why do our scales have seven notes?? and not 8, 9, 10 or 11?

[tapper mike]

Aciddose,

Don't waste your time with the mall security rats who's only goal is to protect the status quo.

While I disagree with some of your findings you concept does have several very well grounded points.

I would only suggest to you watch.
http://www.thesonicsky.com/

[jancivil]

Hi @Jancivil and thanks for the lectures. Enlightning.

But you seem kind of upset?

Are you not taking AD too seriously on this? Given my quote before it seems like he already has admitted that it is all based on intuitions that do not need to be tested or proven to reflect reality. Thus all you say will confirm the theory, may it be explained by denial of facts, ignorance or misconceptions. What more do we need to let it go?

Yeah, he has proved beyond all doubt he is not a person to take seriously. The arrogance of telling not only myself, but others that just have refuted him we don't know what we're doing, compounds my irritation with the insult that the whole exercise is. I am offended by someone trying to get over like that. Anyone doing that pisses me off some. To toss a wiki link on just intonation at me? This happens to be an abiding interest of mine that I'm knowledgable in and experienced in its application. I know this guy is all talk and the talk is obvious dilettantism. He knows better, I would think, BUT NO, he has to win.

Nothing wrong with thinking out of the box and try to explain things differently than usual. Problem is if the whole deal is based on ex nihilo premises, mysteriously implicit deductions that do not have to be stated to be evident and infallible circular conclusions.

Out of nothing or out of the anus, hard to say.

I am afraid we have lost in this respect. The theory cannot be wrong and no one can argue against it because no one really knows it.

May this be baffling bullshit, just bullshit or just very baffling. The strategy works: People give up and last man standing is the winner (I guess….)

Cheer(s) (up)

Yep. This is essentially religious quality of bullshit, he actually has tried to justify maths as a governor of human action, as if the numbers do something in themselves that the physicality of things, the acoustical considerations, the considerations of vibrations in the body, are secondary to. The cart as the necessary driver of the horse entirely because he doesn't care for the horse as much. Reasoning is out the window in such a case, but I enjoyed writing what I did.

[jancivil]

Aciddose,

Don't waste your time with the mall security rats who's only goal is to protect the status quo.

While I disagree with some of your findings you concept does have several very well grounded points

Ok, this is awkward. You haven't contributed at all to the discussion but you found the opportunity to do this sideswipe in a drunken driveby. Yet, I found it crucial to my own survival and sobriety that I take things on rather than hide, so let's talk about what you really meant there:

Still resenting that you were not able to dance around your own incompetence and fakery being caught out in these pages, Mike? Why don't you tie this to *'voice leading', what? I can see why you'd identify with what he did, particularly as faced with someone that knows about the thing.

What does this 'status quo' do? What does that mean? If anything 'aciddose' has tried to make maths 'the reason' - for things whose reasons really lie in what is done - in order to shore up a notion which looks like an unexamined hegemony based in a quite narrow experience. Standing for the status quo of 'seven' is one thing but further he has this bizarre attachment to his own ad culum premises which are magical and golden (to his own brand as Fat Bastard would say).

But do take an opportunity to take sides against, well, me. Lacking the chops or the strength to show what you do want to use from him in service of that. Who do YOU think you're getting over on? So transparent. Do you think this is a good tack, having lost the confidence of the more grounded people here (I just got it, knowing what *things are actually called is 'defending the status quo' and then that isn't enough, 'mall security'... still not enough, 'rats'.)? Wow, dude.

Stay hydrated, you know.

[stringtapper]

I think your theory has one big flaw: Music was based on hexachords when it was predominantly melodic, and only when harmony started to become more important (with the raising of opera, accompanied melody, figured bass, etc.) did things started to change. Therefore, it is more correct, IMO, to say the the seven note "scales" (again, an incorrect term, IMO), AKA the tonal system, based on just two modes (major/minor) was the responsible for the establishment of the seven note modes, with the leading tone (the seventh note) as a very important element, harmonically speaking.
So, in the end it was not the melody (which was not at all enriched by the adding of another note), but the harmony that was the reason for the arising of the system.
Again, in classical music it isn't predominant anymore (and this is for more than 100 years now). It's just pop music that still stick to it.

That's the crux of it right there. I was only able to skirt around it by talking about the advent of tonality, but you nailed it.

Harmony, functional harmony, after all is the primary thing that distinguishes tonal practice from previous practice in western music. (Of course it was a continuum, a gradual process.)

I think one would be hard-pressed to say that a Machaut motet contains little "melodic flexibility."

[IncarnateX]

BTW: Do any of you remember Max Cohen? The protagonist from the movie "Pi"



http://en.wikipedia.org/wiki/Pi_(film)

One, Mathematics is the language of nature. Two, Everything around us can be represented and understood through numbers. Three: If you graph the numbers of any system, patterns emerge. Therefore, there are patterns everywhere in nature. Evidence: The cycling of disease epidemics;the wax and wane of caribou populations; sun spot cycles; the rise and fall of the Nile. So, what about the stock market? The universe of numbers that represents the global economy. Millions of hands at work, billions of minds. A vast network, screaming with life. An organism. A natural organism. My hypothesis: Within the stock market, there is a pattern as well... Right in front of me... hiding behind the numbers. Always has been.

And what he had to do to himself to stop his own ramblings?

As far as musical expression goes in terms of number of notes within a scale, the soundtrack to this wonderful thriller should be some of the most non-expressive music ever. It is pure techno with all the usual rules applied to it: Minimalistic use of note steps and non of harmony. Nevertheless the main composer, Clint Mansell, got instantly famous and as far as my personal taste for music concerns, this is a frigging mind blowing soundtrack -expressions are not in the number of notes used but in the dark and powerful moods of the compositions. (There are a lot of other artists too on the album though such as Massive attack and Aphex Twins)

And the morale: Dear mathematicians - Watch your sanity at every turn of your thinking. It is so easy to loose and so hard to regain.

Cheers

[vurt]

clint had been around for many years previous
pop will eat itself werent exactly unknown ha!

the bbc recently did a mini series on film music, the bit with clint is worth digging around for, although the whole 3 episodes are also interesting

[jancivil]

I think your theory has one big flaw: Music was based on hexachords when it was predominantly melodic, and only when harmony started to become more important (with the raising of opera, accompanied melody, figured bass, etc.) did things started to change. Therefore, it is more correct, IMO, to say the the seven note "scales" (again, an incorrect term, IMO), AKA the tonal system, based on just two modes (major/minor) was the responsible for the establishment of the seven note modes, with the leading tone (the seventh note) as a very important element, harmonically speaking.

I was waiting for precisely this. I didn't want to do it because I knew there was someone with more focus and a better lingo for it.

[jancivil]

BTW: Do any of you remember Max Cohen? The protagonist from the movie "Pi"

One, Mathematics is the language of nature.

I remember that monologue. I really find that whole tack idiotic and that is a great bit of writing in revealing succinctly the incoherence innate to it. That perfectly reinforces what I said: as if nature required an understanding of mathematics in order to proceed. The cart has to drive the horse, it's beautiful enlugh to be charged with that, owing to its capacity for reduction.

[jancivil]

The reason for that is likely that there are not enough notes in 12TET closely approximating "just" (as in just intonation) fractions to allow you to pick a set of 8 notes that provides an advantage over a similar set of 7 - that the 8-note scale will be a 7-note scale with "one extra note", and that it will likely be dissonant.

Word salad par excellence!

'advantage' FOR WHAT?! There is absolutely no musical context in these remarks. This is all of it an utter failure which lies in a stupidly obstinate insistence in trying to make maths the driver of musical thought.

There are reasons one would choose an 8 note scale and the advantage speaks for itself. The symmetrical octatonic over a dominant seventh in jazz ("it will likely be dissonant"? This can't happen with seven notes, then.). There are reasons for a seven tone set for a certain advantage over six, contextually. et cetera... There are ideas that drive choices. Is this really so beyond you that you have to fabricate this silly shit?

Fernando showed a tendency in the west where decisions were made, out of aesthetics and a desire to do things with musical materials that gave rise to a seventh degree; as music become more involved with harmony - and toward an idea of ascension and uplift, 'raised seventh to the octave' - materials were suited for it.

Cf., my rhetorical question, why did the Chinese not embrace it? If you give a traditional Chinese player a simple seven note type of tune - coincidently, I saw this illustrated in a film as this discussion unfolded, perfect: Yankee Doodle Dandy, the violinist charged with delivering that [at a party in order to make a point] avoided the seventh! I noticed that; that is realism.

I wouldn't say that it can add nothing to melody, but seven vis a vis five or six doesn't through itself enhance melodic activity! What a silly thing to propose then.

not enough notes in 12TET closely approximating "just" (as in just intonation) fractions to allow you to pick a set of 8 notes that provides an advantage over a similar set of 7

You're just making it up as you go along for troll jollies? If you are serious, you have proven to be a total noob or that you're just really incompetent.

22 tones in an octave, 'just' ratios:

256:243
16:15
10:9
9:8
32:27
6:5
5:4
81:64
4:3
27:20
45:32
64:45
3:2
128:81
8:5
5:3
27:16
16:9
9:5
15:8
243:128
2:1

- the ADVANTAGE of this being, eg: look at 9:8, the major tone (major second from 1) vis a vis the major tone from the 3:2. In a 12-note just intonation map, the 3:2 x 9:8 is off by the syntonic comma (given the usual 5:3; we're making this compromise throughout). So it's provided by 27:16. There is no 'more dissonant' intrinsic to the thought; quite the opposite, the entire idea is to obtain MORE CONSONANCE of the 'perfect' fifth inclusively.
if you wanted to build a perfectly consonant triad at twelve places, here is the perfect map for it.

For that matter, if you wanted to build regular major and minor triads off the symmetrical octatonic... well, YOU DO THE MATH. It's as though you have yet to test this ONCE.

So, your premise is hereby demonstrated to be false. You seem to be tossing shit to see if it will stick. You don't actually believe this crap do you?

[IncarnateX]

I remember that monologue. I really find that whole tack idiotic and that is a great bit of writing in revealing succinctly the incoherence innate to it. That perfectly reinforces what I said: as if nature required an understanding of mathematics in order to proceed. The cart has to drive the horse, it's beautiful enlugh to be charged with that, owing to its capacity for reduction.

Well basically it is just old school Platonism. The world of ideal abstractions is the real world, while the natural world is an imperfect derivation. That mathematicians are at risk loosing themselves in this kind of idealism goes with the dedicated interest. Not that I really believe AD is an academically trained mathematician, in which case he would be very explicit with the foundation and meaning of his premises, their deductions and the results. Mathematical intuitions are not worth shit without proof, especially to mathematicians and he would know it and never claim his theory to be true without it.

[JumpingJackFlash]

I don't have much time, so I haven't read the entire thread (but I can imagine what people are coming out with).

The answer has very little (if anything) to do with frequencies or the overtone series (etc.), the answer is simply because they evolved that way.

It's not mathematics, it's evolution.
(I'm sure we've discussed this exact same thing on here before).

[IncarnateX]

(but I can imagine what people are coming out with).

No you can't

it's evolution.

So at some point in history previous scales mutated into the 7-notes scale and became dominant through natural selection because they increased the organism's chance for survival?

[jancivil]

The reason for that is likely that there are not enough notes in 12TET closely approximating "just" (as in just intonation) fractions to allow you to pick a set of 8 notes that provides an advantage over a similar set of 7

22 tones in an octave, 'just' ratios:

[/list]

So what is the point in justifying 12 ET approximations - wait, you're justifying your magic seven? You're chasing your tail. The origin of seven note rows does not lie in equal temperament. Which approximates the intervals that were found to happen from phenomena, sound-producing apparati. 12 ET was done for an actual reason. The need to tweak 'just' was not just to find a hobby, and it was not directly a tweak of just. It was a final solution to the 'comma' approach to temperament. Along the journey there were things like quarter-comma meantone. The point was to reduce the error (by which we mean, the out-of-tuneness perceived in the musical context) when one proceeded more and more distantly from the white keys. HISTORICALLY, the beginnings of temperament lie here (3:2 won't multiply out 12x to arrive with unity [result 531441/4096, or folded back 531441/524288 ≠1] so the adjustment, eg., comma of Pythagoras was calculated.). {Oh, BTW, if one wants a reason for twelve, THERE IT IS, 3:2 vis a vis 2:1. In other words, two things that suited the ear and were found in examination of nature [strings vibrating] were conceived of in terms 'we should work this out'.}

- that the 8-note scale will be a 7-note scale with "one extra note", and that it will likely be dissonant.

It must occur to anyone that has the symmetrical octatonic and the why of it, that you don't. It isn't any seven with one added; there is an idea behind it. It appears you don't know what you're doing with the term 'dissonance'. It seems abundantly clear that this notion was never tested, at any rate.

[IncarnateX]

Well this is indeed fun but why do you bother Jancivil? To me it is quite easy.
First of all, like we already has agreed upon, the very premise for a discussion like this is highly questionable, namely that somehow unknown forces of math dictates the use of 7 note scale beyond human history , culture, inventions of instruments, aesthetics etc.

Secondly: If we are accepting the premise after all, it is quite obvious that AD wouldn't be able to distinguish conjecture from a mathematical proof even if the former was a puddle pissing up his leg and the latter a rottweiler attached to his ass.

He likes to argue on basis of wiki articles. Okay then let us stick to the wiki:

http://en.wikipedia.org/wiki/Mathematical_proof
(my underlines)

In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms.[2][3][4] Proofs are examples of deductive reasoning and are distinguished from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproven statement that is believed true is known as a conjecture.

Now in addition to this we can mention that even a perfect mathematical proof can be based on axioms that are not self-evident and that even my be false once they are tested in themselves.

I am not even sure that AD understands your arguments, because I am not sure whether he really understands his own.

Anyway, AD has gone home and it doesn't seems like he will come back to play. I enjoy reading your arguments, but you are probably waisting your breath here. Just saying

[IncarnateX]

Hell, I am even going to help AD out of this and provide the final mathematical proof for you all that 7 actually is the magical number of the 12 note system. Yes you read me right, here it comes:

Given that Y is any number between 1-12 corresponding to a twelve note scale:


Y x 7
______ = 7 (y multiplied by 7 divided with y equals 7 )

Y


Let us take it to a test:


Y
1) 1 x 7 = 7 , 7:1 = 7
2) 2 x 7 = 14, 14:2= 7
3) 3 x 7 = 21, 21:3= 7
4) 4 x 7= 28, 28:4 = 7
5) 5 x 7 = 35, 35:5 = 7
6) 6 x 7 = 42, 42:6 = 7
7) 7 x 7 = 49, 49:7 = 7
8] 8 x 7 = 56, 56:8 = 7
9) 9 x 7 = 63, 63:9 = 7
10) 10 x 7 = 70,70:10 = 7
11) 11 x 7 = 77, 77:11 = 7
12) 12 x 7 = 84, 84:12 = 7

Thus it is proven that 7 is the magical number of a 12 note scale with regard to musical expression and that the development of the tempered 12 note system is dictated by higher mathematical forces. Any uses of other scales are in this respect evolutionary inferior may that regard the chinese people, arabs, techno producers or whatever you freaked out flying monkeys can come up with. If you cannot see this, you are truly idiots.

Now piss off twats.