putative Gogo scale is that it fits uncomfortably with the other tunings mentioned in this section: It gives us the scale {C,D,E,G,Bb}, which is anhemitonic in the sense that it has no semitones, in other words in the etymological sense of anhemitonic, but it is not anhemitonic in the more pertinent sense that the term, regardless of its etymology, means a scale transpositionally equivalent to {C,D,E,G,A}. TheScotch 12:11, 27 January 2007 (UTC)

According to Grove Music Online, which I've just checked, Gogo vocal practice (and it's vocal practice, not instrumental practice) does not make use of what we are accustomed to think of as scales at all; it does not compress its pitches into the span of a single octave and then "[transpose them] to other octaves". Expert Gogo musicians actually sing the fourth through ninth (and occasionally tenth) harmonics above a fundamental. We get C,E,G,Bb,C,D but never C,D,E,G,Bb. This necessarily makes the frequency proportions accurately 4:5:6:7:8:9 (obviating the tendency toward "imposition" I mentioned earlier), but leaving the passage as it now stands very dubious. TheScotch 13:00, 27 January 2007 (UTC)

I think I've fixed this now without losing any substantive actual information (aside from the blues scale tunings). TheScotch 06:56, 9 February 2007 (UTC)

Blues scale
One sentence and six notes hardly does justice to the blues scale, a major building block of American folk, rock, country, jazz, blues, not to mention George Gershwin and Harold Arlen. Ortolan88 17:49, 25 Nov 2004 (UTC)

 * Write more! Hyacinth 19:15, 26 Nov 2004 (UTC)

 * Agreed, it's quite easy to miss too. I'm going to take it out and stubify it. Rico 16:42, 5 August 2005 (UTC)
 * ...or not. I thought we'd have had tags implemented by now. Can't access Lilypond from here. Rico 16:57, 5 August 2005 (UTC)

Isn't the blues scale six different notes in an octave? as in a minor pentatonic scale with one extra note, the blues note. 66.41.59.162 01:43, 21 March 2006 (UTC)

 * Says who? —Keenan Pepper 04:56, 21 March 2006 (UTC)

 * Well, at the moment, the article itself says the blues scale is the pentatonic minor scale with an additional note, the blue note. That would be six. Then, the example eliminates the fifth altogether, replacing it with the "augmented fourth". (I've always thought it was universally called a flat fifth, but whatever.) In any case, the fifth is used in all the blues that I've heard. I think the example needs to be corrected. I don't know where people are getting the graphics of the staves, though. --Trweiss 15:42, 6 December 2006 (UTC)

[I've moved my comments to the lower section]Bedesboy 12:37, 5 January 2007 (UTC)

Pelog
Samuel, please explain regarding pelog in this article. As is it is misleading. Hyacinth 04:42, 19 Dec 2004 (UTC)

 * Hyacinth, I've put a short explanation in the Pelog page.  I don't think it is needed here because this is just a link to that page.  To be brief, Pelog (and also Slendro for that matter) can be thought of as a subset of a larger 7 tone scale.  This varies a bit between Java and Bali.  It is like how the black note pentatonic scale can be thought of as a subset of the 7 tone scale of F#, Gb, C# or Db.  In a good deal of Indonesian music Pelog only uses 5 tones and is indeed Pentatonic.

 * Up until recently, Balinese Gamelan Gong Kebyar only used 5 tone pelog instruments, Only the Suling (flutes) and Rebab (string instrument) could play more tones, but until recently, this was only as ornamentation. Recently, they have started to make 7 tone instruments called "Semeran Dana", but this is the exception, not the norm.

 * In Java, the Pelog instruments have more than 5 tones, but often the music will only use 5 tones. I don't know all that much about Javanese musical theory, but I believe there are 3 modes that are normally used, that come out of that 7 tone scale.

 * So I believe it is correct to call Pelog a pentatonic scale.
 * --Samuel Wantman 07:04, 19 Dec 2004 (UTC)

Someone has recently replaced this:

"The pentatonic scales used in Indonesian gamelan music are called slendro and pelog."

...with this:

"The slendro scale used in Javanese gamelan music is pentatonic, with roughly equally spaced intervals. Another scale, pelog, has seven tones, but is generally played using one of several pentatonic subsets, which are roughly analogous to different keys or modes."

Pelog is not so much a heptatonic (seven-note) scale as a scale system out of which hemitonic pentatonic scales are formed, and there do indeed exist gamelan instruments in Bali (which preserved intact until fairly recently older Javanese culture--as Java itself did not after the Muslims entered) with only five tones per octave and pelog tunings, one of the most popular of which is called selisir.

Also: The degree to which slendro is "equally spaced" has been greatly exaggerated. As I've pointed out before, tunings vary from gamelan to gamelan, but most slendro tunings are much closer to the conventional anhemitonic pentatonic scale than to an equally tempered scale. TheScotch 07:41, 27 April 2007 (UTC)

 * You can find the passage in question under the rubric "Further pentatonic musical traditions". TheScotch 07:48, 27 April 2007 (UTC)

Blues again
afaik, in a the bluesscale is minor scale _plus_ an _additional_ b5. (I just changed that) Maybe someone can update the gfx, or tell me I'm wrong. Tobias (from german wiki)

p.s. so... that would also mean, blues scale isn't a pentatonic, right?
 * "Blues scale" is a poorly defined concept: see . There are blue notes, a well-defined concept (though varying in historical usage). But whether the "blues scale" is a modificiation of the minor scale, or of the major scale (with a flatted third degree)—and how many notes it has—varies from teacher to teacher. —Wahoofive (talk) 17:32, 10 August 2005 (UTC)

 * I think common usage falls on Tobias's side, but common sense is with Wahoofive. There's no single scale that defines or sums up "blues" as a genre, a tradition or even a technique, but if you pick up a scale book, chances are it will list a thing called "the blues scale" that looks exactly as Tobias describes. Anyway IMHO it has no place in an article on pentatonic scales what with its being, as has already been pointed out, hexatonic. Ornette 16:03, 28 April 2006 (UTC)

I'd say the discussion of the blues scale here is pretty unsatisfactory as it stands and could do with a lot more explantion. I'd contend that as blues scale isn't simply a type of pentatonic. I guess one of the problems is that different musicians think of the scale in different ways and there's no formally "correct" definition. For example, I think the pentatonic-type blues scale discussed in this article reflects the POV of a guitarist, as it's the sort of scale you get from playing a "blues box" on a fretboard. I'm a pianist, and for me the blues scale consists of ten notes: (I'll put this in C rather than messing about with numerals): C D Eb E F Gb G A Bb C. I'm sure a ton of people would disagree with my interpretation, though, and Wikipedia needs to reflect the diversity of opinion. What do you reckon about creating a separate article to cover the topic? Unless anyone objects, I'll make a start....Bedesboy 12:36, 5 January 2007 (UTC)

Yes, I think it would be best if the blues scale section here were simply deleted altogether. (It seems to me likely that the b3 and b7 blues notes resulted from the superimposition of a minor pentatonic scale onto a major diatonic scale, which is to say that the blues scale has something to do with the pentatonic scale, but if such a connection is discussed it would be better discussed in a separate article.) TheScotch 07:12, 20 January 2007 (UTC)

It's gone. TheScotch 12:17, 27 January 2007 (UTC)

Clarification needed?
Is it only me or is the following sentence incoherent (aside from being ungrammatical)? I'd just cut it, but it sounds like it's trying to say something interesting. Can someone clarify? Ornette 15:59, 28 April 2006 (UTC)
 * Only certain divisions of the octave, 12 and 20 included, allow uniqueness, coherence, and transpositional simplicity, and that only the diatonic and pentatonic subsets of the 12 tone chromatic set follow these constraints (Balzano, 1980, 1982).

 * What is incoherent or hard to understand about it? What's wrong with the grammar? Why would you remove it? Hyacinth 21:18, 5 June 2006 (UTC)

It sounds a lot like rambling to me.... It isn't at all clear, and I get completely lost in reading it, the 4th or 5th time, and still can't make sense. Does it mean that you divide an octave by 12 and 20(how do you do that?) to achieve... (well... whatever it is it's trying to say) -It is Completely confusing, and unclear -if you understand it, well you are probably the person who wrote it -or a music professor. User:Guest 17:44, 31 July 2006

What's wrong with the grammar? The that is syntactically nonsensical. Either the that needs to go or else something like "Balzano says that" needs to be added to the beginning of the sentence--which brings us to the next obvious problem: As far as I can tell the article never explains who Balzano is or what he published in 1980 and in 1982. Balzano is apparently redefining terms such as simplicity and coherence to give them precise mathematical meaning, and I suspect you'd have actually to read his papers or books to discover what that meaning is--whether or not you happen to be "a music professor". TheScotch 13:08, 12 November 2006 (UTC)

The passage currently reads "Only certain divisions of the octave, 12 and 20 included, allow uniqueness, coherence, and transpositional simplicity, and only the diatonic and pentatonic subsets of the 12 tone chromatic set follow these constraints (Balzano, 1980, 1982). The major and minor pentatonic scales possess Myhill's property." The deletion of the that is a decided improvement, but I still find nothing in the article to explain who "Balzano" is or what he published in 1980 or in 1982. Unless we get some clarification soon the entire passage is going. Consider yourself warned. TheScotch 07:34, 20 January 2007 (UTC)

Gone. TheScotch 12:17, 27 January 2007 (UTC)

Orff?
Which version of the pentatonic scale did Orff recommend for kids to improvise on... so it always sounds good.?

minor mistake
I removed the following:

Another common minor pentatonic is constructed from the scale tones I, II, iii, V, VI.

From the minor pentatonic section because this is the major pentatonic.

Also I changed the scale tones 1,2,3,5,6 listed in the major pentatonic to the more conventional roman numerals I, II, iii, V, VI. Should scale tones be written in capital or lower case? They are pretty inconsistant in this article. —The preceding unsigned comment was added by 61.68.142.241 (talk • contribs).

 * No, I think the original author meant the lowercase Roman numerals to mean minor intervals above the tonic, which is a little non-standard because Roman numerals usually refer to chords, but it's definitely not just "inconsistant" [sic]. —Keenan Pepper 04:17, 2 September 2006 (UTC)

inconsistency
Why is the octave, which has seven notes before it repeats the first called the octave but the pentatonic scale which has five notes before it repeats called the pentatonic scale?

Should this apparent inconsistency be mentioned in the article?

It could be, but I think that would absorb more light than it would shed--or something. Our names for intervals are derived from the diatonic scale, and they're pretty firmly embedded. If we could change them easily then probably we would have changed them long ago, considering that an obvious arithmetical error is involved. The distance between the first and third notes of a diatonic scale should logically be two, not three, yet we call this interval a "third". Atonal theory bypasses these ordinal expressions altogether, logically numbering the equally tempered scale from zero to twelve and deriving chromatic intervals by simple subtraction. TheScotch 13:03, 12 November 2006 (UTC)

 * I think you answered your own question. The octave is an interval, not a scale.  Correct me if I'm wrong, but I've never heard of a major/minor/etc scale being referred to as an "Octave Scale", perhaps for the exact reason you mentioned.

 * Regarding intervals, they're called "thirds" NOT because of the distance between them, but because of their position relative to the first note of the scale. In C Major, the note E is not a "third" above(or "tenth" or "seventh" etc.) because there are three  notes in between, (or two, or even one depending on how you're looking at it) but because it is the third note of the scale.  C is, obviously, a part of the scale, thus it is "one", "unison", "first", or whatever you like to call it. The note "D" is the second note of the scale, thus it is the interval of a "second" (or "ninth" etc.).  The rest follows from that --Crabbyass 16:28, 12 November 2006 (UTC)
 * Furthermore, the octatonic scale does have eight distinct notes before it repeats. —Wahoofive (talk) 03:43, 13 November 2006 (UTC)

Re: "The octave is an interval, not a scale."

Yes, and its name derives from the seven-note diatonic scale. It would be perfectly consistent to call the same acoustical relation in respect to the proto-diatonic anhemitonic pentatonic scale a sixth. I don't think that would be a good idea, however, for two reasons: 1) It would be needlessly confusing, and 2) it would be perpetuating the illogic of our diatonic interval names.

Re: "Regarding intervals, they're called 'thirds' NOT because of the distance between them, but because of their position relative to the first note of the scale. In C Major, the note E is not a 'third'" above(or 'tenth' or seventh' etc.) because there are three notes in between, (or two, or even one depending on how you're looking at it) but because it is the third note of the scale."

Unfortunately, that is not what the term interval means. Interval means distance, and the ancients who invented these interval names failed to recognize zero as a number. (Notice that your system wouldn't work for measuring the interval D-E, for example, unless you switched suddenly to a D scale. That would be revising history--considering that these ancients I mentioned didn't transpose--, as well as extremely limiting and contrary to how we practically make use of interval theory.)

Re: "Furthermore, the octatonic scale does have eight distinct notes before it repeats."

Well, I think that's pretty much why we call it the octatonic scale--some of us; I prefer to use jazz nomenclature here and call it the diminished scale, considering that there is at least one other eight-note scale just as interesting. Anyway, if we were to name intervals in terms of an eight-note diminished scale rather than in terms of a seven-note diatonic scale and in a analogous fashion, we would necessarily have to call the 2:1 frequency relation a ninth. I advise against doing that--at least in wikipedia--for the same reason I advise against making an analogous pentatonic interval-naming system. TheScotch 18:48, 14 November 2006 (UTC)

Re: "I think you answered your own question." It occurs to me now that there may be some understanding here. My contribution to this section (under the heading "inconsistency") begins with "it could be". The two questions above my "it could be" were written by someone else, someone who neglected to sign his contribution. TheScotch 09:29, 31 December 2006 (UTC)

spelling the blues scale
Does it make any difference if we call the note a "sharp four" or a "flat five"? I was taught a "sharp four" - but when I teach my own students - I prefer to use the term "flat five" since it is consistent with "flat three" and "flat seven" William'sboy 17:43, 15 December 2006 (UTC)

Spelling and "calling" are different things. A chromatic pitch will generally be spelled with a sharp if its resolution ascends and spelled with a flat if its resolution descends. We can have F, F#, G, ascending, for example, and G, Gb, F, descending. Contrary to arbitrary jazz pedagogy, there is in fact no such entity as a "blues scale" because blues notes are alternate inflections, but if we put that circumstance aside for the moment and consider C Eb F F# G Bb C a C blues scale, then it should be clear that its second and sixth pitches are spelled with flats because they don't resolve. In real music these pitches are just as likely to resolve as not and we might have something like C D# E F G. "Calling", you should never use the term sharp at all (in respect to scale degrees, that is), but rather raised. Despite the variable spelling, blues notes are generally considered to be lowered inflections, not raised inflections. So call them "lowered" and spell them according to how they resolve in the particular passage in question. TheScotch 09:22, 31 December 2006 (UTC)
 * (late in the game, but...) "There is no such entity as a 'blues scale' "? I suppose if you want to impose a highly abstracted and restrictive theoretical definition of what a "scale" is, you may be right.  But that is to ignore both the lingua franca and the musical practice of millions of actual working musicians, and really to disserve the encyclopedia, however much you may look down on "arbitrary jazz pedagogy."  Definitions may occasionally vary, but that's a different matter.
 * As far as spelling goes, harmonic (or melodic) function should dictate notation -- ie the blues scale should have "#4" going up and "b5" coming down, but in practice even classical composers are often inconsistent with that, especially when double-flats or double-sharps are called for (much to my personal frustration when trying to solfege a score). As for never using "sharp" to mean raised or "flat" to mean lowered wrt scale degrees, I admire your aspirations for precise language, but that's a mighty big tide you're swimming against.
 * I guess this is the place to ask...after all the above discussion on the blues scale(s), all mention of it seems to have been wiped off the page...I thought perhaps it had been forked and I should add a quick "see also" link, but "blues scale" currently redirects to hexatonic scale, a term jazz and pop musicians never use, but classical theorists do-- for the whole tone scale (wrong, whoops). I don't have time right now do dig stuff out of the history, but I would have thought a new article (even a stub) w/ the material from here, and a link interpolated into the jazz discussion here, would be the sensible way to go...— Turangalila  talk 05:20, 17 April 2007 (UTC)

1. "Actual working musicians" actually working with blues material actually use blues notes in various ways, as I've pointed out above.

2. Note my repeated use of the term generally to qualify my remarks about spelling.

3. I also assumed that someone had made a "blues scale" page and have just a few minutes ago discovered to my surprise the redirection to "hexatonic scale". I'm editing this page now. The whole-tone scale does have six pitches per octave, but I've never heard anyone, classical theorist or other, refer to it as the hexatonic scale (in the way that classical theorists tend to refer to what jazz musicians call the diminished scale as the octatonic scale). Before I chanced upon it, the hexatonic scale page here mentioned three hexatonic scales: the whole scale, the augmented scale, and the blues scale. This seems to me reasonable, considering that these are arguably the three most famous specimens. I'll try to make some decisions (or maybe just remarks) about linking after I've edited the hexatonic scale page a bit more. TheScotch 07:15, 29 April 2007 (UTC)

 * For now, I've simply added a blues scale link to the See also section of this page (the pentatonic scale page, that is). TheScotch 08:09, 29 April 2007 (UTC)

 * I think we're using the word scale a bit differently. You're thinking of it as a basis for actual creative music-making, whereas for me scale immediately conjurs up the practice room, and there the blues scale is all too real.  Of course most bluesers & jazzers will use blue notes in different ways, just as most non-jazz composers will mix modes freely; but the "morning routine" of a good (or at least diligent) jazz player often runs through scales (& arpeggios) in all keys, in a sequence like:  major-minor-dominant-pentatonic-diminished-blues (& perhaps whole-tone & augmented &c &c...).  Pedagogically a common exercise is to have students improvise blues choruses specifically restricting themselves to the blues scale.  I think Jamey Aebersold has a whole book on it... Actually even in "real" improvising, when a soloist gets too far afield melodically during a more traditional blues number, somebody'll yell "Play the blues, man," meaning stick (close) to the blues scale — this has happened to me personally :-).
 * Anyhoo, I'm sure you're right that "hexatonic" is a genus not a species... not sure what I was thinking there. On spelling, what I was trying to say in my own garbled way was that your guidance is right, but unfortunately general practice often ignores it.  Thanks for the updates... I may dig out the history here & fork a blues-scale article at some point, but I've way overcommitted myself WP-wise at the moment...  — Turangalila   talk  18:26, 29 April 2007 (UTC)

 * It is perhaps worth pointing out that hexatonic has been in the article for a long time as a generic classification (see the box that has been incorporated at the end: Scales in Equally tempered music). Myself, I think that box is not well thought out at all (especially for its inclusion of diatonic as a well-defined category, for its spurious implicit claim to completeness, etc.). It could be turned into something valuable, but it needs "workshopping", and as it stands articles are diminished by incorporating it.
 * –  Noetica ♬♩ Talk 22:25, 29 April 2007 (UTC)

I’m not happy about the box either. For one thing, it’s titled “Scales in Equally tempered music”, and the “Tuning section” section here never once mentions equal-temperament. Yes, I admit I’ve edited this section myself, but it never once mentioned equal-temperament before I got hold of it either, and back then it was significantly more arithmetically specific (and arithmetically suspect, I contend), more arithmetically specifically oblivious to equal-temperament. For another thing, not only is the box incomplete, as you point out, it’s also likely to remain incomplete. I doubt anyone is ever going to write an article about "tritonic" or "ditonic" (dyatonic?) scales. Why do we stop with octatonic? I’m guessing it’s just because that’s where the box maker’s Greek ran out. He couldn’t conjure up nonatonic, decatonic, or hendacatonic. TheScotch 09:00, 4 May 2007 (UTC)
 * Shouldn't they be enneatonic, decatonic, and hendecatonic? Double sharp (talk) 10:34, 24 May 2015 (UTC)

Diatonic and chromatic
The article uses the term "diatonic" in more than one sense, but without adequate explanation. This term, along with chromatic, is the cause of serious uncertainties at several Wikipedia articles, and in the broader literature. Some of us thought that both terms needed special coverage, so we started up a new article: Diatonic and chromatic. Why not have a look, and join the discussion? Be ready to have comfortable assumptions challenged! –  Noetica ♬♩ Talk 05:59, 6 April 2007 (UTC)

If you can tell us specifically where and how this article uses the term diatonic equivocally, we can probably fix it. Otherwise we're left only to guess. TheScotch 11:49, 6 April 2007 (UTC)

 * TheScotch, I suggested that you look at Diatonic and chromatic, and the talk page for that article. If you do that you will see more detail about the problem I mention here. But let's look at the six uses this article makes of the term:
 * It omits two pitches from a diatonic scale.
 * the Pythagorean diatonic and chromatic scales...
 * If we consider the anhemitonic scale a subset of a just diatonic scale...
 * over several chords diatonic to the same key
 * at the teacher's discretion until the complete diatonic scale is being used.
 * By interval : diatonic | chromatic | whole tone
 * So the term is first used in "diatonic scale", implicitly assuming that term in a certain restricted sense: roughly, the scale equivalent to the modern major scale, or to some "range" of that scale, or some scale using the same mix of tones and semitones (Use 1). But the reader is given no direct guidance about which of several available senses of diatonic scale is intended. In Use 2 diatonic scale is cryptically qualified as "Pythagorean", but there no explanation or link to help the reader, here. In Use 3 there is mention of a "just diatonic scale", with no link or explanation. In Use 4, the term is used in the phrase "diatonic to a key". But in this derivative use of diatonic it is not clear which chords are in fact "diatonic to key". In the context, in this article, only a major key is spoken of. But this usage is generally unruly. (Is the chord G-B♮-D "diatonic to" C minor? Is the chord E♭-G-B♮? Different sources give different answers.) And it is not likely to be understood by the reader who is a novice in music theory. In Use 5 we return to the uses implicit in Uses 1, 2, and 3. But in Use 6, in the table at the end of the article, the term diatonic appears in a supposed three-way division of the kinds of scales used in Western music, which therefore implicitly assigns the harmonic and melodic minors as "diatonic". This is incompatible with Uses 1, 2, and 3, but compatible with usage explicit or implicit in some other Wikipedia articles, and in several respected published sources.
 * Now, we know what's going on! I, for example, understand this article with no difficulty. But articles need to to be written for non-specialist readers. This one isn't: and one reason is its careless use of a term which is far more problematic than most "experts" appreciate.
 * –  Noetica ♬♩ Talk 12:42, 6 April 2007 (UTC)

I'm still going to have to hunt these passages down. Your first three instances require only that one knows the meaning of the term diatonic, and presumably that can be found by clicking on the term. Diatonic to in your #4 should perhaps be replaced with "belonging to", but, then again, belonging to might not be precisely what's meant. You haven't quoted enough of #5 to give me the an idea what its about. I'll take a look at #6.

When you say, "Be ready to have comfortable assumptions challenged!" I fear you're proffering "original research". Should we, in any case, really be using an article's discussion page to advertise another article? TheScotch 07:16, 7 April 2007 (UTC)

I've looked over these instances now. I don't find anything objectionable about any of them. The sixth is simply a link to another article. I haven't read that other article, but if it's faulty, its faults should be addressed on its own discussion page. TheScotch 07:32, 7 April 2007 (UTC)

 * Scotch, you should look at the article Diatonic and chromatic, because I fear you've missed Noetica's point -- the term "diatonic" is ambiguous, and the ambiguity is extensively documented on that page. Noetica's concern is that the word is used here in at least some cases as if its meaning were clear, when it's not. The recommendation of authors on that page is that article avoid the term when possible, replacing it with something more specific. —Wahoofive (talk) 16:07, 7 April 2007 (UTC)

1) The term diatonic is a very basic musical term. Every musician at every level needs to know it, and I can't imagine what anyone would be doing here who is not in some sense a musician--but if someone happens to be ignorant of the term, for whatever reason, he can look it up.

2) Advocating that the term diatonic be done away with is "original research", and if any wikipedia article does it, it needs to reverted immediately.

3) I'm not going to allow myself to bullied into reading anyone's "original research". Criticisms of this article need either to be stated clearly here or else kept to oneself. TheScotch 05:26, 8 April 2007 (UTC)

 * Scotch, here are three responses to your three points:
 * 1) Yes, diatonic is a fundamental term. It is also used in a number of different senses, as is amply shown at Diatonic and chromatic. Budding musicians will consult these articles in Wikipedia, in order to come to an understanding of such terms. Many experienced musicians will also come here, to check their usage of terms or to find material relevant to their teaching, etc. Yes, they can "look it up", but where? At Wikipedia, I hope! As things stand in the literature, if they go elsewhere they will often get incomplete or misleading definitions for diatonic and chromatic.
 * 2) No one is suggesting that the term be done away with: just that it be used uniformly or at least understandably, and that if this is impossible then other terms might be more apt. For example, say that the most usual pentatonic scale (the major pentatonic scale) can be derived by omitting two notes from the major scale, not from the diatonic scale. Why use a contested and unclear term, when such an easy and accurate alternative is available?
 * 3) Who's bullying anyone? [Note: I corrected the this from whose, later, prompted by Scotch. See below.–  Noetica ♬♩ Talk 00:50, 11 April 2007 (UTC)] Who imposes markers on articles (to which they have not contributed) suggesting that they are "original research", as at Diatonic and chromatic? I have made criticisms of this article, and I have done so only here. That's why we have talk pages.
 * Let's all work together on these things, OK?
 * –  Noetica ♬♩ Talk 00:15, 9 April 2007 (UTC)

Re: "No one is suggesting that the term be done away with:

These are precisely Wahoofive's words: "The recommendation of authors on that page is that article avoid the term when possible." Obviously, this is suggesting the term be done away with, at least as far as this article goes.

 * (I interpolate my comments in italics, signing each one.)
 * No, Scotch. By your own citing of these, there is a difference. "Avoid the term where possible" does not express the same intent as "that the term be done away with".–  Noetica ♬♩ Talk 00:50, 11 April 2007 (UTC)

Re: "At Wikipedia, I hope! As things stand in the literature, if they go elsewhere they will often get incomplete or misleading definitions for diatonic and chromatic.":

Clearly, you are saying that your definition of these terms is significantly different from the standard definitions, and just as clearly you are therefore--if you are right that they're significantly different, that is--undertaking "original research" here and advancing your own agenda.

 * No, I have no "agenda": unless that be to take note of various definitions given in standard sources, including Wikipedia. No, there is nothing that I identify as "my" definition, of any of the terms in question. No, none of this is "original research". And we strive to cite all our sources, at Diatonic and chromatic. Have a look. But note: not one of those sources does a better job of clarifying the ways these terms are used than our article does. If you disagree, show me one. –  Noetica ♬♩ Talk 00:50, 11 April 2007 (UTC)

Re: "Why use a contested and unclear term, when such an easy and accurate alternative is available?":

You and your cohorts are the only ones contesting it and the only ones who find it unclear. The major scale is different from the diatonic scale in that it unmistakably implies a particular tonal center, and tonal centers are entirely irrelevant to the process of deriving a pentatonic subset from the diatonic scale (which is, of course, an historically backward procedure--I didn't put this bit in the article). TheScotch 20:30, 10 April 2007 (UTC)

 * No. Look at discussions on the web (I could point you to them, if you like). They illustrate the deep confusion that people are in about these terms. I appreciate your point about the differences between major and diatonic; but the pentatonic scale is not historically "derived" from either, is it? We can show its structure, though, by appeal to the major scale, as effectively and more clearly than by appeal to some diatonic scale – a term which is given several meanings in the literature. –  Noetica ♬♩ Talk 00:50, 11 April 2007 (UTC)
 *  [Note added later:] To be fair, the article does derive the (major) pentatonic from the major scale. But it does so with mention of the "diatonic scale" in the previous sentence. We might wonder why that mention is desirable; and if it is desirable, why is it not equally desirable in the section that follows, on the minor pentatonic scale? Incidentally (and perhaps of some importance), that section starts this way: "There are two different pentatonic scales in common usage that are referred to as minor." Well, only one is named and dealt with. I presume that the other would be of this structure: C-D-E♭-G-A♭[-C]. Is that right? Whatever the other form is, let it be added. Confusing and incomplete, otherwise. It is possible that the two forms intended are the one shown starting on C, and the one shown starting on A. But this would be odd indeed. These two have the same internal structure exactly. Finally, as things stand there may be inconsistency in the use of the term minor as applied to pentatonic scale between this section and the later section called Further pentatonic musical traditions. Perhaps that needs attention also.
 * –  Noetica ♬♩ Talk 03:23, 11 April 2007 (UTC)

Re: "Whose [sic] bullying anyone?":

 * Ouch! Quite right, of course. As one who edits at Apostrophe, and as the one who added to that article the list of possessive forms that do not use the apostrophe, I am in pain when I see my slip here. My excuse is that I had not slept all night. I was editing (not in Wikipedia). –  Noetica ♬♩ Talk 00:50, 11 April 2007 (UTC)

Very clearly, you are using this discussion page to advertise and promote work you have done elsewhere, and you and your cohorts have repeatedly urged me, specifically, to go there. This doesn't seem to me at all proper behavior, and I think I am entirely justified in considering it an intrusion.

 * No. How can it be an intrusion? I have not touched this article (though I might, yet). I only draw attention to issues arising from it, on the talk page. That's why we have talk pages! People can go to Talk:Diatonic and chromatic if they like. Much will be explained there (better than cluttering this page, yes?). No one's compelling anyone, or bullying anyone. My "cohorts"? A bit pejorative, don't you think? A number of concerned editors who have identified an issue, and who have been working hard for clarity, and to serve users of Wikipedia. –  Noetica ♬♩ Talk 00:50, 11 April 2007 (UTC)

Re: "Who imposes markers on articles (to which they have not contributed) suggesting that they are "original research", as at Diatonic and chromatic?"

Whether I have contributed to it are not is entirely irrelevant--and in any case you can hardly expect me to be enthusiastic about the prospect of being immediately mobbed. I make my case in the discussion page of that article, and you need to confine your contesting of my editing of that article to the discussion page there. TheScotch 20:30, 10 April 2007 (UTC)

 * Perhaps it is irrelevant. I don't really care. The fact is that you chose not to contribute, but to slap a marker on the article that it doesn't deserve. If you have reservations about particular statements of the article, discuss them at its talk page. You did that once, and the matter was addressed swiftly. That's pretty good, isn't it? I thanked you for contributing to the talk page. It is interesting that you do not thank me for contributing at this talk page. As it stands, this article still has problems with terms that need to be addressed. You would do well to attend to fix those, rather than raising objections to public commentary of a sort that Wikipedia allows for and encourages. –  Noetica ♬♩ Talk 00:50, 11 April 2007 (UTC)

Merge from Mongolian scale
Support. The Mongolian_Scale is essentially the same scale with a different name. --Stephen Burnett 22:50, 8 April 2007 (UTC)

Examples
"Please, can we have some examples? Like ones we can hear. Or is Wikipedia a text-only medium?"
 * Well ... I uploaded two example MIDI files: [[Image:PentMajor.mid]] and [[Image:PentMinor.mid]] . The problem is, it doesn't look nice when you put it into the page. I guess this is because they are not really image files. I have no idea if that's the way you're supposed to do it, or if you're even supposed to at all. Any advice, anyone? --Stephen Burnett 02:50, 10 April 2007 (UTC)

 * Problem now fixed. --Stephen Burnett 18:53, 12 April 2007 (UTC)

2nd minor pentatonic?
Currently, under "Minor pentatonic scale", the article says: There are two different pentatonic scales in common usage that are referred to as minor...but then goes on to discuss only the "relative" (black-key) minor pentatonic. Did a sentence or paragraph get lost? Either way this doesn't relate well to the "Further pentatonic musical traditions" section, which contains several allusions to "the minor pentatonic scale", and one to "a minor pentatonic scale" for the shakahuchi. This could all be resolved by just cutting that first sentence, but that probably wouldn't be right...— Turangalila talk 05:33, 17 April 2007 (UTC)

 * I agree, Turangalila. See what I wrote above, on 11 April 2007:
 * "Incidentally (and perhaps of some importance), that section starts this way: 'There are two different pentatonic scales in common usage that are referred to as minor.' Well, only one is named and dealt with. I presume that the other would be of this structure: C-D-E♭-G-A♭[-C]. Is that right? Whatever the other form is, let it be added. Confusing and incomplete, otherwise. It is possible that the two forms intended are the one shown starting on C, and the one shown starting on A. But this would be odd indeed. These two have the same internal structure exactly. Finally, as things stand there may be inconsistency in the use of the term minor as applied to pentatonic scale between this section and the later section called Further pentatonic musical traditions. Perhaps that needs attention also."
 * This was ignored. (I know the scale I mention exists!) I think there is a great deal to be fixed in this article, but as things stand I am not in a position (for reasons of time and "politics") to attend to this myself. I wish those who do look after this page would respond to such comments as yours and mine.
 * –  Noetica ♬♩ Talk 05:47, 17 April 2007 (UTC)

If you wanted, you could call various hemitonic pentatonic scales minor, not just C-D-Eb-G-Ab, but also C-Db-Eb-G-Ab, C-D-Eb-G-A, C-Eb-F-G-B, and so on. (All of these scale forms are used in Java and Bali, and at least three of them are used in Japanese traditional music.) The only pentatonic scale commonly called minor, however, is the minor mode of the anhemitonic pentatonic scale, and I think the article should stick to this one. (I'm sorry I didn't see the comment of yours to which you refer. Maybe you wedged into one of your diatonic and chromatic harangues--I stopped reading these because I wearied of having perpetually to repeat myself. In general, though, I don't think you should you should feel neglected just because no one's yet responded to a comment of yours. Wikipedia is a big place, and most contributors have lives.) TheScotch 20:26, 17 April 2007 (UTC)

 * The section we're discussing here also includes this assertion: "This minor pentatonic contains all three tones of the root note's minor triad." I suspect whoever wrote it is confusing root with tonic, but I can't tell for sure. If I can get around to it, I'll tinker with this section on Thursday. TheScotch 20:34, 17 April 2007 (UTC)

 * Scotch, I note your attempt at trenchant invective with detached amusement. I can only speculate about the insecurity that leads to you such an effort. Meanwhile, how about fixing this article's manifest inadequacies, which have been pointed out by several observers independently? I would do it myself if I had the time: but I somehow feel you wouldn't like it if I did.
 * –  Noetica ♬♩ Talk 00:50, 18 April 2007 (UTC)

Leaving editor relationship issues aside, I've boldly gone ahead and changed that first sentence for now, basically paraphrasing The Scotch's first comment here. I'm still curious what other mode it was referring to... Anyway, double-check me, but I think that at least leaves the article unambiguous wrt self-reference, which will have to do for now. — Turangalila talk 02:10, 18 April 2007 (UTC)

 * I weakened the first assertion just slightly, changing can to might, and I removed equivocal references in this section to chord members. TheScotch 06:44, 20 April 2007 (UTC)
 * 'looks OK. — Turangalila  talk 13:50, 20 April 2007 (UTC)

Explanation of a passage
Could someone please explain me this passage? Or say it in other words. I don't understand what does "they work well over several chords diatonic to the same key"? "Diatonic to the same key"? What are we trying to do if we substitute something with a note from the pentatonic scale?
 * "Pentatonic scales are useful for improvisors in modern jazz, pop, and rock contexts because they work well over several chords diatonic to the same key, often better than the parent scale. For instance, over a C major triad (C, E, G) in the key of C major, the note F can be perceived as dissonant as it is a half step above the major third (E) of the chord. It is for this reason commonly avoided. Using the major pentatonic scale is an easy way out of this problem. The scale tones 1, 2, 3, 5, 6 (from the major pentatonic) are either major triad tones (1, 3, 5) or common consonant extensions (2, 6) of major triads. For the corresponding relative minor pentatonic, scale tones 1, ♭3, 4, 5, ♭7 work the same way, either as minor triad tones (1, ♭3, 5) or as common extensions (4, ♭7), as they all avoid being a half step from a chord tone."

 * Please sign your posts on talk pages per Sign your posts on talk pages. Thanks! Hyacinth (talk) 03:23, 21 January 2008 (UTC)

Yo scale
It seems to me that the picture of the Yo scale should have the starting note repeated at the end, since the other pentatonic pictures show the starting note at the end. I would do this if I knew how, but I don't Wikidsoup   [talk]  19:14, 19 January 2008 (UTC)

 * There should be some sort of standard or guideline for images of musical scales. See: WikiProject Music. Hyacinth (talk) 03:39, 21 January 2008 (UTC)

Removed sentence because of logic error
If they could be and were put into a single octave, however, they would make a pentatonic scale with these frequency proportions: 1:9/8:5/4:3/2:7/4. Falsehood implies anything and everything. Please rethink what you're trying to convey and then formulate that in such a way that it makes sense. Shinobu (talk) 10:34, 17 May 2008 (UTC)

 * As does misunderstanding, or perhaps it implies everything and nothing only to some. What don't you understand about it? Hyacinth (talk) 19:21, 3 March 2010 (UTC)

Dorian Pentatonic
Is there a reason why there's no mention of the dorian pentatonic - I, II, ♭III, V, VI, ( I )  ? ~ —Preceding unsigned comment added by Possecomitatus (talk • contribs) 15:17, 5 April 2009 (UTC)

including, but not limited to
"Including, but not limited to" is lawyer-speak and is unnecessary since "including" implies additional items already. --Unimath (talk) 12:32, 2 September 2009 (UTC)

Language
This article reads like it was written by scientists. Can someone please decipher this? —Preceding unsigned comment added by 67.247.24.23 (talk) 15:10, 5 November 2009 (UTC)

 * What, specifically, is hard to understand? Hyacinth (talk) 19:18, 3 March 2010 (UTC)

Additional citations
I removed the "refimprove" template from May 2008 calling for additional citations for verification since there is no explanation on this talk page. Hyacinth (talk) 19:17, 3 March 2010 (UTC)

Dryness
This article is about as exciting as a dead gibbon. While the technical, academic definition is fine, surely there could be some room for something more human? When I think pentatonic scale, I think of how amazing it is that pretty much anything played in the pentatonic scale sounds good. That's a major part of what I'd talk about if I were to explain it to someone else. What's the point of music if not to evoke feelings in people? —Preceding unsigned comment added by Nevster (talk • contribs) 04:52, 23 June 2010 (UTC)

Black keys

 * Other popular children's songs are almost pentatonic. For example, the almost-pentatonic nature of the Gershwin lullaby "Summertime", is evident when it is played in the key of E-flat minor. In that key, the melody can be played almost entirely on the black keys of a piano, except just once per verse, where a white key is needed.

This passage sounds awkward. Why is the pentatonic nature evident when played in the key of E-flat minor? The song won't sound any less pentatonic in any other key. . This seems a convoluted way of saying that "in E-flat minor, the song can be played using almost only black keys". It has already been said that the black keys of the piano form a pentatonic scale, but it seems weird to make this fact a criteria for deciding whether a song's scale is pentatonic. — Preceding unsigned comment added by Rcaetano (talk • contribs) 10:46, 14 August 2011 (UTC)

Removed sentence on the great highland bagpipe
"The pentatonic scale is also used on the Great Highland Bagpipe." The mentioning of Great highland bagpipe on its own here is misleading and can lead to wrong conclusions - the great highland bagpipe has a MIXOLYDIAN scale, written most often to A but actually audibly closer to Bb mixolydian. To say that it "uses pentatonic" scale could be said of the piano as well - you can play a pentatonic scale on the piano - piano nevertheless has quite a bit more than just that. For reasons of avoiding confusion of the scale of the Highland Bagpipe I thus removed the sentence. 91.152.177.51 (talk) 00:15, 16 October 2011 (UTC)

Table Alignment
I do not know how to align the pythagorean table. 75.152.126.183 (talk) 22:03, 7 February 2013 (UTC)

Okay, I figured out most of it. It still does not look like other table of the sort with staggered step ratios. 75.152.126.183 (talk) 22:53, 7 February 2013 (UTC)

Heptatonic origin
Intro comes out saying heptatonic scale originated in Medieval Europe. Seems dubious to me. Web search gave no ready confirmation. I would suspect somewhere East has record of hepta much earlier. Middle East, Subcontinent, Persia... ? Nissimnanach (talk) 16:41, 19 February 2020 (UTC)Nissimnanach
 * Just a little bit earlier (at least as early as the 18th century BC), and you have got the geography pinned down rather well.—Jerome Kohl (talk) 17:39, 19 February 2020 (UTC)

"Complete in terms of tonality"?
The section "Major pentatonic scale" currently claims that the scale is "complete in terms of tonality." Does anyone know what that's about? I know what tonality is, but I'm not sure what that statement could be referring to. On the one hand, it's possible to create the sensation of changing key in it if you tune it in a way that gives priority to the fifths (such as Pythagorean tuning), but you can also achieve that in scales with less notes. On the other hand, it doesn't offer all the possibilities for functional harmony that we're accustomed to in diatonic music, especially with a larger chromatic scale available, and if that's your criterion for "tonal completeness" than it falls short. I kind of imagine that the author had something else in mind but I'm not sure what it would be. Mesocarp (talk) 02:30, 30 November 2022 (UTC)
 * My guess is they just meant that all three notes of the major triad were present. If so, useless info. I vote get rid of it. —Wahoofive (talk) 01:04, 1 December 2022 (UTC)
 * Okay, I went ahead and took it out. I wouldn't be surprised if you're right; if you do follow the Pythagorean/circle of fifths approach to constructing it, the major third is the last note to arrive, so maybe they did feel like it was special on that basis. I agree though that if that is what they meant, it doesn't really say much about the scale in any general sense, and there's no citation besides. Mesocarp (talk) 02:07, 1 December 2022 (UTC)

oVERDONE
This page is so overdone that it's useless. 104.157.227.172 (talk) 22:05, 20 February 2024 (UTC)

title: Talk:Pentatonic scale


text:
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de:Benutzer:Stw fr:Utilisateur:Stw nl:Gebruiker:Stw

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:Stw


text:
Talk:Function (mathematics)

Function evaluation
A mini edit war has started about the paragraph on function evaluation. This paragraph was confusely written, and I rewrote it boldy for clarifiation. Nevertheless, some problems remain, for which I am not sure of the best solution. In summary, fixing this paragraph of the lead requires more work and more discussion, for which the tag cn is of no help. D.Lazard (talk) 17:39, 24 March 2024 (UTC)
 * Although very sketchy, this paragraph is too long for the lead. I am not sure of the part of it that belong to the lead and of the best place for details.
 * redirects here. This deserves more than two lines in the lead. Maybe a specific article?
 * Very often, "function evaluation" refers more properly to "expression evaluation". The confusion between these two concepts is the cause of many errors by beginners in the use of computer algebra systems. is a redirect to Expression (mathematics) that I created recently. Nevertheless, the treatment of evaluation (mathematics) remains insufficient and confusing in Wikipedia.
 * Although very common, the vertical-bar notation for evaluation is not clearly defined in Wikipedia. I added recently a description of it at Expression evaluation, but this is still insufficient. This vertical bar notation, is a particular case of a restriction, if one consider $$x=a$$ as an abbreviation of $$\{x|x=a\}.$$ Maybe, a description of the vertical-bar notation for evaluation could be added at Restriction.

 * The lead section of this article seems like an inappropriate place for the only discussion of this "vertical bar notation" which is not used anywhere else in the article. It's confusing, distracting, and only tangentially relevant. It should be put somewhere else in the article or in another article. Readers aren't going to look for it here, and readers who come across it here aren't going to find it valuable in context. –jacobolus (t) 17:43, 24 March 2024 (UTC)
 * One problem with this vertical bar notation is that it's hard to find clear sources describing its history/use. My guess is that it evolved out of the related notation for the bounds of a definite integral, as found in introductory calculus books/courses. There's a discussion of the earliest use (under "bar notation") in https://jeff560.tripod.com/calculus.html –jacobolus (t) 18:20, 24 March 2024 (UTC)
 * The use of "often" and "commonly" are unsourced and unnecessary. The second sentence has not one, but two parenthetical clauses. Yikes! The third sentence, unnecessarily restricts itself to talk about function evaluation to the case when the expression "depends on x". This, "depends on x", is ambiguous as an intuitive notion and it hasn't been defined in the article as a formal concept. Thatwhichislearnt (talk) 13:35, 25 March 2024 (UTC)
 * I agree that is not sufficient to elaborate on the vertical bar and evaluation, however, I consider(ed) is necessary - I apologize for my part of the "mini edit war" (I didn't intend to fight). I also agree that the vertical bar needn't be adressed in the lead, or even shouldn't be adressed there. However, it should be explained somewhere (not sure whether inside this article). And I, too, have seen the notation only in computations of definite integral [and in the recent versions of this article's lead].
 * Defining the vertical bar based on restriction appears to be one possibility, which also nicely motivates the notation. Another possibility would be to define it based on substitution (logic), i.e. $$e \vert_{x=a}$$ means the substitution application $$e \{ x \mapsto a \}$$, or the evaluation of it. I'm not sure about an explanation of "expression evaluation". Maybe it should be based on (item "Functions" at) First-order_logic, which defines evaluation of an expression in terms of evaluation of its constituent functions. (First-order logic doesn't care about how to obtain a function's result value for given inputs. If a function is defined by an expression in turn, its constituent functions (usually $$+, -, *, /, ...$$) need to be evaluated, which leads to the standard arithmetical algorithms. However, a function may well be non-computable, and it may be impossible to obtain its result value. — In computer science, term rewriting systems are capable of defining every computable function. A subclass of them, the canonical term rewrite systems, guarantee that every function defined by them can be evaluated in finitely many steps to a unique normal form, i.e. a term that can't be rewritten any further; such terms are considered "values" in this setting. Arithmetical algorithms, for example, can be written as term rewriting systems that are canonical when applied to variable-free inputs, cf. "ground confluent".) - Jochen Burghardt (talk) 20:33, 25 March 2024 (UTC)

"Overriding (mathematics)" listed at Redirects for discussion
The redirect [//en.wikipedia.org/w/index.php?title=Overriding_(mathematics)&redirect=no Overriding (mathematics)] has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached. Tea2min (talk) 11:59, 26 April 2024 (UTC)

Function is Overloaded in definition and meaning, this article should be a survey
The function as relation or mapping in the single and multiple-valued and in classical functions, continuous functions, smooth functions, and about the language of functions, and domains and ranges and images and codomains, is very overloaded. This article is picking a course of opinion which does not represent its wide and varied usage, function the term. Over time, as other aspects of mathematics solidified, it's "function" the term that is most loosely thrown about, then as with regards to relations that are admitted to various sub-fields, each claiming their own definition of function has those are each distinct and different ant not compatible. This article, which could be called "mappings" instead as that's largely what it defines, does not from the outset affect to describe the development of the definition over time, nor does it very well reflect the most usual sort of arithmetic definition with which most people are familiar, or as with regards to domain and range. Mathematics is not merely differential geometry, and the definition of function is among the very most general and general throughout. So, this article should largely start explaining that "function theory" is its own sort of world, and a history and survey of "this is what is called a function historically or in these various settings", then with regards to an opinion of "this is a function today and in the most usual setting", which it is largely arguable that this article does not reflect, instead expect.

It reminds one of "graph", "chart", and "plot", about diagrams of functions, drawing a function.

Functions are modern, and Cartesian thus including the multi-valued, and not just classical functions, smooth classical continuous functions that are single-valued, and not just differential geometry's functions with neither vertical nor horizontal tangent, "functions" in mathematics are very general, and sub-fields that restrict the definition for their own purpose are presumptious that their definition is implicit, where it is not.

This article is opinionated and needs context in itself why the definition of function is so broad that it's about its own sub-field of mathematics, in matters of relation.

This article needs a brief survey of the development of the term over time, and to point to the many different intended interpretations of the term.

This article needs a thorough introduction detailing the survey of the meaning of the term "function" over time as mathematics has grown, and, specifically not removing what has become its fuller definition, in the interest of su-fields that would restrict its meaning for their own purposes in notation, where instead they should declare their own regions of syntax, because general usage does not agree.

This article has problems and hides them. 97.113.179.80 (talk) 15:03, 19 May 2024 (UTC)

 * Are you volunteering to track down a pile of sources and write that draft? –jacobolus (t) 21:01, 19 May 2024 (UTC)
 * Keeping in mind the goal of simultaneously being readable to middle-schoolers and providing pointers to current research-level mathematics... —David Eppstein (talk) 21:03, 19 May 2024 (UTC)

Why Set Theory?
As noted somewhere above, the intent was to introduce something that is usable in schools mathematics courses. Ok, nice. But why not mention it explicitly? Why not say right away (I guess it was before) that this definition is specific for set theories.

Or we could add a section dedicated to the history of the term an the notion. Leibnitz, Newton, Cauchy had no clue about functions being their graphs ("pairs of values").

To me, it's a shame to promote just one specific view of things, the school-level mathematics. It's so XX century, the century were everything was "defined" as sets. These days mathematicians must be familiar with model theory, and see clearly that functions as "sets of pairs of sets" is just a model (in sets).

Vlad Patryshev (talk) 00:38, 17 June 2024 (UTC)

title: Talk:Function (mathematics)


text:
Metalloprotein

Metalloprotein is a generic term for a protein that contains a metal ion cofactor. A large proportion of all proteins are part of this category. For instance, at least 1000 human proteins (out of ~20,000) contain zinc-binding protein domains although there may be up to 3000 human zinc metalloproteins.

Abundance
It is estimated that approximately half of all proteins contain a metal. In another estimate, about one quarter to one third of all proteins are proposed to require metals to carry out their functions. Thus, metalloproteins have many different functions in cells, such as storage and transport of proteins, enzymes and signal transduction proteins, or infectious diseases. The abundance of metal binding proteins may be inherent to the amino acids that proteins use, as even artificial proteins without evolutionary history will readily bind metals.

Most metals in the human body are bound to proteins. For instance, the relatively high concentration of iron in the human body is mostly due to the iron in hemoglobin.

Coordination chemistry principles
In metalloproteins, metal ions are usually coordinated by nitrogen, oxygen or sulfur centers belonging to amino acid residues of the protein. These donor groups are often provided by side-chains on the amino acid residues. Especially important are the imidazole substituent in histidine residues, thiolate substituents in cysteine residues, and carboxylate groups provided by aspartate. Given the diversity of the metalloproteome, virtually all amino acid residues have been shown to bind metal centers. The peptide backbone also provides donor groups; these include deprotonated amides and the amide carbonyl oxygen centers. Lead(II) binding in natural and artificial proteins has been reviewed.

In addition to donor groups that are provided by amino acid residues, many organic cofactors function as ligands. Perhaps most famous are the tetradentate N4 macrocyclic ligands incorporated into the heme protein. Inorganic ligands such as sulfide and oxide are also common.

Storage and transport metalloproteins
These are the second stage product of protein hydrolysis obtained by treatment with slightly stronger acids and alkalies.

Oxygen carriers
Hemoglobin, which is the principal oxygen-carrier in humans, has four subunits in which the iron(II) ion is coordinated by the planar macrocyclic ligand protoporphyrin IX (PIX) and the imidazole nitrogen atom of a histidine residue. The sixth coordination site contains a water molecule or a dioxygen molecule. By contrast the protein myoglobin, found in muscle cells, has only one such unit. The active site is located in a hydrophobic pocket. This is important as without it the iron(II) would be irreversibly oxidized to iron(III). The equilibrium constant for the formation of HbO2 is such that oxygen is taken up or released depending on the partial pressure of oxygen in the lungs or in muscle. In hemoglobin the four subunits show a cooperativity effect that allows for easy oxygen transfer from hemoglobin to myoglobin.

In both hemoglobin and myoglobin it is sometimes incorrectly stated that the oxygenated species contains iron(III). It is now known that the diamagnetic nature of these species is because the iron(II) atom is in the low-spin state. In oxyhemoglobin the iron atom is located in the plane of the porphyrin ring, but in the paramagnetic deoxyhemoglobin the iron atom lies above the plane of the ring. This change in spin state is a cooperative effect due to the higher crystal field splitting and smaller ionic radius of Fe2+ in the oxyhemoglobin moiety.

Hemerythrin is another iron-containing oxygen carrier. The oxygen binding site is a binuclear iron center. The iron atoms are coordinated to the protein through the carboxylate side chains of a glutamate and aspartate and five histidine residues. The uptake of O2 by hemerythrin is accompanied by two-electron oxidation of the reduced binuclear center to produce bound peroxide (OOH−). The mechanism of oxygen uptake and release have been worked out in detail.

Hemocyanins carry oxygen in the blood of most mollusks, and some arthropods such as the horseshoe crab. They are second only to hemoglobin in biological popularity of use in oxygen transport. On oxygenation the two copper(I) atoms at the active site are oxidized to copper(II) and the dioxygen molecules are reduced to peroxide,.

Chlorocruorin (as the larger carrier erythrocruorin) is an oxygen-binding hemeprotein present in the blood plasma of many annelids, particularly certain marine polychaetes.

Cytochromes
Oxidation and reduction reactions are not common in organic chemistry as few organic molecules can act as oxidizing or reducing agents. Iron(II), on the other hand, can easily be oxidized to iron(III). This functionality is used in cytochromes, which function as electron-transfer vectors. The presence of the metal ion allows metalloenzymes to perform functions such as redox reactions that cannot easily be performed by the limited set of functional groups found in amino acids. The iron atom in most cytochromes is contained in a heme group. The differences between those cytochromes lies in the different side-chains. For instance cytochrome a has a heme a prosthetic group and cytochrome b has a heme b prosthetic group. These differences result in different Fe2+/Fe3+ redox potentials such that various cytochromes are involved in the mitochondrial electron transport chain.

Cytochrome P450 enzymes perform the function of inserting an oxygen atom into a C−H bond, an oxidation reaction.

Rubredoxin

Rubredoxin is an electron-carrier found in sulfur-metabolizing bacteria and archaea. The active site contains an iron ion coordinated by the sulfur atoms of four cysteine residues forming an almost regular tetrahedron. Rubredoxins perform one-electron transfer processes. The oxidation state of the iron atom changes between the +2 and +3 states. In both oxidation states the metal is high spin, which helps to minimize structural changes.

Plastocyanin
Plastocyanin is one of the family of blue copper proteins that are involved in electron transfer reactions. The copper-binding site is described as distorted trigonal pyramidal. The trigonal plane of the pyramidal base is composed of two nitrogen atoms (N1 and N2) from separate histidines and a sulfur (S1) from a cysteine. Sulfur (S2) from an axial methionine forms the apex. The distortion occurs in the bond lengths between the copper and sulfur ligands. The Cu−S1 contact is shorter (207 pm) than Cu−S2 (282 pm). The elongated Cu−S2 bonding destabilizes the Cu(II) form and increases the redox potential of the protein. The blue color (597 nm peak absorption) is due to the Cu−S1 bond where S(pπ) to Cu(dx2−y2) charge transfer occurs.

In the reduced form of plastocyanin, His-87 will become protonated with a pKa of 4.4. Protonation prevents it acting as a ligand and the copper site geometry becomes trigonal planar.

Iron
Iron is stored as iron(III) in ferritin. The exact nature of the binding site has not yet been determined. The iron appears to be present as a hydrolysis product such as FeO(OH). Iron is transported by transferrin whose binding site consists of two tyrosines, one aspartic acid and one histidine. The human body has no mechanism for excretion of iron. This can lead to iron overload problems in patients treated with blood transfusions, as, for instance, with β-thalassemia. Iron is actually excreted in urine and is also concentrated in bile which is excreted in feces.

Copper
Ceruloplasmin is the major copper-carrying protein in the blood. Ceruloplasmin exhibits oxidase activity, which is associated with possible oxidation of Fe(II) into Fe(III), therefore assisting in its transport in the blood plasma in association with transferrin, which can carry iron only in the Fe(III) state.

Calcium
Osteopontin is involved in mineralization in the extracellular matrices of bones and teeth.

Metalloenzymes
Metalloenzymes all have one feature in common, namely that the metal ion is bound to the protein with one labile coordination site. As with all enzymes, the shape of the active site is crucial. The metal ion is usually located in a pocket whose shape fits the substrate. The metal ion catalyzes reactions that are difficult to achieve in organic chemistry.

Carbonic anhydrase
In aqueous solution, carbon dioxide forms carbonic acid
 * CO2 + H2O H2CO3

This reaction is very slow in the absence of a catalyst, but quite fast in the presence of the hydroxide ion
 * CO2 + OH− hydrogencarbonate

A reaction similar to this is almost instantaneous with carbonic anhydrase. The structure of the active site in carbonic anhydrases is well known from a number of crystal structures. It consists of a zinc ion coordinated by three imidazole nitrogen atoms from three histidine units. The fourth coordination site is occupied by a water molecule. The coordination sphere of the zinc ion is approximately tetrahedral. The positively-charged zinc ion polarizes the coordinated water molecule, and nucleophilic attack by the negatively-charged hydroxide portion on carbon dioxide proceeds rapidly. The catalytic cycle produces the bicarbonate ion and the hydrogen ion as the equilibrium:
 * H2CO3  + H+

favouring dissociation of carbonic acid at biological pH values.

Vitamin B12-dependent enzymes
The cobalt-containing Vitamin B12 (also known as cobalamin) catalyzes the transfer of methyl (−CH3) groups between two molecules, which involves the breaking of C−C bonds, a process that is energetically expensive in organic reactions. The metal ion lowers the activation energy for the process by forming a transient Co−CH3 bond. The structure of the coenzyme was famously determined by Dorothy Hodgkin and co-workers, for which she received a Nobel Prize in Chemistry. It consists of a cobalt(II) ion coordinated to four nitrogen atoms of a corrin ring and a fifth nitrogen atom from an imidazole group. In the resting state there is a Co−C sigma bond with the 5′ carbon atom of adenosine. This is a naturally occurring organometallic compound, which explains its function in trans-methylation reactions, such as the reaction carried out by methionine synthase.

Nitrogenase (nitrogen fixation)
The fixation of atmospheric nitrogen is an energy-intensive process, as it involves breaking the very stable triple bond between the nitrogen atoms. The nitrogenases catalyze the process. One such enzyme occurs in Rhizobium bacteria. There are three components to its action: a molybdenum atom at the active site, iron–sulfur clusters that are involved in transporting the electrons needed to reduce the nitrogen, and an abundant energy source in the form of magnesium ATP. This last is provided by a mutualistic symbiosis between the bacteria and a host plant, often a legume. The reaction may be written symbolically as
 * N2 + 16 MgATP + 8 e− → 2 NH3 + 16 MgADP +16 Pi + H2

where Pi stands for inorganic phosphate. The precise structure of the active site has been difficult to determine. It appears to contain a MoFe7S8 cluster that is able to bind the dinitrogen molecule and, presumably, enable the reduction process to begin. The electrons are transported by the associated "P" cluster, which contains two cubical Fe4S4 clusters joined by sulfur bridges.

Superoxide dismutase
The superoxide ion, is generated in biological systems by reduction of molecular oxygen. It has an unpaired electron, so it behaves as a free radical. It is a powerful oxidizing agent. These properties render the superoxide ion very toxic and are deployed to advantage by phagocytes to kill invading microorganisms. Otherwise, the superoxide ion must be destroyed before it does unwanted damage in a cell. The superoxide dismutase enzymes perform this function very efficiently.

The formal oxidation state of the oxygen atoms is −1⁄2. In solutions at neutral pH, the superoxide ion disproportionates to molecular oxygen and hydrogen peroxide.
 * 2 + 2 H+ → O2 + H2O2

In biology this type of reaction is called a dismutation reaction. It involves both oxidation and reduction of superoxide ions. The superoxide dismutase (SOD) group of enzymes increase the rate of reaction to near the diffusion-limited rate. The key to the action of these enzymes is a metal ion with variable oxidation state that can act either as an oxidizing agent or as a reducing agent.
 * Oxidation: M(n+1)+ + → Mn+ + O2
 * Reduction: Mn+ + + 2 H+ → M(n+1)+ + H2O2.

In human SOD, the active metal is copper, as Cu(II) or Cu(I), coordinated tetrahedrally by four histidine residues. This enzyme also contains zinc ions for stabilization and is activated by copper chaperone for superoxide dismutase (CCS). Other isozymes may contain iron, manganese or nickel. The activity of Ni-SOD involves nickel(III), an unusual oxidation state for this element. The active site nickel geometry cycles from square planar Ni(II), with thiolate (Cys2 and Cys6) and backbone nitrogen (His1 and Cys2) ligands, to square pyramidal Ni(III) with an added axial His1 side chain ligand.

Chlorophyll-containing proteins
Chlorophyll plays a crucial role in photosynthesis. It contains a magnesium enclosed in a chlorin ring. However, the magnesium ion is not directly involved in the photosynthetic function and can be replaced by other divalent ions with little loss of activity. Rather, the photon is absorbed by the chlorin ring, whose electronic structure is well-adapted for this purpose.

Initially, the absorption of a photon causes an electron to be excited into a singlet state of the Q band. The excited state undergoes an intersystem crossing from the singlet state to a triplet state in which there are two electrons with parallel spin. This species is, in effect, a free radical, and is very reactive and allows an electron to be transferred to acceptors that are adjacent to the chlorophyll in the chloroplast. In the process chlorophyll is oxidized. Later in the photosynthetic cycle, chlorophyll is reduced back again. This reduction ultimately draws electrons from water, yielding molecular oxygen as a final oxidation product.

Hydrogenase
Hydrogenases are subclassified into three different types based on the active site metal content: iron–iron hydrogenase, nickel–iron hydrogenase, and iron hydrogenase. All hydrogenases catalyze reversible H2 uptake, but while the [FeFe] and [NiFe] hydrogenases are true redox catalysts, driving H2 oxidation and H+ reduction
 * H2 2 H+ + 2 e−

the [Fe] hydrogenases catalyze the reversible heterolytic cleavage of H2.
 * H2 H+ + H−

Ribozyme and deoxyribozyme
Since discovery of ribozymes by Thomas Cech and Sidney Altman in the early 1980s, ribozymes have been shown to be a distinct class of metalloenzymes. Many ribozymes require metal ions in their active sites for chemical catalysis; hence they are called metalloenzymes. Additionally, metal ions are essential for structural stabilization of ribozymes. Group I intron is the most studied ribozyme which has three metals participating in catalysis. Other known ribozymes include group II intron, RNase P, and several small viral ribozymes (such as hammerhead, hairpin, HDV, and VS) and the large subunit of ribosomes. Several classes of ribozymes have been described.

Deoxyribozymes, also called DNAzymes or catalytic DNA, are artificial DNA-based catalysts that were first produced in 1994. Almost all DNAzymes require metal ions. Although ribozymes mostly catalyze cleavage of RNA substrates, a variety of reactions can be catalyzed by DNAzymes including RNA/DNA cleavage, RNA/DNA ligation, amino acid phosphorylation and dephosphorylation, and carbon–carbon bond formation. Yet, DNAzymes that catalyze RNA cleavage reaction are the most extensively explored ones. 10-23 DNAzyme, discovered in 1997, is one of the most studied catalytic DNAs with clinical applications as a therapeutic agent. Several metal-specific DNAzymes have been reported including the GR-5 DNAzyme (lead-specific), the CA1-3 DNAzymes (copper-specific), the 39E DNAzyme (uranyl-specific) and the NaA43 DNAzyme (sodium-specific).

Calmodulin

Calmodulin is an example of a signal-transduction protein. It is a small protein that contains four EF-hand motifs, each of which is able to bind a Ca2+ ion.

In an EF-hand loop protein domain, the calcium ion is coordinated in a pentagonal bipyramidal configuration. Six glutamic acid and aspartic acid residues involved in the binding are in positions 1, 3, 5, 7 and 9 of the polypeptide chain. At position 12, there is a glutamate or aspartate ligand that behaves as a bidentate ligand, providing two oxygen atoms. The ninth residue in the loop is necessarily glycine due to the conformational requirements of the backbone. The coordination sphere of the calcium ion contains only carboxylate oxygen atoms and no nitrogen atoms. This is consistent with the hard nature of the calcium ion.

The protein has two approximately symmetrical domains, separated by a flexible "hinge" region. Binding of calcium causes a conformational change to occur in the protein. Calmodulin participates in an intracellular signaling system by acting as a diffusible second messenger to the initial stimuli.

Troponin
In both cardiac and skeletal muscles, muscular force production is controlled primarily by changes in the intracellular calcium concentration. In general, when calcium rises, the muscles contract and, when calcium falls, the muscles relax. Troponin, along with actin and tropomyosin, is the protein complex to which calcium binds to trigger the production of muscular force.

Transcription factors

Many transcription factors contain a structure known as a zinc finger, a structural module in which a region of protein folds around a zinc ion. The zinc does not directly contact the DNA that these proteins bind to. Instead, the cofactor is essential for the stability of the tightly folded protein chain. In these proteins, the zinc ion is usually coordinated by pairs of cysteine and histidine side-chains.

Other metalloenzymes
There are two types of carbon monoxide dehydrogenase: one contains iron and molybdenum, the other contains iron and nickel. Parallels and differences in catalytic strategies have been reviewed.

Pb2+ (lead) can replace Ca2+ (calcium) as, for example, with calmodulin or Zn2+ (zinc) as with metallocarboxypeptidases.

Some other metalloenzymes are given in the following table, according to the metal involved.

title: Metalloprotein


text:
Talk:Dinaric race

serious?
Is this serious? just wondering --AN 19:42 Feb 20, 2003 (UTC)

There is indeed a "Dinaric" type in physical anthropology. Actually, Dinaric types are found throughout the world, but are common in the West Balkans. I am not sure if Slobodan Milosevic is the best example, as he is rather short and stocky he would be more of an "Alpine".

Anyway, this classification is serious (or at least was serious until the 1960's), though of course, most scientists have moved away from these sorts of physical catagories, and now focus on genetic differences among populations.

Other such categorizations include "Nordic", "Alpine", "Mediterranean", and so on. I am sure a lot of people find these highly questionable.

 * It has to be taken into consideration that a HUGE proportion of the world's population is racially mixed to some extent or another, and to say the least that complicates any attempts at classification. Gringo300 10:13, 3 November 2005 (UTC)

You should add that modern Dinarics are the tallest people in the world:

Pineau JC,Delamarche P,Bozinovic S.[Average height of adolescents in the Dinaric Alps] "This study contributes to an update of average heights among European populations. Our investigation covering 2705 boys and 2842 girls aged 17 years, shows that, contrary to the general belief, adolescents of the Dinaric Alps are, on average, the tallest in Europe. With an average height of 185,6 cm, they are taller than Dutch adolescents (184 cm on average). Above all, the density of very tall subjects appears to be characteristic of the Dinaric Alps, since 28% measure 190 cm or more in height, as opposed to only 20% in Holland and 1.5% in France. Although our information is not complete, adolescent girls in the Dinaric Alps, with an average height of 171 cm come a close second to girls in Holland."

Areas
The article mentioned Northern Italy being a Dinaric area. Could the southern regions of Switzerland also be considered as such? And what about Croatia?

 * Italian speaking area of Switzerland are also Dinaric, with some other strains.Croatia is not particulary Dinaric since Dalmatia is mostly Atlantid while the Zagreb centered area of Zagorje is mostly Alpine with some Nordic and Dinaric strains.Alpines are also the main population of Croatia's Slavonia region.
 * Are the Czech Republic, Slovakia, and Hungary also Dinaric areas?
 * Came across this information from http://med1nuc11.dfc.unifi.it/linnets/troe/texts/p36.htm:
 * Although the Czechs themselves are predominantly Alpine, the Moravians and Slovaks are frequently Dinaric.
 * As for the Hungarians, haven’t found anything yet.

Not found in Hungary? Hahaha! I live in Hungary, and the Dinarid relatively common in Hungary (mostly Southern Transdanubia), but Budapest and Northern Hungary mostly Alpinid, Baltid with some Nordid influence. — Preceding unsigned comment added by 62.165.206.39 (talk • contribs)

softeners
It seems that "We are all the same" crowd took over the article, with the usual softeners and euphemisms and other PC jargon acrobations.As long as we all pay cash, we are all equal, right?A head,two arms, two legs, five fingers each and you are good at everything like everybody else.......

 * I'm not sure what an "acrobation" is, but I don't see any PC jargon here. As far as I am aware the concept of a "Dinaric race" is not used in modern anthropology. However, if you have examples of mainstream professional modern usage, add them. The main criticism of the concept that's included here comes from the notoriously PC Carelton Coon! Paul B 11:20, 2 March 2006 (UTC)

Serbia, or Montenegro?

 * According to the Dinaric model, Dinarics are to be found today in the mountainous areas of the western Balkans (Croatia, Bosnia and Herzegovina, Serbia and Montenegro, most of northwestern Bulgaria, northwestern Republic of Macedonia and northern Albania).

Between Serbia and Montenegro, would it be safe to say that mountainous Montenegro is the more Dinaric of the two? I’m asking because we may soon have to replace Serbia and Montenegro with simply Montenegro once the latter officially declares independence, and because Serbia from what I know is mostly plains, except for Kosovo.

 * I see that Serbia and Montenegro in that quoted passage was split into Serbia and Montenegro. However, given that Serbia is relatively flat (and the passage states that Dinarics are found mostly in the “the mountainous areas of the western Balkans”), do we still need to include it in the enumeration, or should we remove it?

 * [[Image:Deniker's Races de l'Europe (1899).jpg|thumb|250px]]

Well it's difficult to say. Deniker's orginal map seems to exclude most of Serbia, but Serbia is left white, and thus not allocated to any labelled "race" at all, as you can see (click image to enlarge). Paul B 10:54, 26 May 2006 (UTC)

 * Serbians living in the political entity 'Republic of Serbia' are predominantly Dinaric, although to a certain extents they represent the southeastern periphery of the Dinaric race, and also place of settlement of many Serbs from Montenegro and other more uniformly Dinaric areas.Günther's, Coon's, maps and studies of that particular area seem to suggest that at least the single most prevalent type among these Eastern Serbs is that of Dinaric race, with several other Caucasoid variants also present in the population.

 * Off topic, it is a pity for the science that these categorizations have been abandoned for the several last decades, when it is obvious that even a layman may easily categorize various Caucasoid variants at a glance, after studing several classic books on the subject. A tour over Europe would quickly confront any skeptic with the fact that these categories ,indeed, do exist, both as pockets of populations, in transitional zones, and as more compact, simmilar stocks over wider areas. —Preceding unsigned comment added by 80.77.159.210 (talk • contribs)

 * The "Dinaric race"-concept can be really valid, when viewed genetically. Dinarics are the "cleanest" descendants of paleolithic hunters of the gravettian culture, who found a refuge around the Adriatic Sea in the end of the last ice age. This is obvious from the fact that the area with the most dense presence of the "Dinaric race" has the highest percentage of Y-haplogroup I. But don't worry, the old concepts will be revived again, after the social utopias created by Pc egalitarians crash everywhere in the world.Centrum99 09:04, 20 November 2006 (UTC) Centrum99 09:04, 20 November 2006 (UTC)

Sources? Direct copy?
There are no sources other than a Franz Boas reference at the end, but the 3rd and 4th and last paragraph all sound as if they come directly from a textbook. Should these sections be in block quotes? Where is this outdated material coming from, anyway?--Parkwells (talk) 00:46, 19 November 2007 (UTC)

 * The article is quite clear about the sources for the idea - originally Deniker and then Günther, Coon and the other usual-suspects among mid-20th century anthropologists, including text books such as Meyers Blitz-Lexikon. Coon wrote about "dinarics" repeatedly in the Races of Europe and numerous essays ("Occipital flattening among the Dinarics") etc. I don't know if the passage in the middle is a quotation or not. I did try to find out if it was a while ago, but couldn't find a source. Paul B (talk) 09:18, 19 November 2007 (UTC)

 * What I meant was that some of those paragraphs sounded like direct quotes from an early 20th c. encyclopedia or textbook. I think the article needs to be supplemented with at least a paragraph or more about how this approach was discredited, or why contemporary anthropologists don't use it - what was the criticism or new information.--Parkwells (talk) 13:10, 19 November 2007 (UTC)

 * Yes, I knew what you meant. That's why I said "I don't know if the passage in the middle is a quotation or not. I did try to find out if it was a while ago, but couldn't find a source." It sounded cut-n-pasteish to me too, but I could find no evidence that it was. Maybe I just didn't look hard enough. I don't think the idea was ever discredited as such. It just came to be seen as largely useless. Even Coon eventually uses the term simply to mean nothing more than a local "type". It wasn't killed off so much as died out. Paul B (talk) 15:10, 19 November 2007 (UTC)

I am Shocked by the use of the word race since genetic proved that their is but one Human race, and therefore I propose that all race word should be changed by ethny...

any comment? —Preceding unsigned comment added by 82.124.254.206 (talk) 15:01, 30 April 2009 (UTC)

 * It's called a race, like it or not. Paul B (talk) 22:25, 30 April 2009 (UTC)
 * I am shocked that people can't use their own brain and parrot these demagogic, ideological statements over and over again like a hypnotized herd of sheep. Centrum99 (talk) 23:50, 9 March 2011 (UTC)

Really no genetic basis?
"The Dinaric race (or Adriatic race or Epirotic race) is one of the sub-categories of the Europid (White; Caucasian) race into which it was divided by physical anthropologists in the early 20th century. Such racial typologies have been increasingly criticized for several reasons, especially since the rise of molecular anthropology."

A funny statement, really, considering that genetics clearly showed that Dinaric highlanders are predominantly Slavicized Paleolithic autochthons, former bearers of the Gravettian culture. Centrum99 (talk) 22:40, 11 February 2011 (UTC)

 * Bully for them. Does being "Slavicized Paleolithic autochthons" makes them a race? I thought almost all Europeans are "Paleolithic autochthons". The French are Latinized Paleolithic autochthons. The British are Anglicized Paleolithic autochthons.... Paul B (talk) 17:27, 12 February 2011 (UTC)
 * Dinarics are not a race, but an easily defined anthropological type. Centrum99 (talk) 23:41, 9 March 2011 (UTC)
 * What I find especially funny is that molecular anthropology rather supports these racial typologies - because every distinct physical type developed due to a founder effect and long isolation. And this is clearly visible in DNA. If Dinarics were isolated much longer from their neighbours, they would inevitably developed into a separate race. I wonder, if authors copying these obsolete statements from the beginnings of population genetics actually check, what has changed in the meantime. Centrum99 (talk) 23:48, 9 March 2011 (UTC)

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Pseudoscience and Present Tense
Why is this article so often in the present tense? This is racist pseudoscience masquerading as modern data. Steven Carleton Coons, who is referenced heavily throughout the page as a reliable source, was discredited during his own lifetime (according to the first paragraph in his own Wikipedia page!). This page needs major cleanup, as many of these contributions are blatantly racist. R2Unit (talk) 22:25, 21 June 2024 (UTC)

title: Talk:Dinaric race


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National Foundation for Educational Research

The National Foundation for Educational Research (NFER) is an educational research charity which creates a range of insights on educational policy and practice that aim to strengthen practice in the classroom and inform and influence policymakers and other key decision makers.

NFER’s expertise covers a wide range of education topics, issues and research methods, including:

 * Accountability
 * Assessment Classroom Practice
 * Education to Employment
 * Social Mobility
 * School Funding
 * School Workforce
 * Systems and Structures
 * Covid-19 Recovery

NFER’s research experts are divided up into six teams:

 * Centre for Assessment
 * Centre for Policy and Practice: Programmes
 * Centre for Policy and Practice: Development
 * Centre for Research Planning and Knowledge Management
 * Centre for International Education
 * Centre for Statistics

NFER also have teams who conduct a wide range of data management activities, design and develop a range of evidence-based products and services for schools and conduct a significant number of education related randomised controlled trials, surveys and evaluations. These activities are undertaken for government departments and agencies, and other non-profit organisations around the world. The Foundation also undertakes a range of internally funded projects exploring the key issues in education.

NFER’s clients include government departments and agencies at international, national and local levels, third sector organisations, private and public companies, employers and other organisations with an interest in education. The independent, not-for-profit organisation invests any surplus funds directly back into its programme of research to address key questions in education.

Originally founded in 1946 as the Centre for Educational Research and Development in England and Wales, NFER's head office is located in Slough, with a separate regional office located in York.