# Music interval

What is the title above?
"Muwashah of Arab - Andalusia..."
Well, If I'm not mistaken, Andalusia is a region in southern Spain. Near Gibraltar strait, again "Gibraltar" comes from "Jeb Al Tarik", a general in Arab?

atyy
They can't communicate, but their "music" interval is most likely ##\sqrt[12]{2}##.

The ##\sqrt[12]{2}## is very Western, and late. The Chinese had it, but it doesn't seem they used it extensively in their music. It was developed into Western "common practice harmony". In contrast, the expressive tools in Arabic music use a different kind of modulation, between melodic modes, and not so much harmony. According to some Arab music theorists, they use ##\sqrt[24]{2}## http://en.wikipedia.org/wiki/Arab_tone_system. The diatonic scale is much earlier, but it doesn't involve the ##\sqrt[12]{2}##.

Stephanus
jtbell
Mentor
But then why 12? It's the simplest, and after that, most musicians are too inaccurate - even great ones - Menuhin was not able to play the quarter tones in the Bartok sonata accurately, so Bartok wrote him an "easier version". However, there historically been attempts to use 41 and 53, as those are the next closest.

http://en.wikipedia.org/wiki/41_equal_temperament
http://en.wikipedia.org/wiki/53_equal_temperament

The American composer Easley Blackwood has experimented with writing music in equal-tempered scales with 13 through 24 notes to the octave:

http://www.cedillerecords.org/albums/microtonal

http://en.wikipedia.org/wiki/Easley_Blackwood,_Jr [Broken].

[added: I can't make the second link post properly. The URL is supposed to end in a period, but the forum software insists on putting the period outside the URL. When you follow the link, you'll get an error page from Wikipedia. If you then add the period by hand in your browser's address bar and hit "enter", you'll go to the correct page. Or just use Google to search for Easley Blackwood.]

Last edited by a moderator:
Stephanus
Okay,... I think 12 is the "magic number" for music.
Not that the smallest number that have 4 factors. 2,3,4,6, but

The point is that the 12-equal-interval scale (or equal temperament) contains within it good approximations for ratios such as 2:1 (octave), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third). These ratios sound good to the human ear because the notes share some of the same harmonics.

5:3 (perfect sixth, La)
9:5 (perfect sixth, Si)
But 5:3 or 9:5 the divider and modifier distance is not 1, 5:3 is 2, whereas 9:5 is 4
I don't know if this is a good cause for 12 interval

Mark44
Mentor
Speaking of language.
Do you think music is a kind of language?
Not really. Music can convey some emotions, maybe, but I don't see how it could be used to convey much more than that.

Stephanus
Not really. Music can convey some emotions, maybe, but I don't see how it could be used to convey much more than that.
Twenty six Alphabets + 10 numbers covers 3 octaves in diatonic scale.
In the movie "Close Encounter of the Third Kind", the alien and human use music to communicate.
Okay it's just a movie, but for diferent species with different vocal cords and trained ears just to hear their own vocal cord, perhaps music is a kind of communication tool.

Staff Emeritus
5:3 (perfect sixth, La)
9:5 (perfect sixth, Si)
But 5:3 or 9:5 the divider and modifier distance is not 1, 5:3 is 2, whereas 9:5 is 4
I don't know if this is a good cause for 12 interval

You really should read the article that Greg pointed you to.

There is no perfect sixth. There is a major sixth, and a minor sixth.

Stephanus
You really should read the article that Greg pointed you to.

There is no perfect sixth. There is a major sixth, and a minor sixth.

Pythagorean
Gold Member
I think one issues in this thread is that 12-tone and equal-temperament (2^(1/12)) are not the same thing.

Before equal temperament, Pythagoras used perfect fifths to construct the 12 tone scale. As arty pointed out, thus made it difficult to modulate keys, because the errors in Pythagoras' method got larger as you got "further away" (distance measured on circle of fifths, probably) from the key in which the perfect fifths were constructed.

So there were lots of 12 tone scales, and methods of interval cobstruction and 2^(1/12) is really quite a recent one. It's advantage is that it's consistent - all the intervals are exactly the same from the first degree to the second regardless of key.

I think 12 tones (and 24) work so well because of the numerous factors you mentioned (2,3,4,6). I know there are other divisions - the most important thing is the octave (2:1), as it's relevant to how our brain processes audio signals audio signals. After that, the fifth (3:2) is the next most important, then it probably gets rather subjective, emergent, and cultural after that (Even the fifth isn't universally used like the octave is).

Stephanus
I think 12 tones (and 24) work so well because of the numerous factors you mentioned (2,3,4,6)

But, the more I think of it, the more I disagree with my previous statement. It's not that 12 can be divided by 2,3,4 or six.
It's that, as DrGreg before pointed out,
...2:1 (octave), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third). These ratios sound good to the human ear because the notes share some of the same harmonics.

Minor third: 2(1/12) x 3 ≈ 6:5
Major third: 2(1/12) x 4 ≈ 5:4
Perfect fourth: 2(1/12) x 5 ≈ 4:3
Perfect fifth: 2(1/12) x 7 ≈ 3:2
Octave: 2(1/12) x 12 is of course 2:1
Don't you think so Pythagorean?

I guess this is the answer of my curiousity for years. So simple
Okay..., one more question for anybody.
π, e, golden ratio, they are all, I think, universally accepted. I mean really universally. Any civilization even outside the earth will use those constants. What about $\sqrt[12]{2}$, is it universally used?

Any idea?

Pythagorean
Gold Member
But, the more I think of it, the more I disagree with my previous statement. It's not that 12 can be divided by 2,3,4 or six.
It's that, as DrGreg before pointed out,

Minor third: 2(1/12) x 3 ≈ 6:5
Major third: 2(1/12) x 4 ≈ 5:4
Perfect fourth: 2(1/12) x 5 ≈ 4:3
Perfect fifth: 2(1/12) x 7 ≈ 3:2
Octave: 2(1/12) x 12 is of course 2:1
Don't you think so Pythagorean?

I guess this is the answer of my curiousity for years. So simple
Okay..., one more question for anybody.
π, e, golden ratio, they are all, I think, universally accepted. I mean really universally. Any civilization even outside the earth will use those constants. What about $\sqrt[12]{2}$, is it universally used?

Any idea?
My point was that these are two distinct issues. One is the issue of how many notes you subdivide the octave by, the other is how you distribute that subdivision. There's not one way to do it, the only reason that Dr Greg can talk about approximating these ratios in the first place is because these are the ratios that are already desired, and these ratios come from higher order subdivisions (dividing the string in half, thirds, and fourths).

Stephanus