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Pentatonic scale

#22
Pentatonic scales can go a long way. Using them as 'shapes' for improvision by not starting on the root can yield great results. It's a great means of finding/creating new melodic ideas using all manor of wacky chord extensions. There are of course a billion options - it is an area worthy of investigation, suffice to say.

E.g.
F Major pent built on the 7th of G7 gives you the 7th, root, 9th, 11th and 5th - pretty easy going stuff - you could use that in a straight ahead blues
G B D F + F G A C D

F minor pent built on the 7th of G7 gives you the 7th, b9th, #9th, 11th and b13th - some stronger ones in there, not to be used without due care and attention! :eyebrow:
G B D F + F Ab Bb(A#) C Eb

Hey, this is good stuff! :D ..it's one of many things I need to use more of to start finding my way into the upper extensions more often and hopefully build up the confidence to move away from those roots in solos ;)


Oh and all the stuff about the origin of pentatonic sclae and the like, very interesting, thanks all!
 
#23
WillBuckingham said:
My point was that a 12-tone system arose independantly in two musical systems because it is the result of natural physical properties.
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The pentatonic definitely arose because of natural physical properties. To my mind, the pentatonic is the musical counterpart to Noam Chomsky's root grammars -- the sort of grammars you find in creole or pidgin languages (in fact pentatonics appear in similar cultural situations).

12 ... I don't know. With the Greeks and Babylonians, the number arises from dividing the circle with a compass. I'm not sure why it is a special number in China, but China has a lot of numerical superstitions. I need to read about this.

And I don't think 12 is really a natural number for scales. The early keyboards had anywhere from 9 to 18 notes per octave ... a lot of times split in the center. This was before Bach championed equal temperment, and you needed the extra (in the case of the 18 note keyboard) keys to be able to play in various keys that were further away from C.

The Japanese Koto music uses a 54 note scale, arabic music has a complex system of magamat, where you get microtones -- I think they generally work out to around 21 to 27 tones per octave. I don't know that 12 is all that special ... it is just what we are used to, and what has become standardized in published music (a fairly recent phenomenon)
 
#24
OK. Let's start with an octave (you can do this on a bass string, if so inclined). If the fundamental is a C natural, and we start dividing the string in half (the simplest ratio) we get a series of octaves.

If we go to the next simplest ratio that we can sound on a vibrating string (3:2) we get what we call perfect fifth, if we keep dividing by 3's, we get a series of perfect fifths: C, G, D, A, E, B, F#, C#, G#, D#, A#, E# (or F), and B# (or C). !!! our 12 tones!!!

If we put all these tones into one octave then we would have our octave divided into 12 equal parts. We mess around with these intervals so that non-perfect intervals, like 3rds, sound more like they would when played naturally, but I don't think that's the important part.

So if we take the ratio of 1/3, and divide every note that we find by this ratio, we discover (not invent) a 12-tone system. I think that there is a fundamental difference between this system and one like the Javanese tradition, where the octave is (arbitrarily) sliced up into 5 or 7 parts.

So our system is the very simplest derivation of tones out of the ratio of 1/3 (the simplest interval after 2:1, which wouldn't be a very interesting system -all octaves-). Its not just one of any number of possilbe or random systems that someone could come up with.

P.S. This is my understanding of this stuff, but I could well be wrong.
 
#25
WillBuckingham said:
If we put all these tones into one octave then we would have our octave divided into 12 equal parts. We mess around with these intervals so that non-perfect intervals, like 3rds, sound more like they would when played naturally, but I don't think that's the important part.
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That's not quite right. We would get something close to an equally divided octave, but a little off. By the time you've traveled around a full circle of fifths you'll be at B#, but it won't be in tune with the C you started at.
 
#26
WillBuckingham said:
If we go to the next simplest ratio that we can sound on a vibrating string (3:2) we get what we call perfect fifth, if we keep dividing by 3's, we get a series of perfect fifths: C, G, D, A, E, B, F#, C#, G#, D#, A#, E# (or F), and B# (or C). !!! our 12 tones!!!
Click to expand...


OK ... I'll buy that. And you are going to have intonation problems, but that's what happened with the Pythagoeans. I suppose if there hadn't been a musical demand for all of the 12-tones, because say they appear in one or another of the scales or modes that you are regularly using, then there would have been no need for equal temperment.
 
#27
I don't think 12 tones is anywhere near as perfect as it's being made out to be. Sure, if you make a chain of fifths you'll get a 12 tone octave... almost. If you use 12 tones which are equally spaced then you get a scale which matches exact frequency ratios... sort of. Thirds are way off, and you don't even come close to a true harmonic seventh. To me, 12 equally spaced (important because we like to transpose) tones is special only because it's the smallest set that even comes close to exact frequency ratios. 12 tones isn't natural or best, just the smallest number that's usable for traditional western music. It's just barely good enough, rather than perfect. I could see that arguement applying to 31 tones (but not 19, since the fifths are way off), but not to 12.
 
#31
lemur821 said:
I don't think 12 tones is anywhere near as perfect as it's being made out to be. Sure, if you .... yadda, yadda ...
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Once you go beyond the pentatonic, you will have intonation problems. This is what makes the pentatonic so fundamental. On the other hand, it is usually argued that humans aren't able to differentiate easily any dissonances up to about + or - 5 cents... this is the basis for most tempered tuning systems.

I have to say, too, that I listen to a lot of Chinese and Arabic music (not my choice :bawl: ) and to me it sounds like fingernails on a blackboard (former) and monkish wailing (latter). Give me the blues any day.
 
#33
WillBuckingham said:
Could you explain how a 31-tone system works?
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It's simple, rather than dividing the octave into 12 tones which are each 100 cents apart you divide it into tones which are each around 39 cents apart (1200 cents / 31 tones = 38.7 cents per tone).
Westland said:
I can't imagine that it would work very well at all :p
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31 tones is a few too many for me.

I used 19- and 31-tone equal division systems as examples because they each make some intervals be more in tune than those in a 12-equal system. 19 tones yields good thirds (and a true harmonic seventh, as I recall) at the expense of the fifths, which are way off, and 31 tones does a good job on all the common intervals.
 
#34
westland said:
Note too that the Pythagorian pentatonic is basically minor ... if you think of building a scale only with 5ths and octaves, you go up a 5th for the 5th, down a 5th for the 4th, down another 5th for the b7, and down another 5th for the b3 (I think I've got this right)... so pentatonic with b3, b7 = minor pentatonic.
Click to expand...

brilliant,
So it's called pentatonic not just because of the 5 notes it use but also because of the 5th intervals they used for creating this scale...

Now i got it. :hyper:
 
#36
WillBuckingham said:
You can construct any scale using perfect intervals, right?

As far as I know, many scales can be constructed using combinations of major and minor tetrachords (4 - note scales). These include all major and minor scales. Some exotic scales may not fit into this pattern but the majority of commonly used scales in Western music are composed of different combinations of major and minor intervals. I do not believe that any scale based on perfect intervals can be used "to construct ANY scale," as you have put it. This is due to the fact that there are ONLY PERFECT 4ths and PERFECT 5ths, whereas no such thing as a perfect 3rd exists. Therefore, sir, you must consider the major and the minor 3rd when constructing any scale.
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#37
OK, the the tuning issues that have been gone over here aside . . .

The fifth of C is G, the fifth of G is D, the fifth of D is A. There's a minor third: A to C. A fifth up from A is an E, drop that down however many octaves and you havce a major third between C and E.

You can find any note - though not "in tune" - by doing this. Please read the whole thread more carefully before spewing out snippits of information that have nothing to do with the thread. Did you even read the post that that quote came from?

Thanks,

Will
 

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