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Post by mrsonde on Jul 20, 2018 19:33:30 GMT 1
Let's start with this one:
Then this one:
Then this one:
Then this one:
Then this one:
Then this one:
Then this one, yet again, after several years of repeated asking:
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Post by jean on Jul 20, 2018 20:23:28 GMT 1
It shouldn't matter how large the "intuitive correction" is, should it? Yes, because if it were larger than the interval of a semitone, it would be notated differently. Because the octave doesnt't divide into twelve so perfectly that any one tuning scheme will do in all contexts*. Hence the approximation that is equal temperament, for example (other temperaments are available.) Singers (if unaccomanied by a fixed-pitch instrument like a piano) don't have to abide by its restrictions. You're 'correcting' it to what fits in the harmonic context it finds itself in. I have never claimed that the science behind what musicians do by instinct isn't important, or isn't understood. Just that there's much more to music than its physical basis. I've explained this to you many times already. Now stop wasting my time, and find those threads yourself if you want to learn more. * This may help.
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Post by mrsonde on Jul 20, 2018 21:56:16 GMT 1
Yes, because if it were larger than the interval of a semitone, it would be notated differently. Nope. Only if it's in the same octave. If it's not - and the vast majority of music of any interest at all is not - then there's no way to notate it differently. Is there? You can do what Irving Berlin did, I suppose - always use the same key, and only compose using the black notes. But anything more complicated than the pentatonic that ranges acorss two or three or more octaves and you soon run into trouble - the only way to semi-solve such harmonic dissonances, following indicated intervals, is to diacritically mark the notes, like Porter or Bernstein and a host of others did, up or down; or artifically announce a key change, as was the common Russian practice, when actually there's no key change at all. But, I repeat, this is besides the point. Why, if your theory is true, is there any sized correction at all? Why not? If it's a collection of arbitrary intervals? It doesn't have to be "perfect" - there is indeed no such quality, is there? According to you - something you've insisted, time and time again? Even in this simplest of musical basics you reveal your incomprehension - the Western scale has nothing to do with dividing the octave, into twelve or any other number. The attempt to approximate to it by equal temperament does, the various atonal temperaments do - but what are they being "corrected" to, by any instrument player other than a pianist? Not to an octave that's been arbitrarily "divided". It's to a scale - including the octave - that has been harmonically discovered, a discovery that took thousands of years to fully formulate and wasn't clearly understood until the 19th Century. (And, to correct yet another of your comical misapprehensions, the "modes" come from this discovery of uneven division of an octave, not the other way around!) It exists, has always existed, it's a discovery, not an invention; and this is what is intuitively "known" by any musician. The problem is the theory does not match this knowledge - it doesn't even try to. Approximation to what? Yes, all sorts of temperaments. But what are they approximating to? Why not? Why "restrictions"? The what context? You and your panel of experts say you don't know what "harmonic" means. You now admit this is what you're correcting the score annotated according to intervals to? No - what you have very vigorously and insultingly objected to, from the start, is my very innocuous unobjectionable claims about the way music is taught in this country, and throughout most of the West. I have stated that the harmonic basis of music, fully discovered in the late 19th Century, has been ignored except for in a dry opening chapter to any music textbook. Thereafter it's never referred to again. Instead a music theory and its notation system that derives haphazardly with all its panoply of ad hoc rules and conventions from the 15th and 16th Century is used - quite hopelessly if anyone seeks to understand how music - its scale, its history and evolution, its progressions, the chords that musically "work" - is constructed. This is what you've objected to, with all your usual barrage of insults. And now you finally admit that harmonic relations between notes is what is intuitively "known" by any musician, so much so that they instinctively correct the scores that fail to convey them. Liar. Utter, blatant, pathetic lie. You have always denied that harmonic relations have anything to do with it. You've claimed that music theory doesn't even use the term. The panel of R3 "experts" you creepily dragged in for your support claimed they didn't even understand the term. So, if you believe you've "explained this many times already", you can give a brief description of how such a harmonic relationship works, can't you? You'll be intimately familiar with such a notion. So - the harmonic relationship between a fifth and a fourth, for the most basic of examples? (In C, from the tonic, before you start to equivocate.) Whatever the "context"? And now explain why if this was followed by a second, (in the same octave!), unless it was followed by a third (which would never happen, or the fourth wouldn't have been there, even in the most free-flowing jazz) you'd follow an inexorable push to flatten that note, even though there's no such indication on the score - and no conventional way to so indicate? Let's see if you can do that: when you have to admit you can't, miss know-it-all, then at last you might have the humility to realise you need to start learning about the foundations of music theory! Proper music theory, that's based on harmonic facts, rather than the "music theory" taught in textbooks - because there is no explanation for this simple universal fact, or any of the hundreds of such facts like it, in those textbooks! Nothing to learn from you! You've made it abundantly clear, always, that how music works is a complete mystery to you: you don't know the first thing about it, even the basic 19th Century science that any first-year student will have learned in their first week. You've taken years to admit you made the simplest of errors from the start. Except you're too much of a blustering liar to even confess that!
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Post by jean on Jul 21, 2018 9:50:11 GMT 1
Yes, because if it were larger than the interval of a semitone, it would be notated differently. Nope. Only if it's in the same octave. If it's not - and the vast majority of music of any interest at all is not - then there's no way to notate it differently. Is there? Nick, you do know that's nonsense, don't you? Let's keep it simple. First, you need to get it into your head that the written notation of any one note indicates a pitch which will vary very slightly according to the context (except of course in the case of a fixed-pitch instrument). Let's take a note. Let's call it C. If the variation necessary to accommodate it to its harmonic context were more than a semitone higher than seemed to be indicated by the notation, (which in practice it never is), the note would be written C#. It's that simple.A terrible and fundamental misunderstanding here. Think of the distance between one octave and the consonance at the octave above as a continuous stream of sound - you can do it yourself as a glissando. Our Western scales give twelve fixed points on this stream. This division into 12 semitones isn't arbirtary, but neither is it the only division possible.
Read the article I linked to above - I think it really will help you to understand. Historically, this is demonstrably untrue, so I don't know why you keep repeating it. Oh, and just one more thing, before I lose the will to live. Nobody ever said that. Someone questioned the fourth harmonic, that's all. I've pointed out before that harmony/harmonic has a range of meanings, which you need to keep distinct if you want to communicate anything. Of course I can. But it's all here on the board, so I'll let you do the work and find the relevant posts yourself.
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Post by mrsonde on Jul 21, 2018 11:40:07 GMT 1
Nick, you do know that's nonsense, don't you? If it was, you could simply point out the notation convention used. There isn't one. It doesn't have any choice! If the variations in the pitch required - not indicated by the score in any way - were not adopted by the musician, it would sound awful. In practice it often is. As I said, only if it's in the same octave. In an adjacent octave, the "variation" required is often more than the pitch change between, say, C and C# in the octave you've moved from. This is just a simple fact. If that variation were not made, any listener would say: you're playing the wrong note! Well? Now, at last, you've finally admitted that the correct harmonic relation is what determines the correct note, rather than its interval. This is what you refused to acknowledge for years. So - now I have no idea what you're arguing about. Do you? Yes, it's yours. Now it does. It was five once, then six, then seven, then eight, then, roughly around the time this hopelessly inadequate musical notation system was invented, it was nine. And, as you've only just finally admitted, these points are not fixed at all! For the umpteenth time of trying to get this through your recalcitrant head - they are only so fixed on the piano, and they are not, except by chance, even in the right "point" to begin with! Obviously! You can make a scale however you choose, and people and whole cultures often have. No thanks. You've suckered me into wasting my time often enough in the past. If there's anything you consider relevant in it to what you wish to say, but for some reason seem incapable of doing, paste it, and I'll respond - waste your own time, thankyou. I understand, thanks. It's you who doesn't. Finally you acknowledge that the Western scale "is not arbitrary", even though you've insisted it is over and over for years. So - do tell us, in what way is it not arbitrary? If you're a bit lost, simply go back to any of those threads you're so concerned about aren't finished - I've explained it to you in face of your denials until I'm blue in the face. As I've explained to you also, again and again, there is no historical evidence that could possibly support your bizarre theory. If anyone didn't know this before, they certainly do so now, because yet again you're totally unable to offer such "demonstration", simply assert that it can be done, if you could be bothered to be so condescending, presumably. There is no possible demonstration of such a patently false idea, as I've pointed out to you at least a dozen times. There's a contention that this is what happened by a writer in antiquity which is simply repeated thereafter. Pure speculation, with no evidence for it whatsoever. And, of course, given that our scale is not arbitrary, as you've just finally admitted, but based on the physics of sound, quite obviously it predates any invention of purely conventional systems like the ancient modes. A rainbow has its colours in a certain order not because the ancient Greek poets decided that's the way they first decided was aesthetically pleasing to them - they're in that order because that's the way the world works. I can find the quote easily enough. "Questioning the fourth harmonic" would certainly be shocking enough from soi-disant "music experts" - though not surprising, seeing as harmonic theory is dropped as soon as a brief discussion of Helmholtz's discoveries are covered in chapter one of any music theory textbook - but your panel claimed not to know what the word harmonic meant! You've done so yourself often enough. And I've pointed out to you before that this is nonsense, if taken literally. The "range of meanings" is no more complicated than the various ways the words resonance/resonant can be used. No distinction of differing meanings is required - certainly not when discussing how music works! It's science madame - physics. Sigh. You lie again. You haven't a clue. And you never have had. It's a very simple question, Jean, requiring a one-sentence answer. It's the basics of music - and you're totally unable to even begin answering.
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Post by jean on Jul 21, 2018 12:36:53 GMT 1
As I said, only if it's in the same octave. In an adjacent octave, the "variation" required is often more than the pitch change between, say, C and C# in the octave you've moved from. This is just a simple fact. If that variation were not made, any listener would say: you're playing the wrong note! Complete and utter nonsense. Please give an example, from any score of your choice, where a written C must be sung or played as a C#. Or take any other note you like. Try ChoralWiki for your example, where there's a range of out-of-copyright scores you can quote from freely. Of course I'm not saying that. I never have. I've pointed out time and again that there is no opposition between harmonic relation and interval. For whatever reason, you persist in seeing two systems at variance with each other. Exactly. That's what I keep telling you. No thanks... If there's anything you consider relevant in it to what you wish to say, but for some reason seem incapable of doing, paste it, and I'll respond[/quote] See my next post. How long ago did I advise you to turn to the Liber Usualis and look at the chants there, each of them helpfully ascribed to the mode it is based on? The evidence is the actual music written. I'm not talking about the ancient modes. I never have been, except to point out that they're not the same as the ones the medieval theoreticians were writing about, whatever nams they gave them.The scales don't have their intervals in 'no special order,' nobody's claimed that. But the colour bands on a rainbow have fuzzy edges, had you not noticed? That's where the analogy ends, though. We can't show that slightly different points in the fuzziness would ever need to be selected so as to enable the colours to harmonise better with each other, because we don't use rainbows that way. And have you still not understood that the modes are scales? The diatonic major and minor are the ones that have survived from that system when the others fell into disuse. (I've explained why this happened.) Please do! And I've pointed out to you before that this is nonsense, if taken literally. [/quote]Wrong again. The everyday meaning and the purely scientific shouldn't be confused - if you want to be understood, that is. (This is discussed at length on one of the old threads. I am sure you can find it for yourself.)
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Post by jean on Jul 21, 2018 12:48:27 GMT 1
This much will do to start with. Read on for something avout a nineteen-note scale. And note how we have to choose to tune the interc=vals so as to 'make the octaves exact'. Why 12 notes to the Octave?
Any moderately curious person will ask themselves at some point why, in western music, is the octave divided into 12 'semi-tones'. From a mathematical point of view, we can easily explain why 12 works nicely.
The Greeks realized that sounds which have frequencies in rational proportion are perceived as harmonius. For example, a doubling of frequency gives an octave. A tripling of frequency gives a perfect fifth one octave higher. They didn't know this in terms of frequencies, but in terms of lengths of vibrating strings. Pythagoras, who experimented with a monochord, noticed that subdividing a vibrating string into rational proportions produces consonant sounds. This translates into frequencies when you know that the fundamental frequency of the string is inversely proportional to its length, and that its other frequencies are just whole number multiples of the fundamental. (actually, the notion of consonance is more complicated than rationality- see, for example, this fascinating article ).
First, we should examine what ratios are "meant" to exist in the western scale. The prominence of the major triad in western music reflects the Greek discoveries mentioned above. Starting with the note C as a fundamental, we get the major triad from the 3rd and 5th overtones, dropping down one and two octaves respectively, obtaining ratios of 3/2 (G:C) and 5/4 (E:C) respectively. Two other prominent features in western music include the V I cadence, and the I,IV,V triads. Both reflect the importance of the 3/2 ratio, with the IV further taking into account the reciprocal of 3/2, namely 2/3 aka 4/3. Musically, the reciprocal ratio corresponds to going down rather than up. While 3/2 corresponds to going up a fifth, 2/3 corresponds to going down a fifth, and 4/3 corresponds to going down a fifth and up an octave. Together, 3/2 and 4/3 divide the octave, so that going up by 3/2 followed by 4/3 gives an octave.
The IV and V triads give us the four new notes, B and D of G,B,D, and F and A of F,A,C. Their ratios, relative to C are 15/8 for B, 9/8 for D, 4/3 for F, and 5/3 for A. The notes formed from the I,IV, and V major triads produce the C major scale: C D E F G A B C. Throwing in reciprocals for each of these intervals yields all the intervals that made up western music until the rise of chromaticism.
1/1 unison C 2/1 octave C
3/2 perfect fifth G 4/3 fourth F 5/4 major third E 8/5 minor 6th Ab
6/5 minor 3rd Eb 5/3 major 6th A
9/8 major 2nd D 16/9 minor 7th Bb
15/8 major 7th B 16/15 minor 2nd C#
While this list of intervals does include a few of the most basic intervals and their reciprocals: unison, perfect 5th, major 3rd, major 6th = 3rd above a 4th (or also a 4th above a 3rd), major 2nd = a 5th above a 5th, and major 7th = a 3rd above a 5th (or also a 5th above a 3rd), some obvious ones are missing (such as 7/4, 25/16 = a 3rd above a 3rd, or 9/5 = a fifth above a minor 3rd).
The tritone (such as C to F#) is also omitted from this list, an interval that did not affect the evolution of the western scale as it was not used in western music until twelve note chromaticism had become firmly established. Actually, a tritone refers to two different possible intervals:
7/5 tritone 10/7 also called a tritone.
The idea behind twelve is to build up a collection of notes using just one ratio. The advantage to doing so is that it allows a uniformity that makes modulating between keys possible. Without a compromise most keys would be unusable as most of the basic intervals would not be captured in the different keys (see the table at the end of this essay).
Unfortunately, no one ratio will do the trick exactly. However, the ratio of 3/2 happens to work reasonably well using 12 steps. With 3/2 as the basis for the scale, none of the above ratios besides a unison, fifth, and major 2nd are captured exactly.
However the most important constraint- namely that we get a repeating pattern going up in octaves, is almost satisfied by this scheme. Namely, after 12 applications of the ratios 3/2, we come back very close to where we started from (always dropping down by an octave, i.e. dividing by 2, each time the ratio exceeds 2):
(3/2)^0 = 1 (3/2)^1 = 1.5 (3/2)^2 = 1.125 (after dividing by 2) (3/2)^3 = 1.6875 (after dividing by 2) (3/2)^4 = 1.2656 (after dividing by 4) (3/2)^5 = 1.8984 (after dividing by 4) (3/2)^6 = 1.4238 (after dividing by 8) (3/2)^7 = 1.0678 (after dividing by 16) (3/2)^8 = 1.6018 (after dividing by 16) (3/2)^9 = 1.2013 (after dividing by 32) (3/2)^10 = 1.8020 (after dividing by 32) (3/2)^11 = 1.3515 (after dividing by 64) (3/2)^12 = 1.0136 (after dividing by 128)
we have returned close to where we started from. (these 12 frequencies correspond to the circle of 5ths. Starting from C, we then get G D A E B F# C# Ab Eb Bb F and back to C).
The chromatic scale reflects this fact. In the 18th and 19th centuries, the chromatic scale was tuned using the idea of 3/2. In the most elegant of these, Thomas Young's tuning, several of the fifths were set exactly to 3/2, and the others were tempered slightly (to make octaves exact).
In the modern equal temperament (which came into practical use during the early part of the 20th century), all fifths are tuned to 2^(7/12)=1.49651..., slightly less than 3/2, and 12 repetitions of this ratio gets us back to where we started (after dropping down 7 octaves)...www.math.uwaterloo.ca/~mrubinst/tuning/12.html
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Post by mrsonde on Jul 21, 2018 13:04:57 GMT 1
I must dash out for a while Jean, but I'll respond to your posts, whatever they say, sometime later. I do hope you've managed to respond to at least some of the points put to you this time? At a glance - I do hope you're simply not just cutting and pasting standard but irrelevant discussions of musical scales from the internet, are you?
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Post by jean on Jul 21, 2018 13:16:28 GMT 1
You invited me to cut and paste matter I found worthy of discussion, so that's exactly what I did.
If it is irrelevant, you'll be able to explain how.
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Post by mrsonde on Jul 21, 2018 13:19:37 GMT 1
As I said, only if it's in the same octave. In an adjacent octave, the "variation" required is often more than the pitch change between, say, C and C# in the octave you've moved from. This is just a simple fact. If that variation were not made, any listener would say: you're playing the wrong note! Complete and utter nonsense. Please give an example, from any score of your choice, where a written C must be sung or played as a C#. Just a quick correction, before I go however: But I didn't give that example, you did. And you fail to understand what I did say completely, as ever, because you can;t be bothered to ever read properly! The written note is not played as another note! As you yourself finally admit, the musician makes the variation required - not to another note on the scale, which if such was indeed required would be written as such, simply an adjustment in pitch, up or down. Now, between octaves, this variation can quite often be more than what is counted as a semi-tone, within the octave you're moving from. In terms of the actual sound - the pitch adjustment required. You understand now? An annotated interval, changed without direction by any singer or musician, apart from a fixed-string player, by a pitch alteration of more than a semi-tone value. I don't need to find such examples on any score. I'll give you a clear and simple instance when I return, and I find the standard pitch values, simply from the mathematics of the musical scale - I've done this before, when you simply ignored it entirely, as is your habit.
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Post by mrsonde on Jul 21, 2018 13:22:26 GMT 1
You invited me to cut and paste matter I found worthy of discussion, so that's exactly what I did. If it is irrelevant, you'll be able to explain how. Good - I'll respond to any point you've made, when I get back. You have made a point, have you? Or the writer of this article has, at least? I do hope so, and it is not, as I strongly suspect, entirely divorced from anything we've been discussing.
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Post by jean on Jul 21, 2018 14:00:22 GMT 1
...But I didn't give that example, you did. You didn't give any example! In practice it would be, if its pitch varied by as much as a semitone from the note as written. If the adjustment is as large as you think it can be, then it is a different note. I have no idea what you mean by between octaves. This is new terminology unknown to practising musicians or even musicologists. You do if you want anyone to understand what you are talking about. I would like to see it in the context of an actual piece of music, please. In standard notation. Remember, what we were talking about when this first came up was the failure of standard notation to give any sort of guide as to the pitch that should be sung or played. You claimed to have devised a much better system of notation, but failed to give an example.
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Post by mrsonde on Jul 21, 2018 15:29:19 GMT 1
Huh? These are truly remarkable voltes faces. But they are at variance with each other! You've just admitted it! And, further, you've admitted that the prescribed interval is what is corrected, to the correct harmonically determined pitch! Not that I've ever laboured this rather minor point. It's of no real significance - as long as the real workings of music is understood. The problem is, it isn't. The whole of Western musicology, as taught in every college, is based on the interval theoretical structure. The harmonic basis is, as I've said from the start, barely mentioned, and certainly never explored. Thus learning and understanding music is ludicrously unnecessarily difficult - the foundation is wrong. Most musicians - by which I mean people who sing, and people who play instruments, the vast majority of them, both amateur and professional - give up on such an incomprehensible hotchpotch of dubious theory, piled on with its subsequent necessarily ad hoc rules and conventions, which quite literally make no sense. Most don't even bother learning the absurdly inadequate 16th Century notation system - there are plenty of other better systems around, after all. The very close analogy I would draw here is between the Four Elements theory of the Greeks and modern atomic theory. The Four Elements theory does not strictly speaking contradict modern physical chemistry - they're not especially "at variance" with each other. But this is not to say they're not different, or that one is not a vastly superior understanding than the other. Music is not based on a ladder of intervals - the idea is simply wrong. You can make it work after a fashion if you insist it is, as most textbooks still do, by squeezing the facts into it and ignoring the bulgy bits that refuse to cooperate. Or you can realise that the whole theory was a mistake - actually, music is based on harmonic relations, which produce ladders of intervals, rather than vice versa. Then, with this superior replacement theory, one can begin to explore what can be done with it - like understanding why certain music works, and certain other "music" doesn't, how it is really constructed, how to construct different sorts of music, that depart from standard intervals but are still based properly on harmonic relations, and so forth. It's a liberation for anyone writing music, a genuine realisation for anyone wishing to understand it, and a key of thank-the-lord simplicity for anyone trying to learn how to play music. That's your level of "expertise", is it, you believe? "Telling" someone who grows oranges there are other fruits besides apples? As I keep telling you whenever you raise this utterly fatuous point, the fact that you're free to invent whatever sort of scale you wish does not negate the fact that the Western scale is grounded in mathematically simple reality - unlike these other scales, this one wasn't invented, it was discovered. There's room for slight variations in the higher harmonics for this to still be true - minor differences, such as Japanese or Indian scales. But not the atonal scales - they don't work, because they've only managed to accidentally preserve the key harmonics of the scale, and supplemented them with others too attenuated to be satisfying as harmonically strong. As I no doubt said then, that music is 11th Century at the earliest. You believe the foundations of music were invented sometime around 1,000 AD, do you? The same sort of evidence that demonstrates the world is made of four elements. Just as true if you're talking about medieval modes, obviously! It's all irrelevant, I'm afraid, interesting to you and your hobby though it might be. The shocking news is thta music - and music theory - existed for many millenia before these modes. It existed all around the world, in fact, in every culture ever encountered, in places that have never heard of any "modes". That wasn't the point, even allowing for your lousy grammar. See above - the Western scale is a discovery, not an invention. Intervals do - but harmonic relations do not. That's why you correct the intervals notated. You getting it now? On the contrary, that's exactly how we use rainbows - the colours in them, anyway. Something else you've never heard about, thought about, or explored, presumably. You and your f*#king barmy ideas about "the modes"! All right - one more time, for old time's sake. So you believe the modes use different harmonic relations to construct their scales, do you? Tell us what they are, please do! Ffs. Okay - my bookmark probably still survives, somewhere. I've never used the "everyday meaning" in these discussions, if ever, whatever you might take that to be! I doubt if I've ever even used the term "harmony" - not in any context where anyone could possibly misunderstand what I was referring to. Presumably, you got confused because you weren't sure whether I was talking about hair shampoo, or something? I remember - you didn't understand what "harmonic" meant. I'm not sure you do now, but that's not my problem. In a discussion about the science of music, you somehow imagined I was using the term in some metaphorical, poetic sense, and got discombulated. I hope you're feeling a little more with it in the intervening years. It's really not a difficult word to grasp, as physics terms go.
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Post by jean on Jul 21, 2018 17:08:00 GMT 1
But they are at variance with each other! No, they're not. Remind me again, how many years have you spent studying in a conservatory?Untrue of classical musicians. If you want to exclude them from the discussion because (as I think you said once) they are a minority, there is no point in my discussing any of this with you because classical music is what do and what I know about. Entirely untrue of classical musicians. They all play from a score in standard notation. What do you think is on those music stands they have in front of them? And if you could look over their shoulders, you'd see it was in standard notation. It always is, since tonic sol-fa fell out of favour in the early years of last century. Soloists (especially) sometimes sing or play in public without a score, true. But they've learned the piece from a score in the first place. Such as? All you're doing here is giving yourself a spurious justification for dismissing music you don't like: Well you think they don't. Others disagree. And yet, as so often, we have assertions without any evidence whatsoever! Well, not exactly. Have you read that article yet? No, that's not what I'm saying. But I do believe the eleventh century was chronologically prior to the eighteenth. Don't you? Well, obviously. But as far as Western music is concerned, the modes are an improtant stage in its development, and precede the diatonic scale. I always was, but you aren't. In the case of the rainbow, the fuzzy edges are there in the physical manifestation of the phenomemnon. As they are in the notes of the scale. The notation we use is the nearest we can get to a representation of a note in any harmonic context. There will be small adjustments in different contexts, of course. That was well known, even before Helmholtz. On the contrary, that's exactly how we use rainbows - the colours in them, anyway. Something else you've never heard about, thought about, or explored, presumably.[/quote] Well, I didn't know that, but it's very interesting, and appears to reinforce what I said rather than contradict it. Tell me more. You and your f*#king barmy ideas about "the modes"! All right - one more time, for old time's sake. So you believe the modes use different harmonic relations to construct their scales, do you? [/quote]No. I've never said that. They made use of different intervals fronm those used in the diatonic scale - the semitones were in different places in the sequence. They didn't need to worry too much about harmonic relations though, because in those early days most music was monophonic. Problems started to arise as polyphony developed, which hastened their demise. But that's another story
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Post by mrsonde on Jul 21, 2018 17:19:57 GMT 1
This much will do to start with. Read on for something avout a nineteen-note scale. Hmmm...and what is it that you wish me to respond to? What point are you trying to make with this standard piece of music textbook theory? I'm pretty certain I've answered it before - or one remarkably similar to it. It's fairly harmless, though scattered with serious historical errors and, of course, the very "Four Elements" theoretical mistake I've just mentioned. If you believe this theory, yes you do. As I pointed out, there are all sorts of facts that don't fit with this theory - this is just one of the less serious. Wind pipes almost certainly came first, actually - we know this. Divisors. This is the standard theory of how the scale arose - it was formulated in the 18th Century, and projected back onto Pythagoras (without of course a scrap of evidence.) What the Greeks meant by "the circle of fifths" is not this C18th theory at all. The pentatonic was without a shred of a doubt discovered before all this multiplication business - you get a pipe, you make holes in it where the resultant sound is good, you have your pentatonic. Double or halve the pipe and you have the octaval relations. This is how every culture ever investigated has discovered the pentatonic - including cultures that have yet to develop arithmetic. The other notes of the diatonic doubtless came about in the same way - especially when you consider that these do not work with this C18th hypothesised method - the calculations go awry within a couple of octaves. The chromatic arises in the same way - there's no reason at all to suppose it didn't, anyway. These are the strongest harmonic relationships when you decide you want a 12-note scale. A very good reason for that - a simple mathematical reason. Not really. If anyone ever did have such a bizarre idea, it's a non-starter. Unfortunately for this theory, the 12-note scale existed before such modulation was ever felt as problematic. That arises with the development of fixed-string instruments. Not a problem, then or now, for the voice or the majority of instruments. Quite so. So it's not a candidate for the foundations of music, is it? No, it doesn't! Try it, if you don't believe me. You're roughly okay with the pentatonic, through several octaves. Otherwise - you're way out, within two or three. So - quite obviously, this is not the basis of the scale at all, is it? QEDYou have that pattern anyway, simply by assuming what is obviously the case, that the scale is the selection of the harmonically strongest notes. They repeat ad infinitum, with of course perfect consonance, if you want. But of course most of your notes are audibly out. So no one actually uses this method, because if they did it would sound bloody awful. This was a common method of tuning a fixed-string instrument, of course - most piano tuners still do. It's a rough and ready method, for getting it approximately right. Then you make the slight adjustment necessary to smooth the temperament. Voila. A couple of centuries out, but never mind. "Slightly less than 3/2" is audible even to the most tone-deaf person. After seven octaves it'd an absolute howler. But no one would try to pass a sevn-octave spread fifth as a fifth, played on the piano. Yes - as I said, standard music theory nonsense. All based on an error, a basic historical misinterpretation, compounded by the historical accident of the piano becoming dominant when music becomes systematically conventionalised. This wouldn't be the disaster it is if in fact music theory then elaborated a theory based on such a ratio-based hypothesis as to how the scale works - but it doesn't, of course. No one calculates ratios when they play or write music. The whole theoretical apparatus that has actually been elaborated from this fundamental error is based on the intervals thus supposedly derived. Thus the harmonic relationship, still preserved if only arithmetically in such ratio language, is lost. It took Helmholtz to discover, or rather rediscover, this harmonic basis of the scale - and all the intervals and chords derivable from it. But by then it was too late. Indisputably true, of course, which is why you find it at the beginning of every textbook. But the above theory was already firmly established, and patently false though it is seemingly cannot be shifted. This can only be because musicologists are not scientists, and the bastions of academia are jealously guarded - scientists can't make an inroad onto their hallowed turf. Fortunately, for the vast majority of people who actually make music, what academia thinks doesn't matter a jot. They play and compose by ear, as musicians always have done.
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