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

[aciddose]

Uh.. if we used all scales equally the percentage of their use would be exactly equal to the ratio of those scales vs. the total.
Since there are more 6-tone scales than any others, they will make up a higher percentage.

Since there are more 5-tone and 7-tone scales than any others, again, they will make up a higher percentage than any others simply due to the fact there are more of them available!

This is so simple as to be mind-blowing that anyone could not immediately comprehend it intuitively.

The only remaining question that must be answered theoretically (as we already know - it is a fact that more scales exist for 5, 6, 7) is why do we see a significant bias toward 7 rather than 5 or 6?

I've answered that.

If the best response you people can come up with is honestly either to make a joke (this I don't mind, it's basically saying "hell, I don't know") or to comment "I'm unconvinced that 7 is magic with regard to any other number" showing immediately you are completely ignorant of the whole basis of what I've just explained, or the worst of all bring some totally irrelevant completely unrelated issue up and assert that it in some way conflicts with what I've said...

[stringtapper]

The only remaining question that must be answered theoretically (as we already know - it is a fact that more scales exist for 5, 6, 7) is why do we see a significant bias toward 7 rather than 5 or 6?

I've answered that.

No, you haven't. As I posted before, your "answer" is that 7-note pitch collections offer greater "melodic flexibility" without explaining what you mean by "melodic flexibility."

I live and work in the world of music scholarship. Bring your theory, devoid of any serious consideration of the history of musical practice, psychoacoustic explanations, etc. and based solely on "math and melodic flexibility" and you would undoubtedly be laughed out of a conference of professional musicologists and music theorists.

[J.F.K.]

The only remaining question that must be answered theoretically (as we already know - it is a fact that more scales exist for 5, 6, 7) is why do we see a significant bias toward 7 rather than 5 or 6?

Evolution. Sort of Darwin in music.

[vurt]

its the final single figure prime.

also, according to the pixies, the god is 7, so maybe thats it?

[aciddose]

The only remaining question that must be answered theoretically (as we already know - it is a fact that more scales exist for 5, 6, 7) is why do we see a significant bias toward 7 rather than 5 or 6?

I've answered that.

No, you haven't. As I posted before, your "answer" is that 7-note pitch collections offer greater "melodic flexibility" without explaining what you mean by "melodic flexibility."

I live and work in the world of music scholarship. Bring your theory, devoid of any serious consideration of the history of musical practice, psychoacoustic explanations, etc. and based solely on "math and melodic flexibility" and you would undoubtedly be laughed out of a conference of professional musicologists and music theorists.

Come up with a better explanation for the facts and I might care what you have to say.

Fact: There is a significant positive bias toward scales with more notes. The consequence of this is that scales with 7 notes out-number scales with both 5 and 6 notes, despite there being far more 5 and 6 note scales available.

Fact: The bias toward more notes seems to end at 7 with little 8, 9 and 10-note scales being in common use.

Fact: There are a limited number of fractions closely approximating "just" fractions available under 12TET necessitating that larger scales beyond a limit must contain more dissonant members.

My theory explains those facts. I'm open to a better theory, or mathematical proof of my own theory. Am I willing to do it? Why should I? I honestly don't care whether it's truly accurate or not. I know it reflects reality, I know there is no better explanation available and I feel it is very likely to be accurate.

Until someone provides a better explanation I'll stick with this one.

What I really care about is that you are arguing against simple facts where there is absolutely no room for discussion. The fact you are oblivious there makes me question your ability to intuitively see things the way I initially assumed people could see them. I liked the simple version of my explanation a lot more than the long boring version that goes on and on about high-school math.

[aciddose]

Here is a rough definition for "melodic flexibility" since now I'm forced to assume you're incapable of understanding this on your own.

Melodic flexibility: The flexibility available from a set to create complex results.

For example, 1, 2, 3.

111,

222,

333,

123, 132,

213, 231,

312, 321

112, 113,
121, 131,

221, 223,
212, 232,

331, 332,
313, 323,

(Ugh, typing this is a pain. Shouldn't this be obvious?)

With only 3 members in our set we're limited to a fairly simple result. Obviously I've limited the permutations to all those of three-digits in length. This range of uniqueness however extends from that to any number of steps. Any pattern must be built up from a number of lesser patterns much like prime numbers.

Now I'm going way, way, way beyond the point I'd think I'd need to for a 12-yearold, so I'm going to let you work out whether or not 1,2,3,4 yields a more complex result or not.

(It turns out that *gasp and surprise!* the resulting number of patterns is directly proportionate to the number of symbols.)

[stringtapper]

The consequence of this is that scales with 7 notes out-number scales with both 5 and 6 notes, despite there being far more 5 and 6 note scales available.

Well of course this is completely wrong. There are not more 5-note scales than 7-note scales available because there are the exact same number of each (38) and if you studied pitch-class set theory (or read at least one of my previous posts) you would know that.

As to the rest you are apparently obsessed with a clinical answer to the question. You even state that you're open to "mathematical proof" which implies you are not open to any other form of explanation, which means you have a bias for where you are willing to look for answers. Science and scholarship don't work that way. You have to look everywhere.

You say I've given you no explanation of "the facts" but really you have only ignored my explanations, which were about why the shift from hexachordal practice to the diatonic scale occurred, i.e. increasing use of tonal procedures, necessity of a leading tone, etc.

Or do you not know what those things actually mean and that's why you're ignoring them?

[aciddose]

You haven't answered anything by repeating history out of a text-book. For all you know that history never took place and was simply made up to account for the state things are already in.

As far as you're aware we just popped into existence in this very moment.

Do you see now why I don't care?

I'm interested in the actual explanations and how/why things actually work. I don't care in the slightest about history other than as a reference. Obviously any theory must fit history, which mine does.

There are not more 5-note scales than 7-note scales available

Okay, I'm getting very tired of this. I don't know if you do this on purpose or if you are really that slow.

The sum of 5 and 6 note scales is greater than 7 note scales. Read what I said in the post you quoted again until you understand.

If you find yourself jumping back to quote something and point out how it's "obviously incorrect" you didn't spend enough time attempting to understand it.

[aciddose]

...and please. If you're going to start your BS about axioms again try and focus on things like the fact we're concerned with human perception, or that we've "assumed" "just" fractions are preferred. Then go philosophize about that somewhere else.

[IncarnateX]

My theory explains those facts. I'm open to a better theory, or mathematical proof of my own theory. Am I willing to do it? Why should I? honestly don't care whether it's truly accurate or not. I know it reflects reality, I know there is no better explanation available and I feel it is very likely to be accurate.

"I will not prove my theory but I know it is right?" Well that certainly covers your ass. Who can argue against that?

Even if your math made any sense, it will not tell you whether this math governs human activity (like you seem to imply) or is a result human activity ( as we say).

Never mind though, it is becoming too schizo for me to even dare to follow, so you don't have to start over once again.

Cheers

[jancivil]

The only remaining question that must be answered theoretically (as we already know - it is a fact that more scales exist for 5, 6, 7) is why do we see a significant bias toward 7 rather than 5 or 6?

I've answered that.

No, you haven't. As I posted before, your "answer" is that 7-note pitch collections offer greater "melodic flexibility" without explaining what you mean by "melodic flexibility."

I live and work in the world of music scholarship. Bring your theory, devoid of any serious consideration of the history of musical practice, psychoacoustic explanations, etc. and based solely on "math and melodic flexibility" and you would undoubtedly be laughed out of a conference of professional musicologists and music theorists.

Come up with a better explanation for the facts and I might care what you have to say.

Fact

- then a list of notions that have not been demonstrated as facts in any way or form, but are things you pulled out of your ass and seem to believe in and have tried to justify by constantly begging the question.
You don't need to read anything anyone has, you're just obstinately stupid about the whole exercise. What an extreme case of trying to fake knowledge of something you really just aren't suited to do. Your field must be based in mathematics, and you need to reduce things to a facile maths - or I like 'clinical' - explanation you're comfortable with; but this is really simple-minded.

You have these gobsmacking absurdities, 'obviously we have seven as it's one next to six' out of some bogus idea I don't even want to go back and parse. Why is the Chinese melodic tendency to take the six as if omitting one of our seven, then? (There's a reason you're unresponsive, you don't want to deal with the questions, you don't ask yourself questions. What a great proof of Dunning-Kruger, isn't it.) It's cultural, it's historical. You haven't done a survey of world music to have some statistics behind which here are facts! DON'T BULLSHIT!!! There are too many musical systems that don't fit your guesses for it to have any hope of a basis in 'fact'.

And this 'as far as you know there is no history', how can you be taken seriously at all now? it's an idiot gesture to get rid of the whole problem you don't want to deal with. It's just such absolute (and desperate) BULLSHIT at every turn! Do you actually believe this shit? It really does beggar belief at this point.

for someone with 'acid dose' as a handle, I would think you would wonder if people are onto you, that see right through these little baffle them by bullshit exercises, or maybe you could use an actual dose as a mental enema, if you actually have deluded yourself into this garbage as reasoning at all. Sticking to it seems like a big ego trip, like you'll save face at some point. Ain't gon happing. It could not be more transparent to me that you don't do music qua music with this, you're trying to make yourself suitable for music via maths. It isn't working. It's a glaring fraud on parade by now.
We've been here before where you tried to talk about - to EXPLAIN - melody via pure maths. You don't do melody, you don't know what you're doing here and I know it and deep down you do too. This is a lot of word salad and mumbo jumbo. Please do tire yourself out to the point you shut up. It's depressing to see a person do this kind of shit.

[jancivil]

The only remaining question that must be answered theoretically (as we already know - it is a fact that more scales exist for 5, 6, 7) is why do we see a significant bias toward 7 rather than 5 or 6?

Evolution. Sort of Darwin in music.

Bullshit. Where has this bias been demonstrated? Is 'aciddose' an expert in musicology now? What is 'signified' is culture, probably a narrow awareness of culture and bold (arrogant) assumptions as if this, yet another, cart will pull the horse of his other ad culum arguments.

[jancivil]

Evolution.

So this premise is that by an added note or two notes, by conception is per se more 'evolved' than a pentatonic tune?

That's musically just ignorant.

if we set out to say, 'well, it appears that 5, 6, and 7 notes as a sort of scalar basis enjoys widespread usage' it looks like a reasonable statement and would withstand a lot of attacks.

But melody as if governed by maths - as if maths is a kind of overlord or god - is the very definition of absurd. It's like saying that science preceded nature, rather than sets out to understand it. It demands the cart is the necessary driver of the horse.

So, 'as far as you know, history was written just recently to explain how things are' sounds like a joke. How recently? At what point is this nihilistic statement supposed to be actually true? Do we get rid of Schoenberg and assume the dodecaphonic thing was in fact all Boulez in order to criticize himself?
Is it true that JS Bach did not work towards Well-temperament, that's just a story to explain equal temperament? Was there no quarter-comma meantone in play? What in the hell is this idea supposed to do for the discussion except to get rid of what's inconvenient for this wild ad culum argument by this guy 'aciddose'? It's bizarre.

Melody in a given culture was developed; melody begins with singing. You want to gainsay that there are 'just' intonations preferred? To what end? To justify this absurd set of notions inchoately slapped together as if to form some great overarching truth? You look like an idiot.

So to talk of melody we must get into tradition. At the period where Indian Classical Music was codified into theory, they were well exposed to western music. It's going to be hard to know how it sounded before the Mughal Empire and the influence of those musicians.

But as we have it since the 19th century at any rate, here are 10 'Thaats', which are parents to ragas. They are more-or-less 'scalar basis for'. They are seven notes, ie., they are inclusive to the extent of seven. The ragas themselves do five and six a whole lot of the time. Might be five up and six down, and the pre- and proscriptions go on from there. There are a few that do more and one I know of is twelve, either direction.
I'm working with the Raga Marwa recently. It *is* a hexatonic raga. You don't put the seventh note of Marwa Thaat onto it for musical reasons. It would be like insisting the nose is improved by a wart.

These are the 'notes', ie. as you would have them in the west. HOWEVER the 'swaras' are more than notes, they are how the note is SOUNDED, APPROACHED, INFLECTED as it serves the idea, the raga itself. So we get into the meends/the bends, the gamaka, the graces, the ways in which a thing will be done in order to bring the beauty of the raga out. So this 'number of notes' does not live in this box o' seven. It's like a blues third: is there some math that made sure of this emotional inflection before all time began? That's just nutty.

ICM has not changed its basis in some time, anyway. Is this because their musicians do not 'evolve' as a German, eg., Schoenberg? Does the west enjoy this kind of hegemony of ideas where one would be so confident of that?

Well, I'm listening to Ali Akbar Khan do Marwa Raga (and a lot of things) and he's clearly open to music of his time. His Marwa is basically atonal-sounding, and he does never use the fifth it excludes. A great expansive mystery with just that set. Well, and the 'meends' and the inflections and approaches, you know. All sorts of music comes out of this idea and it all seems to convey that 'dusk' atmo as governed by a couple of things one has to heed.

There are theories going back ages to measure these things, at least to ponder them on this level. '22 Srutis', what does that mean? It's going to depend a lot on who you ask. Alain Danielou has gone into serious depth on his idea of it: twelve - two of them, Sa [1] and Pa [3:2] basically inviolate - and 10 more that lie essentially at a syntonic comma [81:80] from these ten that are left; in order to achieve a 3:2 fifth at all the useful levels. In terms of the musical values, it makes perfect sense. It may not show exactly in observation of course.

http://en.wikipedia.org/wiki/Just_inton ... ian_scales

Further, he scientifically set out 53 useful, *audibly perceptible* notes in an octave.
http://www.find.org.in/alain-danielou/s ... nstrument/

Why do the Arabs have their ratios and a 24 or 25 note basis? For their essentially heptatonic lines... This should be understood as rhetoric in the form of a , but I guess I have to explain: 'this is what they like to hear, these are ideas in a cart that is pulled by the horse of musical expression and intention'.

Melody exists of, by and for music and musicians work in it, and things are arrived at TO GET A SOUND. It seems to be that vis a vis singing lines, seven has shown to be a good average. But there are whole systems that do not deal with that as a basis. Does this number hegemony consider all exceptions a proof, or they must be outliers? We are in the realm of making words perform tricks, it's intellectually dishonest to do.

[IncarnateX]

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?

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.

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)

[fmr]

Now comes the only part of what I've said related to this that is theory: My theory is that 7 note scales provide greater melodic flexibility and are the best trade-off between the total number of scales available vs. the number of notes within them. There are too few 8-note scales available to start with to out-number 7-note scales and there are too few notes available in 5-note scales.

Apparently, it also seems that the bias toward "more notes" is not strong enough to overcome the limited number of scales available for greater numbers, 8, 9 and 10, or that having more than 7 notes doesn't in fact provide any significantly greater melodic flexibility.

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.

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.