The Red-Blue Scale and Superpyth

22 Equal Temperament is rich in scales and harmonies. However one thing it does not contain, is the same diatonic scale which exists in 12 ET. What do I mean exactly? Well see, in 12 ET we stack seven fifths to produce the "diatonic scale" which serious tuning dudes call "meantone". It's called such because in 5-limit just intonation, there are two sizes of whole tones: a major and minor whole tone which have the ratios 9/8 and 10/9.   To the untrained ear, these sound VERY similar, there isn't much of a width difference between the two. If you played a JUST major scale then you would get a major whole tone from C to D but a minor whole tone from D to E. This sounds very good but it also has the draw backs of creating wolf intervals when you move around to a different root than C.

NOTE: Wolves are what tuning guys call intervals which were considered "very dissonant" for the day. Most common is wolf-fifths which are nearly a quarter tone flat from a nice 3/2.




So the dudes back in the say saw that in order to play in a much simpler manner, the difference between the two could be made the same producing a MEAN between the two tones.
THUS MEANTONE WAS BORN!!

Now obviously, if your into just intonation then these two probably have quite a different character to you. Even myself, who isn't into differences this tiny, finds them to sound a bit different. I actually prefer 10/9 as a dyad.  This isn't an ultra technical guide and I'm not even qualified to teach such things so I will skim over the other technical ideas of meantone.  However, meantone is the basic diatonic scale, 10/9 is equated with 9/8.

In 22 ET though, it's not the case. In 22 we have something different but similar at the same time. If we stack seven perfect fifths in 22 ET then we get a different temperament called "superpyth".  While meantone equates 9/8 with 10/9, superpyth equates 8/7 with 9/8.  8/7 is a whole tone which is quite a bit wider than 9/8.  You could think of it as a "super wholetone".

What this does is build a scale which has the same virtual structure PROPORTIONALLY as the diatonic scale yet has a completely different set of intervals. While the major scale is 2 2 1 2 2 2 1, this scale is 4 4 1 4 4 4 1.  Notice how they both have the structure of L L s L L L s but the values of the step sizes are different?  Superpyth has really wide large steps and tiny small steps making it sound altogether new. At least to me it does. \O__O/

The Red-Blue Scale 

Because superpyth is a TEMPERAMENT name, it doesn't specify how far we are moving out in a chain of fifths.  It's like you technically could say 12 ET is one big meantone[12] scale, in fact in a tuning such as 31, meantone[12] is a subset. Point is to avoid confusion, I have named the seven tone superpyth scale the "Red-Blue" scale.  Why you may ask?  Well it's kind of like how we call the major scale, the MAJOR scale and minor scale the MINOR scale, it's based on the quality of the thirds. If you have read the basic quick and dirty guide to 22 ET WHICH YOU SHOULD HAVE READ FIRST!  Then you will know what I mean by red and blue thirds.    

I could have named it the "Blue scale" but that is WAY too confusing with the Blues scale. The red scale also would have worked but I then just decided, well it has both types of thirds in it so I'll just call it "Red-Blue."  In addition, Red-blue scale sounds more unique than just Red-scale which is a term in photography.  

Modes of the Red-Blue Scale 

Because Red-Blue scale is proportionally the same as the diatonic, mode names can remain the same. 

MODE NAMES

Lydian - F G A B C D E F  or 4 4 4 1 4 4 1     

Mixolydian - G A B C D E F G or 4 4 1 4 4 1 4 

Aeolian - A B C D E F G A or 4 1 4 4 1 4 4 

Locrian - B C D E F G A B or 1 4 4 1 4 4 4 

Ionian - C D E F G A B C or 4 4 1 4 4 4 1 

Dorian - D E F G A B C D or 4 1 4 4 4 1 4
Phrygian - E F G A B C D E or 1 4 4 4 1 4 4  

Lydian, Mixolydian, Ionian have red triads on the root.
Aeolian, Dorian, and Phrygian have blue triads on the root.
Locrian has a blue third on the root but the root triad also has a yellow fifth on it rather than a white fifth.

You can play any diatonic music from 12 ET on the red-blue scale but it will probably sound wonky and very different. One particular difference between the Red-blue scale and the diatonic scale of 12 ET is that Blue triads which are more similar to minor are MORE harmonious and stable than Red triads which are less harmonious and less stable. So in essence, if you choose to think of Red as major and Blue as minor then they are basically reversed in this scale.

Superpyth[12] 

We can go beyond the normal Red-blue scale to a larger scale of superpyth[12] which I call the "Supertonic scale." It contains twelve notes in the scale. Unlike 12 EDO, this scale is not evenly spaced but rather very uneven, it is a larger sort of diatonic scale and has the potential for music which goes way beyond simple diatonic music.  

The scale's basic structure is 3 1 3 1 3 1 1 3 1 3 1 1 

That's enough for now.