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

[crazyfiltertweaker]

The iconic number seven will play a central role here, because not only the week has seven days, and not only the world has seven wonders, but also the major scale consists of seven notes are known to

This "explaination" is the only one I have found about this...

But it dont gives a real answer for the question.

"Why have our western scales 7 tones?"

And not 8, 9, 10 or 11?

Yes I know 12 tones are chromatic and atonal. But every other amount is not chromatic, why 7 notes? And why two half steps?

In EVERY single theorie book I have read they give me just such answers, which tell me nothing. But Im searching for a real answer, an answer which EXPLAINS it, which answer the "why".

Especially the question why it dont have more or less.

Yes I know there are some other scales which have less (pentatonic as example) or more (some blues scales) but why is the 7 tone scale so popular? This is the big question for me!

[SJ_Digriz]

In EVERY single theorie book I have read they give me just such answers, which tell me nothing. But Im searching for a real answer, an answer which EXPLAINS it, which answer the "why".

The math of frequencies.

[crazyfiltertweaker]

yes you mean intervalls but where is the math in the number 7?

[Sendy]

It's a "best-ish fit" for the simple harmonic ratios which sound pleasing to the ear.

There are other best-ish fits but no perfect fit because maths.

[SJ_Digriz]

yes you mean intervalls but where is the math in the number 7?

As Sendy indicated of the "pleasing" divisions/ratios, the 8th brings you back the octave.

[SJ_Digriz]

It's a "best-ish fit" for the simple harmonic ratios which sound pleasing to the ear.

There are other best-ish fits but no perfect fit because maths.

That is where the fun starts, as the division only holds within the 8 intervals! Western music has tended to agree on a comprised "spread" approach to the intervals. But lots of tuning options, even within the 8 intervals exist.

[vurt]

its because bach had only 7 fingers

[fmr]

If you do some research, you'll find that there are other. And they are not called "scales" (the term is irritating) but modes. There is the pentatonic mode, the hexatonic mode (whole tone mode), and there are modes with more than seven notes (research Messiaen). And Harry Partch used a mode with sixteen notes.
So, no, "my scales" can have several number of notes, not only seven (depends on what I want).

[aciddose]

Similar to how 360 degrees are divided well by many integers, 12 semitones line up nearest to the desired integer fractions.

If you're going to ask this question I assume you've done the math?

frequency = root * (2 ^ 1/semitones) ^ offset

Then you need to find the ratio between notes, from offset = 0 to semitones.

Then find the LCM for those fractions.

You want to be seeing lots of small integers, try adjusting the number of semitones up and down and see what you get.

As for why we have seven whole tones, again look at the resulting fractions.

You should see that the whole tone is a small integer while the sharp/flat is accented by (2 ^ 1/semitones).

While it seems random, it does actually make logical sense once you do the math.

[jancivil]

a lot of that is just bullshit. you're making carts pull horses.

As for why we have seven whole tones, again look at the resulting fractions.

I'm not sure which mistake you're making there. Which fractions? The seven tone scale is not symmetrical in the west. there are six whole tones in an octave (said to be a 'symmetrical scale') that are twice the size of semitones. The twelve equal to an octave is twelfth root of two.

That whole-tone scale was kind of an arbitrary, experimental device for a certain effect coming out of the French avant-garde. Possibly influenced by exposure to the east but I'm not prepared to write that up.

12 equal divisions of the octave, in terms of western music was a compromise for a perceived reason that belongs to a practice within a particular culture.
The first parsing of 2:1 in terms of string vibrations should be traced to the 'ancient' greeks, but the idea was probably not to obtain twelve tones in a row. These were ratios found dividing string length. 2:1; 3:1; 4:1; and drawing them within the scope of the 2:1, 3:2, 4:3 etc. Then it was noticed that 3 and 2 were a-geometric so-to-speak (will never resolve; 3:2s never gibe with any 2:1) and 'temperament' - in terms of 'commas' to correct the problems - was born.
The development of seven tones as a convention, or 'the reasons' for 'seven out of twelve' reside in a lot of history over a relatively long period.

While certain Chinese 'theorists' developed a more-or-less 12 equal divisions of 2:1 'octave' in antiquity, LONG before we see it in the West, one can observe that generally Chinese music goes with a hexatonic form of scale. Why would that be true and the heptatonic ways be true from the European standpoint? Culture, decisions, consensus, stuff happened.

[Painmooser]

and the harmonics basically come down to frequencies of higher order..

you can look at the analyzer and play some DUR and some strange synth tones..

nice is when it looks like teeth -if it looks more like noise it gets more disharmonic.

why we like harmonic? well I do also like disharmonic, thats a thing you can teach yourself..

listen:

its the beauty and the ugly side of nature - it just is 'being' and not 'being nice ' or 'not nice'.. I like that.

[Sendy]

A wizard did it.

[aciddose]

http://en.wikipedia.org/wiki/Equal_temp ... intonation

My preference is:

Code: Select all

		1/1,	
		18/17,
		//d
		9/8,
		19/16,
		//e
		5/4,
		//f
		4/3,
		10/7,
		//g
		3/2,
		19/12,
		//a
		5/3,
		21/12,
		//b
		15/8

Which is mostly just intonation but with some slight offsets. Been a while since I tweaked these ratios but I believe I made them sit much closer to equal temperament.

Notice the "sharps" are all larger integer ratios than the "whole tones".

Now if you calculate the actual ratios of equal temperament as I prescribed you'll find any claim about "long history" to be pure bullshit.

It's all in the math.

If anything, I might accept the argument that the history of musical scales represents an approximation over time to an emergent preference rooted in our perception of pitch and ratios of pitch.

[Flandersh]

Matthias Rieger's work on Helmholtz may shed light on this question.

[jancivil]

http://en.wikipedia.org/wiki/Equal_temp ... intonation

My preference is:
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Which is mostly just intonation but with some slight offsets. Been a while since I tweaked these ratios but I believe I made them sit much closer to equal temperament.

Notice the "sharps" are all larger integer ratios than the "whole tones".

Now if you calculate the actual ratios of equal temperament as I prescribed you'll find any claim about "long history" to be pure bullshit.

It's all in the math.

If anything, I might accept the argument that the history of musical scales represents an approximation over time to an emergent preference rooted in our perception of pitch and ratios of pitch.

Your preference for what? That is, for what music? Who are you kidding, do you think?! What music is this perfect for, all music? Trust me, it simple won't be. I think you're bullshitting some more. "Notice the 'sharps'<are all larger integer ratios than the "whole tones">?
9:8, or 10:9, or for that matter 8:7 or a number of other ratios might be called after the convention 'whole tone'. Pythagorean 'ditone' 81:64. etc. SO WHAT?!

Why is 'whole tones' in scare quotes? Did you not like your error to be noticed and you fabricated this less-than-meaningful sentence? Can you fabricate something now to get '7 whole tones' into an octave? Are you indicating disagreement with what I said about whole tones?? I think it's designed to be baffling bullshit. I don't think you have the first clue, frankly and it's an insult to people's intelligence that do.
As you "prescribed". I work with this kind of thing all the time (I'm one of the editors of these wiki pages, in fact.). I said you're bullshitting and all you've done is illustrate it some more. You aren't kidding me, I assure you.

"Been a while since I tweaked these ratios but I believe I made them sit much closer to equal temperament." Why not just use equal temperament? Who are you kidding, do you think? The reason MUSICIANS use this have to do with musical reasons, for a type of inflection in melody, that they don't get in 12 ET. An Arabic type of flat 'Re' via 25:24, shorter than 16:15 or 256:243, for instance. If we get into maqam, there are quite some things to experience and understand here.

Or, using samples to obtain a concord in an ensemble where the more natural/more what the musician does in that ensemble is let's say closer to 5:4 than the ET M3 which is 13.69¢ sharper. So Vienna Instruments can use the scala implementation and set the root.