The Neutral Scale

I'm writing today about a scale I had forgotten about. The neutral scale which to xen theorist is known as "Maqamic"[7] or "Mohajira"[7] depending on how it's tuned. The neutral scale is basically the middle ground between major and minor. Consider this, if we take the natural minor scale and raise the third sixth and seventh we get a major scale. But if we only raised those pitches by around half that distance which ironically is a 1/4 tone then we would have the neutral scale. Neutral land is very weird as all the major chords and minor intervals and chords are equated with each other to produce chords which sound both dark yet a little sweet and pungent.  The sound actually to me at least resembles train whistles and clock chimes. The sound is a bit hard to describe in general. They are extremely mellow yet not as crisp or stark as minor.

Structure 

The major scale has a structure of L L s L L L s while the minor has L s L L s L L. In this particular case, the L represents a whole step while s is a semitone. However, in a neutral scale, the s step represents a neutral tone being roughly mid-way between the whole tone and semitone. Thus we get
L n n L n L n  as the neutral scale.

The diagram above shows Major in purple, Neutral in pink, and Minor in blue and how they relate to one another. Notice how two neutral steps makes up the same distance as L + s or s + L.  Here we used n to represent neutral but in reality, we would simply use two step sizes normally except that the small step represents a neutral tone rather than a semitone.  The result is L s s L s L s.

The Neutral Scale Alphabet

If we wish to base music in a neutral tonality, we may want to create a new set of altered letters to write music. The alphabet C D E F G A B C is all connected by a single chain of fifths from F as is the minor scale from Ab, C D Eb F G Ab Bb C. However the neutral scale isn't actually built from a chain of fifths but two separate chains of fifths. Four of the letters connect by one chain and the other three letters by another. 

The simplest way to do this would be to use some sort of sign to indicate an off-set from a chain of fifths. Here I use arrows to indicate and raise or lowering of a pitch rather than # and b which have meanings of their own. These arrows represent a smaller value, more like a 1/4 tone but it depends on how the scale is tuned. 

C D E↓ F G A↓ B↓ C   The ↓ sign is pronounced "Down".

The above makes perfect sense to someone who understands music notation but there is another option which is cleaner though less intuitive. That is to drop E A and B for alternative letters to indicate they are not part of the same fifths chain. I like using greek letters so I wanted to find three letters which weren't just greek versions of the letters and followed the same pattern thus I used η κ and λ or Eta, Kappa, and Lambda to represent these notes. The lowercase was more snazzy looking to me so I chose this as the alphabet:  c d η f g κ λ c 

The alphabet: 

This isn't very difficult to learn as the large steps occur on letters which come from the same alphabet. Thus κ to λ is a large step but d to η is a small step.