The Neutral and Double Neutral Scales

Hello.

I'm going to describe some nerdy stuff here so buckle up. Also keep in mind that the theoretical ideas here are kinda just made up, so they might be shaky in places. With that in mind, I still feel like some of this stuff is useful, and sounds good.

Some non-western music systems make extensive use of quarter tones. In all honesty, I haven't made a proper attempt to look into how those systems work. What I'm doing here is trying to develop a harmonic framework for quarter tones, inside of which the popular system of 12 tone harmony can fit, allowing for many more possible key centers and chord qualities.

But first, some terms. Some people might use different words for some of this stuff, but as far as I can tell, the microtonal community (more specifically the quarter tone community) is not even remotely united. As a result, there seem to be few standard practices or agreed upon theoretical frameworks. Some have been proposed but none seem to have really caught on. It's because of this that I'm just freely making up some of my terminology. So if i sound like I don't know what I'm talking about here and there, forgive me.

Anyway,

NEUTRAL THIRDS

The Neutral Third is an interval of 350 cents, or 7 quarter steps. This is directly between the Major Third and Minor Third. This is also the distance halfway between any pitch and its fifth*. Think of it like this: the Tritone is to the Octave as the Neutral Third is to the Fifth.

THE NEUTRAL THIRD CIRCLE

The Neutral Third Circle is the primary diagram of harmonic relationships that I'm using for quarter tone harmony. You'll see this a lot in this post and in future posts. You may notice that this is just two Circles of Fifths separated by a Neutral Third, interlocked. Think of it like this: the Whole tone Scale is to the Chromatic Scale as the Chromatic Scale is to the Quarter Tone Scale.

NEUTRAL SCALES

Neutral scales are scales built out of stacked Neutral Thirds. This is significant because the Major Scale is built in fifths, so there are common tones between Major and Neutral scales.

THE DOUBLE NEUTRAL SCALE

The Double Neutral Scale is comprised of two Neutral Scales separated by a Tritone. One way to generate this scale is by using the same scale formula as for the major scale: 2212221. Even though it is generated from the same step-number formula as a major scale, it's important to remember that a 2 here represents a half step and a 1 represents a quarter step. As a result, this scale pattern repeats at the Tritone before it repeats at the Octave. While the Tritone is the characteristic symmetrical structure of the Major Scale, the Diminished 7 Chord is the characteristic symmetrical structure of the Double Neutral Scale.

THE DECATONIC SCALE

The Decatonic scale is what's left over after you remove a Double Neutral Scale's characteristic Diminished 7 chord. This scale contains at least two rather consonant Pentatonic Scales.

SUPERMAJOR TONIC CHORD AND BEYOND

The Supermajor Tonic Chord is to the Double Neutral Scale as the Major Triad is to the Major Scale. I'll go further into this and related concepts, such as Built-In Bitonality and the significance of the Diminished Seven Chord, in the next post.

In the mean time, here's a clip of two Supermajor Tonic Chords, separated by a Tritone, thereby making up a Decatonic Scale:

And here is a little sketch of a thing I made using the Double Neutral Scale and just freely picking notes and chords. This is a really preliminary thing but it still shows that there are some interesting sounds in there:

Thanks for reading! This topic will be covered more extensively in future posts, and I also plan to explore this through composition. So subscribe to this blog if you're interested in where this could go!

P.S. - If there is something that I'm completely oblivious to which makes all of this theory irrelevant or redundant (like an already existing system of some kind that is robust and widely used) just let me know!!